aspen property models
TRANSCRIPT
Physical Property Models
Aspen Physical Property System
Version Number: V8.4November 2013
Copyright (c) 1981-2013 by Aspen Technology, Inc. All rights reserved.
Aspen Physical Property System and the aspen leaf are trademarks or registered trademarks of Aspen Technology,Inc., Burlington, MA.
All other brand and product names are trademarks or registered trademarks of their respective companies.
This software includes NIST Standard Reference Database 103b: NIST Thermodata Engine Version 7.1
This document is intended as a guide to using AspenTech's software. This documentation contains AspenTechproprietary and confidential information and may not be disclosed, used, or copied without the prior consent ofAspenTech or as set forth in the applicable license agreement. Users are solely responsible for the proper use ofthe software and the application of the results obtained.
Although AspenTech has tested the software and reviewed the documentation, the sole warranty for the softwaremay be found in the applicable license agreement between AspenTech and the user. ASPENTECH MAKES NOWARRANTY OR REPRESENTATION, EITHER EXPRESSED OR IMPLIED, WITH RESPECT TO THIS DOCUMENTATION,ITS QUALITY, PERFORMANCE, MERCHANTABILITY, OR FITNESS FOR A PARTICULAR PURPOSE.
Aspen Technology, Inc.200 Wheeler RoadBurlington, MA 01803-5501USAPhone: (1) (781) 221-6400Toll Free: (888) 996-7100URL: http://www.aspentech.com
Contents 1
Contents
Contents..................................................................................................................1
1 Introduction.........................................................................................................5
Units for Temperature-Dependent Parameters .....................................................6Pure Component Temperature-Dependent Properties............................................6Extrapolation Methods ......................................................................................9
2 Thermodynamic Property Models .......................................................................11
Equation-of-State Models ................................................................................ 15ASME Steam Tables.............................................................................. 16BWR-Lee-Starling................................................................................. 16Benedict-Webb-Rubin-Starling ............................................................... 18GERG2008 Equation of State ................................................................. 21Hayden-O'Connell ................................................................................ 22HF Equation-of-State ............................................................................ 25IAPWS-95 Steam Tables ....................................................................... 29Ideal Gas ............................................................................................ 29Lee-Kesler........................................................................................... 30Lee-Kesler-Plöcker ............................................................................... 31NBS/NRC Steam Tables ........................................................................ 33Nothnagel ........................................................................................... 33Copolymer PC-SAFT EOS Model.............................................................. 35Peng-Robinson..................................................................................... 48Standard Peng-Robinson ....................................................................... 50Peng-Robinson-MHV2 ........................................................................... 52Predictive SRK (PSRK) .......................................................................... 52Peng-Robinson-Wong-Sandler................................................................ 53Redlich-Kwong..................................................................................... 53Redlich-Kwong-Aspen ........................................................................... 54Redlich-Kwong-Soave ........................................................................... 55Redlich-Kwong-Soave-Boston-Mathias .................................................... 57Redlich-Kwong-Soave-Wong-Sandler ...................................................... 59Redlich-Kwong-Soave-MHV2.................................................................. 59Schwartzentruber-Renon....................................................................... 60Soave-Redlich-Kwong ........................................................................... 62SRK-Kabadi-Danner.............................................................................. 64SRK-ML............................................................................................... 67VPA/IK-CAPE Equation-of-State ............................................................. 67Peng-Robinson Alpha Functions.............................................................. 72Huron-Vidal Mixing Rules ...................................................................... 84MHV2 Mixing Rules ............................................................................... 85Predictive Soave-Redlich-Kwong-Gmehling Mixing Rules ........................... 87Wong-Sandler Mixing Rules ................................................................... 89
2 Contents
Activity Coefficient Models ............................................................................... 91Bromley-Pitzer Activity Coefficient Model................................................. 91Chien-Null ........................................................................................... 94Constant Activity Coefficient .................................................................. 96COSMO-SAC ........................................................................................ 96Electrolyte NRTL Activity Coefficient Model (GMENRTL) ............................. 99ENRTL-SAC ....................................................................................... 112Hansen ............................................................................................. 117Ideal Liquid ....................................................................................... 119NRTL (Non-Random Two-Liquid) .......................................................... 119NRTL-SAC Model ................................................................................ 120Pitzer Activity Coefficient Model............................................................ 140Polynomial Activity Coefficient ............................................................. 152Redlich-Kister .................................................................................... 153Scatchard-Hildebrand ......................................................................... 154Three-Suffix Margules......................................................................... 155Symmetric and Unsymmetric Electrolyte NRTL Activity Coefficient Model... 156UNIFAC Activity Coefficient Model......................................................... 177UNIFAC (Dortmund Modified)............................................................... 179UNIFAC (Lyngby Modified)................................................................... 180UNIQUAC Activity Coefficient Model ...................................................... 181Van Laar Activity Coefficient Model ....................................................... 183Wagner Interaction Parameter ............................................................. 184Wilson Activity Coefficient Model .......................................................... 185Wilson Model with Liquid Molar Volume ................................................. 186
Vapor Pressure and Liquid Fugacity Models...................................................... 187General Pure Component Liquid Vapor Pressure ..................................... 187API Sour Model .................................................................................. 192Braun K-10 Model .............................................................................. 192Chao-Seader Pure Component Liquid Fugacity Model .............................. 193Grayson-Streed Pure Component Liquid Fugacity Model .......................... 193Kent-Eisenberg Liquid Fugacity Model ................................................... 194Maxwell-Bonnell Vapor Pressure Model.................................................. 195Solid Antoine Vapor Pressure Model ...................................................... 195
General Pure Component Heat of Vaporization ................................................. 196DIPPR Heat of Vaporization Equation .................................................... 196Watson Heat of Vaporization Equation .................................................. 197PPDS Heat of Vaporization Equation ..................................................... 197IK-CAPE Heat of Vaporization Equation ................................................. 198NIST TDE Watson Heat of Vaporization Equation .................................... 198Clausius-Clapeyron Equation ............................................................... 199Pure-Component Heat of Sublimation Polynomial ................................... 199Phase Change Heat of Sublimation Model .............................................. 199
Molar Volume and Density Models .................................................................. 200API Liquid Molar Volume ..................................................................... 201Brelvi-O'Connell ................................................................................. 202Chueh-Prausnitz Liquid Molar Volume Model .......................................... 203Clarke Aqueous Electrolyte Volume....................................................... 205COSTALD Liquid Volume ..................................................................... 207Debye-Hückel Volume......................................................................... 208Liquid Constant Molar Volume Model..................................................... 210General Pure Component Liquid Molar Volume ....................................... 210Rackett/Campbell-Thodos Mixture Liquid Volume ................................... 215
Contents 3
Modified Rackett Liquid Molar Volume ................................................... 216Rackett Extrapolation Method .............................................................. 217General Pure Component Solid Molar Volume......................................... 219Liquid Volume Quadratic Mixing Rule .................................................... 221
Heat Capacity Models ................................................................................... 221Aqueous Infinite Dilution Heat Capacity................................................. 221Criss-Cobble Aqueous Infinite Dilution Ionic Heat Capacity ...................... 222General Pure Component Liquid Heat Capacity....................................... 222General Pure Component Ideal Gas Heat Capacity.................................. 227General Pure Component Solid Heat Capacity ........................................ 231
Solubility Correlations................................................................................... 233Henry's Constant................................................................................ 234Water Solubility ................................................................................. 235Hydrocarbon Solubility........................................................................ 235
Other Thermodynamic Property Models........................................................... 236Cavett .............................................................................................. 236Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacity... 237Pure-Component Solid Enthalpy Polynomial ........................................... 239Electrolyte NRTL Enthalpy Model (HMXENRTL) ....................................... 240Electrolyte NRTL Gibbs Free Energy Model (GMXENRTL) .......................... 242Liquid Enthalpy from Liquid Heat Capacity Correlation............................. 244Enthalpies Based on Different Reference States ..................................... 245Helgeson Equations of State ................................................................ 250Quadratic Mixing Rule ......................................................................... 253Ideal Mixing Rule ............................................................................... 253
3 Transport Property Models ...............................................................................255
Viscosity Models........................................................................................... 257Andrade Liquid Mixture Viscosity .......................................................... 258General Pure Component Liquid Viscosity .............................................. 259API Liquid Viscosity ............................................................................ 262API 1997 Liquid Viscosity .................................................................... 262Aspen Liquid Mixture Viscosity ............................................................. 263ASTM Liquid Mixture Viscosity.............................................................. 264General Pure Component Vapor Viscosity .............................................. 265Chapman-Enskog-Brokaw-Wilke Mixing Rule ......................................... 268Chung-Lee-Starling Low-Pressure Vapor Viscosity .................................. 270Chung-Lee-Starling Viscosity ............................................................... 272Dean-Stiel Pressure Correction ............................................................ 274IAPS Viscosity for Water...................................................................... 274Jones-Dole Electrolyte Correction ......................................................... 275Letsou-Stiel ....................................................................................... 277Lucas Vapor Viscosity ......................................................................... 277TRAPP Viscosity Model ........................................................................ 279Twu Liquid Viscosity ........................................................................... 279Viscosity Quadratic Mixing Rule............................................................ 281
Thermal Conductivity Models ......................................................................... 281Chung-Lee-Starling Thermal Conductivity.............................................. 282IAPS Thermal Conductivity for Water .................................................... 283Li Mixing Rule .................................................................................... 284Riedel Electrolyte Correction ................................................................ 284General Pure Component Liquid Thermal Conductivity ............................ 285
4 Contents
Solid Thermal Conductivity Polynomial .................................................. 288General Pure Component Vapor Thermal Conductivity............................. 288Stiel-Thodos Pressure Correction Model................................................. 291Vredeveld Mixing Rule......................................................................... 291TRAPP Thermal Conductivity Model....................................................... 292Wassiljewa-Mason-Saxena Mixing Rule ................................................. 293
Diffusivity Models ......................................................................................... 293Chapman-Enskog-Wilke-Lee (Binary).................................................... 294Chapman-Enskog-Wilke-Lee (Mixture) .................................................. 295Dawson-Khoury-Kobayashi (Binary) ..................................................... 295Dawson-Khoury-Kobayashi (Mixture).................................................... 296Nernst-Hartley ................................................................................... 297Wilke-Chang (Binary) ......................................................................... 298Wilke-Chang (Mixture) ........................................................................ 299
Surface Tension Models................................................................................. 300Liquid Mixture Surface Tension ............................................................ 300API Surface Tension ........................................................................... 300IAPS Surface Tension for Water ........................................................... 301General Pure Component Liquid Surface Tension.................................... 301Onsager-Samaras .............................................................................. 304Modified MacLeod-Sugden ................................................................... 306
4 Nonconventional Solid Property Models ...........................................................307
General Enthalpy and Density Models ............................................................. 307General Density Polynomial ................................................................. 307General Heat Capacity Polynomial ........................................................ 308
Enthalpy and Density Models for Coal and Char................................................ 309General Coal Enthalpy Model ............................................................... 312IGT Coal Density Model ....................................................................... 319IGT Char Density Model ...................................................................... 320
5 Property Model Option Codes ...........................................................................321
Option Codes for Transport Property Models .................................................... 321Option Codes for Activity Coefficient Models .................................................... 323Option Codes for Equation of State Models ...................................................... 325Soave-Redlich-Kwong Option Codes ............................................................... 328Option Codes for K-Value Models.................................................................... 330Option Codes for Enthalpy Models .................................................................. 330Option Codes for Gibbs Free Energy Models..................................................... 332Option Codes for Liquid Volume Models........................................................... 334
Index ..................................................................................................................335
1 Introduction 5
1 Introduction
This manual describes the property models available in the Aspen PhysicalProperty System and defines the parameters used in each model. Thedescription for each model lists the parameter names used to enter values onthe Methods | Parameters forms.
This manual also lists the pure component temperature-dependent propertiesthat the Aspen Physical Property System can calculate from a model thatsupports several equations or submodels. See Pure Component Temperature-Dependent Properties (below).
Many parameters have default values indicated in the Default column. A dash(–) indicates that the parameter has no default value and you must provide avalue. If a parameter is missing, calculations stop. The lower limit and upperlimit for each parameter, when available, indicate the reasonable bounds forthe parameter. The limits are used to detect grossly erroneous parametervalues.
The property models are divided into the following categories:
Thermodynamic property models
Transport property models
Nonconventional solid property models
The property types for each category are discussed in separate sections. Thefollowing table (below) provides an organizational overview of this manual.The tables labeled Thermodynamic Property Models, Transport PropertyModels, and Nonconventional Solid Property Models present detailed lists ofmodels. These tables also list the Aspen Physical Property System modelnames, and their possible use in different phase types, for pure componentsand mixtures.
Electrolyte and conventional solid property models are presented inThermodynamic Property Models.
Categories of ModelsCategory Sections
ThermodynamicProperty Models
Equation-of-State ModelsActivity Coefficient Models (Including Electrolyte Models)Vapor Pressure and Liquid Fugacity ModelsHeat of Vaporization ModelsMolar Volume and Density ModelsHeat Capacity ModelsSolubility CorrelationsOther
6 1 Introduction
Category Sections
Transport PropertyModels
Viscosity ModelsThermal Conductivity ModelsDiffusivity ModelsSurface Tension Models
Nonconventional SolidProperty Models
General Enthalpy and Density ModelsEnthalpy and Density Models for Coal and Char
Units for Temperature-Dependent ParametersSome temperature-dependent parameters may be based on expressionswhich involve logarithmic or reciprocal temperature terms. When thecoefficient of any such term is non-zero, in many cases the entire expressionmust be calculated assuming that all the coefficients are in absolutetemperature units. In other cases, terms are independent from one another,and only certain terms may require calculation using absolute temperatureunits. Notes in the models containing such terms explain exactly whichcoefficients are affected by this treatment.
When absolute temperature units are forced in this way, this affects the unitsfor coefficients you have entered as input parameters. If your inputtemperature units are Fahrenheit (F), then Rankine (R) is used instead. Ifyour input units are Celsius (C), then Kelvin (K) is used instead.
If only constant and positive powers of temperature are present in theexpression, then your specified input units are used.
If the parameters include temperature limits, the limits are always interpretedin user input units even if the expression is forced to absolute units.
Some equations may include a dimensionless parameter, the reducedtemperature Tr = T / Tc. This reduced temperature is calculated usingabsolute temperature units. In most cases, input parameters associated withsuch equations do not have temperature units.
Pure Component Temperature-Dependent PropertiesThe following table lists the pure component temperature-dependentproperties that the Aspen Physical Property System can calculate from ageneral model that supports several equations or submodels.
For example, the Aspen Physical Property System can calculate heat ofvaporization using these equations:
Watson
DIPPR
PPDS
IK-CAPE
1 Introduction 7
NIST TDE Watson
Pure Component Temperature-Dependent Properties
Property
Submodel-SelectionParameterElementNumber Available Submodels
DIPPR EquationNumbers(† = default)
Solid Volume THRSWT/1 Aspen, DIPPR, IK-CAPE,NIST
100
Liquid Volume THRSWT/2 Aspen (Rackett), DIPPR,PPDS, IK-CAPE, NIST
105†, 116 for wateronly
Liquid VaporPressure
THRSWT/3 Aspen (Extended Antoine),Wagner, BARIN, PPDS,PML, IK-CAPE, NIST
101
Heat ofVaporization
THRSWT/4 Aspen (Watson), DIPPR,PPDS, IK-CAPE, NIST
106
Solid HeatCapacity
THRSWT/5 Aspen, DIPPR, BARIN, IK-CAPE, NIST
100†, 102
Liquid HeatCapacity
THRSWT/6 DIPPR, PPDS, BARIN, IK-CAPE, NIST
100†, 114
Ideal Gas HeatCapacity
THRSWT/7 Aspen, DIPPR, BARIN,PPDS, IK-CAPE, NIST
107, 127†
Second VirialCoefficient
THRSWT/8 DIPPR 104
Liquid Viscosity TRNSWT/1 Aspen (Andrade), DIPPR,PPDS, IK-CAPE, NIST
101†, 115
Vapor Viscosity TRNSWT/2 Aspen (Chapman-Enskog-Brokaw), DIPPR, PPDS, IK-CAPE, NIST
102
Liquid ThermalConductivity
TRNSWT/3 Aspen (Sato-Riedel),DIPPR, PPDS, IK-CAPE,NIST
100
Vapor ThermalConductivity
TRNSWT/4 Aspen (Stiel-Thodos),DIPPR, PPDS, IK-CAPE,NIST
102
Liquid SurfaceTension
TRNSWT/5 Aspen (Hakim-Steinberg-Stiel), DIPPR, PPDS, IK-CAPE, NIST
106
Which equation is actually used to calculate the property for a givencomponent depends on which parameters are available. If parameters areavailable for more than one equation, the Aspen Physical Property Systemuses the parameters that were entered or retrieved first from the databanks.The selection of submodels is driven by the data hierarchy, and controlled bythe submodel-selection parameters.
The thermodynamic properties use the THRSWT (thermo switch) submodel-selection parameter, and the transport properties use the TRNSWT (transportswitch) submodel-selection parameter.
8 1 Introduction
As the previous table shows, a property is associated with an element of thesubmodel-selection parameter. For example, THRSWT element 1 controls thesubmodel for solid volume.
The following table shows the values for THRSWT or TRNSWT, and thecorresponding submodels.Parameter Values(Equation Number) Submodel
0 Aspen
1 to 127 DIPPR
200 to 211 BARIN
301 to 302 PPDS or property-specific methods
400 PML
401 to 404 IK-CAPE
501 to 515 NIST
All built-in databank components have model-selection parameters (THRSWT,TRNSWT) that are set to use the correct equations that are consistent withthe available parameters. For example, suppose that parameters for theDIPPR equation 106 are available for liquid surface tension. For thatcomponent, TRNSWT element 5 is set to 106 in the databank. If you areretrieving data from an in-house or user databank, you should store theappropriate values for THRSWT and TRNSWT in the databank, using theappropriate equation number. Otherwise, the Aspen Physical Property Systemwill search for the parameters needed for the Aspen form of the equations.
If a component is available in more than one databank, the Aspen PhysicalProperty System uses the data and equations based on the databank listorder on the Components Specifications Selection sheet. For example,suppose the databank search order is ASPENPCD, then PURE25, and that theAspen Physical Property System cannot find the parameters for a particularsubmodel (equation) in the ASPENPCD databank. If the PURE25 databankcontains parameters for another equation, the Aspen Physical PropertySystem will use that equation (most likely the DIPPR equation) to calculatethe property for that component.
If your calculation contains any temperature-dependent property parameters,(such as CPIGDP for DIPPR ideal gas heat capacity, entered on the Methods| Parameters | Pure Component form), the Aspen Physical PropertySystem sets the corresponding THRSWT and TRNSWT elements for thatcomponent to the default values shown in the table above. This defaultsetting might not always be correct. If you know the equation number, youshould enter it directly on the Methods | Parameters | Pure Componentform. For example, suppose you want to use the:
DIPPR equation form of heat of vaporization (DHVLDP) for a component
Aspen equations for the remaining temperature dependent properties
Set the fourth element of the THRSWT parameter to 106, and the 1-3 and 5-8elements to 0. If you want to set the other temperature-dependent propertiesto use what is defined for that component in the databank, leave the elementblank.
The following table lists the available DIPPR equations and the correspondingequation (submodel) number.
1 Introduction 9
Available DIPPR EquationsEquationNumber Equation Form
100
101
102
103
104
105
106
107
114
115
116
127
For equations 114 and 116, t = 1-Tr.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
The following sections describe the Aspen, DIPPR, BARIN, IK-CAPE, PPDS, andNIST equations for each property. For descriptions of the the BARIN equationsfor heat capacity and enthalpy, see BARIN Equations for Gibbs Energy,Enthalpy, Entropy, and Heat Capacity.
Extrapolation MethodsMany temperature dependent property models have upper and lowertemperature limits. The Aspen Physical Property System usually extrapolateslinearly beyond such limits. It calculates the slope of the property-versus-temperature curve, or the ln(property)-versus-temperature curve for modelsexpressed in logarithmic form, at the upper or lower temperature limit. Fortemperatures beyond the limit, it uses a linear model with this slope whichmeets the curve from the equation at the temperature limit. Thus the modelis:
10 1 Introduction
For T beyond the upper or lower limit, where Tlim is that limit and Z is theproperty or ln(property) as appropriate. Some liquid molar volume models areactually molar density models which then return the reciprocal of the densityas the liquid molar volume. In these models, the extrapolation occurs for thedensity calculation.
There are certain exceptions, detailed below.
Exception 1: Logarithmic Properties Based on ReciprocalTemperature
This applies to property models expressed in the form (where a(T) includesany additional dependency on temperature):
For these models, the extrapolation maintains the slope of ln(property) versus1/T. This applies to the Extended Antoine vapor pressure equation and theAndrade and DIPPR liquid viscosity equations. Note that the equation forHenry's Constant is extrapolated by ln(Henry) versus T.
Exception 2: Aspen Ideal Gas Heat Capacity
The Aspen Ideal Gas Heat Capacity model has an explicit equation forextrapolation at temperatures below the lower limit, which is described in themodel. At high temperatures it follows the usual rule of extrapolatingproperty-versus-temperature linearly.
Exception 3: No Extrapolation
The equations for certain models are used directly at all temperatures, so thatno extrapolation is performed. These models are the Wagner vapor pressureequation, the Aly and Lee equation for the DIPPR Ideal Gas Heat Capacity(using the CPIGDP parameter), and the Water Solubility and HydrocarbonSolubility models. The equations for temperature-dependent binaryinteraction parameters are also used directly at all temperatures with noextrapolation.
2 Thermodynamic Property Models 11
2 Thermodynamic PropertyModels
This section describes the available thermodynamic property models in theAspen Physical Property System. The following table provides a list ofavailable models, with corresponding Aspen Physical Property System modelnames. The table provides phase types for which the model can be used andinformation on use of the model for pure components and mixtures.
Aspen Physical Property System thermodynamic property models includeclassical thermodynamic property models, such as activity coefficient modelsand equations of state, as well as solids and electrolyte models. The modelsare grouped according to the type of property they describe.
Thermodynamic Property Models
Phases: V = Vapor; L = Liquid; S = Solid. An X indicates applicable to Pure orMixture.
Equation-of-State Models
A pure component equation of state model calculates PHIL, PHIV, DHL, DHV,DGL, DGV, DSL, DSV, VL, and VV. Most mixture equation of state modelscalculate PHILMX, PHIVMX, DHLMX, DHVMX, DGLMX, DGVMX, DSLMX,DSVMX, VLMX, and VVMX. Those marked with * only calculate DHLMX,DHVMX, DGLMX, DGVMX, DSLMX, DSVMX, VLMX, and VVMX. The alphafunctions and mixing rules are options available in some of the models.Property Model Model Name(s) Phase(s)Pure Mixture
ASME Steam Tables ESH2O0,ESH2O V L X —
BWR-Lee-Starling ESBWR0, ESCSTBWR V L X X
Benedict-Webb-Rubin-Starling ESBWRS, ESBWRS0 V L X X
GERG2008 — V L X X
Hayden-O'Connell ESHOC0,ESHOC V X X
HF equation-of-state ESHF0, ESHF V X X
IAPWS-95 Steam Tables — V L X —
Ideal Gas ESIG0, ESIG V X X
Lee-Kesler * ESLK V L — X
Lee-Kesler-Plöcker ESLKP0,ESLKP V L X X
12 2 Thermodynamic Property Models
Property Model Model Name(s) Phase(s)Pure Mixture
NBS/NRC Steam Tables ESSTEAM0,ESSTEAM V L X —
Nothnagel ESNTH0,ESNTH V X X
PC-SAFT ESPSAFT, ESPSAFT0 V L X X
Peng-Robinson ESPR0, ESPR V L X X
Standard Peng-Robinson ESPRSTD0,ESPRSTD V L X X
Peng-Robinson-Wong-Sandler * ESPRWS0,ESPRWS V L X X
Peng-Robinson-MHV2 * ESPRV20,ESPRV2 V L X X
Predictive SRK * ESRKSV10, ESRKSV1 V L X X
Redlich-Kwong ESRK0, ESRK V X X
Redlich-Kwong-Aspen ESRKA0,ESRKA V L X X
Redlich-Kwong-Soave ESRKSTD0,ESRKSTD V L X X
Redlich-Kwong-Soave-Boston-Mathias
ESRKS0, ESRKS V L X X
Redlich-Kwong-Soave-MHV2 * ESRKSV20, ESRKSV2 V L X X
Redlich-Kwong-Soave-Wong-Sandler *
ESRKSWS0, ESRKSWSV L X X
Schwartzentruber-Renon ESRKU0,ESRKU V L X X
Soave-Redlich-Kwong ESSRK0, ESSRK V L X X
SRK-Kabadi-Danner ESSRK0, ESSRK V L X X
SRK-ML ESRKSML0, ESRKSML V L X X
VPA/IK-CAPE equation-of-state ESVPA0, ESVPA V X X
Peng-Robinson Alpha functions — V L X —
RK-Soave Alpha functions — V L X —
Huron-Vidal mixing rules — V L — X
MHV2 mixing rules — V L — X
PSRK mixing rules — V L — X
Wong-Sandler mixing rules — V L — X
Activity Coefficient Models (Including Electrolyte Models)
These models calculate GAMMA.Property Model Model Name Phase(s)Pure Mixture
Bromley-Pitzer GMPT2 L — X
Chien-Null GMCHNULL L — X
Constant Activity Coefficient GMCONS S — X
COSMO-SAC COSMOSAC L — X
Electrolyte NRTL GMENRTL, GMELC,GMENRHG
L L1 L2 — X
ENRTL-SAC (patent pending) ENRTLSAC L — X
Hansen HANSEN L — X
Ideal Liquid GMIDL L — X
NRTL (Non-Random-Two-Liquid) GMRENON L L1 L2 — X
NRTL-SAC (patent pending) NRTLSAC L — X
Pitzer GMPT1 L — X
2 Thermodynamic Property Models 13
Property Model Model Name Phase(s)Pure Mixture
Polynomial Activity Coefficient GMPOLY L S — X
Redlich-Kister GMREDKIS L S — X
Scatchard-Hildebrand GMXSH L — X
Symmetric Electrolyte NRTL GMENRTLS L — X
Three-Suffix Margules GMMARGUL L S — X
UNIFAC GMUFAC L L1 L2 — X
UNIFAC (Lyngby modified) GMUFLBY L L1 L2 — X
UNIFAC (Dortmund modified) GMUFDMD L L1 L2 — X
UNIQUAC GMUQUAC L L1 L2 — X
Unsymmetric Electrolyte NRTL GMENRTLQ L — X
van Laar GMVLAAR L — X
Wagner interaction parameter GMWIP S — X
Wilson GMWILSON L — X
Wilson model with liquid molarvolume
GMWSNVOL L — X
Vapor Pressure and Liquid Fugacity ModelsProperty Model Model
NameProperty Phase(s)Pure Mixture
General Pure Component LiquidVapor Pressure
PL0XANT PL L L1 L2 X —
API Sour SWEQ PHILMX L — X
Braun K-10 BK10 PHILMX L — X
Chao-Seader PHL0CS PHIL L X —
Grayson-Streed PHL0GS PHIL L X —
Kent-Eisenberg ESAMINE PHILMX,GLMX,HLMX,SLMX
L — X
Maxwell-Bonnell PL0MXBN PL L L1 L2 X —
Solid Antoine PS0ANT PS S X —
Heat of Vaporization Models
These models calculate DHVL.Property Model Model Name Phase(s)Pure Mixture
General Pure Component Heatof Vaporization
DHVLWTSN L X —
Clausius-Clapeyron Equation DHVLCC L X —
Heat of Sublimation Models
These models calculate DHVS.Property Model Model Name Phase(s)Pure Mixture
Pure-Component Heat ofSublimation Polynomial
DHVSPOLY S X —
14 2 Thermodynamic Property Models
Property Model Model Name Phase(s)Pure Mixture
Phase Change Heat ofSublimation Model
DHVSGEN S X —
Molar Volume and Density Models
These models calculate VL (pure liquid), VLMX (liquid mixture), or VS (puresolid), except for Brelvi-O'Connell which calculates VLPM.Property Model Model Name Phase(s)Pure Mixture
API Liquid Volume VL2API L — X
Brelvi-O'Connell VL1BROC L — X
Chueh-Prausnitz VL0CPRKT, VL2CPRKT L X X
Clarke Aqueous ElectrolyteVolume
VAQCLK L — X
COSTALD Liquid Volume VL0CTD,VL2CTD L X X
Debye-Hückel Volume VAQDH L — X
Liquid Constant Molar Volume VL0CONS L X —
General Pure Component LiquidMolar Volume
VL0RKT,VL2RKT L X —
Rackett/Campbell-ThodosMixture Liquid Volume
VL2RKT L X X
Modified Rackett VL2MRK L X X
General Pure Component SolidMolar Volume
VS0POLY S X —
Liquid Volume Quadratic MixingRule
VL2QUAD L — X
Heat Capacity ModelsProperty Model Model
NameProperty Phase(s)Pure Mixture
Aqueous Infinite Dilution HeatCapacity Polynomial
— — L — X
Criss-Cobble Aqueous InfiniteDilution Ionic Heat Capacity
— — L — X
General Pure Component LiquidHeat Capacity
— CPL L X —
General Pure Component IdealGas Heat Capacity
— CPIG V X X
General Pure Component SolidHeat Capacity
— CPS S X —
Solubility Correlation ModelsProperty Model Model
NameProperty Phase(s)Pure Mixture
Henry's constant HENRY1 HNRY,WHNRY
L — X
Water solubility — — L — X
Hydrocarbon solubility — — L — X
2 Thermodynamic Property Models 15
Other ModelsProperty Model Model
NamePropertyPhase(s)Pure Mixture
Cavett Liquid Enthalpy DepartureDHL0CVT,DHL2CVT
DHL,DHLMX
L X X
BARIN Equations for GibbsEnergy, Enthalpy, Entropy andHeat Capacity
— — S L V X —
Bromley-Pitzer Enthalpy HAQPT2 HLMX L — X
Bromley-Pitzer Gibbs Energy GAQPT2 GLMX L — X
Electrolyte NRTL Enthalpy HMXENRTL,HAQELC,HMXELC,HMXENRHG
HLMX L — X
Electrolyte NRTL Gibbs Energy GMXENRTL,GAQELC,GMXELC,GMXENRHG
HLMX L — X
Enthalpies Based on DifferentReference States
DHL0HREF DHL L V X X
Helgeson Equations of State — — L — X
Liquid Enthalpy from Liquid HeatCapacity Correlation
DHL0DIP — L X X
Pitzer Enthalpy HAQPT1 HLMX L — X
Pitzer Gibbs Energy GAQPT1 GLMX L — X
Pure-Component Solid EnthalpyPolynomial
HS0POLY HS S X —
Quadratic Mixing Rule — — L V — X
Equation-of-State ModelsThe Aspen Physical Property System has the following built-in equation-of-state property models. This section describes the equation-of-state propertymodels available.Model Type
ASME Steam Tables Fundamental
BWR-Lee-Starling Virial
Benedict-Webb-Rubin-Starling Virial
GERG2008 Fundamental/mixing rules
Hayden-O'Connell Virial and association
HF Equation-of-State Ideal and association
Huron-Vidal mixing rules Mixing rules
IAPWS-95 Steam Tables Fundamental
Ideal Gas Ideal
Lee-Kesler Virial
Lee-Kesler-Plöcker Virial
MHV2 mixing rules Mixing rules
16 2 Thermodynamic Property Models
Model Type
NBS/NRC Steam Tables Fundamental
Nothnagel Ideal
PC-SAFT Association
Peng-Robinson Cubic
Standard Peng-Robinson Cubic
Peng-Robinson Alpha functions Alpha functions
Peng-Robinson-MHV2 Cubic
Peng-Robinson-Wong-Sandler Cubic
Predictive SRK Cubic
PSRK mixing rules Mixing rules
Redlich-Kwong Cubic
Redlich-Kwong-Aspen Cubic
Standard Redlich-Kwong-Soave Cubic
Redlich-Kwong-Soave-Boston-Mathias Cubic
Redlich-Kwong-Soave-MHV2 Cubic
Redlich-Kwong-Soave-Wong-Sandler Cubic
RK-Soave Alpha functions Alpha functions
Schwartzentruber-Renon Cubic
Soave-Redlich-Kwong Cubic
SRK-Kabadi-Danner Cubic
SRK-ML Cubic
VPA/IK-CAPE equation-of-state Ideal and association
Wong-Sandler mixing rules Mixing rules
ASME Steam TablesThe ASME steam tables are implemented like any other equation-of-state inthe Aspen Physical Property System. The steam tables can calculate anythermodynamic property of water or steam and form the basis of the STEAM-TA property method. There are no parameter requirements. The ASME steamtables are less accurate than the NBS/NRC steam tables.
References
ASME Steam Tables, Thermodynamic and Transport Properties of Steam,(1967).
K. V. Moore, Aerojet Nuclear Company, prepared for the U.S. Atomic EnergyCommision, ASTEM - A Collection of FORTRAN Subroutines to Evaluate the1967 ASME equations of state for water/steam and derivatives of theseequations.
BWR-Lee-StarlingThe Benedict-Webb-Rubin-Lee-Starling equation-of-state is the basis of theBWR-LS property method. It is a generalization by Lee and Starling of the
2 Thermodynamic Property Models 17
virial equation-of-state for pure fluids by Benedict, Webb and Rubin. Theequation is used for non-polar components, and can manage hydrogen-containing systems.
General Form:
Where:
Mixing Rules:
Where:
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCBWR Tci TC X 5.0 2000.0 TEMPERATURE
VCBWR Vci* VC X 0.001 3.5 MOLE-
VOLUME
BWRGMA iOMEGA X -0.5 3.0 —
BWRKV ij0 X -5.0 1.0 —
BWRKT ij0 X -5.0 1.0 —
Binary interaction parameters BWRKV and BWRKT are available in the AspenPhysical Property System for a large number of components from Brulé et al.(1982) and from Watanasiri et al. (1982). (See Physical Property Data,Chapter 1).
References
M.R. Brulé, C.T. Lin, L.L. Lee, and K.E. Starling, AIChE J., Vol. 28, (1982) p.616.
Brulé et al., Chem. Eng., (Nov., 1979) p. 155.
Watanasiri et al., AIChE J., Vol. 28, (1982) p. 626.
18 2 Thermodynamic Property Models
Benedict-Webb-Rubin-StarlingThe Benedict-Webb-Rubin-Starling equation-of-state is the basis of the BWRSproperty method. It is a modification by Han and Starling of the virialequation-of-state for pure fluids by Benedict, Webb and Rubin. This equation-of-state can be used for hydrocarbon systems that include the common lightgases, such as H2S, CO2 and N2.
The form of the equation-of-state is:
Where:
2 Thermodynamic Property Models 19
kij = kji
In the mixing rules given above, A0i, B0i, C0i, D0i, E0i, ai, bi, ci, di, i, i are pure
component constants which can be input by the user. For methane, ethane,propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, n-heptane, n-octane, ethylene, propylene, nitrogen, carbon dioxide, andhydrogen sulfide, values of the parameters in the table below are available inthe EOS-LIT databank in the Aspen Properties Enterprise Database.
If the values of these parameters are not given, and not available from thedatabank, the Aspen Physical Property System will calculate them using thecritical temperature, the critical volume (or critical density), the acentricfactor and generalized correlations given by Han and Starling.
When water is present, by default Benedict-Webb-Rubin-Starling uses thesteam table to calculate the enthalpy, entropy, Gibbs energy, and molarvolume of water. The total properties are mole-fraction averages of thesevalues with the properties calculated by the equation of state for othercomponents. Fugacity coefficient is not affected. An option code can disablethis use of the steam table.
For best results, the binary parameter kij must be regressed using phase-equilibrium data such as VLE data.ParameterName/Element
SymbolDefault MDS LowerLimit
UpperLimit
Units
BWRSTC Tci TC x 5.0 2000.0 TEMPERATURE
BWRSVC Vci VC x 0.001 3.5 MOLE-VOLUME
BWRSOM i OMEGA x –0.5 2.0 –
BWRSA/1 B0i fcn(i ,Vci , Tci) x – – MOLE-VOLUME
BWRSA/2 A0i fcn(i ,Vci , Tci) x – – PRESSURE * MOLE-VOL^2
BWRSA/3 C0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^2 *MOLE-VOLUME^2
BWRSA/4 ifcn(i ,Vci , Tci) x – – MOLE-VOLUME^2
BWRSA/5 bi fcn(i ,Vci , Tci) x – – MOLE-VOLUME^2
BWRSA/6 ai fcn(i ,Vci , Tci) x – – PRESSURE * MOLE-VOL^3
BWRSA/7 i fcn(i ,Vci , Tci) x – – MOLE-VOLUME^3
BWRSA/8 ci fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^2 *MOLE-VOLUME^3
BWRSA/9 D0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^3 *MOLE-VOLUME^2
BWRSA/10 di fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE * MOLE-VOLUME^3
20 2 Thermodynamic Property Models
ParameterName/Element
SymbolDefault MDS LowerLimit
UpperLimit
Units
BWRSA/11 E0i fcn(i ,Vci , Tci) x – – PRESSURE *TEMPERATURE^4 *MOLE-VOLUME^2
BWRAIJ kij – x – – –
Constants Used with the correlations of Han and StarlingParameter Methane Ethane Propane n-Butane
B0i 0.723251 0.826059 0.964762 1.56588
A0i 7520.29 13439.30 18634.70 32544.70
C0i 2.71092x108 2.95195x109 7.96178x109 1.37436x1010
D0i 1.07737x1010 2.57477x1011 4.53708x1011 3.33159x1011
E0i 3.01122x1010 1.46819x1013 2.56053x1013 2.30902x1012
bi 0.925404 3.112060 5.462480 9.140660
ai 2574.89 22404.50 40066.40 71181.80
di 47489.1 702189.0 1.50520x107 3.64238x107
i 0.468828 0.909681 2.014020 4.009850
ci 4.37222x108 6.81826x109 2.74461x1010 7.00044x1010
i1.48640 2.99656 4.56182 7.54122
Parameter n-Pentane n-Hexane n-Heptane n-Octane
B0i 2.44417 2.66233 3.60493 4.86965
A0i 51108.20 45333.10 77826.90 81690.60
C0i 2.23931x1010 5.26067x1010 6.15662x1010 9.96546x1010
D0i 1.01769x1012 5.52158x1012 7.77123x1012 7.90575x1012
E0i 3.90860x1013 6.26433x1014 6.36251x1012 3.46419x1013
bi 16.607000 29.498300 27.441500 10.590700
ai 162185.00 434517.00 359087.00 131646.00
di 3.88521x107 3.27460x107 8351150.0 1.85906x108
i 7.067020 9.702300 21.878200 34.512400
ci 1.35286x1011 3.18412x1011 3.74876x1011 6.42053x1011
i11.85930 14.87200 24.76040 21.98880
References
M. Benedict, G. B. Webb, and L. C. Rubin, J. Chem. Phys., Vol. 8, (1940), p.334.
M. S. Han, and K. E. Starling , "Thermo Data Refined for LPG. Part 14:Mixtures", Hydrocarbon Processing, Vol. 51, No. 5, (1972), p. 129.
K. E. Starling, "Fluid Themodynamic Properties for Light Petroleum Systems",Gulf Publishing Co., Houston, Texas (1973).
2 Thermodynamic Property Models 21
References for Parameter Data
K.E. Starling and M.S. Han, "Thermo data refined for LPG, part 14 Mixtures,"Hydrocarbon Processing, (May 1972), pp. 129-132.
K.E. Starling and M.S. Han, "Thermo data refined for LPG, part 15 Industrialapplications," Hydrocarbon Processing, (June 1972), pp. 107-115.
K.E. Starling, "Fluid Thermodynamic Properties for Light Petroleum Systems,"Gulf Publishing Co., Houston, Texas (1973).
GERG2008 Equation of StateThe GERG2008 equation-of-state model is the basis for the GERG2008property method.
The equation of state is based on a multi-fluid approximation explicit in thereduced Helmholtz free energy:
(1)
Where the ideal-gas contribution o and residual contribution r at a given
mixture density, temperature, and molar composition are:
(2)
(3)
Where the reduced mixture density and inverse reduced mixture
temperature are:
(4)
In eq. (2), the ideal-gas contribution of the reduced Helmholtz free energy forcomponent i is given by:
(5)
In eq. (3), the pure substance contribution to the residual part of the reducedHelmholtz free energy for component i is given by:
(6)
22 2 Thermodynamic Property Models
In eq. (3), the mixture contribution to the residual part of the reducedHelmholtz free energy is given by:
(7)
The reduced mixture density is given by:
(8)
And the reduced mixture temperature is given by:
(9)
Where:
R = molar gas constant = 8.314472 J/mol-K.
c,i and Tc,i = critical density and critical temperature
nooi,k and o
oi,k = Coefficients and parameters of eq. (5) for pure components
noi,k, doi,k, toi,k, and coi,k = coefficients and exponents of eq. (6) for purecomponents
Fij = Composition dependent factor
nij,k = Coefficients and dij,k, tij,k, ij,k, ij,k, ij,k, and ij,k = the exponents in eq.
(7) for all binary specific and generalized departure functions
v,ij and v,ij in eq. (8) and T,ij and T,ij in eq. (9) = Binary interaction
parameters
Reference
"The GERG-2004 Wide-Range Equation of State for Natural Gases and OtherMixtures" O. Kunz, R. Klimeck, W. Wagner, M. Jaeschke; GERG TM15 2007;ISBN 978-3-18-355706-6; Published for GERG and printed in Germany byVDI Verlag GmbH (2007).
Kunz, O., Wagner, W., "The new GERG-2004 XT08 wide-range equation ofstate for natural gases and other mixtures." To be submitted to Fluid PhaseEquilibria (beginning of 2010).
Hayden-O'ConnellThe Hayden-O'Connell equation-of-state calculates thermodynamic propertiesfor the vapor phase. It is used in property methods NRTL-HOC, UNIF-HOC,UNIQ-HOC, VANL-HOC, and WILS-HOC, and is recommended for nonpolar,polar, and associating compounds. Hayden-O'Connell incorporates thechemical theory of dimerization. This model accounts for strong association
2 Thermodynamic Property Models 23
and solvation effects, including those found in systems containing organicacids, such as acetic acid. The equation-of-state is:
Where:
For nonpolar, non-associating species:
, with
, where
For polar, associating species:
, with
, where
For chemically bonding species:
, and
Cross-Interactions
The previous equations are valid for dimerization and cross-dimerization ifthese mixing rules are applied:
24 2 Thermodynamic Property Models
= 0 unless a special solvation contribution can be justified (for example, iand j are in the same class of compounds). Many values are present in theAspen Physical Property System.
Chemical Theory
When a compound with strong association is present in a mixture,the entire mixture is treated according to the chemical theory of dimerization.
The chemical reaction for the general case of a mixture of dimerizingcomponents i and j is:
Where i and j refer to the same component.
The equation-of-state becomes:
with
In this case, molar volume is equal to V/nt.
This represents true total volume over the true number of species nt.However, the reported molar volume is V/na.
This represents the true total volume over the apparent number of species na.If dimerization does not occur, na is defined as the number of species. V/na
reflects the apparently lower molar volume of an associating gas mixture.
The chemical equilibrium constant for the dimerization reaction on pressurebasis Kp, is related to the true mole fractions and fugacity coefficients:
Where:
yi and yj = True mole fractions of monomers
yij = True mole fraction of dimer
i = True fugacity coefficient of component i
Kij = Equilibrium constant for the dimerization of i and j, on apressure basis
=
2 Thermodynamic Property Models 25
ij = 1 for i=j
= 0 for
Apparent mole fractions yia are reported, but in the calculation real mole
fractions yi, yj, and yij are used.
The heat of reaction due to each dimerization is calculated according to:
The sum of the contributions of all dimerization reactions, corrected for theratio of apparent and true number of moles is added to the molar enthalpy
departure .Parameter Name/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
RGYR rigyr — — 10-11 5x10-9 LENGTH
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
HOCETA 0.0 X — — —
The binary parameters HOCETA for many component pairs are available in theAspen Physical Property System. These parameters are retrievedautomatically when you specify any of the following property methods: NRTL-HOC, UNIF-HOC, UNIQ-HOC, VANL-HOC, and WILS-HOC.
References
J.G. Hayden and J.P. O'Connell, "A Generalized Method for Predicting SecondVirial Coefficients," Ind. Eng. Chem., Process Des. Dev., Vol. 14,No. 3,(1975), pp. 209 – 216.
HF Equation-of-StateHF forms oligomers in the vapor phase. The non-ideality in the vapor phase isfound in important deviations from ideality in all thermodynamic properties.The HF equation accounts for the vapor phase nonidealities. The model isbased on chemical theory and assumes the formation of hexamers.
Species like HF that associate linearly behave as single species. For example,they have a vapor pressure curve, like pure components. The component onwhich a hypothetical unreacted system is based is often called the apparent(or parent) component. Apparent components react to the true species.Electrolyte Calculation in Physical Property Methods discusses apparent andtrue species. Abbott and van Ness (1992) provide details and basicthermodynamics of reactive systems.
The temperature-dependent hexamerization equilibrium constant, can fit theexperimentally determined association factors. The built-in functionality is:
26 2 Thermodynamic Property Models
(1)
The constants C0 and C1 are from Long et al. (1943), and C2 and C3 are set to0. The correlation is valid between 270 and 330 K, and can be extrapolated toabout 370 K (cf. sec. 4). Different sets of constants can be determined byexperimental data regression.
Molar Volume Calculation
The non-ideality of HF is often expressed using the association factor, f,indicating the ratio of apparent number of species to the real number orspecies. Assuming the ideal gas law for all true species in terms of (p, V, T)behavior implies:
(2)
Where the true number of species is given by 1/f. The association factor iseasily determined from (p, V, T) experiments. For a critical evaluation of datarefer to Vanderzee and Rodenburg (1970).
If only one reaction is assumed for a mixture of HF and its associated species,(refer to Long et al., 1943), then:
(3)
If p1 represents the true partial pressure of the HF monomer, and p6
represents the true partial pressure of the hexamer, then the equilibriumconstant is defined as:
(4)
The true total pressure is:
p = p1 + p6 (5)
If all hexamer were dissociated, the apparent total pressure would be thehypothetical pressure where:
pa = p1 + 6p6 = p + 5p6 (6)
When physical ideality is assumed, partial pressures and mole fractions areproportional. The total pressure in equation 5 represents the true number ofspecies. The apparent total pressure from equation 6 represents the apparentnumber of species:
(7)
Note that the outcome of equation 7 is independent of the assumption ofideality. Equation 7 can be used to compute the number of true species 1/ffor a mixture containing HF, but the association factor is defined differently.
2 Thermodynamic Property Models 27
If p1 and p6 are known, the molar volume or density of a vapor containing HFcan be calculated using equations 2 and 7. The molar volume calculated is thetrue molar volume for 1 apparent mole of HF. This is because the volume of 1mole of ideal gas (the true molar volume per true number of moles) is alwaysequal to about 0.0224 m3/mol at 298.15 K.
True Mole Fraction (Partial Pressure) Calculation
If you assume the ideal gas law for a mixture containing HF, the apparent HFmole fraction is:
(8)
The denominator of equation 8 is given by equation 6. The numerator (theapparent partial pressure of HF) is the hypothetical partial pressure only if allof the hexamer was dissociated. If you substitute equation 4, then equation 8becomes:
(9)
K is known from Long et al., or can be regressed from (p,V,T) data. Theapparent mole fraction of HF, ya, is known to the user and the simulator, butp1, or y = p1/p must also be known in order to calculate the thermodynamicproperties of the mixture. Equation 9 must be solved for p1.
Equation 9 can be written as a polynomial in p1 of degree 6:
K(6 - 5ya)(p1)6 + p1 - pya = 0 (9a)
A second order Newton-Raphson technique is used to determine p1. Then p6
can be calculated by equation 5, and f is known (equation 7).
Gibbs Energy and Fugacity
The apparent fugacity coefficient is related to the true fugacity coefficient andmole fractions:
(10)
Equation 10 represents a correction to the ideal mixing term of the fugacity.The ratio of the true number of species to the apparent number of species issimilar to the correction applied in equation 2. Since the ideal gas law isassumed, the apparent fugacity coefficient is given by the equation. Allvariables on the right side are known.
(11)
For pure HF, ya = 1:
28 2 Thermodynamic Property Models
From the fugacity coefficient, the Gibbs energy departure of the mixture orpure apparent components can be calculated:
(12)
(12a)
Enthalpy and Entropy
For the enthalpy departure, the heat of reaction is considered. For anarbitrary gas phase reaction:
(13)
(14)
Where i* is the pure component thermodynamic potential or molar Gibbs
energy of a component. Equation 4 represents the first two terms of thegeneral equation 14. The second or third equality relates the equilibriumconstant to the Gibbs energy of reaction, which is thus related to the enthalpyof reaction:
(15)
All components are assumed to be ideal. The enthalpy departure is equal tothe heat of reaction, per apparent number of moles:
(16)
(17)
From the Gibbs energy departure and enthalpy departure, the entropydeparture can be calculated:
(18)
Temperature derivatives for the thermodynamic properties can be obtainedby straightforward differentiation.
Usage
The HF equation-of-state should only be used for vapor phase calculations. Itis not suited for liquid phase calculations.
The HF equation-of-state can be used with any activity coefficient model fornonelectrolyte VLE. Using the Electrolyte NRTL model and the data packageMHF2 is strongly recommended for aqueous mixtures (de Leeuw andWatanasiri, 1993).
2 Thermodynamic Property Models 29
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
ESHFK/1 C0 43.65 — — — —
ESHFK/2 C1 -8910 — — — —
ESHFK/3 C2 0 — — — —
ESHFK/4 C3 0 — — — —
References
M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions ContainingReactive Species, a Guide to Fundamentals and Applications," Fluid Phase Eq.,Vol. 77, (1992) pp. 53 – 119.
V. V. De Leeuw and S. Watanasiri, "Modelling Phase Equilibria and Enthalpiesof the System Water and Hydroflouric Acid Using an HF Equation-of-state inConjunction with the Electrolyte NRTL Activity Coefficient Model," Paperpresented at the 13th European Seminar on Applied Thermodynamics, June 9– 12, Carry-le-Rouet, France, 1993.
R. W. Long, J. H. Hildebrand, and W. E. Morrell, "The Polymerization ofGaseous Hydrogen and Deuterium Flourides," J. Am. Chem. Soc., Vol. 65,(1943), pp. 182 – 187.
C. E. Vanderzee and W. WM. Rodenburg, "Gas Imperfections andThermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.Thermodynamics, Vol. 2, (1970), pp. 461 – 478.
IAPWS-95 Steam TablesThe IAPWS-95 Steam Tables are implemented like any other equation-of-state in the Aspen Physical Property System. These steam tables can calculateany thermodynamic property of water. The tables form the basis of theIAPWS-95 property method. There are no parameter requirements. They arethe most accurate steam tables in the Aspen Physical Property System.
References
Wanger W. and A. Pruß, ”The IAPWS Formation 1995 for the ThermodynamicProperties of Ordinary Water Substance for General and Scientific Use,” J.Phys. Chem. Ref. Data, 31(2), 387- 535, 2002.
Ideal GasThe ideal gas law (ideal gas equation-of-state) combines the laws of Boyleand Gay-Lussac. It models a vapor as if it consisted of point masses withoutany interactions. The ideal gas law is used as a reference state for equation-of-state calculations, and can be used to model gas mixtures at low pressures(without specific gas phase interactions).
The equation is:
p = RT / Vm
30 2 Thermodynamic Property Models
Lee-KeslerThis equation-of-state model is based on the work of Lee and Kesler (1975).In this equation, the volumetric and thermodynamic properties of fluids basedon the Curl and Pitzer approach (1958) have been analytically represented bya modified Benedict-Webb-Rubin equation-of-state (1940). The modelcalculates the molar volume, enthalpy departure, Gibbs free energydeparture, and entropy departure of a mixture at a given temperature,pressure, and composition for either a vapor or a liquid phase. Partialderivatives of these quantities with respect to temperature can also becalculated.
Unlike the other equation-of-state models, this model does not calculatefugacity coefficients.
The compressibility factor and other derived thermodynamic functions ofnonpolar and slightly polar fluids can be adequately represented, at constantreduced temperature and pressure, by a linear function of the acentric factor.In particular, the compressibility factor of a fluid whose acentric factor is , isgiven by the following equation:
Z = Z(0) + Z(1)
Where:
Z(0) = Compressibility factor of a simple fluid ( = 0)
Z(1) = Deviation of the compressibility factor of the real fluid from Z(0)
Z(0) and Z(1) are assumed universal functions of the reduced temperature andpressure.
Curl and Pitzer (1958) were quite successful in correlating thermodynamicand volumetric properties using the above approach. Their applicationemployed tables of properties in terms of reduced temperature and pressure.A significant weakness of this method is that the various properties (forexample, entropy departure and enthalpy departure) will not be exactlythermodynamically consistent with each other. Lee and Kesler (1975)overcame this drawback by an analytic representation of the tables with anequation-of-state. In addition, the range was extended by including new data.
In the Lee-Kesler implementation, the compressibility factor of any fluid hasbeen written in terms of a simple fluid and a reference as follows:
In the above equation both Z(0) and Z(1) are represented as generalizedequations of the BWR form in terms of reduced temperature and pressure.Thus,
Equations for the enthalpy departure, Gibbs free energy departure, andentropy departure are obtained from the compressibility factor using standardthermodynamic relationships, thus ensuring thermodynamic consistency.
2 Thermodynamic Property Models 31
In the case of mixtures, mixing rules (without any binary parameters) areused to obtain the mixture values of the critical temperature and pressure,and the acentric factor.
This equation has been found to provide a good description of the volumetricand thermodynamic properties of mixtures containing nonpolar and slightlypolar components.Symbol Parameter Name Default Definition
Tc TCLK TC Critical temperature
Pc PCLK PC Critical pressure
OMGLK OMEGA Acentric factor
References
M. Benedict, G. B. Webb, and L. C. Rubin, J. Chem. Phys., Vol. 8, (1940), p.334.
R. F. Curl and K.S. Pitzer, Ind. Eng. Chem., Vol. 50, (1958), p. 265.
B. I. Lee and M.G. Kesler, AIChE J., Vol. 21, (1975), p. 510.
Lee-Kesler-PlöckerThe Lee-Kesler-Plöcker equation-of-state is the basis for the LK-PLOCKproperty method. This equation-of-state applies to hydrocarbon systems thatinclude the common light gases, such as H2S and CO2. It can be used in gas-processing, refinery, and petrochemical applications.
The general form of the equation is:
Where:
The fo and fR parameters are functions of the BWR form. The fo parameter isfor a simple fluid, and fR is for reference fluid n-octane.
The mixing rules are:
Vcm =
=
=
Zm =
32 2 Thermodynamic Property Models
Where:
Vcij =
Tcij =
Zci =
kij = kji
The binary parameter kij is determined from phase-equilibrium dataregression, such as VLE data. The Aspen Physical Property System stores thebinary parameters for a large number of component pairs. These binaryparameters are used automatically with the LK-PLOCK property method. Ifbinary parameters for certain component pairs are not available, they can beestimated using built-in correlations. The correlations are designed for binaryinteractions among the components CO, CO2, N2, H2, CH4 alcohols andhydrocarbons. If a component is not CO, CO2, N2, H2, CH4 or an alcohol, it isassumed to be a hydrocarbon.ParameterName/Element
SymbolDefault MDS LowerLimit
UpperLimit
Units
TCLKP Tci TC x 5.0 2000.0 TEMPERATURE
PCLKP pci PC x PRESSURE
VCLKP Vci VC x 0.001 3.5 MOLE-VOLUME
OMGLKP I OMEGA x -0.5 2.0 —
LKPZC ZciMethod 1: fcn()
Method 2:fcn(pci,Vci,Tci)
x 0.1 0.5 —
LKPKIJ kijfcn(TciVci / TcjVcj) x 5.0 5.0 —
Method 1 is the default for LKPZC; Method 2 can be invoked by setting thevalue of LKPZC equal to zero.
Binary interaction parameters LKPKIJ are available for a large number ofcomponents in the Aspen Physical Property System, from Knapp et al.
References
B.I. Lee and M.G. Kesler, AIChE J., Vol. 21, (1975) p. 510; errata: AIChE J.,Vol. 21, (1975) p. 1040.
V. Plöcker, H. Knapp, and J.M. Prausnitz, Ind. Eng. Chem., Process Des. Dev.,Vol. 17, (1978), p. 324.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-LiquidEquilibria for Mixtures of Low Boiling Substances." Dechema Chemistry DataSeries, Vol. VI.
2 Thermodynamic Property Models 33
NBS/NRC Steam TablesThe NBS/NRC Steam Tables are implemented like any other equation-of-statein the Aspen Physical Property System. These steam tables can calculate anythermodynamic property of water. The tables form the basis of theSTEAMNBS and STMNBS2 property methods. There are no parameterrequirements. The STMNBS2 model uses the same equations as STEAMNBSbut with different root search method. The STEAMNBS method isrecommended for use with the SRK, BWRS, MXBONNEL and GRAYSON2property methods.
References
L. Haar, J.S. Gallagher, and J.H. Kell, "NBS/NRC Steam Tables," (Washington:Hemisphere Publishing Corporation, 1984).
NothnagelThe Nothnagel equation-of-state calculates thermodynamic properties for thevapor phase. It is used in property methods NRTL-NTH, UNIQ-NTH, VANL-NTH, and WILS-NTH. It is recommended for systems that exhibit strong vaporphase association. The model incorporates the chemical theory ofdimerization to account for strong association and solvation effects, such asthose found in organic acids, like acetic acid. The equation-of-state is:
Where:
b =
bij =
nc = Number of components in the mixture
The chemical reaction for the general case of a mixture of dimerizingcomponents i and j is:
The chemical equilibrium constant for the dimerization reaction on pressurebasis Kp is related to the true mole fractions and fugacity coefficients:
Where:
yi and yj = True mole fractions of monomers
34 2 Thermodynamic Property Models
yij = True mole fraction of dimer
i = True fugacity coefficient of component i
Kij = Equilibrium constant for the dimerization of i and j, on apressure basis
When accounting for chemical reactions, the number of true species nt in themixture changes. The true molar volume V/nt is calculated from theequation-of-state. Since both V and nt change in about the same proportion,this number does not change much. However, the reported molar volume isthe total volume over the apparent number of species: V/na. Since theapparent number of species is constant and the total volume decreases withassociation, the quantity V/na reflects the apparent contraction in anassociating mixture.
The heat of reaction due to each dimerization can be calculated:
The heat of reaction for the mixed dimerization of components i and j is bydefault the arithmetic mean of the heats of reaction for the dimerizations of
the individual components. Parameter is a small empirical correctionfactor to this value:
The sum of the contributions of all dimerization reactions, corrected for theratio of apparent and true number of moles, is added to the molar enthalpydeparture:
The equilibrium constants can be computed using either built-in calculationsor parameters you entered.
Built-in correlations:
The pure component parameters b, d, and p are stored in the AspenPhysical Property System for many components.
Parameters you entered:
In this method, you enter Ai, Bi, Ci, and Di on the Methods | Parameters |Pure Component | T-Dependent form. The units for Kii is pressure-1; useabsolute units for temperature. If you enter Kii and Kjj, then Kij is computedfrom
If you enter Ai, Bi, Ci, and Di, the equilibrium constants are computed usingthe parameters you entered. Otherwise the equilibrium constants arecomputed using built-in correlations.
2 Thermodynamic Property Models 35
ParameterName/Element
Symbol Default LowerLimit
Upper Limit Units
TC Tci — 5.0 2000.0 TEMPERATURE
TB Tbi — 4.0 2000.0 TEMPERATURE
PC pci — 105 108 PRESSURE
NTHA/1 bi 0.199 RTci / pci 0.01 1.0 MOLE-VOLUME
NTHA/2 di 0.33 0.01 3.0 —
NTHA/3 pi 0 0.0 1.0 —
NTHK/1 Ai — — — PRESSURE
NTHK/2 Bi 0 — — TEMPERATURE
NTHK/3 Ci 0 — — TEMPERATURE
NTHK/4 Di 0 — — TEMPERATURE
NTHDDH 0† — — MOLE-ENTHALPY
† For the following systems, the values given in Nothnagel et al., 1973 areused by default:
Methyl chloride/acetone
Acetonitrile/acetaldehyde
Acetone/chloroform
Chloroform/diethyl amine
Acetone/benzene
Benzene/chloroform
Chloroform/diethyl ether
Chloroform/propyl formate
Chloroform/ethyl acetate
Chloroform/methyl acetate
Chloroform/methyl formate
Acetone/dichloro methane
n-Butane/n-perfluorobutane
n-Pentane/n-perfluoropentane
n-Pentane/n-perfluorohexane
References
K.-H. Nothnagel, D. S. Abrams, and J.M. Prausnitz, "Generalized Correlationfor Fugacity Coefficients in Mixtures at Moderate Pressures," Ind. Eng. Chem.,Process Des. Dev., Vol. 12, No. 1 (1973), pp. 25 – 35.
Copolymer PC-SAFT EOS ModelThis section describes the Copolymer Perturbed-Chain Statistical AssociatingFluid Theory (PC-SAFT). This equation-of-state model is used through the PC-SAFT property method.
The copolymer PC-SAFT represents the completed PC-SAFT EOS modeldeveloped by Sadowski and co-workers (Gross and Sadowski, 2001, 2002a,2002b; Gross et al., 2003; Becker et al., 2004; Kleiner et al., 2006). Unlike
36 2 Thermodynamic Property Models
the PC-SAFT EOS model (POLYPCSF) in Aspen Plus, the copolymer PC-SAFTincludes the association and polar terms and does not apply mixing rules tocalculate the copolymer parameters from its segments. Its applicability coversfluid systems from small to large molecules, including normal fluids, water,alcohols, and ketones, polymers and copolymers and their mixtures.
References
Gross, J., & Sadowski, G. (2001). Perturbed-Chain SAFT: An equation of statebased on a perturbation theory for chain molecules. Ind. Eng. Chem. Res.,40, 1244-1260.
Gross, J., & Sadowski, G. (2002a). Modeling polymer systems using theperturbed-chain statistical associating fluid theory equation of state. Ind. Eng.Chem. Res., 41, 1084-1093.
Gross, J., & Sadowski, G. (2002b). Application of the Perturbed-Chain SAFTEquation of State to Associating Systems. Ind. Eng. Chem. Res., 41, 5510-5515.
Gross, J., Spuhl, O., Tumakaka, F., & Sadowski, G. (2003). ModelingCopolymer Systems Using the Perturbed-Chain SAFT Equation of State. Ind.Eng. Chem. Res., 42, 1266-1274.
Becker, F., Buback, M., Latz, H., Sadowski, G., & Tumakaka, F. (2004).Cloud-Point Curves of Ethylene-(Meth)acrylate Copolymers in Fluid Ethene upto High Pressures and Temperatures – Experimental Study and PC-SAFTModeling. Fluid Phase Equilibria, 215, 263-282.
Kleiner, M., Tumakaka, F., Sadowski, G., Latz, H., & Buback, M. (2006).PhaseEquilibria in Polydisperse and Associating Copolymer Solutions: Poly(ethane-co-(meth)acrylic acid) – Monomer Mixtures. Fluid Phase Equilibria, 241, 113-123..
Copolymer PC-SAFT Fundamental Equations
The copolymer PC-SAFT model is based on the perturbation theory. Theunderlying idea is to divide the total intermolecular forces into repulsive andattractive contributions. The model uses a hard-chain reference system toaccount for the repulsive interactions. The attractive forces are further dividedinto different contributions, including dispersion, polar, and association.
Using a generated function, , the copolymer PC-SAFT model in general can
be written as follows:
where hc, disp, assoc, and polar are contributions due to hard-chain fluids,
dispersion, association, and polarity, respectively.
The generated function is defined as follows:
2 Thermodynamic Property Models 37
where ares is the molar residual Helmholtz energy of mixtures, R is the gas
constant, T is the temperature, is the molar density, and Zm is the
compressibility factor; ares is defined as:
where a is the Helmholtz energy of a mixture and aig is the Helmholtz energyof a mixture of ideal gases at the same temperature, density and composition
xi. Once is known, any other thermodynamic function of interest can be
easily derived. For instance, the fugacity coefficient i is calculated as follows:
with
where is a partial derivative that is always done to the mole fractionstated in the denominator, while all other mole fractions are consideredconstant.
Applying to the departure equations, departure functions of enthalpy,
entropy, and Gibbs free energy can be obtained as follows:
Enthalpy departure:
Entropy departure:
Gibbs free energy departure:
The following thermodynamic conditions must be satisfied:
38 2 Thermodynamic Property Models
Hard-chain Fluids and Chain Connectivity
In PC-SAFT model, a molecule is modeled as a chain molecule by a series offreely-jointed tangent spheres. The contribution from hard-chain fluids as areference system consists of two parts, a nonbonding contribution (i.e., hard-sphere mixtures prior to bonding to form chains) and a bonding contributiondue to chain formation:
where is the mean segment in the mixture, hs is the contribution from
hard-sphere mixtures on a per-segment basis, and chain is the contribution
due to chain formation. Both and hs are well-defined for mixtures
containing polymers, including copolymers; they are given by the followingequations:
where mi, i, and i are the segment number, the segment diameter, and
the segment energy parameter of the segment type in the copolymer
component i, respectively. The segment number mi is calculated from the
segment ratio parameter ri:
where Mi is the total molecular weight of the segment type in the
copolymer component i and can be calculated from the segment weightfraction within the copolymer:
where wi is the weight fraction of the segment type in the copolymer
component i, and Mi is the molecular weight of the copolymer component i.
Following Sadowski and co-worker’s work ( Gross et al., 2003; Becker et al.,2004), the contribution from the chain connectivity can be written as follows:
2 Thermodynamic Property Models 39
with
where Bii is defined as the bonding fraction between the segment type and the segment type within the copolymer component i, is the number of
the segment types within the copolymer component i, and ghsi,j(di,j) is the
radial distribution function of hard-sphere mixtures at contact.
However, the calculation for Bii depends on the type of copolymers. We
start with a pure copolymer system which consists of only two different types
of segments and ; this gives:
with
We now apply these equations to three common types of copolymers; a)alternating, b) block, and c) random.
For an alternating copolymer, m = m; there are no or adjacent
sequences. Therefore:
For a block copolymer, there is only one pair and the number of and
pairs depend on the length of each block; therefore:
For a random copolymer, the sequence is only known in a statistical sense. If
the sequence is completely random, then the number of adjacent pairs is
proportional to the product of the probabilities of finding a segment of type and a segment of type in the copolymer. The probability of finding a
segment of type is the fraction of segments z in the copolymer:
40 2 Thermodynamic Property Models
The bonding fraction of each pair of types can be written as follows:
where C is a constant and can be determined by the normalization conditionset by Equation 2.70; the value for C is unity. Therefore:
A special case is the Sadowski’s model for random copolymer with two typesof segments only ( Gross et al., 2003; Becker et al., 2004). In this model, thebonding fractions are calculated as follows:
When z < z
When z < z
The generalization of three common types of copolymers from two types of
different segments to multi types of different segments within a copolymer
is straightforward.
For a generalized alternative copolymer, m = m = ... = mr = m/ ; there
are no adjacent sequences for the same type of segments. Therefore,
For a generalized block copolymer, there is only one pair for each adjacent
type of segment pairs ( ) and the number of pairs for a same type
depends on the length of the block; therefore:
2 Thermodynamic Property Models 41
For a generalized random copolymer, the sequence is only known in astatistical sense. If the sequence is completely random, then the number of
adjacent pairs is proportional to the product of the probabilities of finding
a segment of type and a segment of type in the copolymer. The
probability of finding a segment of type is the fraction of segments z in
the copolymer:
The bonding fraction of each pair of types can be written as follows:
where C is a constant and can be determined by the normalization condition.Therefore,
That is,
Put C into the equation above, we obtain:
Copolymer PC-SAFT Dispersion Term
The equations for the dispersion term are given as follows:
42 2 Thermodynamic Property Models
where i,j and i,j are the cross segment diameter and energy parameters,
respectively; only one adjustable binary interaction parameter, i,j is
introduced to calculate them:
In above equations, the model constants a1i, a2i, a3i, b1i, b2i, and b3i are fittedto pure-component vapor pressure and liquid density data of n-alkanes (Gross and Sadowski, 2001).
Association Term for Copolymer Mixtures - 2BModel
The association term in PC-SAFT model in general needs an iterativeprocedure to calculate the fraction of a species (solvent or segment) that arebounded to each association-site type. Only in pure or binary systems, thefraction can be derived explicitly for some specific models. We start with
2 Thermodynamic Property Models 43
general expressions for the association contribution for copolymer systems asfollows:
where A is the association-site type index, is the association-site
number of the association-site type A on the segment type in the
copolymer component i, and is the mole fraction of the segment type in the copolymer component i that are not bonded with the association-sitetype A; it can be estimated as follows:
with
where is the cross effective association volume and is thecross association energy; they are estimated via simple combination rules:
where and are the effective association volume and theassociation energy between the association-site types A and B, of the
segment type in the copolymer component i, respectively.
The association-site number of the site type A on the segment type in the
copolymer component i is equal to the number of the segment type in the
copolymer component i,
where Ni is the number of the segment type in the copolymer component i
and M is the molecular weight of the segment type . In other words, the
association-site number for each site type within a segment is the same;therefore, we can rewrite the equations above as follows:
44 2 Thermodynamic Property Models
To calculate , this equation has to be solved iteratively for eachassociation-site type associated with a species in a component. In practice,further assumption is needed for efficiency. The commonly used model is theso-called 2B model ( Huang and Radosz, 1990; Gross and Sadowski, 2002b).It assumes that an associating species (solvent or segment) has twoassociation sites, one is designed as the site type A and another as the sitetype B. Similarly to the hydrogen bonding, type A treats as a donor site withpositive charge and type B as an acceptor site with negative charge; only thedonor-acceptor association bonding is permitted and this concept applies toboth pure systems (self-association such as water) and mixtures (both self-association and cross-association such as water-methanol). Therefore, we canrewrite these equations as follows:
It is easy to show that
Therefore
References
Huang, S. H., & Radosz, M. (1990). Equation of State for Small, Large,Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res., 29, 2284.
2 Thermodynamic Property Models 45
Gross, J., & Sadowski, G. (2002b). Application of the Perturbed-Chain SAFTEquation of State to Associating Systems. Ind. Eng. Chem. Res., 41, 5510-5515.
Polar Term for Copolymer PC-SAFT
The equations for the polar term are given by Jog et al. (2001) as follows:
In the above equations, I2() and I3() are the pure fluid integrals and i
and (xp)i are the dipole moment and dipolar fraction of the segment type
within the copolymer component i, respectively. Both and
are dimensionless. In terms of them, we can have:
Rushbrooke et al. (1973) have shown that
Then I2() and I3() are computed in terms of by the expressions:
46 2 Thermodynamic Property Models
Reference
Jog, P. K., Sauer, S. G., Blaesing, J., & Chapman, W. G. (2001), Applicationof Dipolar Chain Theory to the Phase Behavior of Polar Fluids and Mixtures.Ind. Eng. Chem. Res., 40, 4641.
Rushbrooke, G. S., & Stell, G., Hoye, J. S. (1973), Molec. Phys., 26, 1199.
Ominik, A., Chapman, W.G., Kleiner, M., & Sadowski, G. (2005), Modeling ofPolar Systems with the Perturbed-Chain SAFT Equation of State. Investigationof the Performance of Two Polar Terms. Ind. Eng. Chem. Res., 44, 6928
Sauer, S.G., & Chapman (2003), A Parametric Study if Dipolar Chain Theorywith Applications to Ketone Mixtures. Ind. Eng. Chem. Res., 42, 5687
Copolymer PC-SAFT EOS Model Parameters
Pure parameters
Each non-association species (solvent or segment) must have a set of three
pure-component parameter; two of them are the segment diameter and the
segment energy parameter . The third parameter for a solvent is the
segment number m and for a segment is the segment ratio parameter r. Foran association species, two additional parameters are the effective association
volume (AB) and the association energy (AB). For a polar species, two
additional parameters are the dipole moment and the segment dipolar
fraction xp.
Binary parameters
There are three types of binary interactions in copolymer systems: solvent-solvent, solvent-segment, and segment-segment. The binary interaction
parameter i,j allows complex temperature dependence:
with
where Tref is a reference temperature and the default value is 298.15 K.
The following table lists the copolymer PC-SAFT EOS model parametersimplemented in Aspen Plus. Some values for these parameters can be foundin the PC-SAFT and POLYPCSF databanks.
2 Thermodynamic Property Models 47
ParameterName/Element
Symbol Default LowerLimit
UpperLimit
MDS UnitsKeyword
Comments
PCSFTM m — — — X — Unary
PCSFTV — — — X — Unary
PCSFTU /k — — — X TEMP Unary
PCSFTR r — — — X — Unary
PCSFAU AB/k — — — X TEMP Unary
PCSFAV AB — — — X — Unary
PCSFMU — — — X — Unary
PCSFXP xp — — — X — Unary
PCSKIJ/1 ai,j0.0 — — X — Binary,
Symmetric
PCSKIJ/2 bi,j0.0 — — X — Binary,
Symmetric
PCSKIJ/3 ci,j0.0 — — X — Binary,
Symmetric
PCSKIJ/4 di,j0.0 — — X — Binary,
Symmetric
PCSKIJ/5 ei,j0.0 — — X — Binary,
Symmetric
PCSKIJ/6 Tref 298.15 — — X TEMP Binary,Symmetric
Parameter Input and Regression for CopolymerPC-SAFT
Since the copolymer PC-SAFT is built based on the segment concept, theunary (pure) parameters must be specified for a solvent or a segment.Specifying a unary parameter for a polymer component (homopolymer orcopolymer) will be ignored by the simulation. For a non-association and non-polar solvent, three unary parameters PCSFTM, PCSFTU, and PCSFTV must bespecified. For a non-association and non-polar segment, these three unaryparameters PCSFTR, PCSFTU, and PCSFTV must be specified. For anassociation species (solvent or segment), two additional unary parametersPCSFAU and PCSFAV must be specified. For a polar species (solvent orsegment), two additional unary parameters PCSFMU and PCSFXP must bespecified.
Note that the SI units for the segment diameter (PCSFTV) and dipole
moment (PCSFMU) are much too large to be practical. The implementation
of PC-SAFT in Aspen Plus has the unit in Angstroms (Å) for the segmentdiameter and in Debye (D) for the dipole moment; these units are not allowedto be changed in PC-SAFT.
The binary parameter PCSKIJ can be specified for each solvent-solvent pair,or each solvent-segment pair, or each segment-segment pair. By default, thebinary parameter is set to be zero.
48 2 Thermodynamic Property Models
A databank called PC-SAFT contains both unary and binary PC-SAFTparameters available from literature; it must be used with the PC-SAFTproperty method. The unary parameters available for segments are stored inthe SEGMENT databank. If unary parameters are not available for a species(solvent or segment) in a calculation, the user can perform an Aspen PlusData Regression Run (DRS) to obtain unary parameters. For non-polymercomponents (mainly solvents), the unary parameters are usually obtained byfitting experimental vapor pressure and liquid molar volume data. To obtainunary parameters for a segment, experimental data on liquid density of thehomopolymer that is built by the segment should be regressed. Once theunary parameters are available for a segment, the ideal-gas heat capacityparameter CPIG may be regressed for the same segment using experimentalliquid heat capacity data for the same homopolymer. In addition to unaryparameters, the binary parameter PCSKIJ for each solvent-solvent pair, oreach solvent-segment pair, or each segment-segment pair, can be regressedusing vapor-liquid equilibrium (VLE) data in the form of TPXY data in AspenPlus.
Note: In Data Regression Run, a homopolymer must be defined as anOLIGOMER type, and the number of the segment that builds the oligomermust be specified.
Peng-RobinsonThe Peng-Robinson equation-of-state is the basis for the PR-BM propertymethod. The model has been implemented with choices of different alphafunctions (see Peng-Robinson Alpha Functions) and has been extended toinclude advanced asymmetric mixing rules.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
By default, the PENG-ROB property method uses the literature version of thealpha function and mixing rules (see Standard Peng-Robinson). The PR-BMproperty method uses the Boston-Mathias alpha function and standard mixingrules. These default property methods are recommended for hydrocarbonprocessing applications such as gas processing, refinery, and petrochemicalprocesses. Their results are comparable to those of the property methods thatuse the standard Redlich-Kwong-Soave equation-of-state.
When advanced alpha function and asymmetric mixing rules are used withappropriately obtained parameters, the Peng-Robinson model can be used toaccurately model polar, non-ideal chemical systems. Similar capability is alsoavailable for the Soave-Redlich-Kwong model.
The equation for the Peng-Robinson model as used in the PR-BM propertymethod is:
Where:
2 Thermodynamic Property Models 49
b =
a = a0+a1
a0 =
(the standard quadratic mixing term, where kij hasbeen made temperature-dependent)
kij =
kij = kji
a1
(an additional, asymmetric term used to modelhighly non-linear systems)
lij =
In general, .
ai =
bi =
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm = Molar volume calculated by the equation of statewithout the correction
c =
(the Peneloux volume correction term)
ci =
(the Peneloux volume correction term for purecomponents, calculated from the criticaltemperature and pressure and the Rackettparameter)
For best results, the binary parameters kij and lij must be determined fromregression of phase equilibrium data such as VLE data. The Aspen PhysicalProperty System also has built-in kij and lij for a large number of componentpairs in the EOS-LIT databank from Knapp et al. These parameters are usedautomatically with the PENG-ROB property method. Values in the databank
50 2 Thermodynamic Property Models
can be different than those used with other models such as Soave-Redlich-Kwong or Redlich-Kwong-Soave, and this can produce different results.
The model has option codes which can be used to customize the model, byselecting a different alpha function and other model options. See Peng-Robinson Alpha Functions for a description of the alpha functions. See OptionCodes for Equation of State Models (under ESPR and ESPR0) for a list of theoption codes.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
PRTC Tci TC x 5.0 2000.0 TEMPERATURE
PRPC pci PC x 105 108 PRESSURE
OMGPR iOMEGA x -0.5 2.0 —
PRZRA zRA RKTZRA x — — —
PRKBV/1 kij(1) 0 x — — —
PRKBV/2 kij(2) 0 x — — TEMPERATURE
PRKBV/3 kij(3) 0 x — — TEMPERATURE
PRKBV/4 Tlower 0 x — — TEMPERATURE
PRKBV/5 Tupper 1000 x — — TEMPERATURE
PRLIJ/1 lij(1) 0 x — — —
PRLIJ/2 lij(2) 0 x — — TEMPERATURE
PRLIJ/3 lij(3) 0 x — — TEMPERATURE
PRLIJ/4 Tlower 0 x — — TEMPERATURE
PRLIJ/5 Tupper 1000 x — — TEMPERATURE
References
D.-Y. Peng and D. B. Robinson, "A New Two-Constant Equation-of-state," Ind.Eng. Chem. Fundam., Vol. 15, (1976), pp. 59–64.
P.M. Mathias, H.C. Klotz, and J.M. Prausnitz, "Equation of state mixing rulesfor multicomponent mixtures: the problem of invariance," Fluid PhaseEquilibria, Vol 67, (1991), pp. 31-44.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-LiquidEquilibria for Mixtures of Low Boiling Substances." Dechema Chemistry DataSeries, Vol. VI.
Standard Peng-RobinsonThe Standard Peng-Robinson equation-of-state is the original formulation ofthe Peng-Robinson equation of state with the standard alpha function (seePeng-Robinson Alpha Functions). It is the basis for the PENG-ROB propertymethod and it is recommended for hydrocarbon processing applications suchas gas processing, refinery, and petrochemical processes. Its results arecomparable to those of the standard Redlich-Kwong-Soave equation of state.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
2 Thermodynamic Property Models 51
The equation for this model is:
Where:
b =
a =
ai =
bi =
kij =
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm = Molar volume calculated by the equation of statewithout the correction
c =
(the Peneloux volume correction term)
ci =
(the Peneloux volume correction term for purecomponents, calculated from the criticaltemperature and pressure and the Rackettparameter)
The model has option codes which can be used to customize the model, byselecting a different alpha function and other model options. See Peng-Robinson Alpha Functions for a description of the alpha functions. See OptionCodes for Equation of State Models (under ESPRSTD and ESPRSTD0) for a listof the option codes.
For best results, the binary parameter kij must be determined from regressionof phase equilibrium data such as VLE data. The Aspen Physical PropertySystem also has built-in kij for a large number of component pairs in the EOS-LIT databank. These parameters are used automatically with the PENG-ROBproperty method. Values in the databank can be different than those usedwith other models such as Soave-Redlich-Kwong or Redlich-Kwong-Soave,and this can produce different results.
52 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCPRS Tci TC x 5.0 2000.0 TEMPERATURE
PCPRS pci PC x 105 108 PRESSURE
OMGPRS iOMEGA x -0.5 2.0 —
PRSZRA zRA RKTZRA x — — —
PRKBV/1 kij(1) 0 x - - -
PRKBV/2 kij(2) 0 x - - TEMPERATURE
PRKBV/3 kij(3) 0 x - - TEMPERATURE
PRKBV/4 Tlower 0 x - - TEMPERATURE
PRKBV/5 Tupper 1000 x - - TEMPERATURE
PRLIJ/1 lij(1) 0 x — — —
PRLIJ/2 lij(2) 0 x — — TEMPERATURE
PRLIJ/3 lij(3) 0 x — — TEMPERATURE
PRLIJ/4 Tlower 0 x — — TEMPERATURE
PRLIJ/5 Tupper 1000 x — — TEMPERATURE
References
D.-Y. Peng and D. B. Robinson, "A New Two-Constant Equation-of-state," Ind.Eng. Chem. Fundam., Vol. 15, (1976), pp. 59–64.
Peng-Robinson-MHV2This model uses the Peng-Robinson equation-of-state for pure compounds.The mixing rules are the predictive MHV2 rules. Several alpha functions canbe used in the Peng-Robinson-MHV2 equation-of-state model for a moreaccurate description of the pure component behavior. The pure componentbehavior and parameter requirements are described in Standard Peng-Robinson, or in Peng-Robinson Alpha Functions.
The MHV2 mixing rules are an example of modified Huron-Vidal mixing rules.A brief introduction is provided in Huron-Vidal Mixing Rules. For more details,see MHV2 Mixing Rules.
Predictive SRK (PSRK)This model uses the Redlich-Kwong-Soave equation-of-state for purecompounds. The mixing rules are the predictive Holderbaum rules, or PSRKmethod. Several alpha functions can be used in the PSRK equation-of-statemodel for a more accurate description of the pure component behavior. Thepure component behavior and parameter requirements are described inStandard Redlich-Kwong-Soave and in Soave Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
2 Thermodynamic Property Models 53
The PSRK method is an example of modified Huron-Vidal mixing rules. A briefintroduction is provided in Huron-Vidal Mixing Rules. For more details, seePredictive Soave-Redlich-Kwong-Gmehling Mixing Rules.
Peng-Robinson-Wong-SandlerThis model uses the Peng-Robinson equation-of-state for pure compounds.The mixing rules are the predictive Wong-Sandler rules. Several alphafunctions can be used in the Peng-Robinson-Wong-Sandler equation-of-statemodel for a more accurate description of the pure component behavior. Thepure component behavior and parameter requirements are described in Peng-Robinson, and in Peng-Robinson Alpha Functions.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
The Wong-Sandler mixing rules are an example of modified Huron-Vidalmixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. Formore details see Wong-Sandler Mixing Rules., this chapter.
Redlich-KwongThe Redlich-Kwong equation-of-state can calculate vapor phasethermodynamic properties for the following property methods: NRTL-RK,UNIFAC, UNIF-LL, UNIQ-RK, VANL-RK, and WILS-RK. It is applicable forsystems at low to moderate pressures (maximum pressure 10 atm) for whichthe vapor-phase nonideality is small. The Hayden-O'Connell model isrecommended for a more nonideal vapor phase, such as in systemscontaining organic acids. It is not recommended for calculating liquid phaseproperties.
The equation for the model is:
p =
Where:
=
b =
ai =
bi =
54 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
References
O. Redlich and J.N.S. Kwong, "On the Thermodynamics of Solutions V. AnEquation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,(1949), pp. 223 – 244.
Redlich-Kwong-AspenThe Redlich-Kwong-Aspen equation-of-state is the basis for the RK-ASPENproperty method. It can be used for hydrocarbon processing applications. It isalso used for more polar components and mixtures of hydrocarbons, and forlight gases at medium to high pressures.
The equation is the same as Redlich-Kwong-Soave:
p =
A quadratic mixing rule is maintained for:
a =
An interaction parameter is introduced in the mixing rule for:
b =
For ai an extra polar parameter is used:
ai =
bi =
The interaction parameters are temperature-dependent:
ka,ij =
kb,ij =
For best results, binary parameters kij must be determined from phase-equilibrium data regression, such as VLE data.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKA Tci TC x 5.0 2000.0 TEMPERATURE
PCRKA pci PC x 105 108 PRESSURE
2 Thermodynamic Property Models 55
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
OMGRKA iOMEGA x -0.5 2.0 —
RKAPOL i0 x -2.0 2.0 —
RKAKA0 ka,ij0 0 x -5.0 5.0 —
RKAKA1 ka,ij1 0 x -15.0 15.0 TEMPERATURE
RKAKB0 kb,ij0 0 x -5.0 5.0 —
RKAKB1 kb,ij1 0 x -15.0 15.0 TEMPERATURE
References
Mathias, P.M., "A Versatile Phase Equilibrium Equation-of-state", Ind. Eng.Chem. Process Des. Dev., Vol. 22, (1983), pp. 385 – 391.
Redlich-Kwong-SoaveThis is the standard Redlich-Kwong-Soave equation-of-state, and is the basisfor the RK-SOAVE property method. It is recommended for hydrocarbonprocessing applications, such as gas-processing, refinery, and petrochemicalprocesses. Its results are comparable to those of the Peng-Robinsonequation-of-state.
The equation is:
Where:
a0 is the standard quadratic mixing term:
a1 is an additional, asymmetric (polar) term:
b =
ai =
bi =
kij = kji
56 2 Thermodynamic Property Models
; ;
The parameter ai is calculated according to the standard Soave formulation(see Soave Alpha Functions, equations 1, 2, 3, 5, and 6).
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm is the molar volume calculated from the equation of state without thecorrection
RKSCMP is the Composition Independent Fugacity Calculation Flag. This is asimplification which improves calculation speed. Set it to 1 for eachcomponent for which you want to enable this simplification. For thesecomponents, the calculated fugacity coefficient of that component is simplythe pure-component fugacity coefficient. This parameter defaults to zero.
RKSWF is the group contribution parameter for the Kabadi-Danner water-hydrocarbon mixing rule, used only when this feature is enabled via optioncode. See SRK-Kabadi-Danner for details.
The model uses option codes which are described in Soave-Redlich-KwongOption Codes.
For best results, binary parameters kij must be determined from phase-equilibrium data regression (for example, VLE data). The Aspen PhysicalProperty System also has built-in kij for a large number of component pairs inthe EOS-LIT databank from Knapp et al. These binary parameters are usedautomatically with the RK-SOAVE property method. Values of kij in thedatabank can be different than those used with other models such as Soave-Redlich-Kwong or Standard Peng-Robinson, and this can produce differentresults.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKSS Tci TC x 5.0 2000.0 TEMPERATURE
PCRKSS pci PC x 105 108 PRESSURE
OMRKSS iOMEGA x -0.5 2.0 —
RKSZRA zRA RKTZRA x — — —
RKSCMP — 0 x — — —
RKSWF Gi 0 x — — —
RKSKBV/1 kij(1) 0 x -5.0 5.0 —
RKSKBV/2 kij(2) 0 x — — TEMPERATURE
2 Thermodynamic Property Models 57
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
RKSKBV/3 kij(3) 0 x — — TEMPERATURE
RKSKBV/4 Tk,lower 0 x — — TEMPERATURE
RKSKBV/5 Tk,upper 1000 x — — TEMPERATURE
RKSLBV/1 lij(1) 0 x — — —
RKSLBV/2 lij(2) 0 x — — TEMPERATURE
RKSLBV/3 lij(3) 0 x — — TEMPERATURE
RKSLBV/4 Tl,lower 0 x — — TEMPERATURE
RKSLBV/5 Tl,upper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.
J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand Temperatures by the Use of a Cubic Equation-of-state," Ind. Eng. Chem.Res., Vol. 28, (1989), pp. 1049 – 1955.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
H. Knapp, R. Döring, L. Oellrich, U. Plöcker, and J. M. Prausnitz. "Vapor-LiquidEquilibria for Mixtures of Low Boiling Substances." Dechema Chemistry DataSeries, Vol. VI.
Redlich-Kwong-Soave-Boston-MathiasThe Redlich-Kwong-Soave-Boston-Mathias equation-of-state is the basis forthe RKS-BM property method. It is the Redlich-Kwong-Soave equation-of-state with the Boston-Mathias alpha function (see Soave Alpha Functions). Itis recommended for hydrocarbon processing applications, such as gas-processing, refinery, and petrochemical processes. Its results are comparableto those of the Peng-Robinson-Boston-Mathias equation-of-state.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
The equation is:
p =
Where:
a0 is the standard quadratic mixing term:
58 2 Thermodynamic Property Models
a1 is an additional, asymmetric (polar) term:
b =
ai =
bi =
kij = kji
; ;
The parameter ai is calculated by the standard Soave formulation atsupercritical temperatures. If the component is supercritical, the Boston-Mathias extrapolation is used (see Soave Alpha Functions).
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm is the molar volume calculated from the equation of state without thecorrection
RKSCMP is the Composition Independent Fugacity Calculation Flag. This is asimplification which improves calculation speed. Set it to 1 for eachcomponent for which you want to enable this simplification. For thesecomponents, the calculated fugacity coefficient of that component is simplythe pure-component fugacity coefficient. This parameter defaults to zero.
RKSWF is the group contribution parameter for the Kabadi-Danner water-hydrocarbon mixing rule, used only when this feature is enabled via optioncode. See SRK-Kabadi-Danner for details.
The model uses option codes which are described in Soave-Redlich-KwongOption Codes.
For best results, binary parameters kij must be determined from phase-equilibrium data regression (for example, VLE data).ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKS Tci TC x 5.0 2000.0 TEMPERATURE
PCRKS pci PC x 105 108 PRESSURE
2 Thermodynamic Property Models 59
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
OMGRKS iOMEGA x -0.5 2.0 —
RKSZRA zRA RKTZRA x — — —
RKSCMP — 0 x — — —
RKSWF Gi 0 x — — —
RKSKBV/1 kij(1) 0 x -5.0 5.0 —
RKSKBV/2 kij(2) 0 x — — TEMPERATURE
RKSKBV/3 kij(3) 0 x — — TEMPERATURE
RKSKBV/4 Tk,lower 0 x — — TEMPERATURE
RKSKBV/5 Tk,upper 1000 x — — TEMPERATURE
RKSLBV/1 lij(1) 0 x — — —
RKSLBV/2 lij(2) 0 x — — TEMPERATURE
RKSLBV/3 lij(3) 0 x — — TEMPERATURE
RKSLBV/4 Tl,lower 0 x — — TEMPERATURE
RKSLBV/5 Tl,upper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 – 1203.
Redlich-Kwong-Soave-Wong-SandlerThis equation-of-state model uses the Redlich-Kwong-Soave equation-of-statefor pure compounds. The predictive Wong-Sandler mixing rules are used.Several alpha functions can be used in the Redlich-Kwong-Soave-Wong-Sandler equation-of-state model for a more accurate description of the purecomponent behavior. The pure component behavior and parameterrequirements are described in Standard Redlich-Kwong-Soave, and in SoaveAlpha Functions.
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
The Wong-Sandler mixing rules are an example of modified Huron-Vidalmixing rules. A brief introduction is provided in Huron-Vidal Mixing Rules. Formore details, see Wong-Sandler Mixing Rules.
Redlich-Kwong-Soave-MHV2This equation-of-state model uses the Redlich-Kwong-Soave equation-of-statefor pure compounds. The predictive MHV2 mixing rules are used. Severalalpha functions can be used in the RK-Soave-MHV2 equation-of-state modelfor a more accurate description of the pure component behavior. The purecomponent behavior and its parameter requirements are described inStandard Redlich-Kwong-Soave, and in Soave Alpha Functions.
60 2 Thermodynamic Property Models
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
The MHV2 mixing rules are an example of modified Huron-Vidal mixing rules.A brief introduction is provided in Huron-Vidal Mixing Rules. For more details,see MHV2 Mixing Rules.
Schwartzentruber-RenonThe Schwartzentruber-Renon equation-of-state is the basis for the SR-POLARproperty method. It can be used to model chemically nonideal systems withthe same accuracy as activity coefficient property methods, such as theWILSON property method. This equation-of-state is recommended for highlynon-ideal systems at high temperatures and pressures, such as in methanolsynthesis and supercritical extraction applications.
The equation for the model is:
p =
Where:
a =
b =
c =
ai =
bi =
ci =
(for T < Tci)
(for T Tci)
The latter equation is used to ensure bi-ci remainspositive in supercritical conditions.
g0i = bi (covolume)
g2i =
2 Thermodynamic Property Models 61
g1i =
ka,ij =
lij =
kb,ij =
ka,ij = ka,ji
lij = -lji
kb,ij = kb,ji
The binary parameters ka,ij, kb,ij, and lij are temperature-dependent. In mostcases, ka,ij
0 and lij0 are sufficient to represent the system of interest.
VLE calculations are independent of c. However, c does influence the fugacityvalues and can be adjusted to (liquid) molar volumes. For a wide temperaturerange, adjust ci0 to the molar volume at 298.15K or at boiling temperature.
The ai are calculated using the Extended Mathias Alpha Function, as describedin Soave Alpha Functions.
Warning: Using c1i and c2i can cause anomalous behavior in enthalpy andheat capacity. Their use is strongly discouraged.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKU Tci TC x 5.0 2000.0 TEMPERATURE
PCRKU pci PC x 105 108 PRESSURE
OMGRKU iOMEGA x -0.5 2.0 —
RKUPP0 †† q0i — x — — —
RKUPP1 †† q1i 0 x — — —
RKUPP2 †† q2i 0 x — — —
RKUC0 c0i 0 x — — ‡
RKUC1 c1i 0 x — — ‡
RKUC2 c2i 0 x — — ‡
RKUKA0 ††† ka,ij0 0 x — — —
RKUKA1 ††† ka,ij1 0 x — — TEMPERATURE †
RKUKA2 ††† ka,ij2 0 x — — TEMPERATURE †
RKULA0 ††† lij0 0 x — — —
RKULA1 ††† lij1 0 x — — TEMPERATURE †
RKULA2 ††† lij2 0 x — — TEMPERATURE †
RKUKB0 ††† kb,ij0 0 x — — —
RKUKB1 ††† kb,ij1 0 x — — TEMPERATURE †
RKUKB2 ††† kb,ij2 0 x — — TEMPERATURE †
† When ka,ij2, lij
2, or kb,ij2 is non-zero, then absolute temperature units are
assumed for it and the corresponding ka,ij1, lij
1, or kb,ij1 .
62 2 Thermodynamic Property Models
†† For polar components (dipole moment >> 0), if you do not enter q0i, thesystem estimates q0i, q1i, q2i from vapor pressures using the Antoine vaporpressure model.
††† If you do not enter at least one of the binary parameters ka,ij0, ka,ij
2, lij0,
lij2, kb,ij
0, or kb,ij2 the system estimates ka,ij
0, ka,ij2, lij
0, and lij2 from the UNIFAC
or Hayden O'Connell models.
‡ RKUC0, RKUC1, and RKUC2 are treated as having units m3/kmol. No unitconversion to other molar volume units is done.
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.
J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand Temperatures by the Use of a Cubic Equation-of-State," Ind. Eng. Chem.Res., Vol. 28, (1989), pp. 1049 – 1955.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
Soave-Redlich-KwongThe Soave-Redlich-Kwong equation-of-state is the basis of the SRK propertymethod. This model is based on the same equation of state as the Redlich-Kwong-Soave model. However, this model has several important differences.
A volume translation concept introduced by Peneloux and Rauzy is used toimprove molar liquid volume calculated from the cubic equation of state.
Improvement in speed of computation for equation based calculation isachieved by using composition independent fugacity.
Optional Kabadi-Danner mixing rules for improved phase equilibriumcalculations in water-hydrocarbon systems (see SRK-Kabadi-Danner)
Optional Mathias alpha function
Note: You can choose any of the available alpha functions, but you cannotdefine multiple property methods based on this model using different alphafunctions within the same run.
This equation-of-state can be used for hydrocarbon systems that include thecommon light gases, such as H2S, CO2 and N2.
The form of the equation-of-state is:
Where:
a0 is the standard quadratic mixing term:
2 Thermodynamic Property Models 63
Where:
;
a1 is an additional, asymmetric (polar) term:
Where:
; ;
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm is the molar volume calculated from the equation of state without thecorrection
If the steam table option is used, the enthalpy, entropy, Gibbs energy, andmolar volume of water to be calculated from the steam tables. The totalproperties are mole-fraction averages of these values with the propertiescalculated by the equation of state for other components. Fugacity coefficientis not affected.
For best results, the binary parameter kij must be determined from phaseequilibrium data regression (for example, VLE data). The Aspen PhysicalProperty System also has built-in kij for a large number of component pairs inthe SRK-ASPEN databank, regressed by AspenTech. These parameters areused automatically with the SRK property method. Values of kij in thedatabank can be different than those used with other models such asStandard Redlich-Kwong-Soave or Standard Redlich-Kwong-Soave, and thiscan produce different results.
The model uses option codes which are described in Soave-Redlich-KwongOption Codes.
64 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SRKTC Tci TC x 5.0 2000.0 TEMPERATURE
SRKPC pci PC x 105 108 PRESSURE
SRKOMG iOMEGA x –0.5 2.0 —
SRKZRA zRA RKTZRA x — — —
SRKKIJ/1 kij(1) 0 x — — —
SRKKIJ/2 kij(2) 0 x — — TEMPERATURE
SRKKIJ/3 kij(3) 0 x — — TEMPERATURE
SRKKIJ/4 Tlower 0 x — — TEMPERATURE
SRKKIJ/5 Tupper 1000 x — — TEMPERATURE
SRKLIJ/1 lij(1) 0 x — — —
SRKLIJ/2 lij(2) 0 x — — TEMPERATURE
SRKLIJ/3 lij(3) 0 x — — TEMPERATURE
SRKLIJ/4 Tlower 0 x — — TEMPERATURE
SRKLIJ/5 Tupper 1000 x — — TEMPERATURE
References
G. Soave, "Equilibrium Constants for Modified Redlich-Kwong Equation-of-state," Chem. Eng. Sci., Vol. 27, (1972), pp. 1196 - 1203.
A. Peneloux, E. Rauzy, and R. Freze, "A Consistent Correction For Redlich-Kwong-Soave Volumes", Fluid Phase Eq., Vol. 8, (1982), pp. 7–23.
P.M. Mathias, H.C. Klotz, and J.M. Prausnitz, "Equation of state mixing rulesfor multicomponent mixtures: the problem of invariance," Fluid PhaseEquilibria, Vol 67, (1991), pp. 31-44.
SRK-Kabadi-DannerThe SRK-Kabadi-Danner property model uses the SRK equation-of-state withimproved phase equilibrium calculations for mixtures containing water andhydrocarbons. These improvements are achieved by using the Kabadi-Dannermixing rules.
The form of the equation-of-state is:
Where:
a0 is the standard quadratic mixing term:
2 Thermodynamic Property Models 65
Where:
;
The best values of kwj (w = water) were obtained from experimental data.Results are given for seven homologous series.
Best Fit Values of kwj for Different Homologous Serieswith WaterHomologous series kwj
Alkanes 0.500
Alkenes 0.393
Dialkenes 0.311
Acetylenes 0.348
Naphthenes 0.445
Cycloalkenes 0.355
Aromatics 0.315
aKD is the Kabadi-Danner term for water:
Where:
Gi is the sum of the group contributions of different groups which make up amolecule of hydrocarbon i.
gl is the group contribution parameter for groups constituting hydrocarbons.
Groups Constituting Hydrocarbons and Their GroupContribution ParametersGroup l gl , atm m6 x 105
CH4 1.3580
– CH3 0.9822
– CH2 – 1.0780
> CH – 0.9728
> C < 0.8687
– CH2 – (cyclic) 0.7488
> CH – (cyclic) 0.7352
– CH = CH – (cyclic) † 0.6180
CH2 = CH2 1.7940
CH2 = CH – 1.3450
CH2 = C< 0.9066
66 2 Thermodynamic Property Models
Group l gl , atm m6 x 105
CH CH 1.6870
CH C – 1.1811
– CH = 0.5117
> C = (aromatic) 0.3902
† This value is obtained from very little data. Might not be reliable.
If the Peneloux volume correction is used (option code 4), then the molarvolume is calculated from:
V = Vm - c
Where:
Vm is the molar volume calculated from the equation of state without thecorrection
The model uses option codes which are described in Soave-Redlich-KwongOption Codes.
SRK-Kabadi-Danner uses the same parameters as SRK, with addedinteraction parameters. Do not specify values for the SRKLIJ parameterswhen using SRK-KD.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SRKTC Tci TC x 5.0 2000.0 TEMPERATURE
SRKPC pci PC x 105 108 PRESSURE
SRKOMG i OMEGA x –0.5 2.0 —
SRKWF Gi 0 x — — —
SRKZRA zRA RKTZRA x — — —
SRKKIJ/1 kij(1) 0 x — — —
SRKKIJ/2 kij(2) 0 x — — TEMPERATURE
SRKKIJ/3 kij(3) 0 x — — TEMPERATURE
SRKKIJ/4 Tlower 0 x — — TEMPERATURE
SRKKIJ/5 Tupper 0 x — — TEMPERATURE
References
V. Kabadi and R. P. Danner, "A Modified Soave-Redlich-Kwong Equation ofState for Water-Hydrocarbon Phase Equilibria", Ind. Eng. Chem. Process Des.Dev., Vol. 24, No. 3, (1985), pp. 537-541.
2 Thermodynamic Property Models 67
SRK-MLThe SRK-ML property model is the same as the Soave-Redlich-Kwong modelwith these exceptions:
kij does not equal kji for non-ideal systems; they are unsymmetric, and adifferent set of parameters is used, as shown below.
The lij are calculated from the equation lij = kji - kij
The Peneloux volume correction is disabled by default. (It can be enabledusing option code 4.)
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SMLTC Tci TC x 5.0 2000.0 TEMPERATURE
SMLPC pci PC x 105 108 PRESSURE
SMLOMG iOMEGA x –0.5 2.0 —
SMLZRA zRA RKTZRA x — — —
SMLCMP — 0 x — — —
SRKMLP — † x -2.0 2.0 †
SRKGLP — † x — — †
SMLKIJ/1 kij(1) 0 x — — —
SMLKIJ/2 kij(2) 0 x — — TEMPERATURE
SMLKIJ/3 kij(3) 0 x — — TEMPERATURE
SMLKIJ/4 Tlower 0 x — — TEMPERATURE
SMLKIJ/5 Tupper 1000 x — — TEMPERATURE
The model uses option codes which are described in Soave-Redlich-KwongOption Codes.
Additional Parameters
SMLZRA is used in Peneloux-Rauzy volume translation as described in Soave-Redlich-Kwong. This volume translation feature can be enabled by settingoption code 4 to 1, but is disabled by default (in which case this parameter isnot used).
SMLCMP is the Composition Independent Fugacity Calculation Flag. This is asimplification which improves calculation speed. Set it to 1 for eachcomponent for which you want to enable this simplification. For thesecomponents, the calculated fugacity coefficient of that component is simplythe pure-component fugacity coefficient. This parameter defaults to zero.
SRKMLP is a polar parameter for the Mathias alpha function.
SRKGLP is a vector of parameters for the Gibbons-Laughton alpha function.
VPA/IK-CAPE Equation-of-StateThe VPA/IK-CAPE equation of state is similar to the HF equation of state butallows dimerization, tetramerization and hexamerization to occursimultaneously. The main assumption of the model is that only molecular
68 2 Thermodynamic Property Models
association causes the gas phase nonideality. Attractive forces between themolecules and the complexes are neglected.
There are three kinds of associations, which can be modeled:
Dimerization (examples: formic acid, acetic acid)
Tetramerization (example: acetic acid)
Hexamerization (example: hydrogen fluoride)
To get the largest possible flexibility of the model all these kinds ofassociation can occur simultaneously, for example, in a mixture containingacetic acid and HF. Up to five components can associate, and any number ofinert components are allowed. This is the only difference between this modeland the HF equation of state, which account only the hexamerization of HF.
Symbols
In the following description, these symbols are used:
yi = Apparent concentration
zin = True concentration, for component i and degree ofassociation n=1, 2, 4, 6
zMij = True concentration of cross-dimers of components iand j, for i,j 1 to 5.
p0 = Reference pressure
k = Number of components
Association Equilibria
Every association equilibrium reaction
(1)
(2)
is described by the equilibrium constants
(3)
(4)
By setting
(5)
(6)
2 Thermodynamic Property Models 69
their temperature dependence can be reproduced.
To evaluate the true concentration of every complex zin, the followingnonlinear systems of equations are to be solved:
Total mass balance:The sum of true concentrations is unity.
(7)
Mass balance for every component i>1:The ratio of the monomers of each component i>1 and component i=1occurring in the various complexes must be equal to the ratio of theirapparent concentrations.
(8)
Thus, a system of k nonlinear equations for k unknowns zi1 has beendeveloped. After having solved it, all the zin and zMij can be determined usingequations (3, 4). This is the main step to evaluate all the properties neededfor a calculation.
Specific Volume of the Gas Phase
The compressibility factor is defined by the ratio between the number ofcomplexes and the number of monomers in the complexes.
(9)
The compressibility factor itself is
(10)
70 2 Thermodynamic Property Models
Fugacity Coefficient
As is well-known from thermodynamics, the fugacity coefficient can becalculated by
(11)
Isothermal Enthalpy Departure
According to the ASPEN enthalpy model, an equation of state must supply anexpression to compute the isothermal molar enthalpy departure between zeropressure and actual pressure. In the following section this enthalpy
contribution per mole monomers is abbreviated by ha.
Taking this sort of gas phase non-ideality into account, the specific enthalpyper mole can be written as
(12)
with
(13)
to evaluate ha, a mixture consisting of N monomers integrated in the
complexes is considered. The quota of monomers i being integrated in acomplex of degree n is given by
(14)
and
(16)
respectively. For the reactions mentioned above:
(1)
(2)
the enthalpies of reaction are
(17)
(18)
as the van't Hoff equation
2 Thermodynamic Property Models 71
(19)
holds for this case.
For each monomer being integrated in a complex of degree n, its contribution
to the enthalpy departure is hin / n or hMij / 2, respectively. Hence, ha can
easily be derived by
(20)
Isothermal entropy and Gibbs energy departure:
A similar expression for ga should hold as it does for the enthalpy departure
(eq. 20):
(21)
using
(22)
and
(23)
(24)
Using the association model, more different species occur than can bedistinguished. Thus, the equivalent expression for the entropy of mixingshould be written with the true concentrations. As eq. 24 refers to 1 molemonomers, the expression should be weighted by the compressibility factorrepresenting the true number of moles. The new expression is
(25)
For ga we obtain
(26)
72 2 Thermodynamic Property Models
and, analogously,
(27)
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DMER/1 Ai2 0 X – – –
DMER/2 Bi2 0 X – – TEMPERATURE
TMER/1 Ai4 0 X – – –
TMER/2 Bi4 0 X – – TEMPERATURE
HMER/1 Ai6 0 X – – –
HMER/2 Bi6 0 X – – TEMPERATURE
References
M. M. Abbott and H. C. van Ness, "Thermodynamics of Solutions ContainingReactive Species, a Guide to Fundamentals and Applications," Fluid Phase Eq.,Vol. 77, (1992) pp. 53–119.
V. V. De Leeuw and S. Watanasiri, "Modeling Phase Equilibria and Enthalpiesof the System Water and Hydrofluoric Acid Using an HF Equation-of-state inConjunction with the Electrolyte NRTL Activity Coefficient Model," PaperPresented at the 13th European Seminar on Applied Thermodynamics, June9–12, Carry-le-Rouet, France, 1993.
R. W. Long, J. H. Hildebrand, and W. E. Morrell, "The Polymerization ofGaseous Hydrogen and Deuterium Fluorides," J. Am. Chem. Soc., Vol. 65,(1943), pp. 182–187.
C. E. Vanderzee and W. Wm. Rodenburg, "Gas Imperfections andThermodynamic Excess Properties of Gaseous Hydrogen Fluoride," J. Chem.Thermodynamics, Vol. 2, (1970), pp. 461–478.
Peng-Robinson Alpha FunctionsThe pure component parameters for the Peng-Robinson equation-of-state arecalculated as follows:
(1)
(2)
These expressions are derived by applying the critical constraints to theequation-of-state under these conditions:
(3)
2 Thermodynamic Property Models 73
The parameter is a temperature function. It was originally introduced by
Soave in the Redlich-Kwong equation-of-state. This parameter improves thecorrelation of the pure component vapor pressure.
Note: You can choose any of the alpha functions described here, but youcannot define multiple property methods based on this model using differentalpha functions within the same run.
This approach was also adopted by Peng and Robinson:
(4)
Equation 3 is still represented. The parameter mi can be correlated with theacentric factor:
(5)
Equations 1 through 5 are the standard Peng-Robinson formulation. ThePeng-Robinson alpha function is adequate for hydrocarbons and othernonpolar compounds, but is not sufficiently accurate for polar compounds.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCPR Tci TC X 5.0 2000.0 TEMPERATURE
PCPR pci PC X 105 108 PRESSURE
OMGPR iOMEGA X -0.5 2.0 —
Boston-Mathias Extrapolation
For light gases at high reduced temperatures (> 5), equation 4 givesunrealistic results. The boundary conditions are that attraction between
molecules should vanish for extremely high temperatures, and reduces
asymptotically to zero. Boston and Mathias derived an alternative function fortemperatures higher than critical:
(6)
With
=
=
Where mi is computed by equation 5, and equation 4 is used for subcriticaltemperatures. Additional parameters are not needed.
74 2 Thermodynamic Property Models
Extended Gibbons-Laughton Alpha Function
The extended Gibbons-Laughton alpha function is suitable for use with bothpolar and nonpolar components. It has the flexibility to fit the vapor pressureof most substances from the triple point to the critical point.
Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependentparameters.
This function is equivalent to the standard Peng-Robinson alpha function if
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
PRGLP/1 X — X — — —
PRGLP/2 Y 0 X — — —
PRGLP/3 Z 0 X — — —
PRGLP/4 n 2 X — — —
PRGLP/5 Tlower 0 X — — TEMPERATURE
PRGLP/6 Tupper 1000 X — — TEMPERATURE
Twu Generalized Alpha Function
The Twu generalized alpha function is a theoretically-based function that iscurrently recognized as the best available alpha function. It behaves betterthan other functions at supercritical conditions (T > Tc) and when the acentricfactor is large. The improved behavior at high values of acentric factor isimportant for high molecular weight pseudocomponents. There is no limit onthe minimum value of acentric factor that can be used with this function.
Where the L, M, and N are parameters that vary depending on the equation ofstate and whether the temperature is above or below the critical temperatureof the component.
For Peng-Robinson equation of state:Subcritical T Supercritical T
L(0) 0.272838 0.373949
M(0) 0.924779 4.73020
N(0) 1.19764 -0.200000
L(1) 0.625701 0.0239035
M(1) 0.792014 1.24615
N(1) 2.46022 -8.000000
2 Thermodynamic Property Models 75
Twu Alpha Function
The Twu alpha function is a theoretically-based function that is currentlyrecognized as the best available alpha function. It behaves better than otherfunctions at supercritical conditions (T > Tc).
Where the L, M, and N are substance-dependent parameters that must bedetermined from regression of pure-component vapor pressure data or otherdata such as liquid heat capacity.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
PRTWUP/1 L — X — — —
PRTWUP/2 M 0 X — — —
PRTWUP/3 N 0 X — — —
Mathias-Copeman Alpha Function
This is an extension of the Peng-Robinson alpha function which provides amore accurate fit of vapor pressure for polar compounds.
(7)
For c2,i = 0 and c3,i = 0, this expression reduces to the standard Peng-Robinson formulation if c2,i = mi. You can use vapor pressure data if thetemperature is subcritical to regress the constants. If the temperature issupercritical, c2,i and c3,i are set to 0.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCPR Tci TC X 5.0 2000.0 TEMPERATURE
PCPR pci PC X 105 108 PRESSURE
PRMCP/1 c1,i — X — — —
PRMCP/2 c2,i 0 X — — —
PRMCP/3 c3,i 0 X — — —
Schwartzentruber-Renon-Watanasiri Alpha Function
The Schwartzentruber-Renon-Watanasiri alpha function is:
(8)
Where mi is computed by equation 5. The polar parameters p1,i, p2,i and p3,i
are comparable with the c parameters of the Mathias-Copeman expression.Equation 8 reduces to the standard Peng-Robinson formulation if the polarparameters are zero. Equation 8 is used only for below-critical temperatures.For above-critical temperatures, the Boston-Mathias extrapolation is used.Use equation 6 with:
(9)
76 2 Thermodynamic Property Models
(10)
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCPR Tci TC X 5.0 2000.0 TEMPERATURE
PCPR pci PC X 105 108 PRESSURE
OMGPR iOMEGA X -0.5 2.0 —
PRSRP/1 — X — — —
PRSRP/2 0 X — — —
PRSRP/3 0 X — — —
HYSYS Alpha Function
The HYSYS alpha function uses the same equation as the standard Peng-
Robinson alpha function when < 0.49, and otherwise it uses equation 4
with the following definition of m to correct the behavior for large values of
acentric factor:
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCPR Tci TC X 5.0 2000.0 TEMPERATURE
PCPR pci PC X 105 108 PRESSURE
OMGPR iOMEGA X -0.5 2.0 —
Use of Alpha Functions
The alpha functions in Peng-Robinson-based equation-of-state models isprovided in the following table. You can verify and change the value ofpossible option codes on the Methods | Selected Methods | Models sheet.Alpha function Model name First Option code
Standard PR/Boston-Mathias
ESPR0, ESPRESPRWS0, ESPRWSESPRV20, ESPRV2
000
Standard Peng Robinson ESPRSTD0, ESPRSTD 1
Extended Gibbons-Laughton
ESPR0, ESPR 2
Twu Generalized alphafunction
ESPR0, ESPR 3
Twu alpha function ESPR0, ESPR 4
HYSYS alpha function ESPRSTD0, ESPRSTD 5
Mathias-Copeman ESPR, ESPR0ESPRWS0, ESPRWSESPRV20, ESPRV2
622
2 Thermodynamic Property Models 77
Alpha function Model name First Option code
Schwartzentruber-Renon-Watanasiri
ESPR, ESPR0ESPRWS0, ESPRWSESPRV20, ESPRV2
73 (default)3 (default)
References
J. F. Boston and P.M. Mathias, "Phase Equilibria in a Third-Generation ProcessSimulator" in Proceedings of the 2nd International Conference on PhaseEquilibria and Fluid Properties in the Chemical Process Industries, West Berlin,(17-21 March 1980) pp. 823-849.
D.-Y. Peng and D.B. Robinson, "A New Two-Constant Equation-of-state," Ind.Eng. Chem. Fundam., Vol. 15, (1976), pp. 59-64.
P.M. Mathias and T.W. Copeman, "Extension of the Peng-Robinson Equation-of-state To Complex Mixtures: Evaluation of the Various Forms of the LocalComposition Concept",Fluid Phase Eq., Vol. 13, (1983), p. 91.
J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for Non-IdealSystems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.
G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-of-state," Chem Eng. Sci., Vol. 27, (1972), pp. 1196-1203.
C.H. Twu, J. E. Coon, and J.R. Cunningham, "A New Cubic Equation of State,"Fluid Phase Equilib., Vol. 75, (1992), pp. 65-79.
C.H. Twu, D. Bluck, J.R. Cunningham, and J.E. Coon, "A Cubic Equation ofState with a New Alpha Function and a New Mixing Rule," Fluid Phase Equilib.,Vol. 69, (1991), pp. 33-50.
Soave Alpha Functions
The pure component parameters for the Redlich-Kwong equation-of-state arecalculated as:
(1)
(2)
These expressions are derived by applying the critical constraint to theequation-of-state under these conditions:
(3)
Note: You can choose any of the alpha functions described here, but youcannot define multiple property methods based on this model using differentalpha functions within the same run.
In the Redlich-Kwong equation-of-state, alpha is:
78 2 Thermodynamic Property Models
(4)
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
Soave Modification
The parameter i is a temperature function introduced by Soave in theRedlich-Kwong equation-of-state to improve the correlation of the purecomponent vapor pressure:
(5)
Equation 3 still holds. The parameter mi can be correlated with the acentricfactor:
(6)
Equations 1, 2, 3, 5 and 6 are the standard Redlich-Kwong-Soaveformulation. The Soave alpha function is adequate for hydrocarbons and othernonpolar compounds, but is not sufficiently accurate for polar compounds.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKS Tci TC X 5.0 2000.0 TEMPERATURE
PCRKS pci PC X 105 108 PRESSURE
OMGRKS i OMEGA X -0.5 2.0 —
Boston-Mathias Extrapolation
For light gases at high reduced temperatures (> 5), equation 5 givesunrealistic results. The boundary conditions are that attraction between
molecules should vanish for extremely high temperatures, and reducesasymptotically to zero. Boston and Mathias derived an alternative function fortemperatures higher than critical:
(7)
With
di =
ci =
Where:
2 Thermodynamic Property Models 79
mi = Computed by equation 6
Equation 5 = Used for subcritical temperatures
Additional parameters are not needed.
Mathias Alpha Function
This is an extension of the Soave alpha function which provides a moreaccurate fit of vapor pressure for polar compounds.
(8)
For i=0, equation 8 reduces to the standard Redlich-Kwong-Soaveformulation, equations 5 and 6. For temperatures above critical, the Boston-Mathias extrapolation is used, that is, equation 7 with:
(9)
(10)
The Mathias alpha function is used in the Redlich-Kwong-Aspen model, whichis the basis for the RK-ASPEN property method. This alpha function is alsoavailable as an option for SRK, SRKKD, SRK-ML, RK-SOAVE, and RKS-BM.See Soave-Redlich-Kwong Option Codes for more information.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKA Tci TC X 5.0 2000.0 TEMPERATURE
PCRKA pci PC X 105 108 PRESSURE
OMGRKA i OMEGA X -0.5 2.0 —
† i — X -2.0 2.0 —
† RKAPOL for Redlich-Kwong-Aspen, SRKPOL for SRK and SRKKD, SRKMLP forSRK-ML, RKSPOL for RKS-BM, or RKSSPO for RK-SOAVE.
Extended Mathias Alpha Function
An extension of the Mathias approach is:
(11)
Where mi is computed by equation 6. If the polar parameters p1,i, p2,i and p3,i
are zero, equation 11 reduces to the standard Redlich-Kwong-Soaveformulation. You can use vapor pressure data to regress the constants if thetemperature is subcritical. Equation 11 is used only for temperatures belowcritical.
The Boston-Mathias extrapolation is used for temperatures above critical, thatis, with:
(12)
80 2 Thermodynamic Property Models
(13)
This alpha function is used in the Redlich-Kwong-UNIFAC model which is thebasis for the SR-POLAR property method.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKU Tci TC X 5.0 2000.0 TEMPERATURE
PCRKU pci PC X 105 108 PRESSURE
OMGRKU i OMEGA X -0.5 2.0 —
RKUPP0 p1,i — X — — —
RKUPP1 p2,i 0 X — — —
RKUPP2 p3,i 0 X — — —
Mathias-Copeman Alpha Function
The Mathias-Copeman alpha function is suitable for use with both polar andnonpolar components. It has the flexibility to fit the vapor pressure of mostsubstances from the triple point to the critical point.
(14)
For c2,i=0 and c3,i=0 this expression reduces to the standard Redlich-Kwong-Soave formulation if c1,i=mi. If the temperature is subcritical, use vaporpressure data to regress the constants. If the temperature is supercritical, setc2,i and c3,i to 0.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKS Tci TC X 5.0 2000.0 TEMPERATURE
PCRKS pci PC X 105 108 PRESSURE
RKSMCP/1 c1,i — X — — —
RKSMCP/2 c2,i 0 X — — —
RKSMCP/3 c3,i 0 X — — —
Schwartzentruber-Renon-Watanasiri Alpha Function
The Schwartzentruber-Renon-Watanasiri alpha function is:
(15)
Where mi is computed by equation 6 and the polar parameters p1,i, p2,i andp3,i are comparable with the c parameters of the Mathias-Copemanexpression. Equation 15 reduces to the standard Redlich-Kwong-Soaveformulation if the polar parameters are zero. Equation 15 is very similar tothe extended Mathias equation, but it is easier to use in data regression. It isused only for temperatures below critical. The Boston-Mathias extrapolation isused for temperatures above critical, that is, use equation 7 with:
(16)
2 Thermodynamic Property Models 81
(17)
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCRKS Tci TC X 5.0 2000.0 TEMPERATURE
PCRKS pci PC X 105 108 PRESSURE
OMGRKS i OMEGA X -0.5 2.0 —
RKSSRP/1 p1,i — X — — —
RKSSRP/2 p2,i 0 X — — —
RKSSRP/3 p3,i 0 X — — —
Extended Gibbons-Laughton Alpha Function
The extended Gibbons-Laughton alpha function is suitable for use with bothpolar and nonpolar components. It has the flexibility to fit the vapor pressureof most substances from the triple point to the critical point.
Where Tr is the reduced temperature; Xi, Yi and Zi are substance dependentparameters.
This function is equivalent to the standard Soave alpha function if
This function is not intended for use in supercritical conditions. To avoidpredicting negative alpha, when Tri>1 the Boston-Mathias alpha function isused instead.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SRKGLP/1 X — X — — —
SRKGLP/2 Y 0 X — — —
SRKGLP/3 Z 0 X — — —
SRKGLP/4 n 2 X — — —
SRKGLP/5 Tlower 0 X — — TEMPERATURE
SRKGLP/6 Tupper 1000 X — — TEMPERATURE
Twu Generalized Alpha Function
The Twu generalized alpha function is a theoretically-based function that iscurrently recognized as the best available alpha function. It behaves betterthan other functions at supercritical conditions (T > Tc) and when the acentricfactor is large. The improved behavior at high values of acentric factor isimportant for high molecular weight pseudocomponents. There is no limit onthe minimum value of acentric factor that can be used with this function.
82 2 Thermodynamic Property Models
Where the L, M, and N are parameters that vary depending on the equation ofstate and whether the temperature is above or below the critical temperatureof the component.
For Soave-Redlich-Kwong:Subcritical T Supercritical T
L(0) 0.544000 0.379919
M(0) 1.01309 5.67342
N(0) 0.935995 -0.200000
L(1) 0.544306 0.0319134
M(1) 0.802404 1.28756
N(1) 3.10835 -8.000000
Twu Alpha Function
The Twu alpha function is a theoretically-based function that is currentlyrecognized as the best available alpha function. It behaves better than otherfunctions at supercritical conditions (T > Tc).
Where the L, M, and N are substance-dependent parameters that must bedetermined from regression of pure-component vapor pressure data or otherdata such as liquid heat capacity.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
*/1 L — X — — —
*/2 M 0 X — — —
*/3 N 0 X — — —
* Parameter name is RKSTWUP for ESRKS & ESRKS0, SRKTWUP for ESSRK &ESSRK0, RKSSTWUP for ESRKSTD & ESRKSTD0, and RKSMTWUP forESRKSML & ESRKSML0.
Use of Alpha Functions
The use of alpha functions in Soave-Redlich-Kwong based equation-of-statemodels is given in the following table. You can verify and change the value ofpossible option codes on the Methods | Selected Methods | Models sheet.Alpha Function Model Name First Option Code
original RK ESRK0, ESRK —
standard RKS ESRKSTD0, ESRKSTD*
—1, 2 (default)
2 Thermodynamic Property Models 83
Alpha Function Model Name First Option Code
standard RKS/Boston-Mathias *ESRKSWS0, ESRKSWSESRKSV10, ESRKV1ESRKSV20, ESRKSV2
0111
Gibbons-Laughton with Patelextension
* 3
Mathias/Boston-Mathias ESRKA0, ESRKA —
Mathias for T < Tc; Boston-Mathias for T > Tc
* 4
Extended Mathias/Boston-Mathias
ESRKU0, ESRKU —
Mathias-Copeman ESRKSV10, ESRKSV1ESRKSV20, ESRKSV2ESRKS, ESRKS0,ESRKSML, ESRKSML0,ESRKSW, ESRKSW0,ESSRK, ESSRK0
226666
Schwartzentruber-Renon-Watanasiri
ESPRWS0, ESPRWSESRKSV10, ESRKSV1ESRKSV20, ESRKSV2ESRKS, ESRKS0,ESRKSML, ESRKSML0,ESRKSW, ESRKSW0,ESSRK, ESSRK0
3 (default)3 (default)3 (default)7777
Twu * 8
Twu generalized * 5
* ESRKSTD0, ESRKSTD, ESRKS0, ESRKS, ESSRK, ESSRK0, ESRKSML,ESRKSML0. The default alpha function (option code 2) for these models is thestandard RKS alpha function, except that the Grabovsky-Daubert alpha
function is used for H2: = 1.202 exp(-0.30228xTri)
References
J. F. Boston and P.M. Mathias, "Phase Equilibria in a Third-Generation ProcessSimulator" in Proceedings of the 2nd International Conference on PhaseEquilibria and Fluid Properties in the Chemical Process Industries, West Berlin,(17-21 March 1980), pp. 823-849.
P. M. Mathias, "A Versatile Phase Equilibrium Equation-of-state", Ind. Eng.Chem. Process Des. Dev., Vol. 22, (1983), pp. 385–391.
P.M. Mathias and T.W. Copeman, "Extension of the Peng-Robinson Equation-of-state To Complex Mixtures: Evaluation of the Various Forms of the LocalComposition Concept", Fluid Phase Eq., Vol. 13, (1983), p. 91.
O. Redlich and J. N. S. Kwong, "On the Thermodynamics of Solutions V. AnEquation-of-state. Fugacities of Gaseous Solutions," Chem. Rev., Vol. 44,(1949), pp. 223–244.
J. Schwartzentruber and H. Renon, "Extension of UNIFAC to High Pressuresand Temperatures by the Use of a Cubic Equation-of-state," Ind. Eng. Chem.Res., Vol. 28, (1989), pp. 1049–1055.
84 2 Thermodynamic Property Models
J. Schwartzentruber, H. Renon, and S. Watanasiri, "K-values for Non-IdealSystems:An Easier Way," Chem. Eng., March 1990, pp. 118-124.
G. Soave, "Equilibrium Constants for a Modified Redlich-Kwong Equation-of-state," Chem Eng. Sci., Vol. 27, (1972), pp. 1196-1203.
C.H. Twu, W.D. Sim, and V. Tassone, "Getting a Handle on Advanced CubicEquations of State", Chemical Engineering Progress, Vol. 98 #11 (November2002) pp. 58-65.
Huron-Vidal Mixing RulesHuron and Vidal (1979) used a simple thermodynamic relationship to equatethe excess Gibbs energy to expressions for the fugacity coefficient ascomputed by equations of state:
(1)
Equation 1 is valid at any pressure, but cannot be evaluated unless someassumptions are made. If Equation 1 is evaluated at infinite pressure, themixture must be liquid-like and extremely dense. It can be assumed that:
(2)
(3)
Using equations 2 and 3 in equation 1 results in an expression for a/b thatcontains the excess Gibbs energy at an infinite pressure:
(4)
Where:
(5)
The parameters 1and 2depend on the equation-of-state used. In general a
cubic equation-of-state can be written as:
(6)
Values for 1and 2 for the Peng-Robinson and the Soave-Redlich-Kwong
equations of state are:Equation-of-state 1 2
Peng-Robinson
Redlich-Kwong-Soave 1 0
This expression can be used at any pressure as a mixing rule for theparameter. The mixing rule for b is fixed by equation 3. Even when used atother pressures, this expression contains the excess Gibbs energy at infinite
2 Thermodynamic Property Models 85
pressure. You can use any activity coeffecient model to evaluate the excessGibbs energy at infinite pressure. Binary interaction coefficients must beregressed. The mixing rule used contains as many binary parameters as theactivity coefficient model chosen.
This mixing rule has been used successfully for polar mixtures at highpressures, such as systems containing light gases. In theory, any activitycoefficient model can be used. But the NRTL equation (as modified by Huronand Vidal) has demonstrated better performance.
The Huron-Vidal mixing rules combine extreme flexibility with thermodynamicconsistency, unlike many other mole-fraction-dependent equation-of-statemixing rules. The Huron-Vidal mixing rules do not allow flexibility in thedescription of the excess molar volume, but always predict reasonable excessvolumes.
The Huron-Vidal mixing rules are theoretically incorrect for low pressure,because quadratic mole fraction dependence of the second virial coefficient (ifderived from the equation-of-state) is not preserved. Since equations of stateare primarily used at high pressure, the practical consequences of thisdrawback are minimal.
The Gibbs energy at infinite pressure and the Gibbs energy at an arbitraryhigh pressure are similar. But the correspondence is not close enough tomake the mixing rule predictive.
There are several methods for modifying the Huron-Vidal mixing rule to makeit more predictive. The following three methods are used in Aspen PhysicalProperty System equation-of-state models:
The modified Huron-Vidal mixing rule, second order approximation(MHV2)
The Predictive SRK Method (PSRK)
The Wong-Sandler modified Huron-Vidal mixing rule (WS)
These mixing rules are discussed separately in the following sections. Theyhave major advantages over other composition-dependent equation-of-statemixing rules.
References
M.- J. Huron and J. Vidal, "New Mixing Rules in Simple Equations of State forrepresenting Vapour-liquid equilibria of strongly non-ideal mixtures," FluidPhase Eq., Vol. 3, (1979), pp. 255-271.
MHV2 Mixing RulesDahl and Michelsen (1990) use a thermodynamic relationship between excessGibbs energy and the fugacity computed by equations of state. Thisrelationship is equivalent to the one used by Huron and Vidal:
(1)
86 2 Thermodynamic Property Models
The advantage is that the expressions for mixture and pure componentfugacities do not contain the pressure. They are functions of compacity V/b
and :
(2)
Where:
(3)
and
(4)
With:
(5)
The constants 1 and 2, which depend only on the equation-of-state (see
Huron-Vidal Mixing Rules) occur in equations 2 and 4.
Instead of using infinite pressure for simplification of equation 1, the conditionof zero pressure is used. At p = 0 an exact relationship between the
compacity and can be derived. By substitution the simplified equation q()
is obtained, and equation 1 becomes:
(6)
However, q() can only be written explicitly for = 5.8. Only an
approximation is possible below that threshold. Dahl and Michelsen use a
second order polynomial fitted to the analytical solution for 10 < < 13 that
can be extrapolated to low alpha:
(7)
Since q()is a universal function (for each equation-of-state), the
combination of equations 6 and 7 form the MHV2 mixing rule. Excess Gibbsenergies, from any activity coefficient model with parameters optimized at
low pressures, can be used to determine , if i, bi, and b are known. To
compute b, a linear mixing rule is assumed as in the original Huron-Vidalmixing rules:
(8)
This equation is equivalent to the assumption of zero excess molar volume.
The MHV2 mixing rule was the first successful predictive mixing rule forequations of state. This mixing rule uses previously determined activity
2 Thermodynamic Property Models 87
coefficient parameters for predictions at high pressures. UNIFAC was chosenas a default for its predictive character. The Lyngby modified UNIFACformulation was chosen for optimum performance (see UNIFAC (LyngbyModified)). However, any activity coefficient model can be used when itsbinary interaction parameters are known.
Like the Huron-Vidal mixing rules, the MHV2 mixing rules are not flexible inthe description of the excess molar volume. The MHV2 mixing rules aretheoretically incorrect at the low pressure limit. But the practicalconsequences of this drawback are minimal (see Huron-Vidal Mixing Rules,this chapter).
Reference: S. Dahl and M.L. Michelsen, "High-Pressure Vapor-LiquidEquilibrium with a UNIFAC-based Equation-of-state," AIChE J., Vol. 36,(1990), pp. 1829-1836.
Predictive Soave-Redlich-Kwong-GmehlingMixing RulesThese mixing rules by Holderbaum and Gmehling (1991) use a relationshipbetween the excess Helmholtz energy and equation-of-state. They do not usea relationship between equation-of-state properties and excess Gibbs energy,as in the Huron-Vidal mixing rules. The pressure-explicit expression for theequation-of-state is substituted in the thermodynamic equation:
(1)
The Helmholtz energy is calculated by integration. AE is obtained by:
(2)
Where both Ai* and Am are calculated by using equation 1. Ai* and Am arewritten in terms of equation-of-state parameters.
The simplification of constant packing fraction (Vm / b) is used:
(3)
With:
(4)
Therefore:
(5)
The mixing rule is:
(6)
88 2 Thermodynamic Property Models
Where ' is slightly different from for the Huron-Vidal mixing rule:
(7)
Where 1 and 2, depend on the equation-of-state (see Huron-Vidal Mixing
Rules). If equation 6 is applied at infinite pressure, the packing fraction goesto 1. The excess Helmholtz energy is equal to the excess Gibbs energy. TheHuron-Vidal mixing rules are recovered.
The goal of these mixing rules is to be able to use binary interactionparameters for activity coefficient models at any pressure. These parametershave been optimized at low pressures. UNIFAC is chosen for its predictivecharacter. Two issues exist: the packing fraction is not equal to one, and theexcess Gibbs and Helmholtz energy are not equal at the low pressure wherethe UNIFAC parameters have been derived.
Fischer (1993) determined that boiling point, the average packing fraction forabout 80 different liquids with different chemical natures was 1.1. Adoptingthis value, the difference between liquid excess Gibbs energy and liquidexcess Helmholtz energy can be computed as:
(8)
The result is a predictive mixing rule for cubic equations of state. But theoriginal UNIFAC formulation gives the best performance for any binary pairwith interactions available from UNIFAC. Gas-solvent interactions areunavailable. However, it has poor accuracy for highly asymmetric such as CH4– n-C10H22. To address the issue, the Li correction (Li et al., 1998) isapplied.
With the Li correction, the R and Q parameters for groups CH3, CH2, CH, andC in UNIFAC are modified. R* and Q*, the effective values of R and Q, arecalculated based on the original values and nc, the number of alkyl carbons(single-bonded carbons in CH3, CH2, CH, and C groups), as follows, fornc<45:
At the University of Oldenburg in Germany, the UNIFAC groups wereextended with often-occurring gases. New group interactions weredetermined from gas-solvent data, specific to the Redlich-Kwong-Soaveequation-of-state. The new built-in parameters to the Aspen Physical PropertySystem are activated when using the PSRK equation-of-state model.
The PSRK method has a lot in common with the Huron-Vidal mixing rules. Themole fraction is dependent on the second virial coefficient and excess volumeis predicted. These are minor disadvantages.
2 Thermodynamic Property Models 89
References
K. Fischer, "Die PSRK-Methode: Eine Zustandsgleichung unter Verwendungdes UNIFAC-Gruppenbeitragsmodells," (Düsseldorf: VDI Fortschrittberichte,Reihe 3: Verfahrenstechnik, Nr. 324, VDI Verlag GmbH, 1993).
T. Holderbaum and J. Gmehling, "PSRK: A Group Contribution Equation-of-state based on UNIFAC," Fluid Phase Eq., Vol. 70, (1991), pp. 251-265.
J. Li, K. Fischer, and J. Gmehling, "Prediction of vapor-liquid equilibria forasymmetric systems at low and high pressures with the PSRK model," FluidPhase Equilib., 1998, 143, 71-82
Wong-Sandler Mixing RulesThese mixing rules use a relationship between the excess Helmholtz energyand equation-of-state. They do not use a relationship between equation-of-state properties and excess Gibbs energy, as in the Huron-Vidal mixing rules.The pressure-explicit expression for the equation-of-state is substituted in thethermodynamic equation:
(1)
The Helmholtz energy is obtained by integration, AE is obtained by:
(2)
Where both Ai* and Am are calculated by using equation 1. Ai* and Am arewritten in terms of equation-of-state parameters.
Like Huron and Vidal, the limiting case of infinite pressure is used. Thissimplifies the expressions for Ai* and Am. Equation 2 becomes:
(3)
Where depends on the equation-of-state (see Huron-Vidal Mixing Rules).
Equation 3 is completely analogous to the Huron-Vidal mixing rule for theexcess Gibbs energy at infinite pressure. (See equation 4, Huron-Vidal MixingRules.) The excess Helmholtz energy can be approximated by the excessGibbs energy at low pressure from any liquid activity coefficient model. Usingthe Helmholtz energy permits another mixing rule for b than the linear mixingrule. The mixing rule for b is derived as follows. The second virial coefficientmust depend quadratically on the mole fraction:
(4)
With:
(5)
90 2 Thermodynamic Property Models
The relationship between the equation-of-state at low pressure and the virialcoefficient is:
(6)
(7)
Wong and Sandler discovered the following mixing rule to satisfy equation 4(using equations 6 and 7):
The excess Helmholtz energy is almost independent of pressure. It can beapproximated by the Gibbs energy at low pressure. The difference betweenthe two functions is corrected by fitting kij until the excess Gibbs energy fromthe equation-of-state (using the mixing rules 3 and 8) is equal to the excessGibbs energy computed by an activity coeffecient model. This is done at aspecific mole fraction and temperature.
This mixing rule accurately predicts the VLE of polar mixtures at highpressures. UNIFAC or other activity coeffecient models and parameters fromthe literature are used. Gas solubilities are not predicted. They must beregressed from experimental data.
Unlike other (modified) Huron-Vidal mixing rules, the Wong and Sandlermixing rule meets the theoretical limit at low pressure. The use of kij doesinfluence excess molar volume behavior. For calculations where densities areimportant, check whether they are realistic.
References
D. S. Wong and S. I. Sandler, "A Theoretically Correct New Mixing Rule forCubic Equations of State for Both Highly and Slightly Non-ideal Mixtures,"AIChE J., Vol. 38, (1992), pp. 671 – 680.
D. S. Wong, H. Orbey, and S. I. Sandler, "Equation-of-state Mixing Rule forNon-ideal Mixtures Using Available Activity Coefficient Model Parameters andThat Allows Extrapolation over Large Ranges of Temperature and Pressure",Ind Eng Chem. Res., Vol. 31, (1992), pp. 2033 – 2039.
H. Orbey, S. I. Sandler and D. S. Wong, "Accurate Equation-of-statePredictions at High Temperatures and Pressures Using the Existing UNIFACModel," Fluid Phase Eq., Vol. 85, (1993), pp. 41 – 54.
2 Thermodynamic Property Models 91
Activity Coefficient ModelsThe Aspen Physical Property System has the following built-in activitycoefficient models. This section describes the activity coefficient modelsavailable.Model Type
Bromley-Pitzer Electrolyte
Chien-Null Regular solution, local composition
Constant Activity Coefficient Arithmetic
COSMO-SAC Regular solution
Electrolyte NRTL Electrolyte
ENRTL-SAC Segment contribution, electrolyte
Hansen Regular solution
Ideal Liquid Ideal
NRTL (Non-Random-Two-Liquid) Local composition
NRTL-SAC Segment contribution
Pitzer Electrolyte
Polynomial Activity Coefficient Arithmetic
Redlich-Kister Arithmetic
Scatchard-Hildebrand Regular solution
Symmetric Electrolyte NRTL Electrolyte, pure fused saltreference state for ions
Three-Suffix Margules Arithmetic
UNIFAC Group contribution
UNIFAC (Lyngby modified) Group contribution
UNIFAC (Dortmund modified) Group contribution
UNIQUAC Local composition
Unsymmetric Electrolyte NRTL Electrolyte
Van Laar Regular solution
Wagner interaction parameter Arithmetic
Wilson Local composition
Wilson with Liquid Molar Volume Local composition
Bromley-Pitzer Activity Coefficient ModelThe Bromley-Pitzer activity coefficient model is a simplified Pitzer activitycoefficient model with Bromley correlations for the interaction parameters.See Working Equations for a detailed description. This model has predictivecapabilities. It can be used to compute activity coefficients for aqueouselectrolytes up to 6 molal ionic strength, but is less accurate than the Pitzermodel if the parameter correlations are used. The model should not be usedfor mixed-solvent electrolyte systems.
The Bromley-Pitzer model in the Aspen Physical Property System involvesuser-supplied parameters, used in the calculation of binary parameters for theelectrolyte system.
92 2 Thermodynamic Property Models
Parameters (0), (1), (2), (3), and have five elements to account for
temperature dependencies. Elements P1 through P5 follow the temperaturedependency relation:
Where:
Tref = 298.15K
The user must:
Supply these elements using a Methods | Parameters | Binary | T-Dependent form.
Specify Comp ID i and Comp ID j on this form, using the same order thatappears on the Components | Specifications | Selection sheet form.
Parameter Name Symbol No. of ElementsDefault Units
Ionic Unary Parameters
GMBPB ion1 0 —
GMBPD ion1 0 —
Cation-Anion Parameters
GMBPB0 (0) 5 0 —
GMBPB1 (1) 5 0 —
GMBPB2 (2) 5 0 —
GMBPB3 (3) 5 0 —
Cation-Cation Parameters
GMBPTH cc'5 0 —
Anion-Anion Parameters
GMBPTH aa'5 0 —
Molecule-Ion and Molecule-Molecule Parameters
GMBPB0 (0) 5 0 —
GMBPB1 (1) 5 0 —
Working Equations
The complete Pitzer equation (Fürst and Renon, 1982) for the excess Gibbsenergy is (see also equation 4):
(1)
Where:
GE = Excess Gibbs energy
2 Thermodynamic Property Models 93
R = Gas constant
T = Temperature
nw = Kilograms of water
zi = Charge number of ion i
= molality of ion i
Where:
xi = Mole fraction of ion i
xw = Mole fraction of water
Mw = Molecular weight of water (g/mol)
ni = Moles of ion i
B, C, and are interaction parameters, and f(I) is an electrostatic term as
a function of ionic strength; these terms are discussed in Pitzer ActivityCoefficient Model, which has a detailed discussion of the Pitzer model.
The C term and the term are dropped from equation 1 to give the
simplified Pitzer equation.
(2)
Where:
Bij = f(ij(0),ij
(1),ij(2),ij
(3))
Therefore, the simplified Pitzer equation has two types of binary interaction
parameters, 's and ''s. There are no ternary interaction parameters with
the simplified Pitzer equation.
Note that the Pitzer model parameter databank described in Physical PropertyData, Chapter 1, is not applicable to the simplified Pitzer equation.
A built-in empirical correlation estimates the (0) and (1) parameters for
cation-anion pairs from the Bromley ionic parameters, ion and ion (Bromley,
1973). The estimated values of (0)'s and (1)'s are overridden by the user's
input. For parameter naming and requirements, see Bromley-Pitzer ActivityCoefficient Model.
References
L.A. Bromley, "Thermodynamic Properties of Strong Electrolytes in AqueousSolution, " AIChE J., Vol. 19, No. 2, (1973), pp. 313 – 320.
W. Fürst and H. Renon, "Effects of the Various Parameters in the Applicationof Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1Electrolytes," Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, (1982),pp. 396-400.
94 2 Thermodynamic Property Models
Parameter Conversion
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), the parameter
(3) corresponds to Pitzer's (1); (2) is the same in both Aspen Physical
Property System and original Pitzer models. Pitzer refers to the n-m
electrolyte parameters as (1), (2), (0). (0) and (2) retain their meanings in
both models, but Pitzer's (1) is Aspen Physical Property System (3). Be
careful to make this distinction when entering n-m electrolyte parameters.
Chien-NullThe Chien-Null model calculates liquid activity coefficients and it can be usedfor highly non-ideal systems. The generalized expression used in its derivationcan be adapted to represent other well known formalisms for the activitycoefficient by properly defining its binary terms. This characteristic allows themodel the use of already available binary parameters regressed for thoseother liquid activity models with thermodynamic consistency.
The equation for the Chien-Null liquid activity coeficient is:
Where:
Rji = Aji / Aij
Aii = 0
Aij = aij + bij / T
Subscripts i and j are component indices.
The choice of model and parameters can be set for each binary pairconstituting the process mixture by assigning the appropriate value to theICHNUL parameter.
The Regular Solution and Scatchard-Hamer models are regained bysubstituting in the general expression (ICHNUL = 1 or 2).
Vji = Sji = Vj*,l / Vi
*,l
Where:
Vj*,l = Liquid molar volume of component i
The Chien-Null activity coefficient model collapses to the Margules liquidactivity coefficient expression by setting (ICHNUL = 3):
Vji = Sji = 1
The Van Laar Liquid activity coefficient model is obtained when the V and Sparameters in the Chien-Null models are set to the ratio of the cross terms ofA (ICHNUL = 4:)
Vji = Sji = Aji / Aij
2 Thermodynamic Property Models 95
Finally, the Renon or NRTL model is obtained when we make the followingsusbstitutions in the Chien-Null expression for the liquid activity (ICHNUL =5).
Sji = RjiAji / Aij
Aji = 2jiGji
Vji = Gji
The following are defined for the Non-Random Two-Liquid activity coefficientmodel, where:
ij = aij + bij / T
Cij = cij + dij (T - 273.15 K)
cji = cij
dji = dij
The binary parameters CHNULL/1, CHNULL/2, and CHNULL/3 can bedetermined from regression of VLE and/or LLE data. Also, if you haveparameters for many of the mixture pairs for the Margules, Van Laar,Scatchard-Hildebrand, and NRTL (Non-Random-Two-Liquid) activity models,you can use them directly with the Chien-Null activity model after selectingthe proper code (ICHNUL) to identify the source model and entering theappropriate activity model parameters.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
ICHNUL — 3 1 6 —
CHNULL/1 aij 0 — — —
CHNULL/2 bij 0 — — —
CHNULL/3 Vij 0 — — —
The parameter ICHNUL is used to identify the activity model parametersavailable for each binary pair of interest. The following values are allowed forICHNUL:
ICHNUL = 1 or 2, sets the model to the Scatchard-Hamer or regular solutionmodel for the associated binary;
ICHNUL = 3, sets the model to the Three-Suffix Margules activity model forthe associated binary;
ICHNUL = 4, sets the model to the Van Laar formalism for the activity modelfor the associated binary;
ICHNUL = 5, sets the model to the NRTL (Renon) formalism for the activitymodel for the associated binary.
ICHNUL = 6, sets the model to the full Chien-Null formalism for the activitymodel for the associated binary.
When you specify a value for the ICHNUL parameter that is different than thedefault, you must enter the appropriate binary model parameters for the
96 2 Thermodynamic Property Models
chosen activity model directly. The routine will automatically convert theexpressions and parameters to conform to the Chien-Null formulation.
Constant Activity CoefficientThis approach is used exclusively in metallurgical applications where multipleliquid and solid phases can coexist. You can assign any value to the activitycoefficient of component i. Use the Properties | Parameters | PureComponent | Scalar form.The equation is:
i = ai
ParameterName/Element
Symbol Default MDS UpperLimit
LowerLimit
Units
GMCONS ai 1.0 x — — —
COSMO-SACCosmo-SAC is a solvation model that describes the electric fields on themolecular surface of species that are polarizable. It requires a fairlycomplicated quantum mechanical calculation, but this calculation must bedone only once for a particular molecule; then the results can be stored. In itsfinal form, it uses individual atoms as the building blocks for predicting phaseequilibria instead of functional groups. This model formulation provides aconsiderably larger range of applicability than group-contribution methods.
The calculation for liquid nonideality is only slightly more computationallyintensive than activity-coefficient models such as NRTL or UNIQUAC. Cosmo-SAC complements the UNIFAC group-contribution method, because it isapplicable to virtually any mixture.
The Cosmo-SAC model calculates liquid activity coefficients. The equation forthe Cosmo-SAC model is:
With
2 Thermodynamic Property Models 97
Where:
i= Activity coefficient of component i
iSG = Staverman-Guggenheim model for combinatorial
contribution to i
i(m) = Segment activity coefficient of segment m in
component i
S(m) = Segment activity coefficient of segment m in
solvent mixture
pi(m) = Sigma profile of component i
pi(m) = Sigma profile of solvent mixture
= Surface charge density
W(m,n) = Exchange energy between segments m and n
WHB(m,n) = Hydrogen-bonding contribution to exchange energy
between segments m and n
98 2 Thermodynamic Property Models
z = Coordination number, 10
Vi = Molecular volume of component i
Ai = Molecular surface area of component i
aeff = Standard segment surface area, 7.50 Å2
Veff = Standard component volume, 66.69 Å3
Aeff = Standard component surface area, 79.53 Å2
' = Misfit energy constant
The Cosmo-SAC model does not require binary parameters. For eachcomponent, it has six input parameters. CSACVL is the component volumeparameter which is always defined in cubic angstroms, regardless of chosenunits sets. SGPRF1 to SGPRF5 are five molecular component sigma profileparameters; each can store up to 12 points of sigma profile values. All sixinput parameters are obtained from COSMO calculation. The Aspen PhysicalProperty System includes a database of sigma profiles for over 1400compounds from Mullins et al. (2006). The parameters were obtained bypermission from the Virginia Tech Sigma Profile Database website(http://www.design.che.vt.edu/VT-2004.htm). Aspen Technology, Inc. doesnot claim proprietary rights to these parameters.
Note: Starting in version V7.2, additional parameters SGPRF6 and SGPRF7are available in Aspen Plus and Aspen Properties, as part of a plannedexpansion to allow larger sigma profiles to be used. In V7.3.2, threeadditional sets of parameters are added as part of further expansion to modelelectrolyte systems. They are the component ionic sigma profile fromSGPRE1 through SGPRE7, the molecular sigma profile for ionic pair fromSGPBF1 through SGPBF7, and the ionic sigma profile for ionic pair fromSGPBE1 through SGPBE7. However, the model is not yet updated to usethese parameters and you should not yet try to use sigma profiles larger than51 elements.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CSACVL Vi — x — — VOLUME (Å3)
SGPRF1 Ai pi(1-12) — x — — —
SGPRF2 Ai pi(13-24) — x — — —
SGPRF3 Ai pi(25-36) — x — — —
SGPRF4 Ai pi(37-48) — x — — —
SGPRF5 Ai pi(49-51) — x — — —
Option Codes
The primary version of COSMO-SAC is the model by Lin and Sandler (2002).Two other versions are available using an option code, as detailed in the tablebelow:OptionCode
Description
1 COSMO-SAC model by Lin and Sandler (2002)
2 COSMO-RS model by Klamt (1995)
2 Thermodynamic Property Models 99
OptionCode
Description
3 Lin and Sandler model with modified exchange energy (Linet al., 2002)
References
A. Klamt, "Conductor-like Screening Model for Real Solvents: A New Approachto the Quantitative Calculation of Solvation Phenomena," J. Phys. Chem. 99,2224 (1995).
S.-T. Lin, P. M. Mathias, Y. Song, C.-C. Chen, and S. I. Sandler,"Improvements of Phase-Equilibrium Predictions for Hydrogen-BondingSystems from a New Expression for COSMO Solvation Models," presented atthe AIChE Annual Meeting, Indianapolis, IN, 3-8 November (2002).
S.-T. Lin and S. I. Sandler, "A Priori Phase Equilibrium Prediction from aSegment Contribution Solvation Model," Ind. Eng. Chem. Res. 41, 899(2002).
E. Mullins, et al. "Sigma-Profile Database for Using COSMO-BasedThermodynamic Methods," Ind. Eng. Chem. Res. 45, 4389 (2006).
Electrolyte NRTL Activity Coefficient Model(GMENRTL)The Electrolyte NRTL activity coefficient model (GMENRTL) is a versatilemodel for the calculation of activity coefficients. Using binary and pairparameters, the model can represent aqueous electrolyte systems as well asmixed solvent electrolyte systems over the entire range of electrolyteconcentrations. This model can calculate activity coefficients for ionic speciesand molecular species in aqueous electrolyte systems as well as in mixedsolvent electrolyte systems. The model reduces to the well-known NRTLmodel when electrolyte concentrations become zero (Renon and Prausnitz,1969).
The electrolyte NRTL model uses the infinite dilution aqueous solution as thereference state for ions. It adopts the Born equation to account for thetransformation of the reference state of ions from the infinite dilution mixedsolvent solution to the infinite dilution aqueous solution.
Water must be present in the electrolyte system in order to compute thetransformation of the reference state of ions. Thus, it is necessary tointroduce a trace amount of water to use the model for nonaqueouselectrolyte systems.
The Aspen Physical Property System uses the electrolyte NRTL model tocalculate activity coefficients, enthalpies, and Gibbs energies for electrolytesystems. Model development and working equations are provided inTheoretical Basis and Working Equations. The enthalpy and Gibbs energymodels are described separately in Electrolyte NRTL Enthalpy and ElectrolyteNRTL Gibbs Energy.
The adjustable parameters for the electrolyte NRTL model include the:
Pure component dielectric constant coefficient of nonaqueous solvents
100 2 Thermodynamic Property Models
Born radius of ionic species
NRTL parameters for molecule-molecule, molecule-electrolyte, andelectrolyte-electrolyte pairs
The pure component dielectric constant coefficients of nonaqueous solventsand Born radius of ionic species are required only for mixed-solventelectrolyte systems. The temperature dependency of the dielectric constant ofsolvent B is:
Each type of electrolyte NRTL parameter consists of both the nonrandomness
factor, , and energy parameters, . The temperature dependency relations
of the electrolyte NRTL parameters are:
Molecule-Molecule Binary Parameters:
Electrolyte-Molecule Pair Parameters:
Electrolyte-Electrolyte Pair Parameters:
For the electrolyte-electrolyte pair parameters, the two electrolytes mustshare either one common cation or one common anion:
Where:
Tref = 298.15K
Many parameter pairs are included in the electrolyte NRTL model parameterdatabank (see Physical Property Data, Chapter 1).ParameterName
Symbol No. ofElements
Default MDS Units
Dielectric Constant Unary Parameters
CPDIEC AB 1 — — —
BB 1 0 — —
CB 1 298.15 — Kelvin (noconversion)
2 Thermodynamic Property Models 101
ParameterName
Symbol No. ofElements
Default MDS Units
Dielectric Constant Unary Parameters
Ionic Born Radius Unary Parameters
RADIUS ri 1 3x10-10 — LENGTH
Molecule-Molecule Binary Parameters
NRTL/1 ABB' — 0 x —
AB'B — 0 x —
NRTL/2 BBB' — 0 x TEMPERATURE†
BB'B — 0 x TEMPERATURE†
NRTL/3 BB' = B'B— .3 x —
NRTL/4 — — 0 x TEMPERATURE
NRTL/5 FBB' — 0 x TEMPERATURE
FB'B — 0 x TEMPERATURE
NRTL/6 GBB' — 0 x TEMPERATURE
GB'B — 0 x TEMPERATURE
Electrolyte-Molecule Pair Parameters
GMELCC Cca,B 1 0 x —
CB,ca 1 0 x —
GMELCD Dca,B 1 0 x TEMPERATURE†
DB,ca 1 0 x TEMPERATURE†
GMELCE Eca,B 1 0 x —
EB,ca 1 0 x —
GMELCN ca,B = B,ca1 .2 x —
Electrolyte-Electrolyte Pair Parameters
GMELCC Cca',ca'' 1 0 x —
Cca'',ca' 1 0 x —
Cc'a,c''a 1 0 x —
Cc''a,c'a 1 0 x —
GMELCD Dca',ca'' 1 0 x TEMPERATURE †
Dca'',ca' 1 0 x TEMPERATURE†
Dc'a,c''a 1 0 x TEMPERATURE†
Dc''a,c'a 1 0 x TEMPERATURE†
GMELCE Eca',ca'' 1 0 x —
Eca'',ca' 1 0 x —
Ec'a,c''a 1 0 x —
Ec''a,c'a 1 0 x —
GMELCN ca',ca'' = ca'',ca'1 .2 x —
c'a,c''a = c''a,c'a1 .2 x —
† Certain Electrolyte NRTL activity coefficient model parameters are used withreciprocal temperature terms:
CPDIEC
NRTL/2
GMELCD for electrolyte-electrolyte or electrolyte-molecule pairs
102 2 Thermodynamic Property Models
When any of these parameters is specified, absolute temperature units areused for the calculations in this model.
Additional parameters are used in the enthalpy and Gibbs energy models. Seealso Electrolyte NRTL Enthalpy and Electrolyte NRTL Gibbs Energy.
Reference: H. Renon, and J.M. Prausnitz, "Local Compositions inThermodynamic Excess Functions for Liquid Mixtures", AIChE J., Vol. 14, No.1, (1968), pp. 135-144.
Theoretical Basis and Working Equations
In this section, the theoretical basis of the model is explained and the workingequations are given. The different ways parameters can be obtained arediscussed with references to the databank directories and the DataRegression System (DRS). The parameter requirements of the model aregiven in Electrolyte NRTL Activity Coefficient Model.
Development of the Model
The Electrolyte NRTL model was originally proposed by Chen et al., foraqueous electrolyte systems. It was later extended to mixed solventelectrolyte systems (Mock et al., 1984, 1986). The model is based on twofundamental assumptions:
The like-ion repulsion assumption: states that the local composition ofcations around cations is zero (and likewise for anions around anions).This is based on the assumption that the repulsive forces between ions oflike charge are extremely large. This assumption may be justified on thebasis that repulsive forces between ions of the same sign are very strongfor neighboring species. For example, in salt crystal lattices the immediateneighbors of any central ion are always ions of opposite charge.
The local electroneutrality assumption: states that the distribution ofcations and anions around a central molecular species is such that the netlocal ionic charge is zero. Local electroneutrality has been observed forinterstitial molecules in salt crystals.
Chen proposed an excess Gibbs energy expression which contains twocontributions: one contribution for the long-range ion-ion interactions thatexist beyond the immediate neighborhood of a central ionic species, and theother related to the local interactions that exist at the immediateneighborhood of any central species.
The unsymmetric Pitzer-Debye-Hückel model and the Born equation are usedto represent the contribution of the long-range ion-ion interactions, and theNon-Random Two Liquid (NRTL) theory is used to represent the localinteractions. The local interaction contribution model is developed as asymmetric model, based on reference states of pure solvent and purecompletely dissociated liquid electrolyte. The model is then normalized byinfinite dilution activity coefficients in order to obtain an unsymmetric model.This NRTL expression for the local interactions, the Pitzer-Debye-Hückelexpression, and the Born equation are added to give equation 1 for theexcess Gibbs energy (see the following note).
2 Thermodynamic Property Models 103
(1)
This leads to
(2)
Note: The notation using * to denote an unsymmetric reference state is well-accepted in electrolyte thermodynamics and will be maintained here. Thereader should be warned not to confuse it with the meaning of * in classicalthermodynamics according to IUPAC/ISO, referring to a pure component
property. In fact in the context of G or , the asterisk as superscript is never
used to denote pure component property, so the risk of confusion is minimal.For details on notation, see Chapter 1 of Physical Property Methods.
References
C.-C. Chen, H.I. Britt, J.F. Boston, and L.B. Evans, "Local Compositions Modelfor Excess Gibbs Energy of Electrolyte Systems: Part I: Single Solvent, SingleCompletely Dissociated Electrolyte Systems:, AIChE J., Vol. 28, No. 4, (1982),p. 588-596.
C.-C. Chen, and L.B. Evans, "A Local Composition Model for the Excess GibbsEnergy of Aqueous Electrolyte Systems," AIChE J., Vol. 32, No. 3, (1986), p.444-459.
B. Mock, L.B. Evans, and C.-C. Chen, "Phase Equilibria in Multiple-SolventElectrolyte Systems: A New Thermodynamic Model," Proceedings of the 1984Summer Computer Simulation Conference, p. 558.
B. Mock, L.B. Evans, and C.-C. Chen, "Thermodynamic Representation ofPhase Equilibria of Mixed-Solvent Electrolyte Systems," AIChE J., Vol. 32, No.10, (1986), p. 1655-1664.
Long-Range Interaction Contribution
The Pitzer-Debye-Hückel formula, normalized to mole fractions of unity forsolvent and zero for electrolytes, is used to represent the long-rangeinteraction contribution.
with
(3)
(4)
(5)
Where:
104 2 Thermodynamic Property Models
xi = Mole fraction of component i
Ms = Molecular weight of the solvent
A = Debye-Hückel parameter
NA = Avogadro's number
ds = Mass density of solvent
Qe = Electron charge
s= Dielectric constant of the solvent
T = Temperature
k = Boltzmann constant
Ix = Ionic strength (mole fraction scale)
xi = Mole fraction of component i
zi = Charge number of ion i
= "Closest approach" parameter
Taking the appropriate derivative of equation 3, an expression for the activitycoefficient can then be derived.
(6)
The Born equation is used to account for the Gibbs energy of transfer of ionicspecies from the infinite dilution state in a mixed-solvent to the infinitedilution state in aqueous phase.
(7)
Where:
w= Dielectric constant of water
ri = Born radius of the ionic species i
The expression for the activity coefficient can be derived from (7):
(8)
The Debye-Hückel theory is based on the infinite dilution reference state forionic species in the actual solvent media. For systems with water as the onlysolvent, the reference state is the infinite dilution aqueous solution. Formixed-solvent systems, the reference state for which the Debye-Hückeltheory remains valid is the infinite dilution solution with the correspondingmixed-solvent composition. However, the molecular weight Ms, the mass
density ds, and the dielectric constant s for the single solvent need to be
2 Thermodynamic Property Models 105
extended for mixed solvents; simple composition average mixing rules areadequate to calculate them as follows:
(6a)
(7a)
(8a)
(8b)
(8c)
(8d)
Where:
xm = Mole fraction of the solvent m in the solution
Mm = Molecular weight of the solvent m
Vml = Molar volume of the solvent mixture
m= Dielectric constant of the solvent m
Vw* = Molar volume of water using the steam table
xnws = Sum of the mole fractions of all non-watersolvents.
Vnwsl = Liquid molar volume for the mixture of all non-
water solvents. It is calculated using theRackett equation.
It should be understood that equations 6a-8a should be used only in
equations 3, 4, and 7. Ms, ds, and s were already assumed as constants when
deriving equations 6 and 8 for mixed-solvent systems.
Local Interaction Contribution
The local interaction contribution is accounted for by the Non-Random TwoLiquid theory. The basic assumption of the NRTL model is that the nonidealentropy of mixing is negligible compared to the heat of mixing: this is indeedthe case for electrolyte systems. This model was adopted because of itsalgebraic simplicity and its applicability to mixtures that exhibit liquid phasesplitting. The model does not require specific volume or area data.
The effective local mole fractions Xji and Xii of species j and i, respectively, inthe neighborhood of i are related by:
106 2 Thermodynamic Property Models
(9)
Where:
Xj = xjCj
(Cj = zj for ions and Cj = unity for molecules)
Gji =
ji=
ji= Nonrandomness factor
gji and gii are energies of interaction between species j and i, and i and i,
respectively. Both gij and ij are inherently symmetric (gij = gji and ij = ji).
Similarly,
(10)
Where:
Gji,ki =
ji,ki=
ji,ki= Nonrandomness factor
Apparent Binary Systems
The derivations that follow are based on a simple system of one completelydissociated liquid electrolyte ca and one solvent B. They will be later extendedto multicomponent systems. In this simple system, three differentarrangements exist:
In the case of a central solvent molecule with other solvent molecules,cations, and anions in its immediate neighborhood, the principle of localelectroneutrality is followed: the surrounding cations and anions are such thatthe neighborhood of the solvent is electrically neutral. In the case of a central
2 Thermodynamic Property Models 107
cation (anion) with solvent molecules and anions (cations) in its immediateneighborhood, the principle of like-ion repulsion is followed: no ions of likecharge exist anywhere near each other, whereas opposite charged ions arevery close to each other.
The effective local mole fractions are related by the following expressions:
(central solvent cells)(11)
(central cation cells)(12)
(central anion cells)(13)
Using equation 11 through 13 and the notation introduced in equations 9 and10 above, expressions for the effective local mole fractions in terms of theoverall mole fractions can be derived.
i = c, a, or B
(14)
(15)
(16)
To obtain an expression for the excess Gibbs energy, let the residual Gibbsenergies, per mole of cells of central cation, anion, or solvent, respectively, be
, , and . These are then related to theeffective local mole fractions:
(17)
(18)
(19)
The reference Gibbs energy is determined for the reference states ofcompletely dissociated liquid electrolyte and of pure solvent. The referenceGibbs energies per mole are then:
(20)
(21)
(22)
Where:
zc = Charge number on cations
za = Charge number on anions
108 2 Thermodynamic Property Models
The molar excess Gibbs energy can be found by summing all changes inresidual Gibbs energy per mole that result when the electrolyte and solvent intheir reference state are mixed to form the existing electrolyte system. Theexpression is:
(23)
Using the previous relation for the excess Gibbs energy and the expressionsfor the residual and reference Gibbs energy (equations 17 to 19 and 20 to22), the following expression for the excess Gibbs energy is obtained:
(24)
The assumption of local electroneutrality applied to cells with central solventmolecules may be stated as:
(25)
Combining this expression with the expression for the effective local molefractions given in equations 9 and 10, the following equality is obtained:
(26)
The following relationships are further assumed for nonrandomness factors:
(27)
(28)
and,
(29)
It can be inferred from equations 9, 10, and 26 to 29 that:
(30)
(31)
The binary parameters ca,B , ca,B and B,ca are now the adjustable parameters
for an apparent binary system of a single electrolyte and a single solvent.
The excess Gibbs energy expression (equation 24) must now be normalizedto the infinite dilution reference state for ions:
(32)
This leads to:
2 Thermodynamic Property Models 109
(33)
By taking the appropriate derivatives of equation 33, expressions for theactivity coefficients of all three species can be determined.
(34)
(35)
(36)
Multicomponent Systems
The Electrolyte NRTL model can be extended to handle multicomponentsystems.
The excess Gibbs energy expression is:
(37)
Where:
j and k can be any species (a, C, or B)
The activity coefficient equation for molecular components is given by:
110 2 Thermodynamic Property Models
(38)
The activity coefficient equation for cations is given by:
(39)
The activity coefficient equation for anions is given by:
(40)
Where:
(41)
(42)
(43)
2 Thermodynamic Property Models 111
(44)
(45)
(46)
(47)
(48)
It should be understood that and remained constant inequation 37 when deriving the activity coefficients given by equations 38-40.
Parameters
The model adjustable parameters include:
Pure component dielectric constant coefficient of nonaqueous solvents
Born radius of ionic species
NRTL interaction parameters for molecule-molecule, molecule-electrolyte,and electrolyte-electrolyte pairs
Note that for the electrolyte-electrolyte pair parameters, the two electrolytesmust share either one common cation or one common anion.
Each type of the electrolyte NRTL parameter consists of both the
nonrandomness factor, , and energy parameters, .
The pure component dielectric constant coefficients of nonaqueous solventsand Born radius of ionic species are required only for mixed-solventelectrolyte systems.
The temperature dependency relations of these parameters are given inElectrolyte NRTL Activity Coefficient Model.
Heat of mixing is calculated from temperature derivatives of activitycoefficients. Heat capacity is calculated from secondary temperaturederivative of the activity coefficient. As a result, the temperature dependentparameters are critical for modeling enthalpy correctly. It is recommendedthat enthalpy data and heat capacity data be used to obtain thesetemperature dependency parameters. See also Electrolyte NRTL Enthalpy andElectrolyte NRTL Gibbs Energy.
112 2 Thermodynamic Property Models
Obtaining Parameters
In the absence of electrolytes, the electrolyte NRTL model reduces to theNRTL equation which is widely used for non-electrolyte systems. Therefore,molecule-molecule binary parameters can be obtained from binarynonelectrolyte systems.
Electrolyte-molecule pair parameters can be obtained from data regression ofapparent single electrolyte systems.
Electrolyte-electrolyte pair parameters are required only for mixedelectrolytes with a common ion. Electrolyte-electrolyte pair parameters canaffect trace ionic activity precipitation. Electrolyte-electrolyte pair parameterscan be obtained by regressing solubility data of multiple componentelectrolyte systems.
When the electrolyte-molecule and electrolyte-electrolyte pair parameters arezero, the electrolyte NRTL model reduces to the Debye-Hückel limiting law.Calculation results with electrolyte-molecule and electrolyte-electrolyte pairparameters fixed to zero should be adequate for very dilute weak electrolytesystems; however, for concentrated systems, pair parameters are requiredfor accurate representation.
See Physical Property Data, Chapter 1, for the pair parameters available fromthe electrolyte NRTL model databank. The table contains pair parameters forsome electrolytes in aqueous solution at 100C. These values were obtainedby using the Aspen Physical Property Data Regression System (DRS) toregress vapor pressure and mole fraction data at T=100C with SYSOP15S(Handbook of Chemistry and Physics, 56th Edition, CRC Press, 1975, p. E-1).In running the DRS, standard deviations for the temperature (C), vaporpressure (mmHg), and mole fractions were set at 0.2, 1.0, and 0.001,respectively. In addition, complete dissociation of the electrolyte wasassumed for all cases.
Option Codes for Electrolyte NRTL ActivityCoefficient Model (GMENRTL)
The electrolyte NRTL activity coefficient model (GMENRTL) has three optioncodes and the option codes can affect the performance of this model.
Option code 1. Use this option code to specify the default values of pairparameters for water/solute and solvent/solute; the solute represents acation/anion pair. The value (1) sets the default values to zero and the value(3) sets the default values for water/solute to (8,-4) and for solvent/solute to(10,-2). The value (3) is the default choice of the option code.
Option code 2. Not used.
Option code 3. Always leave this option code set to the value (1) to use thesolvent/solvent binary parameters obtained from NRTL parameters.
ENRTL-SACeNRTL-SAC (ENRTLSAC, patent pending) is an extension of the nonrandomtwo-liquid segment activity coefficient model (NRTL-SAC, patent pending) by
2 Thermodynamic Property Models 113
Chen and Song (Ind. Eng. Chem. Res., 2004, 43, 8354) to includeelectrolytes in the solution. It can be used in usable in Aspen Properties andAspen Polymers. It is intended for the computation of ionic activitycoefficients and solubilities of electrolytes, organic and inorganic, in commonsolvents and solvent mixtures. In addition to the three types of molecularparameters defined for organic nonelectrolytes in NRTL-SAC (hydrophobicityX, hydrophilicity Z, and polarity Y- and Y+), an electrolyte parameter, E, isintroduced to characterize both local and long-range ion-ion and ion-moleculeinteractions attributed to ionized segments of electrolytes.
In applying the segment contribution concept to electrolytes, a newconceptual electrolyte segment e corresponding to the electrolyte parameterE, is introduced. This conceptual segment e would completely dissociate to acationic segment (c) and an anionic segment (a), both of unity charge. Allelectrolytes, organic or inorganic, symmetric or unsymmetric, univalent ormultivalent, are to be represented with this conceptual uni-univalentelectrolyte segment e together with previously defined hydrophobic segmentx, polar segments y- and y+, and hydrophilic segment z in NRTL-SAC.
A major consideration in the extension of NRTL-SAC for electrolytes is thetreatment of the reference state for activity coefficient calculations. While theconventional reference state for nonelectrolyte systems is the pure liquidcomponent, the conventional reference state for electrolytes in solution is theinfinite-dilution aqueous solution and the corresponding activity coefficient isunsymmetric. The equation for the logarithm of the unsymmetric activitycoefficient of an ionic species is
With
114 2 Thermodynamic Property Models
2 Thermodynamic Property Models 115
Where:
I, J = Component index
i, j, m, c, a = Conceptual segment index
m = Conceptual molecular segment, x, y-, y+, z
c = Conceptual cationic segment
a = Conceptual anionic segment
i, j = m,c,a
I* = Unsymmetric activity coefficient of an ionic species I
I*lc = NRTL term
I*PDH = Pitzer-Debye-Hückel term
I*FH = Flory-Huggins term
116 2 Thermodynamic Property Models
= Aqueous-phase infinite-dilution reference state
i= Activity coefficient of conceptual segment i
rI = Total segment number of component I
xI = Mole fraction of component I
rI,i = Number of conceptual segment i containing in component I
xi = Segment mole fraction of conceptual segment i in mixtures
ij= NRTL binary non-randomness factor parameter for
conceptual segments
ij= NRTL binary interaction energy parameter for conceptual
segments
A = Debye-Hückel parameter
= Closest approach parameter, 14.9
Ix = Ionic strength (segment mole fraction scale)
= Average solvent molecular weight, g/mol
= Average solvent density, g/cm3
NA = Avogadro’s number
Qe = Absolute electronic charge
= Average solvent dielectric constant
w= Water dielectric constant
rc = Born radius of cationic segment
ra = Born radius of anionic segment
NRTL binary parameters for conceptual segments
The NRTL binary parameters between conceptual molecular segments in aredetermined by available VLE and LLE data between reference moleculesdefined in NRTLSAC.Segment (1) x x y- y+ x
Segment (2) y- z z z y+
121.643 6.547 -2.000 2.000 1.643
211.834 10.949 1.787 1.787 1.834
12 = 210.2 0.2 0.3 0.3 0.2
NaCl is used as the reference electrolyte for the conceptual electrolytesegment e. The NRTL binary parameters between conceptual molecularsegments and the electrolyte segment e are determined from literature dataor preset as follows:
2 Thermodynamic Property Models 117
Segment (1) x y- y+ z
Segment (2) e e e e
1215 12 12 8.885
215 -3 -3 -4.549
12 = 210.2 0.2 0.2 0.2
Parameters used in ENRTLSAC
Each component can have up to five parameters, rI,i (i = x, y-, y+, z, e),although only one or two of these parameters are needed for most solventsand ionic species in practice. Since conceptual segments apply to all species,these five parameters are implemented together as a binary parameter,NRTLXY(I, i) where I represents a component index and i represents aconceptual segment index.
Option codes
There are three option codes in ENRTLSAC. The first is used to enable ordisable the Flory-Huggins term. The other two are only used internally andyou should not change their values. The Flory-Huggins term is included bydefault in eNRTL-SAC model. You can remove this term using the first optioncode. The table below lists the values for the first option code.
0 Flory-Huggins term included (default)
Others Flory-Huggins term removed
References
C.-C. Chen and Y. Song, "Solubility Modeling with a Nonrandom Two-LiquidSegment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).
C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid SegmentActivity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res. 44, 8909(2005).
HansenHansen is a solubility parameter model and is commonly used in the solventselection process. It is based on the regular solution theory and Hansensolubility parameters. This model has no binary parameters and its applicationmerely follows the empirical guide like dissolves like.
The Hansen model calculates liquid activity coefficients. The equation for theHansen model is:
with
118 2 Thermodynamic Property Models
Where:
i= Activity coefficient of component i
Vi = Molar volume of component i
id = Hansen solubility parameter of component i for nonpolar
effect
ip = Hansen solubility parameter of component i for polar effect
ih = Hansen solubility parameter of component i for hydrogen-
bonding effect
i= Volume fraction of component i
xi = Mole fraction of component i
R = Gas constant
T = Temperature
The Hansen model does not require binary parameters. For each component,it has four input parameters.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DELTAD id — x — — PRESSURE^0.5
DELTAP ip — x — — PRESSURE^0.5
DELTAH ih — x — — PRESSURE^0.5
HANVOL Vi — x — — VOLUME
Option codes
The Hansen volume is implemented as an input parameter. If the Hansenvolume is not input by the user it will be calculated by an Aspen Plus internalmethod. You can also request the Aspen Plus method using Option Codes inAspen Plus Interface. The table below lists the option codes.
First Option Code in Hansen model
0 Hansen volume input by user (default)
Other values Hansen volume calculated by Aspen Plus
2 Thermodynamic Property Models 119
Reference
Frank, T. C.; Downey, J. R.; Gupta, S. K. "Quickly Screen Solvents forOrganic Solids," Chemical Engineering Progress 1999, December, 41.
Hansen, C. M. Hansen Solubility Parameters: A User’s Handbook; CRC Press,2000.
Ideal LiquidThis model is used in Raoult's law. It represents ideality of the liquid phase.This model can be used for mixtures of hydrocarbons of similar carbonnumber. It can be used as a reference to compare the results of other activitycoefficient models.
The equation is:
ln i = 0
NRTL (Non-Random Two-Liquid)The NRTL model calculates liquid activity coefficients for the followingproperty methods: NRTL, NRTL-2, NRTL-HOC, NRTL-NTH, and NRTL-RK. It isrecommended for highly non-ideal chemical systems, and can be used for VLEand LLE applications. The model can also be used in the advanced equation-of-state mixing rules, such as Wong-Sandler and MHV2.
The equation for the NRTL model is:
for Tlower T Tupper
Where:
Gij =
ij=
ij =
ii= 0
Gii = 1
aij, bij, eij, and fij are unsymmetrical. That is, aij may not be equal to aji, etc.
Recommended cij Values for Different Types of Mixturescij Mixtures
0.30 Nonpolar substances; nonpolar with polar non-associated liquids; smalldeviations from ideality
0.20 Saturated hydrocarbons with polar non-associated liquids and systems thatexhibit liquid-liquid immiscibility
120 2 Thermodynamic Property Models
cij Mixtures
0.47 Strongly self-associated substances with nonpolar substances
The binary parameters aij, bij, cij, dij, eij, and fij can be determined from VLEand/or LLE data regression. The Aspen Physical Property System has a largenumber of built-in binary parameters for the NRTL model. The binaryparameters have been regressed using VLE and LLE data from the DortmundDatabank. The binary parameters for the VLE applications were regressedusing the ideal gas, Redlich-Kwong, and Hayden O'Connell equations of state.See Physical Property Data, Chapter 1, for details.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
NRTL/1 aij 0 x -100.0 100.0 —
NRTL/2 bij 0 x -30000 30000.0 TEMPERATURE
NRTL/3 cij 0.30 x 0.0 1.0 —
NRTL/4 dij 0 x -0.02 0.02 TEMPERATURE
NRTL/5 eij 0 x — — TEMPERATURE
NRTL/6 fij 0 x — — TEMPERATURE
NRTL/7 Tlower 0 x — — TEMPERATURE
NRTL/8 Tupper 1000 x — — TEMPERATURE
Note: If any of bij, dij, or eij is non-zero, absolute temperature units areassumed for bij, dij, eij, and fij. Otherwise, user input units for temperature areused. The temperature limits are always interpreted in user input units.
The NRTL-2 property method uses data set 2 for NRTL. All other NRTLmethods use data set 1.
References
H. Renon and J.M. Prausnitz, "Local Compositions in Thermodynamic ExcessFunctions for Liquid Mixtures," AIChE J., Vol. 14, No. 1, (1968), pp. 135 –144.
NRTL-SAC ModelNRTL-SAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model and extended to handleelectrolytes, but usable in Aspen Plus or Aspen Properties without AspenPolymers. NRTL-SAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. It can also beused as a general activity coefficient model in Aspen Plus, Aspen Properties,and HYSYS.
Conceptually, the model treats the liquid non-ideality of mixtures containingcomplex organic molecules (solute) and small molecules (solvent) in terms ofinteractions between three pairwise interacting conceptual segments:hydrophobic segment (x), hydrophilic segment (z), and polar segments (y-and y+). In practice, these conceptual segments become the moleculardescriptors used to represent the molecular surface characteristics of eachsolute or solvent molecule. Hexane, water, and acetonitrile are selected asthe reference molecules for the hydrophobic, hydrophilic, and polar segments,
2 Thermodynamic Property Models 121
respectively. The molecular parameters for all other solvents can bedetermined by regression of available VLE or LLE data for binary systems ofsolvent and the reference molecules or their substitutes.
The treatment results in four component-specific molecular parameters:hydrophobicity X, hydrophilicity Z, and polarity Y- and Y+. The two types ofpolar segments, Y- and Y+, are used to reflect the wide variations ofinteractions between polar molecules and water.
NRTL-SAC can also be used to model electrolyte systems. In this case, anelectrolyte segment e, corresponding to the electrolyte parameter E, isintroduced. This conceptual segment e completely dissociates to a cationicsegment (c) and an anionic segment (a), both of unit charge. All electrolytes,organic or inorganic, symmetric or unsymmetric, univalent or multivalent, areto be represented with this conceptual 1-1 electrolyte segment e togetherwith the previously defined hydrophobic segment x, polar segments y- andy+, and hydrophilic segment z in NRTL-SAC. The reference state for ions is bydefault an unsymmetric state based on infinite dilution in aqueous solution,but an option code is available to select the symmetric state of pure fusedsalts. When there are no electrolytes present, the segment e is unused andthe current model reduces to the non-electrolyte version of NRTL-SAC presentin earlier releases.
The conceptual segment contribution approach in NRTL-SAC represents apractical alternative to the UNIFAC functional group contribution approach.This approach is suitable for use in the industrial practice of carrying outmeasurements for a few selected solvents and then using NRTL-SAC toquickly predict other solvents or solvent mixtures and to generate a list ofsuitable solvent systems.
The NRTL-SAC model calculates liquid activity coefficients.
Note: This is the updated version of NRTL-SAC, represented with propertymodel GMNRTLS and property method NRTL-SAC. This version does notrequire the specification of components as oligomers. For the old version, seeNRTLSAC for Segments/Oligomers and ENRTL-SAC.
For the model equations, see NRTL-SAC Model Derivation.
Parameters used in NRTL-SAC
Each component can have up to five parameters, rx,I, ry-,I, ry+,I, rz,I, and re,I,representing the equivalent number of segments of each type for the NRTLactivity coefficient model. Only one or two of these molecular parameters areneeded for most solvents in practice. These parameters are implementedtogether as pure parameter XYZE with five elements representing these fiveparameters. Values for this parameter are available for many commonsolvents in the NRTL-SAC databank.ParameterName/Element
Symbol Default MDS LowerLimit
Upper Limit Units
XYZE/1 rx,I — — — — —
XYZE/2 ry-,I — — — — —
XYZE/3 ry+,I — — — — —
XYZE/4 rz,I — — — — —
122 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
Upper Limit Units
XYZE/5 re,I — — — — —
Electrolytes must be modeled as ion pairs in this system, while the individualions are components in the Aspen Physical Property System, so for these ionpairs, the five parameters are stored in binary parameter BXYZE which haselements corresponding to those of XYZE.ParameterName/Element
Symbol Default MDS LowerLimit
Upper Limit Units
BXYZE/1 rx,CA — — — — —
BXYZE/2 ry-,CA — — — — —
BXYZE/3 ry+,CA — — — — —
BXYZE/4 rz,CA — — — — —
BXYZE/5 re,CA — — — — —
The conceptual segment numbers of a cationic component and
an anionic component come from the dissociation of theircorresponding electrolyte component CA, as defined by the chemical equationdescribing the dissociation of the electrolyte:
with
Since an electrolyte component CA can be measured by up to five conceptual
segments , we can calculate ri,C and ri,A as follows for systems ofsingle electrolyte.
For an electrolyte system where multi-electrolytes may be generated, asimple mixing rule is used:
2 Thermodynamic Property Models 123
where YC is a cationic charge composition fraction and YA is an anionic chargecomposition fraction; they are defined as follows:
Notice that electrolyte here is meant to represent an ion-pair composed of acationic component and an anionic component in the solutions. The result isthat electrolytes are generated from all possible combinations of ions in thesolution; each generated electrolyte is not necessarily associated with an ion-pair through the dissociation.
Option Codes in NRTL-SAC
Three option codes are available for NRTL-SAC to select the reference stateand to optionally exclude the Flory-Huggins and long-range interaction terms:Option CodeValue Meaning
1 0 Reference state for ions is unsymmetric: infinite dilution inaqueous solution (default)
2 Reference state for ions is symmetric: pure fused salts
2 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
3 0 Long-range interaction term included (default)
1 Long-range interaction term removed
References
C.-C. Chen and Y. Song, "Extension of Nonrandom Two-Liquid SegmentActivity Coefficient Model for Electrolytes," Ind. Eng. Chem. Res., 2005, 44,8909.
Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid Segment ActivityCoefficient Model for Electrolytes," Ind. Eng. Chem. Res., 2009, 48, 5522.
NRTL-SAC Reference States
The NRTL-SAC activity coefficient model for component I is composed of the
local composition term, ln Ilc, the Pitzer-Debye-Hückel long-range interaction
term, ln IPDH, and the Flory-Huggins term, I
FH:
(1)
This equation needs to be normalized based on the reference states ofmolecular and ionic components.
124 2 Thermodynamic Property Models
Reference state for molecular components
The reference state for a molecular component is defined as follows:
(2)
This definition is the so-called standard state of pure liquids for molecularcomponents and it is also called the symmetric reference state for molecularcomponents.
Reference state for ionic components
The standard state of pure liquids is hypothetical for ionic components inelectrolyte systems. The symmetric reference state is defined as the purefused salt state of each electrolyte component in the system.
However, the conventional reference state for ionic components is theinfinite-dilution activity coefficient in pure water; it is also called theunsymmetric reference state for ionic components. In NRTL-SAC model, wewill consider both of these reference states; the unsymmetric state is thedefault.
Pure fused salt state of an electrolyte component
For an electrolyte component CA, the pure fused salt state can be defined asfollows:
(3)
(4)
where ± is the mean ionic activity coefficient of the electrolyte component
and is related to the corresponding cationic and anionic activity coefficients C
and A by this expression:
(5)
where C is the cationic stoichiometric coefficient and A is the anionic
stoichiometric coefficient, and =C+A (one mole of salt releases moles of
ions in solution). They are given by the chemical equation describing thedissociation of the electrolyte. Therefore Eq. 5 can be written in terms ofcharge numbers zC and zA:
(6)
At the pure fused salt state:
(7)
(8)
2 Thermodynamic Property Models 125
(9)
The symmetric reference state defined by Eq. 3 is restricted to systemscontaining a single electrolyte component. For multi-electrolyte systems, thesymmetric reference state can be generalized from Eq. 3 as follows:
(10)
where I applies to all molecular components in the system. The symmetricreference state is a molecular-component-free media.
Infinite-dilution aqueous solution
The condition of infinite-dilution solution for ionic components can be writtenas follows:
(11)
This condition applies to all ionic components in the solution. In infinite-dilution aqueous solutions, water must be present and is assumed torepresent the entire solution, so the unsymmetric reference state can bewritten as follows:
(12)
This equation applies to all ionic components in the solution.
NRTL-SAC Local Composition Term
The segment-based excess Gibbs free energy of the local interactions forsystems with multiple molecular segments m and a single electrolyte segmente (with a single cation segment c and anion segment a) can be written asfollows:
(13)
(14)
(15)
(16)
126 2 Thermodynamic Property Models
where I is the component index, i is the segment index, ri,I is the number ofsegment i in component I, xI is the mole fraction of component I, xi is thesegment fraction of segment i, and ns is the total number of all segments inthe system.
Since there is only a single 1-1 electrolyte segment, the pair parametersbetween a molecular segment and the electrolyte segment can be simplifiedas follows:
(17)
(18)
(19)
(20)
We can then rewrite the excess Gibbs free energy as follows:
(21)
with
(22)
The local composition contribution to the segment activity coefficient can becalculated as follows:
(23)
The local composition contribution to the activity coefficients for molecularsegments, the cationic segment, and the anionic segment can be calculatedout as follows:
2 Thermodynamic Property Models 127
(24)
(25)
(26)
The local composition term for the logarithm of the activity coefficient ofcomponent I , before normalization to a chosen reference state, is computedas the sum of the individual segment contributions.
(27)
Specifically, for non-electrolyte (molecular) components, the activitycoefficients are given as follows:
(28)
For a cationic component, we have
128 2 Thermodynamic Property Models
(29)
For an anionic component, we have
(30)
Molecular components
Applying Eq. 1, the normalization for molecular components can be done asfollows:
(31)
where mlc,I is the activity coefficient of the molecular segment m contained in
component I,
(32)
Ionic components with symmetric reference state
Applying Eq. 10, the local composition contribution to the symmetric activitycoefficients for ionic components in multi-electrolyte systems can benormalized as follows:
(33)
(34)
(35)
where I applies to all molecular components in the solution and Ix0 is the ionic
strength at the symmetric reference state. In the case that electrolytes aremade up of only the conceptual 1-1 electrolyte segment and none of themolecular segments, this reference state is equivalent to the molten state ofthe conceptual 1-1 electrolyte.
Ionic components with infinite dilution aqueous solutionreference state
Applying Eq. 12, the unsymmetric activity coefficients for ionic components inaqueous solutions can be normalized as follows:
(36)
(37)
2 Thermodynamic Property Models 129
where and are activity coefficients at the infinite dilution aqueoussolution:
(38)
(39)
NRTL-SAC Long-Range Interaction Term
To account for the long-range ion-ion interactions, the model uses thesymmetric Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1986) on the segmentbasis:
(40)
with
(41)
(42)
where ns is the total segment number of the solution, R is the gas constant,
A is the Debye-Hückel parameter, Ix is the segment-based ionic strength, is the closest approach parameter, NA is Avogadro's number, v and are the
molar volume and dielectric constant of the solvent, Qe is the electron charge,kB is the Boltzmann constant, zi is the charge number of segment i, and Ix
0
represents Ix at the reference state. Since the "single 1-1 electrolyte segmente=ca" is defined in the model, we can obtain:
(43)
For the symmetric reference state,
(44)
And for the unsymmetric reference state,
(45)
The long-range contribution to the activity coefficient of segment i can bederived as follows:
(46)
130 2 Thermodynamic Property Models
For a molecular segment, the activity coefficient can be carried out as follows:
(47)
For the univalent cation or anion segment, the activity coefficient can becarried out as follows:
(48)
The original Debye-Hückel theory is based on a single electrolyte with water
as the solvent. The molar volume v and the dielectric constant for the
single solvent water need to be extended for mixed-solvents based on themolecular solvent properties; a simple composition average mixing rule isproposed to calculate them as follows:
(49)
(50)
where S is a solvent component, MS is the solvent molecular weight, and eachsum is over all solvent components in the solution.
The long range interaction term for the logarithm of the activity coefficient ofcomponent I is computed as the sum of the individual segment contributions.
(51)
Molecular components
For molecular components, the activity coefficients are given as follows:
(52)
From Eq. 47, it is easy to show that the PDH term activity coefficients for allmolecular components are normalized; that is
(53)
where I applies to all molecular components in the system.
2 Thermodynamic Property Models 131
Ionic components with symmetric reference state
Applying Eq. 10, the symmetric activity coefficients for ionic components fromthe long range contribution are given as follows:
(54)
(55)
(56)
where I applies to all molecular components in the solution.
Ionic components with infinite dilution aqueous solution
Applying Eq. 12, the unsymmetric activity coefficients for ionic componentsfrom the long range contribution in aqueous solutions are given as follows:
(57)
(58)
Segment based Born correction term to activity coefficient
If the infinite dilution aqueous solution is chosen as the reference state, weneed to correct the change of the reference state from the mixed-solventcomposition to aqueous solution for the Debye-Hückel term. The Born term(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for thispurpose:
(59)
where ri is the Born radius of segment species i and w is the dielectric
constant of water. GBorn is the Born term correction to the unsymmetric
Pitzer-Debye-Hückel formula Gex,PDH.
The Born correction activity coefficient of component i can be derived asfollows:
(60)
For a molecular segment, the correction to the activity coefficient is zero:
(61)
For the univalent cation or anion segment, the activity coefficient can becarried out as follows:
132 2 Thermodynamic Property Models
(62)
Specifically,
(63)
(64)
The long range interaction term for the logarithm of the activity coefficient ofcomponent I is computed as the sum of the individual segment contributions.
(65)
Activity coefficients given by Eq. 65 are already normalized for molecularcomponents as well as for ionic components with the infinite-dilution aqueoussolution reference state.
References
Pitzer, K.S., J.M. Simonson, "Thermodynamics of Multicomponent, Miscible,Ionic Systems: Theory and Equations," J. Phys. Chem., 1986, 90, 3005-3009.
Robinson, R.A., Stokes, R.H., Electrolyte Solutions, 2nd revised edition,Dover, 1970.
Rashig, A.A., Honig, B., "Reevaluation of the Born Model of Ion Hydration," J.Phys. Chem., 1985, 89, 5588.
NRTL-SAC Flory-Huggins Term
We use the Flory-Huggins term to describe the combinatorial term:
(66)
(67)
where Gex,FH is the Flory-Huggins term for the excess Gibbs energy, I is the
segment fraction of component I, and rI is the number of all conceptualsegments in component I:
(68)
(69)
2 Thermodynamic Property Models 133
The contribution to the activity coefficient of component I from thecombinatorial term is thus:
(70)
Molecular components
It is easy to show that activity coefficients for molecular components from theFlory-Huggins term are normalized; that is
(71)
where I applies to all molecular components in the solution.
Ionic components with symmetric reference state
Applying Eq. 10, the symmetric activity coefficients for ionic components fromthe Flory-Huggins term can be carried out as follows:
(72)
(73)
with
(74)
(75)
(76)
(77)
where I applies to all molecular components in the solution.
Ionic components with infinite dilution aqueous solution
Applying Eq. 12, the unsymmetric activity coefficients for ionic components inaqueous solutions can be carried out as follows:
(78)
(79)
134 2 Thermodynamic Property Models
where and are activity coefficients at the infinite dilutionaqueous solution:
(80)
(81)
Henry Components in NRTL-SAC
Light gases (i.e. Henry components) are usually supercritical at thetemperature and pressure of the system. In that case pure component vaporpressure is meaningless and therefore the pure liquid state at thetemperature and pressure of the system cannot serve as the reference state.The reference state for a Henry component is redefined to be at infinite
dilution (that is, xI0) and at the temperature and pressure of the system.
The liquid phase reference fugacity, fI*,l, becomes the Henry’s constant for
Henry components in the solution, HI, and the activity coefficient, I, is
converted to the infinite dilution reference state through the relationship:
(82)
where is the infinite dilution activity coefficient of Henry component I
(xI0) in the solution. By this definition I* approaches unity as
xI approaches zero. The phase equilibrium relationship for Henry componentsbecomes:
(83)
The Henry’s Law is available in all activity coefficient property methods. Themodel calculates the Henry’s constant for a dissolved gas component in allsolvent components in the mixture:
(84)
(85)
where HIS and are the Henry’s constant and the infinite dilution activitycoefficient of the dissolved gas component i in the solvent component S
(xI0 and xS1, respectively).
Since ionic species exist only in the liquid phase and therefore do notparticipate directly in vapor-liquid equilibria, the activities of Henry
2 Thermodynamic Property Models 135
components are mainly through the local interactions with solvents. We cancalculate all three activity coefficients for Henry components as follows:
(86)
(87)
(88)
with
(89)
(90)
(91)
(92)
(93)
(94)
Notice that xH0 applies to all Henry components in the solution.
NRTLSAC for Segments/Oligomers
This is the original NRTLSAC model added in version 2006, which requiresthat components be defined as oligomers. It is retained for compatibility, butnew models should use the NRTL-SAC model.
NRTL-SAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model, usable in Aspen Properties andAspen Polymers. NRTL-SAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. Conceptually,the model treats the liquid non-ideality of mixtures containing complexorganic molecules (solute) and small molecules (solvent) in terms ofinteractions between three pairwise interacting conceptual segments:hydrophobic segment (x), hydrophilic segment (z), and polar segments (y-and y+). In practice, these conceptual segments become the moleculardescriptors used to represent the molecular surface characteristics of eachsolute or solvent molecule. Hexane, water, and acetonitrile are selected asthe reference molecules for the hydrophobic, hydrophilic, and polar segments,respectively. The molecular parameters for all other solvents can bedetermined by regression of available VLE or LLE data for binary systems ofsolvent and the reference molecules or their substitutes. The treatmentresults in four component-specific molecular parameters: hydrophobicity X,hydrophilicity Z, and polarity Y- and Y+. The two types of polar segments, Y-
136 2 Thermodynamic Property Models
and Y+, are used to reflect the wide variations of interactions between polarmolecules and water.
The conceptual segment contribution approach in NRTL-SAC represents apractical alternative to the UNIFAC functional group contribution approach.This approach is suitable for use in the industrial practice of carrying outmeasurements for a few selected solvents and then using NRTL-SAC toquickly predict other solvents or solvent mixtures and to generate a list ofsuitable solvent systems.
The NRTL-SAC model calculates liquid activity coefficients.
The equation for the NRTL-SAC model is:
with
G = exp(-)
Where:
2 Thermodynamic Property Models 137
I, J = Component index
i, j, m = Conceptual segment indexx, y-, y+, z
I= Activity coefficient of component I
IC = I
FH = Flory-Huggins term for combinatorial contribution to I
IR = I
lc = NRTL term for local composition interaction contribution to
I
I= Segment mole fraction of component I
pI = Effective component size parameter
sI and I= Empirical parameters for pI
rI = Total segment number of component I
xI = Mole fraction of component I
rI,m = Number of conceptual segment m containing in componentI
xi = Segment mole fraction of conceptual segment i in mixtures
im= NRTL binary non-randomness factor parameter for
conceptual segments
im= NRTL binary interaction energy parameter for conceptual
segments
NRTL binary parameters for conceptual segments
The NRTL binary parameters between conceptual segments in NRTLSAC aredetermined by available VLE and LLE data between reference moleculesdefined above.Segment 1 x x y- y+ x
Segment 2 y- z z z y+
121.643 6.547 -2.000 2.000 1.643
211.834 10.949 1.787 1.787 1.834
12 = 210.2 0.2 0.3 0.3 0.2
Parameters used in NRTLSAC
Each component can have up to four parameters, rI,x, rI,y-, rI,y+, and rI,z
although only one or two of these molecular parameters are needed for mostsolvents in practice. Since conceptual segments apply to all molecules, thesefour molecular parameters are implemented together as a binary parameter,NRTLXY(I, m) where I represents a component (molecule) index and mrepresents a conceptual segment index.
In addition, the Flory-Huggins size parameter, FHSIZE , is used in NRTLSACto calculate the effective component size parameter, pI. The Flory-Huggins
combinatorial term can be turned off by setting I = 0 for each component in
mixtures.
138 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units Comment
NRTLXY rI,m — — — — — Binary,symmetric
FHSIZE/1 sI 1.0 — 1E-15 1E15 — Unary
FHSIZE/2 I1.0 — -1E10 1E10 — Unary
Option codes
The Flory-Huggins term is included by default in the NRTLSAC model. You canremove this term using the first option code. The table below lists the valuesfor this option code.
0 Flory-Huggins term included (default)
Others Flory-Huggins term removed
NRTLSAC molecular parameters for common solvents
The molecular parameters are identified for 62 solvents and published.Solvent name rI,x rI,y- rI,y+ rI,z
ACETIC-ACID 0.045 0.164 0.157 0.217
ACETONE 0.131 0.109 0.513
ACETONITRILE 0.018 0.131 0.883
ANISOLE 0.722
BENZENE 0.607 0.190
1-BUTANOL 0.414 0.007 0.485
2-BUTANOL 0.335 0.082 0.355
N-BUTYL-ACETATE 0.317 0.030 0.330
METHYL-TERT-BUTYL-ETHER 1.040 0.219 0.172
CARBON-TETRACHLORIDE 0.718 0.141
CHLOROBENZENE 0.710 0.424
CHLOROFORM 0.278 0.039
CUMENE 1.208 0.541
CYCLOHEXANE 0.892
1,2-DICHLOROETHANE 0.394 0.691
1,1-DICHLOROETHYLENE 0.529 0.208
1,2-DICHLOROETHYLENE 0.188 0.832
DICHLOROMETHANE 0.321 1.262
1,2-DIMETHOXYETHANE 0.081 0.194 0.858
N,N-DIMETHYLACETAMIDE 0.067 0.030 0.157
N,N-DIMETHYLFORMAMIDE 0.073 0.564 0.372
DIMETHYL-SULFOXIDE 0.532 2.890
1,4-DIOXANE 0.154 0.086 0.401
ETHANOL 0.256 0.081 0.507
2 Thermodynamic Property Models 139
Solvent name rI,x rI,y- rI,y+ rI,z
2-ETHOXYETHANOL 0.071 0.318 0.237
ETHYL-ACETATE 0.322 0.049 0.421
ETHYLENE-GLYCOL 0.141 0.338
DIETHYL-ETHER 0.448 0.041 0.165
ETHYL-FORMATE 0.257 0.280
FORMAMIDE 0.089 0.341 0.252
FORMIC-ACID 0.707 2.470
N-HEPTANE 1.340
N-HEXANE 1.000
ISOBUTYL-ACETATE 1.660 0.108
ISOPROPYL-ACETATE 0.552 0.154 0.498
METHANOL 0.088 0.149 0.027 0.562
2-METHOXYETHANOL 0.052 0.043 0.251 0.560
METHYL-ACETATE 0.236 0.337
3-METHYL-1-BUTANOL 0.419 0.538 0.314
METHYL-BUTYL-KETONE 0.673 0.224 0.469
METHYLCYCLOHEXANE 1.162 0.251
METHYL-ETHYL-KETONE 0.247 0.036 0.480
METHYL-ISOBUTYL-KETONE 0.673 0.224 0.469
ISOBUTANOL 0.566 0.067 0.485
N-METHYL-2-PYRROLIDONE 0.197 0.322 0.305
NITROMETHANE 0.025 1.216
N-PENTANE 0.898
1-PENTANOL 0.474 0.223 0.426 0.248
1-PROPANOL 0.375 0.030 0.511
ISOPROPYL-ALCOHOL 0.351 0.070 0.003 0.353
N-PROPYL-ACETATE 0.514 0.134 0.587
PYRIDINE 0.205 0.135 0.174
SULFOLANE 0.210 0.457
TETRAHYDROFURAN 0.235 0.040 0.320
1,2,3,4-TETRAHYDRONAPHTHALENE0.443 0.555
TOLUENE 0.604 0.304
1,1,1-TRICHLOROETHANE 0.548 0.287
TRICHLOROETHYLENE 0.426 0.285
M-XYLENE 0.758 0.021 0.316
WATER 1.000
TRIETHYLAMINE 0.557 0.105
1-OCTANOL 0.766 0.032 0.624 0.335
140 2 Thermodynamic Property Models
Reference
C.-C. Chen and Y. Song, "Solubility Modeling with a Nonrandom Two-LiquidSegment Activity Coefficient Model," Ind. Eng. Chem. Res. 43, 8354 (2004).
Using NRTLSAC
NRTLSAC (patent pending) is a segment contribution activity coefficientmodel, derived from the Polymer NRTL model, usable in Aspen Properties andAspen Polymers. NRTLSAC can be used for fast, qualitative estimation of thesolubility of complex organic compounds in common solvents. For moreinformation about the model, see NRTLSAC for Segments/Oligomers.
Note: A newer version of NRTL-SAC comes with its own property methodnamed NRTL-SAC and does not require the specification of a method andoligomer components as described below.
The NRTLSAC model for Segments/Oligomers in the Aspen Physical PropertySystem is a liquid activity coefficient model called NRTLSAC. To specify it:
1 On the Methods | Specifications sheet, specify method filter ALL.
2 Specify base method NRTLSAC.
In order to use this version of NRTLSAC, all components must be defined asoligomers. Four conceptual segments also must be defined. On theComponents | Polymers | Oligomers sheet, enter a number for at leastone conceptual segment for each oligomer component, as required by thedefinition of an oligomer. These numbers are not used by NRTL-SAC.
On the Methods | Parameters | Binary Interaction | NRTL-1 form, enterthe binary parameters between conceptual segments. In the followingexample, the conceptual segments are named X, Y-, Y+, and Z.Segment 1 X X Y- Y+ X
Segment 2 Y- Z Z Z Y+
AIJ 1.643 6.547 -2.000 2.000 1.643
AJI 1.834 10.949 1.787 1.787 1.834
CIJ 0.2 0.2 0.3 0.3 0.2
On the Methods | Parameters | Binary Interaction | NRTLXY-1 form,enter a non-zero value for at least one of the four parameters for eachcomponent.
Pitzer Activity Coefficient ModelThe Pitzer model was developed as an improvement upon an earlier modelproposed by Guggenheim ( 1935, 1955). The earlier model worked well at lowelectrolyte concentrations, but contained discrepancies at higherconcentrations (>0.1M). The Pitzer model resolved these discrepancies,without resorting to excessive arrays of higher-order terms.
Important: The model can be used for aqueous electrolyte systems, up to 6molal ionic strength. It cannot be used for systems with any other solvent ormixed solvents. Any non-water molecular components are considered solutesand treated as Henry components.
2 Thermodynamic Property Models 141
This section provides theoretical background for the model. All modelequations and parameter requirements are included.
The Pitzer model is commonly used in the calculation of activity coefficientsfor aqueous electrolytes up to 6 molal ionic strength. Do not use this model ifa non-aqueous solvent exists. Henry's law parameters are required for allother components in the aqueous solution. The model development andworking equations are provided in the following sections. Parameterconversion between the Pitzer notation and our notation is also provided.
The Pitzer model in the Aspen Physical Property System involves user-supplied parameters that are used in the calculation of binary and ternaryparameters for the electrolyte system.
Five elements (P1 through P5) account for the temperature dependencies of
parameters (0), (1), (2), (3), C, , and . These parameters follow the
temperature dependency relation:
Where:
Tref = 298.15 K
The user must:
Supply these elements for the binary parameters using a Methods |Parameters | Binary | T-Dependent form.
Supply these elements for on the Methods | Parameters |
Electrolyte Ternary form.
Specify Comp ID i and Comp ID j (and Comp ID k for ) on these forms,
using the same order that appears on the Components SpecificationsSelection sheet.
The parameters are summarized in the following table. There is a Pitzerparameter databank in the Aspen Physical Property System (see PhysicalProperty Data).ParameterName
ProvidesP1 - P5 for
No. ofElements
Default MDS Units
Cation-Anion Parameters
GMPTB0 (0) 5 0 x —
GMPTB1 (1) 5 0 x —
GMPTB2 (2) 5 0 x —
GMPTB3 (3) 5 0 x —
GMPTC C 5 0 x —
Cation-Cation Parameters
GMPTTH cc'5 0 x —
Anion-Anion Parameters
GMPTTH aa'5 0 x —
Ternary Parameters
142 2 Thermodynamic Property Models
ParameterName
ProvidesP1 - P5 for
No. ofElements
Default MDS Units
GMPTPS,GMPTP1,GMPTP2,GMPTP3,GMPTP4
ijk1 (in eachparameter)
0 x —
Molecule-Ion and Molecule-Molecule Parameters
GMPTB0 (0) 5 0 x —
GMPTB1 (1) 5 0 x —
GMPTC C 5 0 x —
Model Development
The Pitzer model analyzes "hard-core" effects in the Debye-Hückel theory. Ituses the following expansion as a radial distribution function:
(1)
Where:
gij = Distribution function
r = Radius
qij =
(pair potential of mean force)
With:
zi = Charge of ion i
Qe = Electron charge
j(r) = Average electric potential for ion j
k = Boltzmann's constant
T = Temperature
This radial distribution function is used in the so-called pressure equation thatrelates this function and the intermolecular potential to thermodynamicproperties. From this relation you can obtain an expression for the osmoticcoefficient.
Pitzer proposes a general equation for the excess Gibbs energy. The basicequation is:
(2)
Where:
GE = Excess Gibbs energy
2 Thermodynamic Property Models 143
R = Gas constant
T = Temperature
nw = Kilograms of water
mi =
(molality of ion i)
With:
xi = Mole fraction of ion i
xw = Mole fraction of water
Mw = Molecular weight of water (g/mol)
ni = Moles of ion i
The function f(I) is an electrostatic term that expresses the effect of long-range electrostatic forces between ions. This takes into account the hard-coreeffects of the Debye-Hückel theory. This term is discussed in detail in the
following section. The parameters ij are second virial coefficients that
account for the short-range forces between solutes i and j. The parameters
ijk account for the interactions between solutes, i, j, k. For ion-ion
interactions, ij is a function of ionic strength. For molecule-ion or molecule-
molecule interactions this ionic strength dependency is neglected. The
dependence of ijk on ionic strength is always neglected. The matrices ij and
ijk are also taken to be symmetric (that is, ij = ji).
Pitzer modified this expression for the Gibbs energy by identifyingcombinations of functions. He developed interaction parameters that can beevaluated using experimental data. He selected mathematical expressions forthese parameters that best fit experimental data.
Pitzer's model can be applied to aqueous systems of strong electrolytes andto aqueous systems of weak electrolytes with molecular solutes. Theseapplications are discussed in the following section.
In the Aspen Physical Property System, this model is applied using thereference state of infinite dilution solution in water for non-water molecularsolutes and ionic species. The properties such as DHAQFM are obtained at 25C and 1 atm.
Application of the Pitzer Model to Aqueous StrongElectrolyte Systems
Pitzer modified his basic equation to make it more useful for data correlationof aqueous strong electrolytes. He defined a set of more directly observableparameters to represent combinations of the second and third virialcoefficients. The modified Pitzer equation is:
144 2 Thermodynamic Property Models
(3)
zi = Charge of ion i
Subscripts c, c', and a, a' denote cations and anions of the solution. B, C, ,
and are interaction parameters. f(I) is an electrostatic term as a function of
ionic strength. The cation-anion parameters B and C are characteristic for anaqueous single-electrolyte system. These parameters can be determined bythe properties of pure (apparent) electrolytes. B is expressed as a function of
(0) and (1), or of (0), (2), and (3) (see equations 11 through 15).
The parameters and are for the difference of interaction of unlike ions of
the same sign from the mean of like ions. These parameters can be measuredfrom common-ion mixtures. Examples are NaCl + KCl + H2O or NaCl + NaNO3
+ H2O (sic, Pitzer, 1989). These terms are discussed in detail later in thissection.
Fürst and Renon (1982) propose the following expression as the Pitzerequation for the excess Gibbs energy:
(4)
The difference between equations 3 and 4 is that Pitzer orders cation beforeanions. Fürst and Renon do not. All summations are taken over all ions i and j(both cations and anions). This involves making the parameter matrices Bij,
Cij, ij, and ijk symmetric, as follows:
Second-order parameters are written Bij if i and j are ions of different sign. Bij
= 0 if the sign of zi = sign of zj, and Bii = 0. Since cations are not orderedbefore anions, Bij = Bji. This eliminates the 2 in the second term in brackets inPitzer's original expression (equation 3). Second-order parameters are written
ij if i and j are ions of the same sign. Thus ij = 0 if the sign of zi is different
from the sign of zj, and ii = 0 with ij = ji.
Third-order parameters are written Cij if i and j are ions with different signs.Cij = 0 if the sign of zi = sign of zj, and Cii = 0 with Cij = Cji. The factor of 2 inthe fifth bracketed term in Pitzer's original expression (equation 3) becomes
1/2 in equation 4. The matrix C is symmetric and is extended to allions to make the equation symmetric.
2 Thermodynamic Property Models 145
ijk is written for three different ions ijk = kij = jki , and ikk = 0. ijk = 0
if the sign of zi =sign of zj =sign of zk. The factor of 1/6 is different from 1/2in the last term in brackets in Pitzer's original expression. Pitzer distinguishesbetween cations and anions. In Pitzer's original model this parameter appears
twice, as cc'a and c'ca. In this modified model, it appears six times, as cc'a;
c'ca; acc'; ac'c; cac'; and c'ac. Fürst and Renon's expression, equation 4,
calculates the expressions for activity coefficients and osmotic coefficients.
Pitzer (1975) modified his model by adding the electrostatic unsymmetricalmixing effects, producing this modified Pitzer equation for the excess Gibbsenergy:
(4a)
Calculation of Activity Coefficients
The natural logarithm of the activity coefficient for ions is calculated fromequation 4a to give:
(5)
Where is neglected and ij and 'ij are the electrostatic unsymmetric mixing
effects:
The X parameters are calculated differently on the option code.
For option code = –1, there is no unsymmetric mixing correction term:
146 2 Thermodynamic Property Models
For option code = 0 (default), the unsymmetric mixing correction term is inpolynomial form:
For option code = 1, the unsymmetric mixing correction term is in integralform:
For water the logarithm of the activity coefficient is calculated similarly, asfollows:
Applying:
to equation 3 and using:
Where Nw = moles water, gives:
(6)
f(I), the electrostatic term, is expressed as a function of ionic strength I :
(7)
I, the ionic strength, is defined as:
2 Thermodynamic Property Models 147
(8)
Taking the derivative of equation 7 with respect to I, gives:
(9)
So that:
(10)
This equation is used in equation 6. In equations 7 and 9, is the usual Debye-Hückel constant for the osmotic coefficient, determined from:
(11)
Where:
NA = Avogadro's constant
dw = Water density
B= Dielectric constant of solvent B
b is an adjustable parameter, which has been optimized in this model to equal1.2.
B and B' need expressions so that equations 5 and 6 can completely be solvedfor the activity coefficients. The parameter B is determined differently fordifferent electrolyte pairings. For 1-n electrolytes (1-1, 1-2, 2-1, and so on)the following expression gives the parameter B:
(12)
with 1=2.0.
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), B is determinedby the following expression:
(13)
with 2 = 12.0 and 3 = 1.4.
By taking appropriate derivatives, expressions for B' can be derived for 1–nelectrolytes:
(14)
148 2 Thermodynamic Property Models
and for n-m electrolytes:
(15)
The parameters (0), (1), (2), (3) and also C, , and can be found in
Pitzer's articles .
After the activity coefficients are calculated, they can be converted to themole fraction scale from the molality scale by the following relations:
For solutes:
(16)
For water as a solvent:
(17)
Where:
m= Activity coefficient (molality scale)
x= Activity coefficient (mole fraction scale)
Application of the Pitzer Model to AqueousElectrolyte Systems with Molecular Solutes
In aqueous weak electrolyte systems with molecular solutes, the second andthird virial coefficients in the basic Pitzer equation for molecule-ion andmolecule-molecule interactions must be considered. The following extensionsof Pitzer's interaction parameters are made.
The second-order parameters Bij are extended to include molecule-moleculeand molecule-ion interaction parameters.
The third-order parameters ijk are extended to molecule-molecule-molecule
interactions. The following expressions relate ijk to Pitzer's original ijk:
iii = 6iii
However, molecule-molecule interactions were not taken into account by
Pitzer and coworkers. So iii is an artificially introduced quantity.
2 Thermodynamic Property Models 149
The equations for activity coefficients and the Gibbs free energy are the sameas equations 3 through 6.
Parameters
The Pitzer model in the Aspen Physical Property System involves user-supplied parameters. These parameters are used in the calculation of binaryand ternary parameters for the electrolyte system. These parameters include
the cation-anion parameters (0), (1), (2), (3) and C, cation-cation
parameter cc', anion-anion parameter aa', cation1-cation2-common anion
parameter cc'a, anion1-anion2-common cation parameter caa', and the
molecule-ion and molecule-molecule parameters (0), (1), and, C. The
parameter names in the Aspen Physical Property System and theirrequirements are discussed in Pitzer Activity Coefficient Model.
Parameter Conversion
For n-m electrolytes, n and m>1 (2-2, 2-3, 3-4, and so on), the parameter
(3) corresponds to Pitzer's (1). (2) is the same in both the Aspen Physical
Property System and original Pitzer models. Pitzer refers to the n-m
electrolyte parameters as (1), (2), (0). (0) and (2) retain their meanings in
both models, but Pitzer's (1) is (3) in the Aspen Physical Property System. Be
careful to make this distinction when entering n-m electrolyte parameters.
Pitzer often gives values of (0), (1), (2), (3), and C
that are corrected by
some factors (see Pitzer and Mayorga (1973) for examples). These factorsoriginate from one of Pitzer's earlier expressions for the excess Gibbs energy:
(18)
Where:
=
na = Mole number of anions
nc = Mole number of cation
Here (0), (1), (2), and (3) are multiplied by a factor of 2ncna. C is multiplied
by a factor of 2(ncna)3/2.
Aspen Physical Property System accounts for these correcting factors. Enterthe parameters without their correcting factors.
For example, Pitzer gives the values of parameters for MgCl2 as:
4/3(0) = 0.4698
4/3(1) = 2.242
150 2 Thermodynamic Property Models
= 0.00979
Perform the necessary conversions and enter the parameters as:
= 0.3524
= 1.6815
= 0.00520
Parameter Sources
Binary and ternary parameters for the Pitzer model for various electrolytesystems are available from Pitzer's series on the thermodynamics ofelectrolytes. These papers and the electrolyte parameters they give are:Reference Parameters available
(Pitzer, 1973) Binary parameters ((0), (1), C) for 13
dilute aqueous electrolytes
(Pitzer and Mayorga, 1973) Binary parameters for 1-1 inorganicelectrolytes, salts of carboxylic acids (1-1),tetraalkylammonium halids, sulfonic acidsand salts, additional 1-1 organic salts, 2-1inorganic compounds, 2-1 organicelectrolytes, 3-1 electrolytes, 4-1 and 5-1electrolytes
(Pitzer and Mayorga, 1974) Binary parameters for 2-2 electrolytes inwater at 25C
(Pitzer and Kim, 1974) Binary and ternary parameters for mixedelectrolytes, binary mixtures without acommon ion, mixed electrolytes with threeor more solutes
(Pitzer, 1975) Ternary parameters for systems mixingdoubly and singly charged ions
(Pitzer and Silvester, 1976) Parameters for phosphoric acid and its buffersolutions
(Pitzer, Roy and Silvester, 1977) Parameters and thermodynamic propertiesfor sulfuric acid
(Silvester and Pitzer, 1977) Data for NaCl and aqueous NaCl solutions
(Pitzer, Silvester, and Peterson, 1978) Rare earth chlorides, nitrates, andperchlorates
(Peiper and Pitzer, 1982) Aqueous carbonate solutions, includingmixtures of sodium carbonate, bicarbonate,and chloride
(Phutela and Pitzer, 1983) Aqueous calcium chloride
(Conceicao, de Lima, and Pitzer, 1983) Saturated aqueous solutions, includingmixtures of sodium chloride, potassiumchloride, and cesium chloride
2 Thermodynamic Property Models 151
Reference Parameters available
(Pabalan and Pitzer, 1987) Parameters for polynomial unsymmetricmixing term
(Kim and Frederick, 1988) Parameters for integral unsymmetric mixingterm
Pitzer References
Conceicao, M., P. de Lima, and K.S. Pitzer, "Thermodynamics of SaturatedAqueous Solutions Including Mixtures of NaCl, KCl, and CsCl, "J. SolutionChem, Vol. 12, No. 3, (1983), pp. 171-185.
Fürst, W. and H. Renon, "Effects of the Various Parameters in the Applicationof Pitzer's Model to Solid-Liquid Equilibrium. Preliminary Study for Strong 1-1Electrolytes," Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 3, (1982),pp. 396-400.
Guggenheim, E.A., Phil. Mag., Vol. 7, No. 19, (1935), p. 588.
Guggenheim, E.A. and J.C. Turgeon, Trans. Faraday Soc., Vol. 51, (1955), p.747.
Kim, H. and W.J. Frederick, "Evaluation of Pitzer Ion Interaction Parametersof Aqueous Mixed Electrolyte Solution at 25C, Part 2: Ternary MixingParameters," J. Chem. Eng. Data, 33, (1988), pp. 278-283.
Pabalan, R.T. and K.S. Pitzer, "Thermodynamics of Concentrated ElectrolyteMixtures and the Prediction of Mineral Solubilities to High Temperatures forMixtures in the system Na-K-Mg-Cl-SO4-OH-H2O," Geochimica Acta, 51,(1987), pp. 2429-2443.
Peiper, J.C. and K.S. Pitzer, "Thermodynamics of Aqueous CarbonateSolutions Including Mixtures of Sodium Carbonate, Bicarbonate, andChloride," J. Chem. Thermodynamics, Vol. 14, (1982), pp. 613-638.
Phutela, R.C. and K.S. Pitzer, "Thermodynamics of Aqueous CalciumChloride," J. Solution Chem., Vol. 12, No. 3, (1983), pp. 201-207.
Pitzer, K.S., "Thermodynamics of Electrolytes. I. Theoretical Basis andGeneral Equations, " J. Phys. Chem., Vol. 77, No. 2, (1973), pp. 268-277.
Pitzer, K.S., J. Solution Chem., Vol. 4, (1975), p. 249.
Pitzer, K.S., "Fluids, Both Ionic and Non-Ionic, over Wide Ranges ofTemperature and Composition," J. Chen. Thermodynamics, Vol. 21, (1989),pp. 1-17. (Seventh Rossini lecture of the commission on Thermodynamics ofthe IUPAC, Aug. 29, 1988, Prague, ex-Czechoslovakia).
Pitzer, K.S. and J.J. Kim, "Thermodynamics of Electrolytes IV; Activity andOsmotic Coefficients for Mixed Electrolytes," J.Am. Chem. Soc., Vol. 96(1974), p. 5701.
Pitzer, K.S. and G. Mayorga, "Thermodynamics of Electrolytes II; Activity andOsmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent,"J. Phys. Chem., Vol. 77, No. 19, (1973), pp. 2300-2308.
Pitzer, K.S. and G. Mayorga, J. Solution Chem., Vol. 3, (1974), p. 539.
152 2 Thermodynamic Property Models
Pitzer, K.S., J.R. Peterson, and L.F. Silvester, "Thermodynamics ofElectrolytes. IX. Rare Earth Chlorides, Nitrates, and Perchlorates, "J. SolutionChem., Vol. 7, No. 1, (1978), pp. 45-56.
Pitzer, K.S., R.N. Roy, and L.F. Silvester, "Thermodynamics of Electrolytes 7Sulfuric Acid," J. Am. Chem. Soc., Vol. 99, No. 15, (1977), pp. 4930-4936.
Pitzer, K.S. and L.F. Silvester, J. Solution Chem., Vol. 5, (1976), p. 269.
Silvester, L.F. and K.S. Pitzer, "Thermodynamics of Electrolytes 8 High-Temperature Properties, Including Enthalpy and Heat Capacity, WithApplication to Sodium Chloride," J. Phys. Chem., Vol. 81, No. 19, (1977), pp.1822-1828.
Polynomial Activity CoefficientThis model represents activity coefficient as an empirical function ofcomposition and temperature. It is used frequently in metallurgicalapplications where multiple liquid and solid solution phases can exist.
The equation is:
Where:
Ai =
Bi =
Ci =
Di =
Ei =
For any component i, the value of the activity coefficient can be fixed:
i = fi
This model is not part of any property method. To use it:
1 On the Methods | Specifications sheet, specify an activity coefficientmodel, such as NRTL.
2 Click the Methods | Selected Methods folder.
3 In the Object Manager, click New.
4 In the Create New ID dialog box, enter a name for the new method.
5 In the Base Property Method field, select NRTL.
6 Click the Models tab.
7 Change the Model Name for GAMMA from GMRENON to GMPOLY.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMPLYP/1 ai1 0 x — — —
GMPLYP/2 ai2 0 x — — —
GMPLYP/3 ai3 0 x — — —
2 Thermodynamic Property Models 153
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMPLYP/4 bi1 0 x — — —
GMPLYP/5 bi2 0 x — — —
GMPLYP/6 bi3 0 x — — —
GMPLYP/7 ci1 0 x — — —
GMPLYP/8 ci2 0 x — — —
GMPLYP/9 ci3 0 x — — —
GMPLYP/10 di1 0 x — — —
GMPLYP/11 di2 0 x — — —
GMPLYP/12 di3 0 x — — —
GMPLYP/13 ei1 0 x — — —
GMPLYP/14 ei2 0 x — — —
GMPLYP/15 ei3 0 x — — —
GMPLYO fi — x — — —
Note: If you specify GMPLYP on the Methods | Parameters | PureComponent | T-Dependent sheet, you can only enter the first 12 elements.If you want to specify values for elements 13 to 15, you should go to theCustomize | Add-Input | Add After sheet and enter the values of all 15elements as in the following example:
PROP-DATA GMPLYP-1IN-UNITS SIPROP-LIST GMPLYPPVAL WATER 0.0 1.5 0.0 &
0.0 0.0 0.0 &0.0 0.0 0.0 &0.0 0.0 0.0 &0.0 16. 0.0
Redlich-KisterThis model calculates activity coefficients. It is a polynomial in the differencebetween mole fractions in the mixture. It can be used for liquid and solidmixtures (mixed crystals).
The equation is:
Where:
nc = Number of components
A1,ij = aij / T + bij
A2,ij = cij / T + dij
A3,ij = eij / T + fij
A4,ij = gij / T + hij
154 2 Thermodynamic Property Models
A5,ij = mij / T + nij
An,ii = An,jj = 0.0
An,ji = An,ij(-1)(n-1)
An,kj = An,jk(-1)(n-1)
For any component i, the value of the activity coefficient can be fixed:
i = vi
Parameter Name/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMRKTB/1 aij 0 x — — —
GMRKTB/2 bij 0 x — — —
GMRKTB/3 cij 0 x — — —
GMRKTB/4 dij 0 x — — —
GMRKTB/5 eij 0 x — — —
GMRKTB/6 fij 0 x — — —
GMRKTB/7 gij 0 x — — —
GMRKTB/8 hij 0 x — — —
GMRKTB/9 mij 0 x — — —
GMRKTB/10 nij 0 x — — —
GMRKTO vi — x — — —
Reference
J. P. Novak, J. Matous, and J. Pick, Studies in Modern Thermodynamics,Volume 7: Liquid-Liquid Equilibria, Appendix 4, Elsevier, 1987.
Scatchard-HildebrandThe Scatchard-Hildebrand model calculates liquid activity coefficients. It isused in the CHAO-SEA property method and the GRAYSON property method.
The equation for the Scatchard-Hildebrand model is:
Where:
Aij =
i=
Vm*,l =
2 Thermodynamic Property Models 155
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — x 5.0 2000.0 TEMPERATURE
GMSHSP iDELTA x 103 105 SOLUPARAM
VLCVT1 Vi*,CVT — x 0.0005 1.0 MOLE-
VOLUME
GMSHVL Vi*,l x 0.01 1.0 MOLE-
VOLUME
GMSHXL kij 0.0 x -5 5 —
Three-Suffix MargulesThis model can be used to describe the excess properties of liquid and solidsolutions. It does not find much use in chemical engineering applications, butis still widely used in metallurgical applications. Note that the binaryparameters for this model do not have physical significance.
The equation is:
Where kij is a binary parameter:
For any component i, the value of the activity coefficient can be fixed:
i = di
Parameter Name/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMMRGB/1 aij 0 x — — TEMPERATURE
GMMRGB/2 bij 0 x — — —
GMMRGB/3 cij 0 x — — —
GMMRGO di — x — — —
References
M. Margules, "Über die Zusammensetzung der gesättigten Dämpfe vonMischungen," Sitzungsber. Akad. Wiss. Vienna, Vol. 104, (1895), p. 1293.
D.A. Gaskell, Introduction to Metallurgical Thermodyanics, 2nd ed., (NewYork: Hemisphere Publishing Corp., 1981), p. 360.
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987).
156 2 Thermodynamic Property Models
Symmetric and Unsymmetric ElectrolyteNRTL Activity Coefficient ModelThe Symmetric Electrolyte NRTL activity coefficient model (GMENRTLS) uses asymmetric reference state for ions as pure fused salts, rather than infinitedilution in aqueous solution. This basis is easier to use for nonaqueous andmixed-solvent systems, and eliminates the need to introduce water intootherwise water-free systems. It also allows the model to reduce to thestandard NRTL model when there are no electrolytes in the system. TheENRTL-SR property method is based on this model.
Chemical constants, enthalpy, and Gibbs free energy are calculated withrespect to the symmetric ionic reference state.
The Unsymmetric Electrolyte NRTL activity coefficient model (GMENRTLQ)uses the same equations as GMENRTLS, but the unsymmetric reference statefor ions (infinite dilution in aqueous solution). The ENRTL-RK property methodis based on this model. Unlike the original Electrolyte NRTL activity coefficientmodel, GMENRTLQ is also used to calculate enthalpy and Gibbs free energyfrom thermodynamics based on the unsymmetric ionic reference state.
These models also handle zwitterions.
Parameters
Both symmetric and unsymmetric models share the same binary and pairparameters. The adjustable model parameters are the symmetric non-random
factor parameters, , and the asymmetric binary interaction energy
parameters, . These parameters exist for molecule-molecule pairs (mm' =
m'm while mm' m'm), molecule-electrolyte pairs (m,ca = ca,m while m,ca ca,m where ca represents an ion pair), and electrolyte-electrolyte pairs (ca,ca'
= ca',ca and ca,c'a = c'a,ca while ca,ca' ca',ca and ca,c'a c'a,ca)
The parameters for ion pairs are temperature-dependent:
2 Thermodynamic Property Models 157
where .
The NRTL parameters are used for molecule-molecule parameters, withtemperature dependence:
The temperature dependency of the dielectric constant is given by:
Option codes can affect the performance of this model. See Option Codes forActivity Coefficient Models for details.
The following table lists the parameters used by GMENRTLS and GMENRTLQ:ParameterName
Symbol No. ofElements
Default MDS Units
Dielectric Constant Unary Parameters
CPDIEC a 1 — — —
b 1 0 — —
Tref 1 298.15 — Kelvin (noconversion)
Ionic Born Radius Unary Parameters
RADIUS ri 1 3x10-10 — LENGTH
Molecule-Molecule Binary Parameters
NRTL/1 aij — 0 x —
aji — 0 x —
NRTL/2 bij — 0 x TEMPERATURE†
bji — 0 x TEMPERATURE†
NRTL/3 cij=cji — .3 x —
NRTL/4 dij=dji — 0 x TEMPERATURE
NRTL/5 eij — 0 x TEMPERATURE
eji — 0 x TEMPERATURE
NRTL/6 fji — 0 x TEMPERATURE
fji — 0 x TEMPERATURE
Electrolyte-Molecule Pair Parameters
GMENCC Cca,m 1 0 x —
158 2 Thermodynamic Property Models
ParameterName
Symbol No. ofElements
Default MDS Units
Dielectric Constant Unary Parameters
Cm,ca 1 0 x —
GMENCD Dca,m 1 0 x TEMPERATURE†
Dm,ca 1 0 x TEMPERATURE†
GMENCE Eca,m 1 0 x —
Em,ca 1 0 x —
GMENCN ca,m = m,ca1 .2 x —
Electrolyte-Electrolyte Pair Parameters
GMENCC Cca,c'a 1 0 x —
Cc'a,ca 1 0 x —
Cca,ca' 1 0 x —
Cca',ca 1 0 x —
GMENCD Dca,c'a 1 0 x TEMPERATURE†
Dc'a,ca 1 0 x TEMPERATURE†
Dca,ca' 1 0 x TEMPERATURE†
Dca',ca 1 0 x TEMPERATURE†
GMENCE Eca,c'a 1 0 x —
Ec'a,ca 1 0 x —
Eca,ca' 1 0 x —
Eca',ca 1 0 x —
GMENCN ca,c'a = c'a,ca1 .2 x —
ca,ca' = ca',ca1 .2 x —
Zwitterions in Symmetric and UnsymmetricElectrolyte NRTL
The Symmetric and Unsymmetric Electrolyte NRTL models supportzwitterions, compounds with both positive and negative charges but netcharge of zero. Zwitterions are defined as:
Components of type Conventional, similar to solvents
Parameter ZWITTER set to 1; all other components in the Aspen PhysicalProperty System default to zero for ZWITTER
Parameter PLXANT/1 less than -1.0E10 so that they are non-volatile.
Zwitterions are handled as follows:
A zwitterion interacts with other molecular species through NRTLparameters only, excluding any interactions through Henry constants andpair parameters.
The activity coefficient is calculated as a solute.
The contribution from zwitterions to the solution enthalpy and Gibbs freeenergy are calculated as solutes using the infinite dilution heat capacitymodel CPAQ0, DGAQFM, and DHAQFM.
2 Thermodynamic Property Models 159
Working Equations for Symmetric andUnsymmetric Electrolyte NRTL
The symmetric and unsymmetric electrolyte NRTL models have twocontributions, one from local interactions that exist at the immediateneighbourhood of any species, and the other from the long-range ion-ioninteractions that exist beyond the immediate neighbourhood of an ionicspecies. To account for the local interactions, the model uses the electrolyteNRTL expression. To account for the long-range interactions, the model usesthe Pitzer-Debye-Hückel (PDH) formula (Pitzer, 1980, 1986). The followingequation is the basis of the electrolyte NRTL model for the excess Gibbs freeenergy of electrolyte systems:
(1)
The excess Gibbs free energy Gmex is defined as:
(2)
where Gm is the Gibbs free energy of electrolyte systems and Gmid is the Gibbs
free energy of an ideal solution at the same conditions of temperature,pressure, and composition.
The activity coefficient i of component i can be derived from Eq. 1 as follows:
(3)
or
(4)
Each of these terms will be discussed in subsequent sections.
Reference States in Electrolyte Systems
The activity coefficient needs to be normalized by choosing a reference statefor any molecular and ionic component, respectively.
Reference state for molecular components
The reference state for a molecular component m is defined as follows:
(5)
This definition is the so-called standard state of pure liquids for molecularcomponents and it is also called the symmetric reference state for molecularcomponents.
160 2 Thermodynamic Property Models
Reference state for ionic components
The standard state of pure liquids is hypothetical for ionic components inelectrolyte systems. Instead, the symmetric reference state is defined as thepure fused salt state of each electrolyte component in the system.
However, the conventional reference state for ionic components is theinfinite-dilution activity coefficients; it is also called the unsymmetricreference state for ionic components.
GMENRTLS uses the symmetric reference state, while GMENRTLQ uses theunsymmetric reference state.
Pure fused salt state of an electrolyte component
For an electrolyte component ca, the pure fused salt state can be defined asfollows:
(6)
(7)
Where ± is the mean ionic activity coefficient of the electrolyte component
and is related to the corresponding cationic and anionic activity coefficients c
and a by this expression:
(8)
where c is the cationic stoichiometric coefficient and a is the anionic
stoichiometric coefficient, and =c+a (one mole of salt releases moles of
ions in solution). They are given by the chemical equation describing thedissociation of the electrolyte:
(9)
with
(10)
Therefore Eq. 4 can be written in terms of charge numbers zc and za:
(11)
At the pure fused salt state, the total moles of ionic components (for onemole of salt) are:
=c+a(12)
therefore
(13)
2 Thermodynamic Property Models 161
(14)
(15)
The symmetric reference state defined by Eq. 6 is restricted to systemscontaining a single electrolyte component. For multi-electrolyte systems, thesymmetric reference state can be generalized from Eq. 6 as follows:
(16)
where m applies to all molecular components in the system. The symmetricreference state is a molecular-component-free medium.
Infinite-dilution aqueous solution
The condition of infinite-dilution aqueous solution for ionic components can bewritten as follows:
xc=xa=0 (17)
This condition applies to all ionic components in the solution, and water mustbe present in the solution for this reference state. In terms of the activitycoefficients for ionic components, the condition for the aqueous solution asthe unsymmetric reference state can be written as follows (where w=water):
(18)
This equation applies to all ionic components in the solution.
Local Interaction Term
In an electrolyte system, all component species can be categorized as one ofthree types: molecular species (solvents), m; cationic species (cations), c;and anionic species (anions), a. The model assumes that there are threetypes of local composition interactions. The first type consists of a centralmolecular species with other molecular species, cationic species, and anionicspecies in the immediate neighbourhood. Here, local electroneutrality ismaintained. The other two types are based on the like-ion repulsionassumption and have either a cationic or anionic species as the centralspecies. They also have an immediate neighbourhood consisting of molecularspecies and oppositely charged ionic species. Accordingly, the excess Gibbsenergy from local interactions for an electrolyte system can be written asfollows:
(19)
or
162 2 Thermodynamic Property Models
(20)
with
(21)
(22)
where the first term is the contribution when a molecular species is at thecenter, the second is the contribution when a cationic species is at the center,and the third term is the contribution when an anionic species is at thecenter. In Eq. 21, Ci=zi (charge number) for ionic species and Ci=1 for
molecular species. Finally, in Eqs. 19 and 20, G and are local binary
quantities related to each other by the NRTL non-random factor parameter :
(23)
The contribution to the activity coefficient of component i can be derived asfollows:
(24)
The results are:
(25)
(26)
2 Thermodynamic Property Models 163
(27)
Binary Parameters
The adjustable binary parameters for these models include molecule-molecule, molecule-electrolyte, and electrolyte-electrolyte binary parameters,where electrolyte here means an ion-pair composed of a cationic species andan anionic species. For each of these types, there are asymmetric binary
interaction energy parameters, , and symmetric non-random factor
parameters, (for calculating G). That is to say that the following are the
adjustable parameters:
(28)
However, as seen in the preceding equations, we need these parameters formolecule-molecule, molecule-cation, molecule-anion, and cation-anion pairs.The molecule-molecule parameters are given directly by the model's
adjustable binary parameters. The remaining parameters cm, am, mc, ma,
ca, ac, cm, am, mc, ma, ca, and ac, are calculated from these parameters.
The parameters for pairs involving cations and anions are calculated from
the adjustable binary parameters by applying a simple composition-averagemixing rule.
(29)
(30)
(31)
(32)
where Yc is a cationic charge composition fraction and Ya is an anionic chargecomposition fraction, defined as follows:
(33)
164 2 Thermodynamic Property Models
(34)
G for these pairs is calculated the same way:
(35)
(36)
(37)
(38)
(39)
(40)
And then the binary parameters are calculated from G using Eq. 23:
(41)
Normalized contributions to activity coefficients
From Eq. 5, it is easy to show that the local interaction contributions toactivity coefficients for all molecular components are normalized; that is
(42)
for all molecular components m in the system.
For ionic components with symmetric reference state, apply Eq. 16 to find:
(43)
(44)
2 Thermodynamic Property Models 165
(45)
(46)
(47)
(48)
where xm0 applies to all molecular components in the solution.
For ionic components with infinite-dilution aqueous solution as referencestate, apply Eq. 18 to get:
(49)
(50)
where and are local interaction contributions to activitycoefficients at infinite dilution aqueous solution:
(51)
(52)
Long-Range Interaction Term
To account for the long-range ion-ion interactions, the Symmetric andUnsymmetric Electrolyte NRTL models use the symmetric Pitzer-Debye-Hückel(PDH) formula (Pitzer, 1986):
166 2 Thermodynamic Property Models
(53)
with
(54)
(55)
where n is the total mole number of the solution, A is the Debye-Hückel
parameter, Ix is the ionic strength, is the closest approach parameter, NA is
Avogadro's number, vs is the molar volume of the solvent, Qe is the electron
charge, s is the dielectric constant of the solvent, kB is the Boltzmann
constant, zi is the charge number of component i, and Ix0 represents Ix at the
reference state.
For the unsymmetric reference state, Ix0 = 0.
For the symmetric reference state, the Debye-Hückel theory is originallybased on a single electrolyte with water as the solvent. Therefore, we canobtain Ix
0 from Eqs. 13 and 14:
(56)
For multi-electrolyte systems with mixed-solvents, Ix0 can take this form:
(57)
(58)
(59)
so that
(60)
where xm0 applies to all molecular components in the solution. This
definition ensures that the excess Gibbs free energy from the long rangeinteractions will be zero at the symmetric reference state regardless of howmany electrolytes are present in the solution.
The contribution to the activity coefficient from component i can be derivedas:
2 Thermodynamic Property Models 167
(61)
For a solvent component, this is:
(62)
For a cation or anion component:
(63)
For the unsymmetric reference state:
(64)
And for the symmetric reference state:
(65)
(66)
(67)
or
(68)
(69)
The Debye-Hückel theory is original based on a single electrolyte with water
as the solvent. The molar volume vs and the dielectric constant s for the
168 2 Thermodynamic Property Models
single solvent need to be extended for mixed-solvents; a simple compositionaverage mixing rule is adequate to calculate them as follows:
(70)
(71)
where s is a solvent component in the mixture and Msis the solvent molecularweight. Each sum is over all solvent components in the solution.
Born term correction
If the infinite dilution aqueous solution is chosen as the reference state, weneed to correct the the Debye-Hückel term for the change of the referencestate from the mixed-solvent composition to aqueous solution. The Born term(Robinson and Stokes, 1970; Rashin and Honig, 1985) is used for thispurpose:
(72)
where NA is the Avogadro constant and R is the gas constant. is theBorn term correction to the unsymmetric Pitzer-Debye-Hückel formula,
, and w is the dielectric constant of water, and ri is the Born radius
of species i.
The Born contribution to the activity coefficient of component i can be derivedas follows:
(73)
For a cation or anion component, this is:
(74)
The correction to the activity coefficient for a solvent component is zero:
(75)
2 Thermodynamic Property Models 169
Henry Components in the Symmetric andUnsymmetric Electrolyte NRTL Models
Light gases (Henry components) are usually supercritical at the temperatureand pressure of the system. In that case, pure component vapor pressure ismeaningless and therefore the pure liquid state at the temperature andpressure of the system cannot serve as the reference state. The referencestate for a Henry component is redefined to be at infinite dilution (that is, at
xi0) and at the temperature and pressure of the system.
The liquid phase reference fugacity, fi*,l, becomes the Henry’s constant for
Henry components in the solution, Hi, and the activity coefficient, i, is
converted to the infinite dilution reference state through the relationship:
(76)
where i
is the infinite dilution activity coefficient of Henry component i
(xi0) in the solution.
By this definition i* approaches unity as xi approaches zero. The phase
equilibrium relationship for Henry components becomes:
(77)
The Henry’s Law is available in all activity coefficient property methods. Themodel calculates the Henry’s constant for a dissolved gas component in allsolvent components in the mixture:
(78)
(79)
where His and is
are the Henry’s constant and the infinite dilution activity
coefficient of the dissolved gas component i in the solvent component s (xi0
and xs1), respectively.
Since ionic species exist only in the liquid phase and therefore do notparticipate directly in vapor-liquid equilibria, the activities of Henrycomponents are mainly through the local interactions with solvents. We cancalculate the activity coefficients for Henry components as follows:
(80)
(81)
(82)
170 2 Thermodynamic Property Models
where xh0 applies to all Henry components in the solution.
Activity Coefficient Basis for Henry Components
Regardless of the reference state for ionic components, there are two
possibilities for the basis of unsymmetric activity coefficients h
of Henry
components: aqueous and mixed-solvent. This can be specified on the Setup| Calculation Options | Reactions sheet. Mixed-solvent is the default.
For mixed-solvent basis, h
is calculated as follows:
(83)
where xh0 applies to all Henry components and xi0 to all ionic
components in the solution.
For aqueous basis, the unsymmetric activity coefficients of Henry componentsare calculated as follows:
(84)
Electrolyte Chemical Equilibria
In determining the composition of an electrolyte system, it is important toknow the equilibrium constants of the reactions taking place. An equilibriumconstant is expressed as the product of the activity of each species raised toits stoichiometric coefficients. Two different scales are used in Aspen Plus: themolality scale and the mole fraction scale but both are based on aqueouselectrolyte chemical equilibrium. For instance, the equilibrium constant for themole fraction scale in Aspen Plus is written in one of these:
(85)
(86)
Where:
K = Equilibrium constant
xw = Water mole fraction
w= Water activity coefficient
xs = Non-water solvent mole fraction
s= Non-water solvent activity coefficient
xi = Mole fraction of solute component (Henry orion)
i* = Unsymmetric activity coefficient of solute
component
i= Stoichiometric coefficient
2 Thermodynamic Property Models 171
The above equations are limited to aqueous electrolyte chemical equilibriaonly. Therefore, the chemical constants in Aspen Plus databanks forelectrolyte systems with infinite dilution aqueous reference state cannot beused for electrolyte systems with the symmetric reference state for ioniccomponents.
The chemical constants for electrolyte systems with the symmetric referencestate can be written in these forms:
(87)
(88)
where i indicates a molecular or ionic component and h represents a Henrycomponent. Eq. 83 or 84 is used for calculation of the unsymmetric activitycoefficients of Henry components. However, the calculation for the activitycoefficients of ionic components is carried out with the symmetric referencestate.
Other Thermophysical Properties
The activity coefficient model can be related to other properties throughfundamental thermodynamic equations. These properties (called excess liquidfunctions) are relative to the ideal liquid mixture at the same condition:
Excess molar liquid Gibbs free energy
(89)
Excess molar liquid enthalpy
(90)
Excess molar liquid entropy
(91)
The excess liquid functions given by Equations 89-91 are calculated from the
same activity coefficient model. In practice, however, the activity coefficient i
is often derived first from the excess liquid Gibbs free energy of a mixturefrom an activity coefficient model:
(92)
with
(93)
172 2 Thermodynamic Property Models
(94)
Where is the liquid Gibbs free energy of mixing; it is defined as thedifference between the Gibbs free energy of the mixture and that of the pure
component and is the ideal Gibbs free energy of mixing. Once theexcess liquid functions are known, the thermodynamic properties of liquidmixtures can be computed as follows:
(95)
(96)
(97)
where Hil and Hi
ig are the enthalpy and ideal gas enthalpy of component i atthe system conditions. Similarly, Gi
l and Giig are the Gibbs free energy and
ideal gas Gibbs free energy of component i at the system conditions. In AspenPlus, both Hi
ig and Giig are computed by the expressions:
(98)
(99)
where is the standard enthalpy of formation of ideal gas at
, is the ideal gas heat capacity, and is the
standard Gibbs free energy of formation of ideal gas at .
However, the above equations are directly not applicable to mixturescontaining ionic components because the ideal gas model becomes invalid forionic components.
The formulation to calculate the enthalpy and Gibbs free energy forelectrolyte systems can be carried out as follows:
(100)
(101)
2 Thermodynamic Property Models 173
(102)
where indexes s, h, and ca are meant to represent the contributions fromsolvents, Henry components and ionic components, respectively.
Solvents
The contribution from solvents can be written as follows:
(103)
(104)
(105)
(106)
(107)
(108)
where is the liquid fugacity coefficient of pure solventcomponent i, pi
sat is the vapor pressure of pure component at the system
temperature T, iv is the vapor fugacity coefficient of pure component at T
and pisat (normally calculated from an equation-of-state model), and
is the Poynting pressure correction from pisat to p,
and Vil is the liquid molar volume at T and p.
Henry components
The contribution from Henry components can be written as follows:
(109)
(110)
174 2 Thermodynamic Property Models
(111)
(112)
(113)
(114)
(115)
Ionic components
The contribution from ionic components can be written as follows:
(116)
(117)
(118)
(119)
(120)
(121)
where Hiref and Gi
ref are the enthalpy and Gibbs free energy of ioniccomponent i at the system conditions with a specified reference state(symmetric or unsymmetric).
The property calculations for solvents and Henry components are the samewhen the reference state is changed. Only for ionic components do theproperty methods need to be specified with a reference state. The methodswith the unsymmetric reference state are available already in Aspen Plus andAspen Properties (e.g. using the infinite dilution heat capacity model CPAQ0,DGAQFM, and DHAQFM). New methods are needed only for the symmetricreference state. Overall, the calculated total enthalpy or Gibbs free energy forthe same electrolyte solution should be the same, regardless of the referencestate specified.
2 Thermodynamic Property Models 175
Enthalpy and Gibbs free energy of ionic components with the symmetricreference state can be written as follows:
(122)
(123)
where and are enthalpy and Gibbs free energy of ionic componenti with the unsymmetric reference state, respectively, and available already in
Aspen Plus and Aspen Properties. Hi and Gi are the new contributions from
the symmetric reference state.
The unsymmetric enthalpy for an ionic component is calculated from
the infinite dilution aqueous phase heat capacity as follows:
(124)
where Tref = 298.15K. By default, is calculated from the aqueousinfinite dilution heat capacity polynomial. If the polynomial model parameters
are not available, is calculated from the Criss-Cobble correlation.
The unsymmetric Gibbs free energy for an ionic component is
calculated from the infinite dilution aqueous phase heat capacity asfollows:
(125)
(126)
where the term RT ln (1000/Mw) is added because and
are based on a molality scale, and is based on a mole fraction scale.
Hi and Gi for the symmetric reference state
The reference state for ionic components in the symmetric electrolyte NRTLmodel is the pure fused salts containing these ions, so the enthalpy or Gibbsfree energy of the ionic components at the symmetric reference state is theenthalpy contributions or the Gibbs free energy contributions of these ions tothe system of the pure fused salts. The condition of the pure fused salts canbe defined as follows:
176 2 Thermodynamic Property Models
(127)
which applies to all molecular components in the solution.
Given that the calculated total enthalpy or total Gibbs free energy of anelectrolyte solution by any reference state should be the same, theformulation of enthalpy or Gibbs free energy of the ionic components at thesymmetric reference state can be derived from the unsymmetric electrolyteNRTL enthalpy or Gibbs free energy calculations at the condition that allmolecular components (solvents and Henry components) approach zero, i.e.the pure fused salts. Applying Eq. 127, the system enthalpy and Gibbs freeenergy with the unsymmetric reference state can be expressed as:
(128)
(129)
where and are the total enthalpy and total Gibbsfree energy of the solution calculated by the unsymmetric electrolyte NRTLmodel at the limit of all molecular components approach zero, that is, the
pure fused salts state, and and are theexcess enthalpy and excess Gibbs free energy of ion i at the same limitcondition.
Applying Eq. 127, the system enthalpy and Gibbs free energy with thesymmetric reference state can be expressed as:
(130)
(131)
Comparing Eqs. 130 and 131 to Eqs. 128 and 129, we can get:
(132)
(133)
Therefore, the enthalpy and Gibbs free energy of ionic components with thesymmetric reference state can be written as:
(134)
(135)
2 Thermodynamic Property Models 177
One of advantages with the symmetric reference state is its capability tomodel non-aqueous electrolyte systems without introducing a trace amount ofwater. However, for calculating system enthalpy, entropy, and Gibbs freeenergy correctly, water must be defined in the component list so that thecorrections showed by Eqs. 132 and 133 can be calculated from theunsymmetric reference state.
References for Symmetric and UnsymmetricElectrolyte NRTL
C.-C. Chen and L.B. Evans, "A Local Composition Model for the Excess GibbsEnergy of Aqueous Electrolyte Systems," AIChE Journal, 1986, 32, 444.
Y. Song and C.-C. Chen, "Symmetric Nonrandom Two-Liquid ActivityCoefficient Model for Electrolytes" (to be published).
K.S. Pitzer, "Electrolytes. From Dilute Solutions to Fused Salts," J. Am. Chem.Soc., 1980, 102, 2902-2906.
K.S. Pitzer and J.M. Simonson, "Thermodynamics of Multicomponent, Miscible,Ionic Systems: Theory and Equations," J. Phys. Chem., 1986, 90, 3005-3009.
R.A. Robinson and R.H. Stokes, Electrolyte Solutions, Second Revised Edition.Butterworths: London, 1970.
A.A. Rashin and B. Honig, "Reevaluation of the Born Model of Ion Hydration,"J. Phys. Chem., 1985, 89 (26), pp 5588–5593.
UNIFAC Activity Coefficient ModelThe UNIFAC model calculates liquid activity coefficients for the followingproperty methods: UNIFAC, UNIF-HOC, and UNIF-LL. Because the UNIFACmodel is a group-contribution model, it is predictive. All published groupparameters and group binary parameters are stored in the Aspen PhysicalProperty System.
The equation for the original UNIFAC liquid activity coefficient model is madeup of a combinatorial and residual term:
ln = ln ic + ln i
r
ln ic =
Where the molecular volume and surface fractions are:
and
Where nc is the number of components in the mixture. The coordinationnumber z is set to 10. The parameters ri and qi are calculated from the groupvolume and area parameters:
178 2 Thermodynamic Property Models
and
Where ki is the number of groups of type k in molecule i, and ng is the
number of groups in the mixture.
The residual term is:
k is the activity coefficient of a group at mixture composition, and ki is the
activity coefficient of group k in a mixture of groups corresponding to pure i.
The parameters k and ki are defined by:
With:
And:
The parameter Xk is the group mole fraction of group k in the liquid:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
UFGRP (k,k, m, m, ...) — — — — —
GMUFQ Qk — — — — —
GMUFR Rk — — — — —
GMUFB bkn — — — — TEMPERATURE
The parameter UFGRP stores the UNIFAC functional group number andnumber of occurrences of each group. UFGRP is stored in the Aspen PhysicalProperty System pure component databank for most components. Fornondatabank components, enter UFGRP on the Components | MolecularStructure | Functional Group sheet. See Physical Property Data, Chapter 3,for a list of the UNIFAC functional groups.
2 Thermodynamic Property Models 179
UNIFAC-PSRK
The PSRK property method uses GMUFPSRK, the UNIFAC-PSRK model, whichis a variation on the standard UNIFAC model. UNIFAC-PSRK has specialgroups defined for the light gases CO2, H2, NH3, N2, O2, CO, H2S, and argon,and the group binary interaction parameters are temperature-dependent,using the values in parameter UNIFPS, instead of the constant value fromGMUFB used above, so that:
Where a, b, and c are the three elements of UNIFPS.
References
Aa. Fredenslund, J. Gmehling and P. Rasmussen, "Vapor-Liquid Equilibriausing UNIFAC," (Amsterdam: Elsevier, 1977).
Aa. Fredenslund, R.L. Jones and J.M. Prausnitz, AIChE J., Vol. 21, (1975), p.1086.
H.K. Hansen, P. Rasmussen, Aa. Fredenslund, M. Schiller, and J. Gmehling,"Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5 Revision andExtension", Ind. Eng. Chem. Res., Vol. 30, (1991), pp. 2352-2355.
UNIFAC (Dortmund Modified)The UNIFAC modification by Gmehling and coworkers (Weidlich andGmehling, 1987; Gmehling et al., 1993), is slightly different in thecombinatorial part. It is otherwise unchanged compared to the originalUNIFAC:
With:
The temperature dependency of the interaction parameters is:
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
UFGRPD (k,k, m, m, ...) — — — — —
GMUFDQ Qk — — — — —
GMUFDR Rk — — — — —
UNIFDM/1 amn,1 0 — — — TEMPERATURE
UNIFDM/2 amn,2 0 — — — TEMPERATURE
UNIFDM/3 amn,3 0 — — — TEMPERATURE
180 2 Thermodynamic Property Models
The parameter UFGRPD stores the group number and the number ofoccurrences of each group. UFGRPD is stored in the Aspen Physical PropertySystem pure component databank. For nondatabank components, enterUFGRPD on the Components | Molecular Structure | Functional Groupsheet. See Physical Property Data, Chapter 3, for a list of the Dortmundmodified UNIFAC functional groups.
References
U. Weidlich and J. Gmehling, "A Modified UNIFAC Model 1. Prediction of VLE,
hE and ," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 1372–1381.
J. Gmehling, J. Li, and M. Schiller, "A Modified UNIFAC Model. 2. PresentParameter Matrix and Results for Different Thermodynamic Properties," Ind.Eng. Chem. Res., Vol. 32, (1993), pp. 178–193.
UNIFAC (Lyngby Modified)The equations for the "temperature-dependent UNIFAC" (Larsen et al., 1987)are similar to the original UNIFAC:
,
Volume fractions are modified:
With:
Where k and ki have the same meaning as in the original UNIFAC, but
defined as:
With:
2 Thermodynamic Property Models 181
The temperature dependency of a is described by a function instead of aconstant:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
UFGRPL (k,k, m, m, ...) — — — — —
GMUFLQ Qk — — — — —
GMUFLR Rk — — — — —
UNIFLB/1 amn,1 0 — — — TEMPERATURE
UNIFLB/2 amn,2 0 — — — TEMPERATURE
UNIFLB/3 amn,3 0 — — — TEMPERATURE
The parameter UFGRPL stores the modified UNIFAC functional group numberand the number of occurrences of each group. UFGRPL is stored in the AspenPhysical Property System pure component databank. For nondatabankcomponents, enter UFGRP on the Components | Molecular Structure |Functional Group sheet. See Physical Property Data, Chapter 3, for a list ofthe Larsen modified UNIFAC functional groups.
Reference: B. Larsen, P. Rasmussen, and Aa. Fredenslund, "A ModifiedUNIFAC Group-Contribution Model for Prediction of Phase Equilibria and Heatsof Mixing," Ind. Eng. Chem. Res., Vol. 26, (1987), pp. 2274 – 2286.
UNIQUAC Activity Coefficient ModelThe UNIQUAC model calculates liquid activity coefficients for these propertymethods: UNIQUAC, UNIQ-2, UNIQ-HOC, UNIQ-NTH, and UNIQ-RK. It isrecommended for highly non-ideal chemical systems, and can be used for VLEand LLE applications. This model can also be used in the advanced equationsof state mixing rules, such as Wong-Sandler and MHV2.
The equation for the UNIQUAC model is:
Where:
i =
182 2 Thermodynamic Property Models
i' =
i =
li =
ti' =
ij=
z = 10
aij, bij, cij, and dij are unsymmetrical. That is, aij may not be equal to aji, etc.
Absolute temperature units are assumed for the binary parameters aij, bij, cij,dij, and eij.
can be determined from VLE and/or LLE data regression. The Aspen PhysicalProperty System has a large number of built-in parameters for the UNIQUACmodel. The binary parameters have been regressed using VLE and LLE datafrom the Dortmund Databank. The binary parameters for VLE applicationswere regressed using the ideal gas, Redlich-Kwong, and Hayden-O'Connellequations of state. See Physical Property Data, Chapter 1, for details.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMUQR ri — x — — —
GMUQQ qi — x — — —
GMUQQ1 qi' q x — — —
UNIQ/1 aij 0 x -50.0 50.0 —
UNIQ/2 bij 0 x -15000.0 15000.0 TEMPERATURE
UNIQ/3 cij 0 x — — TEMPERATURE
UNIQ/4 dij 0 x — — TEMPERATURE
UNIQ/5 Tlower 0 K x — — TEMPERATURE
UNIQ/6 Tupper 1000 K x — — TEMPERATURE
UNIQ/7 eij 0 x — — TEMPERATURE
Absolute temperature units are assumed for elements 2 through 4 and 7 ofUNIQ.
The UNIQ-2 property method uses data set 2 for UNIQ. All other UNIQUACmethods use data set 1.
References
D.S. Abrams and J.M. Prausnitz, "Statistical Thermodynamics of liquidmixtures: A new expression for the Excess Gibbs Energy of Partly orCompletely Miscible Systems," AIChE J., Vol. 21, (1975), p. 116.
2 Thermodynamic Property Models 183
A. Bondi, "Physical Properties of Molecular Crystals, Liquids and Gases," (NewYork: Wiley, 1960).
Simonetty, Yee and Tassios, "Prediction and Correlation of LLE," Ind. Eng.Chem. Process Des. Dev., Vol. 21, (1982), p. 174.
Van Laar Activity Coefficient ModelThe Van Laar model (Van Laar 1910) calculates liquid activity coefficients forthe property methods: VANLAAR, VANL-2, VANL-HOC, VANL-NTH, and VANL-RK. It can be used for highly nonideal systems.
Where:
zi =
Ai =
Bi =
Ci =
Aij =
Cij =
Cij = Cji
Aii = Bii = Cii = 0
aij and bij are unsymmetrical. That is, aij may not be equal to aji, and bij maynot be equal to bji.ParametersName/Element
Symbol DefaultMDS Lower Limit UpperLimit
Units
VANL/1 aij 0 x -50.0 50.0 —
VANL/2 bij 0 x -15000.0 15000.0 TEMPERATURE
VANL/3 cij 0 x -50.0 50.0 —
VANL/4 dij 0 x -15000.0 15000.0 TEMPERATURE
The VANL-2 property method uses data set 2 for VANL. All other Van Laarmethods use data set 1.
References
J.J. Van Laar, "The Vapor Pressure of Binary Mixtures," Z. Phys. Chem., Vol.72, (1910), p. 723.
184 2 Thermodynamic Property Models
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed. (New York: McGraw-Hill, 1987).
Wagner Interaction ParameterThe Wagner Interaction Parameter model calculates activity coefficients. Thismodel is used for dilute solutions in metallurgical applications.
The relative activity coefficient with respect to the reference activitycoefficient of a solute i (in a mixture of solutes i, j, and l and solvent A) is:
Where:
The parameter iref is the reference activity coefficient of solute i:
kij is a binary parameter:
For any component i, the value of the activity coefficient can be fixed:
i = gi
This model is recommended for dilute solutions.Parameter Name/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
GMWIPR/1 ai 0 x — — TEMPERATURE
GMWIPR/2 bi 0 x — — —
GMWIPR/3 ci 0 x — — —
GMWIPB/1 dij 0 x — — TEMPERATURE
GMWIPB/2 eij 0 x — — —
GMWIPB/3 fij 0 x — — —
GMWIPO gi — x — — —
GMWIPS — 0 x — — —
GMWIPS is used to identify the solvent component. You must set GMWIPS to1.0 for the solvent component. This model allows only one solvent.
References
A.D. Pelton and C. W. Bale, "A Modified Interaction Parameter Formalism forNon-Dilute Solutions," Metallurgical Transactions A, Vol. 17A, (July 1986),p. 1211.
2 Thermodynamic Property Models 185
Wilson Activity Coefficient ModelThe Wilson model calculates liquid activity coefficients for the followingproperty methods: WILSON, WILS2, WILS-HOC, WILS-NTH, WILS-RK, WILS-HF, WILS-LR, and WILS-GLR. It is recommended for highly nonideal systems,especially alcohol-water systems. It can also be used in the advancedequation-of-state mixing rules, such as Wong-Sandler and MHV2. This modelcannot be used for liquid-liquid equilibrium calculations.
The equation for the Wilson model is:
Where:
ln Aij = †
The extended form of ln Aij provides more flexibility in fitting phaseequilibrium and enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. Thatis, aij may not be equal to aji, etc.
The binary parameters aij, bij, cij, dij, and eij must be determined from dataregression or VLE and/or heat-of-mixing data. The Aspen Physical PropertySystem has a large number of built-in binary parameters for the Wilsonmodel. The binary parameters have been regressed using VLE data from theDortmund Databank. The binary parameters were regressed using the idealgas, Redlich-Kwong, and Hayden-O'Connell equations of state. See PhysicalProperty Data, Chapter 1, for details.ParameterName/Element
Symbol Default MDS Lower LimitUpperLimit
Units
WILSON/1 aij 0 x -50.0 50.0 —
WILSON/2 bij 0 x -15000.0 15000.0 TEMPERATURE††
WILSON/3 cij 0 x -— — TEMPERATURE††
WILSON/4 dij 0 x — — TEMPERATURE††
WILSON/5 Tlower 0 K x — — TEMPERATURE
WILSON/6 Tupper 1000 K x — — TEMPERATURE
WILSON/7 eij 0 x — — TEMPERATURE††
The WILS-2 property method uses data set 2 for WILSON. All other Wilsonmethods use data set 1.
† In the original formulation of the Wilson model, aij = ln Vj/Vi, cij = dij = eij =0, and
bij = -(ij - ii)/R, where Vj and Vi are pure component liquid molar volume at
25C.
†† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others are
186 2 Thermodynamic Property Models
interpreted in input units. The temperature limits are always interpreted ininput units.
References
G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.
Wilson Model with Liquid Molar VolumeThis Wilson model (used in the method WILS-VOL) calculates liquid activitycoefficients using the original formulation of Wilson (Wilson 1964) except thatliquid molar volume is calculated at system temperature, instead of at 25C.It is recommended for highly nonideal systems, especially alcohol watersystems. It can be used in any activity coefficient property method or in theadvanced equation of state mixing rules, such as Wong Sandler and MHV2.This model cannot be used for liquid liquid equilibrium calculations.
The equation for the Wilson model is:
Where:
ln Aij = †
Vj and Vi are pure component liquid molar volume at the system temperaturecalculated using the General Pure Component Liquid Molar Volume model. Theextended form of ln Aij provides more flexibility in fitting phase equilibriumand enthalpy data. aij, bij, cij, dij, and eij are unsymmetrical. That is, aij maynot be equal to aji, etc.
The binary parameters aij, bij, cij, dij, and eij must be determined from dataregression of VLE and/or heat-of-mixing data. There are no built in binaryparameters for this model.ParameterName/Element
SymbolDefaultMDS LowerLimit
UpperLimit
Units
WSNVOL/1 aij 0 x -50.0 50.0 —
WSNVOL/2 bij 0 x -15000.0 15000.0 TEMPERATURE††
WSNVOL/3 cij 0 x — — TEMPERATURE††
WSNVOL/4 dij 0 x — — TEMPERATURE††
WSNVOL/5 eij 0 x — — TEMPERATURE††
WSNVOL/6 Tlower 0 K x — — TEMPERATURE
WSNVOL/7 Tupper 1000 K x — — TEMPERATURE
Pure component parameters for the General Pure Component Liquid MolarVolume model are also required.
2 Thermodynamic Property Models 187
† In the original formulation of the Wilson model, aij = cij = dij = eij = 0 and
. Vj and Vi are calculated at 25C.
†† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others areinterpreted in input units. The temperature limits are always interpreted ininput units.
Reference: G.M. Wilson, J. Am. Chem. Soc., Vol. 86, (1964), p. 127.
Vapor Pressure and LiquidFugacity ModelsThe Aspen Physical Property System has the following built-in vapor pressureand liquid fugacity models. This section describes the vapor pressure andliquid fugacity models available.Model Type
General Pure Component Liquid VaporPressure
Vapor pressure
API Sour Vapor pressure
Braun K-10 Vapor pressure
Chao-Seader Fugacity
Grayson-Streed Fugacity
Kent-Eisenberg Fugacity
Maxwell-Bonnell Vapor pressure
Solid Antoine Vapor pressure
General Pure Component Liquid VaporPressureThe Aspen Physical Property System has several submodels for calculatingvapor pressure of a liquid. It uses parameter THRSWT/3 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/3is
Then this equation isused
And this parameter is used
0 Extended Antoine PLXANT
200-211 Barin CPLXP1, CPLXP2, CPIXP1, CPIXP2,and CPIXP3
301 Wagner WAGNER
302 PPDS Modified Wagner WAGNER
400 PML LNVPEQ and one of LNVP1, LOGVP1,LNPR1, LOGPR1, LNPR2, LOGPR2
401 IK-CAPE PLPO
501 NIST TDE Polynomial PLTDEPOL
188 2 Thermodynamic Property Models
If THRSWT/3is
Then this equation isused
And this parameter is used
502 NIST Wagner 25 WAGNER25
Extended Antoine Equation
Parameters for many components are available for the extended Antoineequation from the Aspen Physical Property System pure component databank.This equation can be used whenever the parameter PLXANT is available.
The equation for the extended Antoine vapor pressure model is:
Extrapolation of ln pi*,l versus 1/T occurs outside of temperature bounds, until
ln pi*,l reaches 7 + ln pi
*,l(T=C9i). Beyond that point pi*,l is constant at that
value.ParameterName/ Element
Symbol Default MDS LowerLimit
UpperLimit
Units
PLXANT/1 C1i x PRESSURE,TEMPERATURE
PLXANT/2 C2i x TEMPERATURE
PLXANT/3, . . . , 7 C3i, ..., C7i 0 x TEMPERATURE
PLXANT/8 C8i 0 x TEMPERATURE
PLXANT/9 C9i 1000 x TEMPERATURE
If C5i, C6i, or C7i is non-zero, absolute temperature units are assumed for allcoefficients C1i through C7i. The temperature limits are always in user inputunits.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacityfor details about this submodel.
Wagner Vapor Pressure Equation
The Wagner vapor pressure equation is the best equation for correlation. Theequation can be used if the parameter WAGNER is available:
Where:
Tri = T / Tci
pri*,l = pi
*,l / pci
Linear extrapolation of ln pi*,l versus T occurs outside of temperature bounds.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
2 Thermodynamic Property Models 189
PPDS Modified Wagner Vapor Pressure Equation
The PPDS equation also uses the same parameter WAGNER as the standardWagner equation:
Where:
Tri = T / Tci
pri*,l = pi
*,l / pci
Linear extrapolation of ln pi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
WAGNER/1 C1i x
WAGNER/2 C2i 0 x
WAGNER/3 C3i 0 x
WAGNER/4 C4i 0 x
WAGNER/5 C5i 0 x TEMPERATURE
WAGNER/6 C6i 1000 x TEMPERATURE
TC Tci TEMPERATURE
PC pci PRESSURE
NIST Wagner 25 Liquid Vapor Pressure Equation
This equation is the same as the PPDS Modified Wagner equation above, butit uses parameter WAGNER25 instead of WAGNER, and it uses criticalproperties from this parameter set also.
Where:
Tri = T / Tci
Linear extrapolation of ln pi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
WAGNER25/1 C1i x
WAGNER25/2 C2i 0 x
WAGNER25/3 C3i 0 x
WAGNER25/4 C4i 0 x
WAGNER25/5 ln pci 0 x
WAGNER25/6 Tci x TEMPERATURE
190 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
WAGNER25/7 Tlower 0 x TEMPERATURE
WAGNER25/8 Tupper 1000 x TEMPERATURE
IK-CAPE Vapor Pressure Equation
The IK-CAPE model is a polynomial equation. If the parameter PLPO isavailable, the Aspen Physical Property System can use the IK-CAPE vaporpressure equation:
Linear extrapolation of ln pi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
PLPO/1 C1i X PRESSURETEMPERATURE
PLPO/2, ..., 10 C2i , ..., C10i 0 X TEMPERATURE
PLPO/11 C11i 0 X TEMPERATURE
PLPO/12 C12i 1000 X TEMPERATURE
PML Vapor Pressure Equations
The PML vapor pressure equations are modified versions of the Antoine andWagner equations. Each equation comes in two alternate forms, identicalexcept for the use of natural or base-10 logarithms. Parameter LNVPEQ/1specifies the number of the equation used. Each equation uses a separateparameter: LNVP1 for equation 1, LOGVP1 for 2, LNPR1 for 3, LOGPR1 for 4,LNPR2 for 5, and LOGPR2 for 6.
Equation 1 (natural logarithm) and 2 (base 10 logarithm):
Equation 3 (natural logarithm) and 4 (base 10 logarithm):
Equation 5 (natural logarithm) and 6 (base 10 logarithm):
Where:
Tri = T / Tci
2 Thermodynamic Property Models 191
pri*,l = pi
*,l / pci
LNVPEQ/2 and LNVPEQ/3 are the lower and upper temperature limits,respectively.
In equations 1-4, if elements 4, 7, or 8 are non-zero, absolute temperatureunits are assumed for all elements.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
LNVP1/1, ...,8 C1i, ..., C8i x PRESSURETEMPERATURE
LOGVP1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE
LNPR1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE
LOGPR1/1, ..., 8 C1i, ..., C8i x PRESSURETEMPERATURE
LNPR2/1,2 C1i, C2i x
LOGPR2/1,2 C1i, C2i x
LNVPEQ/1 (equationnumber)
LNVPEQ/2 Tlower 0 X TEMPERATURE
LNVPEQ/3 Tupper 1000 X TEMPERATURE
TC Tci TEMPERATURE
PC pci PRESSURE
NIST TDE Polynomial for Liquid Vapor Pressure
This equation can be used for calculating vapor pressure when parameterPLTDEPOL is available.
Linear extrapolation of ln pi*,l versus T occurs outside of temperature bounds.
If elements 2, 3, 6, or 8 are non-zero, absolute temperature units areassumed for all elements.ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
PLTDEPOL/1 C1i X
PLTDEPOL/2 C2i 0 X TEMPERATURE
PLTDEPOL/3 C3i 0 X
PLTDEPOL/4, ..., 8 C4i , ..., C8i 0 X TEMPERATURE
PLTDEPOL/9 Tlower 0 X TEMPERATURE
PLTDEPOL/10 Tupper 1000 X TEMPERATURE
192 2 Thermodynamic Property Models
References
Reid, Prausnitz, and Poling, The Properties of Gases and Liquids, 4th ed.,(New York: McGraw-Hill, 1987).
Harlacher and Braun, "A Four-Parameter Extension of the Theorem ofCorresponding States," Ind. Eng. Chem. Process Des. Dev., Vol. 9, (1970), p.479.
W. Wagner, Cryogenics, Vol. 13, (1973), pp. 470-482.
D. Ambrose, M. B. Ewing, N. B. Ghiassee, and J. C. Sanchez Ochoa "Theebulliometric method of vapor-pressure measurement: vapor pressures ofbenzene, hexafluorobenzene, and naphthalene," J. Chem. Thermodyn. 22(1990), p. 589.
API Sour ModelThe API Sour model is based on the API sour water model for correlating theammonia, carbon dioxide, and hydrogen sulfide volatilities from aqueous sourwater system. The model assumes aqueous phase chemical equilibriumreactions involving CO2, H2S, and NH3. The model is not usable with chemistryin the true component approach. Use the apparent component approach withthis model.
The model is applicable from 20 C to 140 C. The authors developed the modelusing available phase equilibrium data and reported average errors betweenthe model and measured partial pressure data as followsCompound Average Error, %
Up to 60 C Above 60 C
Ammonia 10 36
Carbon dioxide 11 24
Hydrogen sulfide 12 29
Detail of the model is described in the reference below and is too involved tobe reproduced here.
Reference
New Correlation of NH3, CO2, and H2S Volatility Data from Aqueous SourWater Systems, API Publication 955, March 1978 (American PetroleumInstitute).
Braun K-10 ModelThe BK10 model uses the Braun K-10 K-value correlations, which weredeveloped from the K10 charts (K-values at 10 psia) for both real and pseudocomponents. The form of the equation used is an extended Antoine vaporpressure equation with coefficients specific to real components and pseudocomponent boiling ranges.
This method is strictly applicable to heavy hydrocarbons at low pressures.However, our model includes coefficients for a large number of hydrocarbonsand light gases. For pseudocomponents the model covers boiling ranges 450
2 Thermodynamic Property Models 193
– 700 K (350 – 800F). Heavier fractions can also be handled using themethods developed by AspenTech.
References
B.C. Cajander, H.G. Hipkin, and J.M. Lenoir, "Prediction of Equilibrium Ratiosfrom Nomograms of Improved Accuracy," Journal of Chemical EngineeringData, vol. 5, No. 3, July 1960, p. 251-259.
J.M. Lenoir, "Predict K Values at Low Temperatures, part 1," HydrocarbonProcessing, p. 167, September 1969.
J.M. Lenoir, "Predict K Values at Low Temperatures, part 2," HydrocarbonProcessing, p. 121, October 1969.
Chao-Seader Pure Component LiquidFugacity ModelThe Chao-Seader model calculates pure component fugacity coefficient, forliquids. It is used in the CHAO-SEA property method. This is an empiricalmodel with the Curl-Pitzer form. The general form of the model is:
Where:
=
ParameterName/Element
Symbol Default MDS Lower LimitUpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
OMEGA i— — -0.5 2.0 —
References
K.C. Chao and J.D. Seader, "A General Correlation of Vapor-Liquid Equilibriain Hydrocarbon Mixtures," AIChE J., Vol. 7, (1961), p. 598.
Grayson-Streed Pure Component LiquidFugacity ModelThe Grayson-Streed model calculates pure component fugacity coefficients forliquids, and is used in the GRAYSON/GRAYSON2 property methods. It is anempirical model with the Curl-Pitzer form. The general form of the model is:
Where:
194 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS Lower LimitUpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
OMEGA i— — -0.5 2.0 —
References
H.G. Grayson and C.W. Streed, Paper 20-PO7, Sixth World PetroleumConference, Frankfurt, June 1963.
Kent-Eisenberg Liquid Fugacity ModelThe Kent-Eisenberg model calculates liquid mixture component fugacitycoefficients and liquid enthalpy for the AMINES property method.
The chemical equilibria in H2S + CO2 + amine systems are described usingthese chemical reactions:
Where:
R' = Alcohol substituted alkyl groups
The equilibrium constants are given by:
The chemical equilibrium equations are solved simultaneously with thebalance equations. This obtains the mole fractions of free H2S and CO2 insolution. The equilibrium partial pressures of H2S and CO2 are related to therespective free concentrations by Henry's constants:
2 Thermodynamic Property Models 195
The apparent fugacities and partial molar enthalpies, Gibbs energies andentropies of H2S and CO2 are calculated by standard thermodynamicrelationships. The chemical reactions are always considered.
The values of the coefficients for the seven equilibrium constants (A1i, ... A5i)and for the two Henry's constants B1i and B2i are built into the Aspen PhysicalProperty System. The coefficients for the equilibrium constants weredetermined by regression. All available data for the four amines were used:monoethanolamine, diethanolamine, disopropanolamine and diglycolamine.
You are not required to enter any parameters for this model.
References
R.L. Kent and B. Eisenberg, Hydrocarbon Processing, (February 1976),pp. 87-92.
Maxwell-Bonnell Vapor Pressure ModelThe Maxwell-Bonnell model calculates vapor pressure using the Maxwell-Bonnell vapor pressure correlation for all hydrocarbon pseudo-components asa function of temperature. This is an empirical correlation based on APIprocedure 5A1.15, 5A1.13. This model is used in property method MXBONNELfor calculating vapor pressure and liquid fugacity coefficients (K-values).
References
API procedure 5A1.15 and 5A1.13.
Solid Antoine Vapor Pressure ModelThe vapor pressure of a solid can be calculated using the Antoine equation.
Parameters for some components are available for the extended Antoineequation from the Aspen Physical Property System pure component databank.This equation can be used whenever the parameter PSANT is available.
The equation for the solid Antoine vapor pressure model is:
Extrapolation of ln pi*,s versus 1/T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS Lower LimitUpperLimit
Units
PSANT/1 C1i — x — — PRESSURE,TEMPERATURE
PSANT/2 C2i — x — — TEMPERATURE
PSANT/3 C3i 0 x — — TEMPERATURE
PSANT/4 C4i 0 x — — TEMPERATURE
PSANT/5 C5i 1000 x — — TEMPERATURE
196 2 Thermodynamic Property Models
General Pure Component Heatof VaporizationThe Aspen Physical Property System has several submodels for calculatingpure component heat of vaporization. It uses parameter THRSWT/4 todetermine which submodel is used. See Pure Component Temperature-Dependent Properties for details.If THRSWT/4is
Then this equation is usedAnd this parameter isused
0 Watson DHVLWT
106 DIPPR DHVLDP
301 PPDS DHVLDS
401 IK-CAPE DHVLPO
505 NIST TDE Watson equation DHVLTDEW
DIPPR Heat of Vaporization EquationThe DIPPR equation is used to calculate heat of vaporization when THRSWT/4is set to 106. (Other DIPPR equations may sometimes be used. See PureComponent Temperature-Dependent Properties for details.)
The equation for the DIPPR heat of vaporization model is:
Where:
Tri = T / Tci
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
Linear extrapolation of vapHi* versus T occurs outside of temperature bounds,
using the slope at the temperature bound, except that vapHi* is zero for
.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DHVLDP/1 C1i — x — — MOLE-ENTHALPY
DHVLDP/2 C2i 0.38 x — — —
DHVLDP/3, 4, 5 C3i, C4i, C5i 0 x — — —
DHVLDP/6 C6i 0 x — — TEMPERATURE
DHVLDP/7 C7i 1000 x — — TEMPERATURE
TC Tci — — 5.0 2000.0 TEMPERATURE
2 Thermodynamic Property Models 197
Watson Heat of Vaporization EquationThe Watson equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 0. See Pure Component Temperature-DependentProperties for details.
The equation for the Watson model is:
Where:
vapHi*(T1) = Heat of vaporization at temperature T1
Linear extrapolation of vapHi* versus T occurs below the minimum
temperature bound, using the slope at the temperature bound.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
TC Tci — 5.0 2000.0 TEMPERATURE
DHVLWT/1 vapHi*(T1) — 5x104 5x108 MOLE-ENTHALPY
DHVLWT/2 T1 — 4.0 3500.0 TEMPERATURE
DHVLWT/3 ai 0.38 -2.0 2.0 —
DHVLWT/4 bi 0 -2.0 2.0 —
DHVLWT/5 Tmin 0 0.0 1500.0 TEMPERATURE
PPDS Heat of Vaporization EquationThe PPDS equation is used to calculate heat of vaporization when THRSWT/4is set to 301. See Pure Component Temperature-Dependent Properties fordetails.
The equation for the PPDS model is:
where R is the gas constant.
Linear extrapolation of vapHi* versus T occurs outside of temperature bounds,
using the slope at the temperature bound.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — 5.0 2000.0 TEMPERATURE
DHVLDS/1 C1i — — — — —
DHVLDS/2 C2i 0 — — — —
DHVLDS/3 C3i 0 — — — —
DHVLDS/4 C4i 0 — — — —
DHVLDS/5 C5i 0 — — — —
DHVLDS/6 C6i 0 — — TEMPERATURE
198 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DHVLDS/7 C7i 1000 — — TEMPERATURE
IK-CAPE Heat of Vaporization EquationThe IK-CAPE equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 401. See Pure Component Temperature-DependentProperties for details.
The equation for the IK-CAPE model is:
Linear extrapolation of vapHi* versus T occurs outside of temperature bounds,
using the slope at the temperature boundParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DHVLPO/1 C1i — X — — MOLE-ENTHALPY
DHVLPO/2, ...,10
C2i, ..., C10i 0 X — — MOLE-ENTHALPYTEMPERATURE
DHVLPO/11 C11i 0 X — — TEMPERATURE
DHVLPO/12 C12i 1000 X — — TEMPERATURE
NIST TDE Watson Heat of VaporizationEquationThe NIST TDE Watson equation is used to calculate heat of vaporization whenTHRSWT/4 is set to 505. See Pure Component Temperature-DependentProperties for details.
The equation is:
Linear extrapolation of vapHi* versus T occurs outside of temperature bounds,
using the slope at the temperature boundParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DHVLTDEW/1 C1i — X — — —
DHVLTDEW/2, 3,4
C2i, C3i, C4i 0 X — — —
DHVLTDEW/5 Tci — X — — TEMPERATURE
DHVLTDEW/6 nTerms 4 X — — —
2 Thermodynamic Property Models 199
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DHVLTDEW/7 Tlower 0 X — — TEMPERATURE
DHVLTDEW/8 Tupper 1000 X — — TEMPERATURE
Clausius-Clapeyron EquationThe Aspen Physical Property System can calculate heat of vaporization usingthe Clausius Clapeyron equation:
Where:
= Slope of the vapor pressure curve calculated from the ExtendedAntoine equation. (Note that above the critical point, this slopeis zero.)
Vi*,v = Vapor molar volume calculated from the Redlich Kwong
equation of state
Vi*,l = Liquid molar volume calculated from the Rackett equation
For parameter requirements, see General Pure Component Liquid VaporPressure, the General Pure Component Liquid Molar Volume model, andRedlich Kwong.
Pure-Component Heat of SublimationPolynomialThis model calculates molar enthalpy of sublimation using a polynomialmodel:
Linear extrapolation occurs for Hvs versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DHVSPL/1 C1i — x — — MOLE ENTHALPY,TEMPERATURE
DHVSPL/2,...,5 C2i, ..., C5i 0 x — — MOLE ENTHALPY,TEMPERATURE
DHVSPL/6 C6i 0 x — — TEMPERATURE
DHVSPL/7 C7i 1000 x — — TEMPERATURE
Phase Change Heat of Sublimation ModelThis model calculates enthalpy of sublimation from a phase changerelationship. In this calculation, it is not assumed that the compound goesfrom the solid state directly to the vapor state. The model returns the
200 2 Thermodynamic Property Models
difference between the solid enthalpy and vapor (ideal gas) enthalpy at T,taking into account all phase changes and sensible heat from Tref,1 to T.
ParameterName/Element
Symbol DescriptionDefault MDS LowerLimit
UpperLimit
Units
DHFUS Hfusenthalpy offusion atTREF1
— x — — MOLEENTHALPY
TREF1 Tref,1 fusiontemperature
— x — — TEMPERATURE
CPINT HLliquidenthalpychange fromTREF1 toTREF2
— x — — MOLEENTHALPY
DHVAP HVL(Tref,2)enthalpy ofvaporizationat TREF2
— x — — MOLEENTHALPY
TREF2 Tref,2 boiling pointtemperature
— x — — TEMPERATURE
CPIG CpIG ideal gas
heatcapacity
— x — — MOLE-HEAT-CAPACITY
CPSPOL Cps solid heat
capacity— x — — MOLE-HEAT-
CAPACITY
Molar Volume and DensityModelsThe Aspen Physical Property System has the following built-in molar volumeand density models available. This section describes the molar volume anddensity models.Model Type
API Liquid Volume Liquid volume
Brelvi-O'Connell Partial molar liquidvolume of gases
Chueh-Prausnitz Liquid volume
Clarke Aqueous Electrolyte Volume Liquid volume
COSTALD Liquid Volume Liquid volume
Debye-Hückel Volume Electrolyte liquid volume
Liquid Constant Molar Volume Model Liquid volume
General Pure Component Liquid MolarVolume
Liquid volume/liquiddensity
Rackett/Campbell-Thodos Mixture LiquidVolume
Liquid volume
Modified Rackett Liquid volume
2 Thermodynamic Property Models 201
Model Type
General Pure Component Solid Molar Volume Solid volume
Liquid Volume Quadratic Mixing Rule Liquid volume
API Liquid Molar VolumeThis model calculates liquid molar volume for a mixture, using the APIprocedure and the Rackett model. Ideal mixing is assumed:
Where:
xp = Mole fraction of pseudocomponents
xr = Mole fraction of real components
For pseudocomponents, the API procedure is used:
Where:
fcn = A correlation based on API procedure 6A3.5 (API Technical DataBook, Petroleum Refining, 4th edition)
At high density, the Ritter equation is used (adapted from Ritter, Lenoir, andSchweppe, Petrol. Refiner 37 [11] 225 (1958)):
Where SG is the specific gravity, Tb is the mean average boiling point inRankine, T is the temperature of the system in Rankine, and the mass volumeis produced in units of cubic feet per pound-mass.
This procedure is valid over the following conditions:
UOPK: 10.5 - 12.5
API: 0 - 95
Mean Average Boiling Point: 0 - 1100 F
Temperature: 0 - 1000 F
Calculated density: 0.4 - 1.05 g/cc
The effect of pressure is automatically accounted for using procedure 6A3.10.This procedure has the following validity range:
Density at low pressure: 0.7 - 1.0 g/cc
Pressure: 0 - 100,000 psig
For real components, the mixture Rackett model is used:
202 2 Thermodynamic Property Models
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
See the Rackett model for descriptions.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TB Tb — — 4.0 2000.0 TEMPERATURE
API API — — -60.0 500.0 —
TC Tc — — 5.0 2000.0 TEMPERATURE
PC pc — — 105 108 PRESSURE
RKTZRA ZRA ZC — 0.1 0.5 —
There are two versions of this model: VL2API and VL2API5. Model VL2API isused in route VLMX20, while model VL2API5 is used in route VLMX24.
The main difference between the VL2API and VL2API5 models is as follows:
The VL2API model calculates the liquid density for each pseudocomponentusing the API procedure 6A3.5 (or Ritter equation), then computes thedensity of the pseudocomponent mixture as a mole-fraction-weightedaverage.
The VL2API5 model calculates the liquid density of the mixture of thepseudocomponents as a whole. It first computes the specific gravity andmean average boiling point of the pseudocomponent mixture, then uses theAPI procedure 6A3.5 (or Ritter equation) to compute the mixture liquiddensity.
Both models use the same procedure 6A3.10 for pressure correction.Experience shows that VL2API5 is less sensitive to how thepseudocomponents are generated from the same assay (number of cutpoints, etc.).
Brelvi-O'ConnellThe Brelvi-O'Connell model calculates partial molar volume of a supercriticalcomponent i at infinite dilution in pure solvent A. Partial molar volume atinfinite dilution is required to compute the effect of pressure on Henry'sconstant. (See Henry's Constant.)
The general form of the Brelvi-O'Connell model is:
Where:
i = Solute or dissolved-gas component
A = Solvent component
VBO = V1 + TV2
The above correlation applies to both solute and solvent.
The liquid molar volume of solvent is obtained from the Rackett model:
2 Thermodynamic Property Models 203
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC TcA — — 5.0 2000.0 TEMPERATURE
PC pcA — — 105 108 PRESSURE
RKTZRA ZARA ZC x 0.1 1.0 —
VLBROC/1 V1 VC x -1.0 1.0 MOLE-VOLUME
VLBROC/2 V2 0 x -0.1 0.1 TEMPERATURE
References
S.W. Brelvi and J.P. O'Connell, AIChE J., Vol. 18, (1972), p. 1239.
S.W. Brelvi and J.P. O'Connell, AIChE J., Vol. 21, (1975), p. 157.
Chueh-Prausnitz Liquid Molar VolumeModelThe Chueh-Prausnitz model is used to calculate liquid molar volume for purecomponents and mixtures. It uses the Rackett model to calculate thesaturated molar volume then applies a pressure correction term. The mixtureform of the model is described below. The equations reduce to the purecomponent version.
Where
Vm =Liquid molar volume of the mixture
Vms=Liquid molar volume at saturation, calculated using the Rackett
model for mixtures or the General liquid volume model for purecomponents
Zcm=Critical compressibility factor of the mixture = xiZci
Zci =Critical compressibility factor of component i
N =
P =System pressure
204 2 Thermodynamic Property Models
Pvp =Saturation pressure = formixtures, or calculated using the General vapor pressure modelfor pure components
Pcm =Critical pressure of the mixture
T =Temperature
Trm =Reduced temperature = T/Tcm
Tcm =Critical temperature of the mixture
m=Acentric factor of the mixture = xii
i=Acentric factor of component i
Tcm and Pcm are calculated by:
Vcm = xiZciTci/Pci
Tcm = [xiZciTci3/2/Pci]
2/Vcm2
Pcm = ZcmTcm/Vcm
Tci = Critical temperature of component i
Pci = Critical pressure of component i
Note: Reduced temperature Tr is always calculated using absolutetemperature units.Note: Above Tr=0.99 an extrapolation method is used to smooth thetransition to constant molar volume equal to the critical volume.
The parameters required for the model are the same as those for the Rackett
model with the addition of the acentric factor, i
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
VCRKT Vci VC x 0.001 3.5 MOLE-VOLUME
RKTZRA Zi*,RA ZC x 0.1 1.0 —
RKTKIJ kij x -5.0 5.0 —
OMEGA i— — -0.5 2.0 —
Reference
Chueh, P.L. and J.M. Prausnitz, AIChE J. 15, 471 (1969).
2 Thermodynamic Property Models 205
Clarke Aqueous Electrolyte VolumeThe Clarke model calculates liquid molar volume for electrolytes solutions.The model is applicable to mixed solvents and is based on:
Molar volume of molecular solvents (equation 2)
The relationship between the partial molar volume of an electrolyte and itsmole fraction in the solvent (equation 4)
All quantities are expressed in terms of apparent components.
If option code 1 is set to 1, the liquid volume quadratic mixing rule is usedinstead. The default option uses this equation to calculate the liquid molarvolume for electrolyte solutions:
(1)
Where:
Vml = Liquid molar volume for electrolyte solutions.
Vsl = Liquid molar volume for solvent mixtures.
Vel = Liquid molar volume for electrolytes.
Apparent Component Approach
For molecular solvents, the liquid molar volume is calculated by:
(2)
Where:
xw = Mole fraction of water
Vw* = Molar volume of water from the steam table.
xnws = Sum of the mole fractions of all non-watersolvents.
Vnwsl = Liquid molar volume for the mixture of all non-
water solvents. It is calculated using theRackett equation.
For electrolytes:
(3)
(4)
(5)
(6)
Where:
206 2 Thermodynamic Property Models
xca = Apparent mole fraction of electrolyte ca
Vca = Liquid molar volume for electrolyte ca
The mole fractions xca are reconstituted arbitrarily from the true ionicconcentrations, even if you use the apparent component approach. Thistechnique is explained in Electrolyte Calculation in Physical Property Methods.
The result is that electrolytes are generated from all possible combinations ofions in solution. The following equation is consistently applied to determinethe amounts of each possible apparent electrolyte nca:
(7)
Where:
nca = Number of moles of apparent electrolyte ca
zc = Charge of c
zfactor = zc if c and a have the same number ofcharges; otherwise 1.
nc = Number of moles of cation c
na = Number of moles of anion a
For example: given an aqueous solution of Ca2+, Na+, SO42-, Cl- four
electrolytes are found: CaCl2, Na2SO4, CaSO4, and NaCl. The Clarkeparameters of all four electrolytes are used. You can rely on the default,which calculates the Clarke parameters from ionic parameters. Otherwise, youmust enter parameters for any electrolytes that may not exist in thecomponents list. If you do not want to use the default, the first step in usingthe Clarke model is to add any needed components for electrolytes not in thecomponents list.
True Component Approach
The true molar volume is obtained from the apparent molar volume:
(8)
Where:
Vml,t = Liquid volume per number of true species
Vml,a = Liquid volume per number of apparent species, Vm
l
of equation 1
na = Number of apparent species
nt = Number of true species
The apparent molar volume is calculated as explained in the precedingsubsection.
2 Thermodynamic Property Models 207
Temperature Dependence
The temperature dependence of the molar volume of the solution isapproximately equal to the temperature dependence of the molar volume ofthe solvent mixture:
(9)
Where Vml(298.15K) is calculated from equation 1.
ParameterName/Element
ApplicableComponents
Symbol Default Units
VLCLK/1 Cation-Anion † MOLE-VOLUME
VLCLK/2 Cation-Anion Aca 0.020 MOLE-VOLUME
†If VLCLK/1 is missing, it is calculated based on VLBROC and CHARGE asfollows:
(10)
If VLBROC/1 is missing, the default value of -0.0012 is used. See the Brelvi-O'Connell model for VLBROC and also Rackett/Campbell-Thodos MixtureLiquid Volume for additional parameters used in the Rackett equation.
Reference
C.C. Chen, private communication.
COSTALD Liquid VolumeThe equation for the COSTALD liquid volume model is:
Where:
VmR,0 and Vm
R, are functions or Tr for
For , there is a linear interpolation between the liquid density atTr = 0.95 and the vapor density at Tr = 1.05. This model can be used tocalculate saturated and compressed liquid molar volume. The compressedliquid molar volume is calculated using the Tait equation:
Where B and C are functions of T, , Tc, Pc and Psat is the saturated pressure
at T.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
208 2 Thermodynamic Property Models
Mixing Rules:
Where:
To improve results, the Aspen Physical Property System uses a specialcorrelation for water when this model is used. Changing the VSTCTD andOMGCTD parameters for water will not affect the results of the specialcorrelation.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
VSTCTD Vr*,CTD VC X 0.001 3.5 MOLE-VOLUME
OMGCTD rOMEGA X -0.5 2.0 —
References
R.W. Hankinson and G.H. Thomson, AIChE J., Vol. 25, (1979), p. 653.
G.H. Thomson, K.R. Brobst, and R.W. Hankinson, AIChE J., Vol. 28, (1982),p. 4, p. 671.
Debye-Hückel VolumeThe Debye-Hückel model calculates liquid molar volume for aqueouselectrolyte solutions.
The equation for the Debye-Hückel volume model is:
Where:
Vw* is the molar volume for water and is calculated from the ASME steamtable.
Vk is calculated from the Debye-Hückel limiting law for ionic species:
Where:
Vk = Partial molar ionic volume at infinite dilution
2 Thermodynamic Property Models 209
zk = Charge number of ion k
Av = Debye-Hückel constant for volume
b = 1.2
I =
the ionic strength, with
mk = Molarity of ion k
Av is computed as follows:
Where:
A = Debye-Hückel constant for the osmoticcoefficients (Pitzer, 1979)
w= Density of water (kg / m3)
w= Dielectric constant of water (Fm-1), a function
of pressure and temperature (Bradley andPitzer, 1979)
The above equation for Vk can also apply to non-water molecular speciessince the second term on the right is zero; it is assumed to be the infinitedilution partial volume for molecular species.
Vk
in general is calculated from the Brelvi-O'Connell correlation:
Vk
= V1 + TV2
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
VLBROC/1 V1 0 x -1.0 1.0 MOLE-VOLUME
VLBROC/2 V2 0 x -0.1 0.1 TEMPERATURE
References
D. J. Bradley, K. S. Pitzer, "Thermodynamics of Electrolytes," J. Phys. Chem.,83 (12), 1599 (1979).
H.C. Helgeson and D.H. Kirkham, "Theoretical prediction of thethermodynamic behavior of aqueous electrolytes at high pressure andtemperature. I. Thermodynamic/electrostatic properties of the solvent", Am.J. Sci., 274, 1089 (1974).
K.S. Pitzer, "Theory: Ion Interaction Approach," Activity Coefficients inElectrolyte Solutions, Pytkowicz, R. ed., Vol. I, (CRC Press Inc., Boca Raton,Florida, 1979).
210 2 Thermodynamic Property Models
Liquid Constant Molar Volume ModelThis model, VL0CONS, uses a constant value entered by the user as the purecomponent liquid molar volume. It is not a function of temperature orpressure. This is used with the solids handling property method for modelingnonconventional solids.Parameter Name Default MDS Units
VLCONS * x MOLE-VOLUME
* When no value is provided for VLCONS, the General Pure Component LiquidMolar Volume model is used to calculate the liquid molar volume.
General Pure Component Liquid MolarVolumeThe Aspen Physical Property System has several submodels for calculatingliquid molar volume. It uses parameter THRSWT/2 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/2 is This equation is used And this parameter is used
0 Rackett RKTZRA
100-116 DIPPR DNLDIP
301 PPDS DNLPDS
302 PPDS Campbell-Thodos RACKET
401 IK-CAPE VLPO
503 NIST ThermoMLPolynomial
DNLTMLPO
504 NIST TDE expansion DNLEXSAT
514 NIST TDE Rackett DNLRACK
515 NIST COSTALD DNLCOSTD
For liquid molar volume of mixtures, the Rackett mixture equation is alwaysused by default. This is not necessarily consistent with the pure componentmolar volume or density. If you need consistency, select route VLMX26 on theMethods | Selected Methods form. This route calculates mixture molarvolume from the mole-fraction average of pure component molar volumes.
Many of these equations calculate density first, and return calculate liquidmolar volume based on that density:
DIPPR
DIPPR equation 105 is the default DIPPR equation for most substances:
This equation is similar to the Rackett equation.
2 Thermodynamic Property Models 211
DIPPR equation 116 is the default equation for water.
= 1 - T / Tc
Other DIPPR equations, such as equation 100, may be used for somesubstances. Check the value of THRSWT/2 to determine the equation used.See Pure Component Temperature-Dependent Properties for details aboutDIPPR equations.
In either case, linear extrapolation of i*,l versus T occurs outside of
temperature bounds.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLDIP/1 C1i — x — — MOLE-DENSITY †
DNLDIP/2 C2i 0 x — — †
DNLDIP/3 C3i Tci † x — — TEMPERATURE †
DNLDIP/4 C4i 0 x — — †
DNLDIP/5 C5i 0 x — — †
DNLDIP/6 C6i 0 x — — TEMPERATURE
DNLDIP/7 C7i 1000 x — — TEMPERATURE
† For equation 116, the units are MOLE-DENSITY for parameters DNLDIP/1through DNLDIP/5 and the default for DNLDIP/3 is 0. For equation 105,DNLDIP/5 is not used, and absolute temperature units are assumed forDNLDIP/3.
PPDS
The PPDS equation is:
Linear extrapolation of i*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
VC Vci — — 0.001 3.5 MOLE-VOLUME
TC Tci — — 5.0 2000.0 TEMPERATURE
DNLPDS/1 C1i — — — — MASS-DENSITY
DNLPDS/2 C2i 0 — — — MASS-DENSITY
DNLPDS/3 C3i 0 — — — MASS-DENSITY
DNLPDS/4 C4i 0 — — — MASS-DENSITY
DNLPDS/5 C5i 0 x — — TEMPERATURE
DNLPDS/6 C6i 1000 x — — TEMPERATURE
212 2 Thermodynamic Property Models
PPDS Campbell-Thodos
The PPDS Campbell-Thodos model uses a form similar to the mixtureCampbell-Thodos model:
Where:
Tr = T / Tci
Note: This equation uses the same parameter RACKET as the mixtureCampbell-Thodos model, but it uses a different, incompatible definition ofRACKET/3. Our database does not include values for this parameter, but beaware that if you use this parameter in this equation, you cannot use theCampbell-Thodos mixture equation.
Tmin and Tmax define the temperature range where the equation is applicable.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
RACKET/1 C1 R*Tci/Pci — — — MOLE-VOLUME
RACKET/2 C2 RKTZRA x 0.1 1.0 —
RACKET/3 C3 0 x 0 0.11 —
RACKET/4 Tmin 0 x — — TEMPERATURE
RACKET/5 Tmax 1000 x — — TEMPERATURE
TC Tci — — 5.0 2000.0 TEMPERATURE
IK-CAPE
The IK-CAPE equation is:
Linear extrapolation of Vi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
VLPO/1 C1i — X — — MOLE-VOLUME
VLPO/2, ..., 10 C2i, ..., C10i 0 X — — MOLE-VOLUMETEMPERATURE
VLPO/11 C11i 0 X — — TEMPERATURE
VLPO/12 C12i 1000 X — — TEMPERATURE
NIST ThermoML Polynomial
This equation can be used when parameter DNLTMLPO is available.
2 Thermodynamic Property Models 213
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DNLTMLPO/1 C1i — X — — MOLE-DENSITY
DNLTMLPO/2, 3,4
C2i, C3i, C4i 0 X — — MOLE-DENSITYTEMPERATURE
DNLTMLPO/5 nTerms 4 X — — —
DNLTMLPO/6 0 X — — TEMPERATURE
DNLTMLPO/7 1000 X — — TEMPERATURE
Rackett
The Rackett equation is:
Where:
Tr = T / Tci
Note: Reduced temperature Tr is always calculated using absolutetemperature units.Note: Above Tr=0.99 an extrapolation method is used to smooth thetransition to constant molar volume equal to the critical volume.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
RKTZRA Zi*,RA ZC x 0.1 1.0 —
NIST TDE Rackett Parameters
This equation can be used when the parameter DNLRACK is available.
Linear extrapolation of Vi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLRACK/1 Zc — x — — —
DNLRACK/2 n 2/7 x — — —
DNLRACK/3 Tci — x — — TEMPERATURE
214 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLRACK/4 pci 0 x — — PRESSURE
DNLRACK/5 Tlower 0 x — — TEMPERATURE
DNLRACK/6 Tupper 1000 x — — TEMPERATURE
NIST COSTALD Parameters
This equation can be used when the parameter DNLCOSTD is available.
Linear extrapolation of Vi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLCOSTD/1 Voi — x — — VOLUME
DNLCOSTD/2 0 x — — —
DNLCOSTD/3 Tci — x — — TEMPERATURE
DNLCOSTD/4 Tlower 0 x — — TEMPERATURE
DNLCOSTD/5 Tupper 1000 x — — TEMPERATURE
NIST TDE Expansion
This equation can be used when the parameter DNLEXSAT is available.
Linear extrapolation of Vi*,l versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLEXSAT/1 ci— x — — MOLE-
DENSITY
DNLEXSAT/2 C1i — x — — MOLE-DENSITY
DNLEXSAT/3,..., DNLEXSAT/7
C2i, ..., C6i 0 x — — MOLE-DENSITY
DNLEXSAT/8 Tci — x — — TEMPERATURE
2 Thermodynamic Property Models 215
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DNLEXSAT/9 nTerms 6 x — — —
DNLEXSAT/10 Tlower 0 x — — TEMPERATURE
DNLEXSAT/11 Tupper 1000 x — — TEMPERATURE
References
H.G. Rackett, J.Chem. Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.
Rackett/Campbell-Thodos Mixture LiquidVolumeThe Rackett equation calculates liquid molar volume for all activity coefficientbased and petroleum tuned equation of state based property methods. In thelast category of property methods, the equation is used in conjunction withthe API model. The API model is used for pseudocomponents, while theRackett model is used for real components. (See API Liquid Volume .)Campbell-Thodos is a variation on the Rackett model which allows thecompressibility term Zi
*,RA to vary with temperature.
Rackett
The equation for the Rackett model is:
Where:
Tc =
=
ZmRA =
Vcm =
Tr = T / Tc
Note: Reduced temperature Tr is always calculated using absolutetemperature units.Note: Above Tr=0.99 an extrapolation method is used to smooth thetransition to constant molar volume equal to the critical volume.
216 2 Thermodynamic Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
VCRKT Vci VC x 0.001 3.5 MOLE-VOLUME
RKTZRA Zi*,RA ZC x 0.1 1.0 —
RKTKIJ kij x -5.0 5.0 —
Campbell-Thodos
The Campbell-Thodos model uses the same equation as the Rackett model,above, except that Zm
RA is allowed to vary with temperature:
ZmRA =
Campbell-Thodos uses a separate set of parameters, RACKET. Tmin and Tmax
define the temperature range where the equation is applicable.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
RACKET/1 R*Tci/Pci R*Tci/Pci — — — MOLE-VOLUME
RACKET/2 Zi*,RA RKTZRA x 0.1 1.0 —
RACKET/3 di 0 x 0 0.11 —
RACKET/4 Tmin 0 x — — TEMPERATURE
RACKET/5 Tmax 1000 x — — TEMPERATURE
The Campbell-Thodos model is used when RACKET/3 is set to a value lessthan 0.11. Do not change this parameter unless you intend to use this model.
References
H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.
Modified Rackett Liquid Molar VolumeThe Modified Rackett equation improves the accuracy of liquid mixture molarvolume calculation by introducing additional parameters to compute the purecomponent parameter RKTZRA and the binary parameter kij.
The equation for the Modified Rackett model is:
2 Thermodynamic Property Models 217
Where:
Tc =
kij =
=
ZmRA =
Zi*,RA =
Vcm =
Tr = T / Tc
Note: Reduced temperature Tr is always calculated using absolutetemperature units.Note: Above Tr=0.99 an extrapolation method is used to smooth thetransition to constant molar volume equal to the critical volume.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MRKZRA/1 ai RKTZRA x 0.1 0.5 —
MRKZRA/2 bi 0 x — — —
MRKZRA/3 ci 0 x — — —
MRKKIJ/1 Aij x — — —
MRKKIJ/2 Bij 0 x — — —
MRKKIJ/3 Cij 0 x — — —
References
H.G. Rackett, J.Chem, Eng. Data., Vol. 15, (1970), p. 514.
C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, Vol. 17, (1972), p. 236.
Rackett Extrapolation MethodThe Rackett equation has a formula involving an exponent of 1+(1-Tr )2/7
which is invalid above the critical temperature. As a result, a specialextrapolation method is required for this equation. This method involves the
218 2 Thermodynamic Property Models
calculation of an intermediate temperature T00 near the critical temperature.When the temperature exceeds T00, the volume is constant at the criticalvolume. When the temperature is between 0.99Tc and T00, a circle equation isused to smoothly interpolate the volume between the value and slope at0.99Tc and the constant value at T00.
Details
First the volume V0 at 0.99Tc and the critical volume Vc are calculated:
Then the volume difference is calculated, as well as the temperaturedifference required for the circle equation:
From this, the required intermediate temperature T00 can be calculated:
Then the volume V00 at the circle's center can be calculated:
2 Thermodynamic Property Models 219
Finally, the equation of the circle is used to determine any point (T,V) for0.99Tc < T < T00:
General Pure Component Solid MolarVolumeThe Aspen Physical Property System has several submodels for calculatingsolid molar volume. It uses parameter THRSWT/1 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/1 is This equation is used And this parameter is
used
0 Aspen VSPOLY
100 DIPPR DNSDIP
401 IK-CAPE VSPO
503 NIST ThermoMLpolynomial
DNSTMLPO
Aspen Polynomial
The equation for the Aspen solids volume polynomial is:
Linear extrapolation of Vi*,s versus T occurs outside of temperature bounds.
ParameterName
ApplicableComponents
Symbol MDS Default Units
VSPOLY/1 Salts, CI solids C1i x — MOLE-VOLUMETEMPERATURE
VSPOLY/2, ..., 5 Salts, CI solids C2i, ..., C5i x 0 MOLE-VOLUMETEMPERATURE
VSPOLY/6 Salts, CI solids C6i x 0 MOLE-VOLUMETEMPERATURE
VSPOLY/7 Salts, CI solids C7i x 1000 MOLE-VOLUMETEMPERATURE
IK-CAPE Equation
The IK-CAPE equation is:
220 2 Thermodynamic Property Models
Linear extrapolation of Vi*,s versus T occurs outside of temperature bounds.
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
VSPO/1 C1i — X — — MOLE-VOLUME
VSPO/2, ..., 10 C2i, ..., C10i 0 X — — MOLE-VOLUMETEMPERATURE
VSPO/11 C11i 0 X — — TEMPERATURE
VSPO/12 C12i 1000 X — — TEMPERATURE
DIPPR
The DIPPR equation is:
Linear extrapolation of i*,s versus T occurs outside of temperature bounds.
Vi*,s = 1 / i
*,s
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
The model returns solid molar volume for pure components.ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DNSDIP/1 C1i — x — — MOLE-DENSITY
DNSDIP/2, ..., 5 C2i, ..., C5i 0 x — — MOLE-DENSITY,TEMPERATURE
DNSDIP/6 C6i 0 x — — TEMPERATURE
DNSDIP/7 C7i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
Linear extrapolation of i*,s versus T occurs outside of temperature bounds.
Vi*,s = 1 / i
*,s
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
DNSTMLPO/1 C1i — x — — MOLE-DENSITY
DNSTMLPO/2,...,8 C2i, ..., C8i 0 x — — MOLE-DENSITY,TEMPERATURE
DNSTMLPO/9 nTerms 8 x — — —
DNSTMLPO/10 Tlower 0 x — — TEMPERATURE
DNSTMLPO/11 Tupper 1000 x — — TEMPERATURE
2 Thermodynamic Property Models 221
Liquid Volume Quadratic Mixing RuleWith i and j being components, the liquid volume quadratic mixing rule is:
Option CodesOption Code Value Descriptions
1 0 Use normal pure component liquid volume model for allcomponents (default)
1 Use steam tables for water
2 0 Use mole basis composition (default)
1 Use mass basis composition
ParameterParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
VLQKIJ Kij 0 x - - —
This model is not part of any property method. To use it, you will need todefine a property method on the Methods | Selected Methods form.Specify the route VLMXQUAD for VLMX on the Routes sheet of this form, orthe model VL2QUAD for VLMX on the Models sheet.
Heat Capacity ModelsThe Aspen Physical Property System has five built-in heat capacity models.This section describes the heat capacity models available.Model Type
Aqueous Infinite Dilution Heat CapacityPolynomial
Electrolyte liquid
Criss-Cobble Aqueous Infinite DilutionIonic Heat Capacity
Electrolyte liquid
General Pure Component Liquid HeatCapacity
Liquid
General Pure Component Ideal Gas HeatCapacity
Ideal gas
General Pure Component Solid HeatCapacity
Solid
Aqueous Infinite Dilution Heat CapacityThe aqueous phase infinite dilution enthalpies, entropies, and Gibbs energiesare calculated from the heat capacity polynomial. The values are used in thecalculation of aqueous and mixed solvent properties of electrolyte solutions:
222 2 Thermodynamic Property Models
versus T is linearly extrapolated using the slope at C7i for T < C7i
versus T is linearly extrapolated using the slope at C8i for T < C8i
ParameterName/Element
ApplicableComponents
Symbol Default Units
CPAQ0/1 Ions, molecular solutes C1i — TEMPERATURE andHEAT CAPACITY
CPAQ0/2,…,6 Ions, molecular solutes C2i, ..., C6i 0 TEMPERATURE andHEAT CAPACITY
CPAQ0/7 Ions, molecular solutes C7i 0 TEMPERATURE
CPAQ0/8 Ions, molecular solutes C8i 1000 TEMPERATURE
If any of C4i through C6i is non-zero, absolute temperature units areassumed for C1i through C6i . Otherwise, user input units for temperature areused. The temperature limits are always interpreted in user input units.
Criss-Cobble Aqueous Infinite Dilution IonicHeat CapacityThe Criss-Cobble correlation for aqueous infinite dilution ionic heat capacity isused if no parameters are available for the aqueous infinite dilution heatcapacity polynomial. From the calculated heat capacity, the thermodynamicproperties entropy, enthalpy and Gibbs energy at infinte dilution in water arederived:
ParameterName
ApplicableComponents
Symbol Default Units
IONTYP Ions Ion Type 0 —
SO25C Anions MOLE-ENTROPY
Cations MOLE-ENTROPY
General Pure Component Liquid HeatCapacityThe Aspen Physical Property System has several submodels for calculatingliquid heat capacity. It uses parameter THRSWT/6 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/6 is This equation is used And this parameter is used
100 DIPPR CPLDIP
2 Thermodynamic Property Models 223
If THRSWT/6 is This equation is used And this parameter is used
200-211 Barin CPLXP1, CPLXP2
301 PPDS CPLPDS
401 IK-CAPE heat capacitypolynomial
CPLPO
403 IK-CAPE liquid heatcapacity
CPLIKC
503 NIST ThermoMLpolynomial
CPLTMLPO
506 NIST TDE equation CPLTDECS
This liquid heat capacity model is used to calculate pure component liquidheat capacity and pure component liquid enthalpy. To use this model, twoconditions must exist:
One of the parameters for calculating heat capacity (see table) isavailable.
The component is not supercritical (HENRY-COMP).
The model uses a specific method (see Methods in Property CalculationMethods and Routes):
Where
= Reference enthalpy calculated at Tref
= Ideal gas enthalpy
= Vapor enthalpy departure
= Enthalpy of vaporization
Tref is the reference temperature; it defaults to 298.15 K. You can enter adifferent value for the reference temperature. This is useful when you want touse this model for very light components or for components that are solids at298.15K.
Activate this model by specifying the route DHL09 for the property DHL onthe Methods | Selected Methods | Routes sheet. For equation of stateproperty method, you must also modify the route for the property DHLMX touse a route with method 2 or 3, instead of method 1. For example, you canuse the route DHLMX00 or DHLMX30. You must ascertain that the route forDHLMX that you select contains the appropriate vapor phase model and heatof mixing calculations. Click the View button on the form to see details of theroute.
Optionally, you can specify that this model is used for only certaincomponents. The properties for the remaining components are thencalculated by the standard model. Use the parameter COMPHL to specify the
224 2 Thermodynamic Property Models
components for which this model is used. By default, all components with theCPLDIP or CPLIKC parameters use this model.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacityfor details about this submodel.
DIPPR Liquid Heat Capacity
The DIPPR equation is used to calculate liquid heat capacity when parameterTHRSWT/6 is 100.
The DIPPR equation is:
Linear extrapolation occurs for Cp*,l versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPLDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPLDIP/2, ..., 5 C2i, ..., C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPLDIP/6 C6i 0 x — — TEMPERATURE
CPLDIP/7 C7i 1000 x — — TEMPERATURE
TREFHL Tref 298.15 — — — TEMPERATURE
COMPHL — — — — — —
To specify that the model is used for a component, enter a value of 1.0 forCOMPHL.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
PPDS Liquid Heat Capacity
The PPDS equation is used to calculate liquid heat capacity when parameterTHRSWT/6 is 301.
The PPDS equation is:
Where R is the gas constant.
Linear extrapolation occurs for Cp*,l versus T outside of bounds.
2 Thermodynamic Property Models 225
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPLPDS/1 C1i — — — — —
CPLPDS/2 C2i 0 — — — —
CPLPDS/3 C3i 0 — — — —
CPLPDS/4 C4i 0 — — — —
CPLPDS/5 C5i 0 — — — —
CPLPDS/6 C6i 0 — — — —
CPLPDS/7 C7i 0 x — — TEMPERATURE
CPLPDS/8 C8i 0.99 TC x — — TEMPERATURE
IK-CAPE Liquid Heat Capacity
Two IK-CAPE equations can be used to calculate liquid heat capacity. Linearextrapolation occurs for Cp
*,l versus T outside of bounds for either equation.
When THRSWT/6 is 403, the IK-CAPE liquid heat capacity equation is used.The equation is:
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPLIKC/1 C1i —T
x — — MOLE-HEAT-CAPACITY
CPLIKC/2,...,4 C2i, ..., C4i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPLIKC/5 C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE †
CPLIKC/6 C6i 0 x — — TEMPERATURE
CPLIKC/7 C7i 1000 x — — TEMPERATURE
† If C5i is non-zero, absolute temperature units are assumed for C2i throughC5i. Otherwise, user input units for temperature are used. The temperaturelimits are always interpreted in user input units.
When THRSWT/6 is 401, the IK-CAPE heat capacity polynomial is used.Theequation is:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPLPO/1 C1i — X — — MOLE-CAPACITY
CPLPO/2,…,10 C2i, ..., C10i 0 X — — MOLE-CAPACITYTEMPERATURE
CPLPO/11 C11i 0 X — — TEMPERATURE
226 2 Thermodynamic Property Models
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPLPO/12 C12i 1000 X — — TEMPERATURE
See Pure Component Temperature-Dependent Properties for details on theTHRSWT parameters.
NIST Liquid Heat Capacity
Two NIST equations can be used to calculate liquid heat capacity. Linearextrapolation occurs for Cp
*,l versus T outside of bounds for either equation.
When THRSWT/6 is 503, the ThermoML polynomial is used to calculate liquidheat capacity:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPLTMLPO/1 C1i — X — — J/K^2/mol
CPLTMLPO/2,…,5 C2i, ..., C5i 0 X — — J/K^2/mol
CPLTMLPO/6 nTerms 5 X — — —
CPLTMLPO/7 Tlower 0 X — — TEMPERATURE
CPLTMLPO/8 Tupper 1000 X — — TEMPERATURE
When THRSWT/6 is 506, the TDE equation is used to calculate liquid heatcapacity:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPLTDECS/1 C1i — X — — MOLE-HEAT-CAPACITY
CPLTDECS/2,…,4 C2i, ..., C4i 0 X — — MOLE-HEAT-CAPACITY
CPLTDECS/5 B 0 X — — MOLE-HEAT-CAPACITY
CPLTDECS/6 Tci — X — — TEMPERATURE
CPLTDECS/7 nTerms 4 X — — —
CPLTDECS/8 Tlower 0 X — — TEMPERATURE
CPLTDECS/9 Tupper 1000 X — — TEMPERATURE
See Pure Component Temperature-Dependent Properties for details on theTHRSWT parameters.
2 Thermodynamic Property Models 227
General Pure Component Ideal Gas HeatCapacityThe Aspen Physical Property System has several submodels for calculatingideal gas heat capacity. It uses parameter THRSWT/7 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/7 is This equation is used And this parameter is
used
0 Ideal gas heat capacitypolynomial
CPIG
107, 127 DIPPR 107 or 127 CPIGDP
200-211 Barin CPIXP1, CPIXP2, CPIXP3
301 PPDS CPIGDS
400 PML (Modified API) CPIAPI
401 IK-CAPE heat capacitypolynomial
CPIGPO
503 NIST ThermoMLpolynomial
CPITMLPO
513 NIST Aly-Lee CPIALEE
These equations are also used to calculate ideal gas enthalpies, entropies,and Gibbs energies.
Aspen Ideal Gas Heat Capacity Polynomial
The ideal gas heat capacity polynomial is available for components stored inASPENPCD, AQUEOUS, and SOLIDS databanks. This model is also used inPCES.
Cp*,ig is linearly extrapolated using slope at
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPIG/1 C1i — — — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPIG/2, ..., 6 C2i, ..., C6i 0 — — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPIG/7 C7i 0 — — — TEMPERATURE
CPIG/8 C8i 1000 — — — TEMPERATURE
CPIG/9, 10,11
C9i, C10i, C11i — — — — MOLE-HEAT-CAPACITY,TEMPERATURE †
† If C10i or C11i is non-zero, then absolute temperature units are assumed forC9i through C11i. Otherwise, user input temperature units are used for allparameters. User input temperature units are always used for C1i through C8i.
228 2 Thermodynamic Property Models
NIST ThermoML Polynomial
This equation can be used when parameter CPITMLPO is available.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPITMLPO /1 C1i — x — — J/K^2/mol
CPITMLPO /2,..., 6
C2i, ..., C6i 0 x — — J/K^2/mol
CPITMLPO/7 nTerms 6 x — — —
CPITMLPO /8 Tlower 0 x — — TEMPERATURE
CPITMLPO /9 Tupper 1000 x — — TEMPERATURE
DIPPR Equation 107
The DIPPR ideal gas heat capacity equation 107 by Aly and Lee 1981 is:
No extrapolation is used with this equation.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPIGDP/1 C1i — x — — MOLE-HEAT-CAPACITY
CPIGDP/2 C2i 0 x — — MOLE-HEAT-CAPACITY
CPIGDP/3 C3i 0 x — — TEMPERATURE ††
CPIGDP/4 C4i 0 x — — MOLE-HEAT-CAPACITY
CPIGDP/5 C5i 0 x — — TEMPERATURE ††
CPIGDP/6 C6i 0 x — — TEMPERATURE
CPIGDP/7 C7i 1000 x — — TEMPERATURE
†† Absolute temperature units are assumed for C3i and C5i. The temperaturelimits are always interpreted in user input units.
DIPPR Equation 127
The DIPPR ideal gas heat capacity equation 127 is:
2 Thermodynamic Property Models 229
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPIGDP/1 C1i — x — — MOLE-HEAT-CAPACITY
CPIGDP/2 C2i 0 x — — MOLE-HEAT-CAPACITY
CPIGDP/3 C3i 0 x — — TEMPERATURE ††
CPIGDP/4 C4i 0 x — — MOLE-HEAT-CAPACITY
CPIGDP/5 C5i 0 x — — TEMPERATURE ††
CPIGDP/6 C6i 0 x — — MOLE-HEAT-CAPACITY
CPIGDP/7 C7i 0 x — — TEMPERATURE ††
†† Absolute temperature units are assumed for C3i, C5i and C7i.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacityfor details about this submodel.
NIST Aly-Lee
This equation is the same as the DIPPR Aly and Lee equation 107 above, butit uses a different parameter set. Note that elements 6 and 7 of the CPIALEEparameter are not used in the equation.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPIALEE/1 C1i — x — — MOLE-HEAT-CAPACITY
CPIALEE/2 C2i 0 x — — MOLE-HEAT-CAPACITY
CPIALEE/3 C3i 0 x — — TEMPERATURE ††
CPIALEE/4 C4i 0 x — — MOLE-HEAT-CAPACITY
CPIALEE/5 C5i 0 x — — TEMPERATURE ††
CPIALEE/8 C6i 0 x — — TEMPERATURE
CPIALEE/9 C7i 1000 x — — TEMPERATURE
†† Absolute temperature units are assumed for C3i and C5i. The temperaturelimits are always interpreted in user input units.
PPDS
The PPDS equation is:
230 2 Thermodynamic Property Models
where R is the gas constant.
Linear extrapolation of Cp*,ig versus T is performed outside temperature
bounds.ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPIGDS/1 C1i — — — — TEMPERATURE
CPIGDS/2, …, 8 C2i, ..., C8i 0 — — — —
CPIGDS/9 C9i 0 — — — TEMPERATURE
CPIGDS/10 C10i 1000 — — — TEMPERATURE
PML (Modified API)
The equation is:
Linear extrapolation of Cp*,ig versus T is performed outside temperature
bounds.ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPIAPI/1 C1i — X — — MOLE-CAPACITY
CPIAPI/2,…,5 C2i, ..., C5i 0 X — — MOLE-CAPACITYTEMPERATURE††
CPIAPI/6 C6i 0 X — — TEMPERATURE
CPIAPI/7 C7i 1000 X — — TEMPERATURE
†† If C4i or C5i is non-zero, then absolute temperature units are assumed forC2i through C5i. Otherwise, user input temperature units are used for allparameters.
IK-CAPE Heat Capacity Polynomial
The equation is:
Linear extrapolation of Cp*,ig versus T is performed outside temperature
bounds.
2 Thermodynamic Property Models 231
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPIGPO/1 C1i — X — — MOLE-CAPACITY
CPIGPO/2,…,10 C2i, ..., C10i 0 X — — MOLE-CAPACITYTEMPERATURE
CPIGPO/11 C11i 0 X — — TEMPERATURE
CPIGPO/12 C12i 1000 X — — TEMPERATURE
References
Data for the Ideal Gas Heat Capacity Polynomial: Reid, Prausnitz and Poling,The Properties of Gases and Liquids, 4th ed., (New York: McGraw-Hill, 1987).
The Aspen Physical Property System combustion data bank, JANAFThermochemical Data, Compiled and calculated by the Thermal ResearchLaboratory of Dow Chemical Company.
F. A. Aly and L. L. Lee, "Self-Consistent Equations for Calculating the IdealGas Heat Capacity, Enthalpy, and Entropy, Fluid Phase Eq., Vol. 6, (1981), p.169.
General Pure Component Solid HeatCapacityThe Aspen Physical Property System has several submodels for calculatingsolid heat capacity. It uses parameter THRSWT/5 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If THRSWT/5 is This equation is used And this parameter is
used
0 Aspen solid heat capacitypolynomial
CPSPO1
100 or 102 DIPPR CPSDIP
200-211 Barin CPSXP1, CPSXP2, …,CPSXP7
401 IK-CAPE heat capacitypolynomial
CPSPO
503 NIST ThermoMLpolynomial
CPSTMLPO
The enthalpy, entropy, and Gibbs energy of solids are also calculated fromthese equations:
Aspen Solid Heat Capacity Polynomial
The Aspen equation is:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
232 2 Thermodynamic Property Models
ParameterName
ApplicableComponents
Symbol MDS Default Units
CPSPO1/1 Solids, Salts C1i x — †
CPSPO1/2, ..., 6 Solids, Salts C2i, ..., C6i x 0 †
CPSPO1/7 Solids, Salts C7i x 0 †
CPSPO1/8 Solids, Salts C8i x 1000 †
† The units are TEMPERATURE and HEAT-CAPACITY for all elements. If any ofC4i through C6i are non-zero, absolute temperature units are assumed forelements C1i through C6i. Otherwise, user input temperature units areassumed for all elements. The temperature limits are always interpreted inuser input units.
Barin
See Barin Equations for Gibbs Energy, Enthalpy, Entropy, and Heat Capacityfor details about this submodel.
DIPPR
There are two DIPPR equations that may generally be used.
The more common one, DIPPR equation 100, is:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPSDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPSDIP/2,...,5 C2i, ..., C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPSDIP/6 C6i 0 x — — TEMPERATURE
CPSDIP/7 C7i 1000 x — — TEMPERATURE
DIPPR equation 102 is:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPSDIP/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPSDIP/2 C2i — x — — —
CPSDIP/3,4 C3i, C4i 0 x — — TEMPERATURE
CPSDIP/6 C6i 0 x — — TEMPERATURE
CPSDIP/7 C7i 1000 x — — TEMPERATURE
2 Thermodynamic Property Models 233
If C3i or C4i are non-zero or C2i is negative, absolute temperature units areassumed for elements C1i through C4i. Otherwise, user input temperatureunits are assumed for all elements. The temperature limits are alwaysinterpreted in user input units.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
NIST ThermoML Polynomial
The equation is:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPSTMLPO/1 C1i — x — — J/K^2/mol
CPSTMLPO/2,...,5C2i, ..., C5i 0 x — — J/K^2/mol
CPSTMLPO/6 nTerms 5 x — — —
CPSTMLPO/7 Tlower 0 x — — TEMPERATURE
CPSTMLPO/8 Tupper 1000 x — — TEMPERATURE
IK-CAPE Heat Capacity Polynomial
The equation is:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
CPSPO/1 C1i — X — — MOLE-CAPACITY
CPSPO/2,…,10 C10i 0 X — — MOLE-CAPACITYTEMPERATURE
CPSPO/11 C11i 0 X — — TEMPERATURE
CPSPO/12 C12i 1000 X — — TEMPERATURE
Solubility CorrelationsThe Aspen Physical Property System has three built-in solubility correlationmodels. This section describes the solubility correlation models available.Model Type
Henry's constant Gas solubility in liquid
Water solubility Water solubility in organic liquid
234 2 Thermodynamic Property Models
Model Type
Hydrocarbon solubility Hydrocarbon solubility in water-richliquid
Henry's ConstantThe Henry's constant model is used when Henry's Law is applied to calculateK-values for dissolved gas components in a mixture. Henry's Law is availablein all activity coefficient property methods, such as the WILSON propertymethod. The model calculates Henry's constant for a dissolved gas component(i) in one or more solvents (A or B):
Where:
wA =
ln HiA(T, pA*,l) =
Linear extrapolation occurs for ln HiA versus T outside of bounds.
HiA(T, P) =
The parameter is obtained from the Brelvi-O'Connell model. pA*,l is
obtained from the Antoine model. is obtained from the appropriate activitycoefficient model.
The Henry's constants aiA, biA, ciA, diA, and eiA are specific to a solute-solventpair. They can be obtained from regression of gas solubility data. The AspenPhysical Property System has a large number of built-in Henry's constants formany solutes in solvents. These parameters were obtained using data fromthe Dortmund Databank. In addition, a small number of Henry's constantsfrom the literature are available in the BINARY databank. See PhysicalProperty Data, Chapter 1, for details.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
VC VcA — — 0.001 3.5 MOLE-VOLUME
HENRY/1 aiA †† x — — PRESSURE,TEMPERATURE †
HENRY/2 biA 0 x — — TEMPERATURE †
HENRY/3 ciA 0 x — — TEMPERATURE †
HENRY/4 diA 0 x — — TEMPERATURE †
HENRY/5 TL 0 x — — TEMPERATURE
HENRY/6 TH 2000 x — — TEMPERATURE
HENRY/7 eiA 0 x — — TEMPERATURE †
2 Thermodynamic Property Models 235
† If any of biA, ciA, and eiA are non-zero, absolute temperature units areassumed for all coefficients. If biA, ciA, and eiA are all zero, the others areinterpreted in input units. The temperature limits are always interpreted ininput units.
†† If aiA is missing, is set to zero and the weighting factor wA isrenormalized.
Reference for BINARY Databank
E. Wilhelm, R. Battino, and R.J. Wilcock, "Low-Pressure Solubility of Gases inLiquid Water," Chemical Reviews, 1977, Vol. 77, No. 2, pp 219 - 262.
Water SolubilityThis model calculates solubility of water in a hydrocarbon-rich liquid phase.The model is used automatically when you model a hydrocarbon-watersystem with the free-water option. See Free-Water Immiscibility Simplificationin Free-Water and Three-Phase Calculations for details.
The expression for the liquid mole fraction of water in the ith hydrocarbonspecies is:
No extrapolation is used with this equation.
The parameters for about 60 components are stored in the Aspen PhysicalProperty System pure component databank.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
WATSOL/1 C1i fcn(Tbi, SGi, Mi) — -10.0 33.0 —
WATSOL/2 C2i fcn(Tbi, SGi, Mi) — -10000.0 3000.0 TEMPERATURE †
WATSOL/3 C3i 0 — -0.05 0.05 TEMPERATURE †
WATSOL/4 C4i 0 — 0.0 500 TEMPERATURE †
WATSOL/5 C5i 1000 — 4.0 1000 TEMPERATURE †
† Absolute temperature units are assumed for elements 2 through 5.
Hydrocarbon SolubilityThis model calculates solubility of hydrocarbon in a water-rich liquid phase.The model is used automatically when you model a hydrocarbon-watersystem with the dirty-water option. See Free-Water ImmiscibilitySimplification in Free-Water and Rigorous Three-Phase Calculations fordetails.
The expression for the liquid mole fraction of the ith hydrocarbon species inwater is:
236 2 Thermodynamic Property Models
No extrapolation is used with this equation.
The parameters for about 40 components are stored in the Aspen PhysicalProperty System pure component databank.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
HCSOL/1 C1i fcn(carbonnumber) †
— -1000.0 1000.0 —
HCSOL/2 C2i 0 — -100000.0 100000.0 TEMPERATURE ††
HCSOL/3 C3i 0 — -100.0 100.0 TEMPERATURE ††
HCSOL/4 C4i 0 — 0.0 500 TEMPERATURE
HCSOL/5 C5i 1000 — 4.0 1000 TEMPERATURE
† For Hydrocarbons and pseudocomponents, the default values are estimatedby the method given by API Procedure 9A2.17 at 25 C.
†† Absolute temperature units are assumed for elements 2 and 3. Thetemperature limits are always interpreted in user input units.
Reference
C. Tsonopoulos, Fluid Phase Equilibria, 186 (2001), 185-206.
Other Thermodynamic PropertyModelsThe Aspen Physical Property System has some built-in additionalthermodynamic property models that do not fit in any other category. Thissection describes these models:
Cavett Liquid Enthalpy Departure
Barin Equations for Gibbs Energy, Enthalpy, Entropy and Heat Capacity
Electrolyte NRTL Enthalpy
Electrolyte NRTL Gibbs Energy
Liquid Enthalpy from Liquid Heat Capacity Correlation
Enthalpies Based on Different Reference States
Helgeson Equations of State
Quadratic Mixing Rule
Ideal Mixing Rule
CavettThe general form for the Cavett model is:
2 Thermodynamic Property Models 237
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
DHLCVT ZC X 0.1 0.5 —
Barin Equations for Gibbs Energy, Enthalpy,Entropy, and Heat CapacityThe following equations are used when parameters from the Aspen PhysicalProperty System inorganic databank are retrieved.
Gibbs energy:
(1)
Enthalpy:
(2)
Entropy:
(3)
Heat capacity:
(4)
refers to an arbitrary phase which can be solid, liquid, or ideal gas. For each
phase, multiple sets of parameters from 1 to n are present to cover multipletemperature ranges. The value of the parameter n depends on the phase.(See tables that follow.) When the temperature is outside all thesetemperature ranges, linear extrapolation of properties versus T is performedusing the slope at the end of the nearest temperature bound.
The four properties Cp, H, S, and G are interrelated as a result of thethermodynamic relationships:
There are analytical relationships between the expressions describing theproperties Cp, H, S, and G (equations 1 to 4). The parameters an,i to hn,i canoccur in more than one equation.
238 2 Thermodynamic Property Models
The Aspen Physical Property System has other models which can be used tocalculate temperature-dependent properties which the BARIN equations cancalculate. The Aspen Physical Property System uses the parameters inTHRSWT to determine which model is used. See Pure ComponentTemperature-Dependent Properties for details.If this parameter is 200 to 211 Then the BARIN equations are
used to calculate
THRSWT/3 Liquid vapor pressure
THRSWT/5 Solid heat capacity
THRSWT/6 Liquid heat capacity
THRSWT/7 Ideal gas heat capacity
The liquid vapor pressure is computed from Gibbs energy as follows:
ln p = (GL - GV)/RT + ln pref
where p is the vapor pressure, and pref is the reference pressure 101325 Pa.Thus, parameters for both liquid and vapor are necessary to calculate vaporpressure.
Solid Phase
The parameters in range n are valid for temperature: Tn,ls < T < Tn,h
s
When you specify this parameter, be sure to specify at least elements 1through 3.Parameter Name †/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPSXPn/1 Tn,ls — x — — TEMPERATURE
CPSXPn/2 Tn,hs — x — — TEMPERATURE
CPSXPn/3 an,is — x — — ††
CPSXPn/4 bn,is 0 x — — ††
CPSXPn/5 cn,is 0 x — — ††
CPSXPn/6 dn,is 0 x — — ††
CPSXPn/7 en,is 0 x — — ††
CPSXPn/8 fn,is 0 x — — ††
CPSXPn/9 gn,is 0 x — — ††
CPSXPn/10 hn,is 0 x — — ††
† n is 1 through 7. CPSXP1 vector stores solid parameters for the firsttemperature range. CPSXP2 vector stores solid parameters for the secondtemperature range, and so on.
†† TEMPERATURE, ENTHALPY, ENTROPY
Liquid Phase
The parameters in range n are valid for temperature: Tn,ll < T < Tn,h
l
When you specify this parameter, be sure to specify at least elements 1through 3.Parameter Name †/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPLXPn/1 Tn,ll — x — — TEMPERATURE
2 Thermodynamic Property Models 239
Parameter Name †/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPLXPn/2 Tn,hl — x — — TEMPERATURE
CPLXPn/3 an,il — x — — ††
CPLXPn/4 bn,il 0 x — — ††
CPLXPn/5 cn,il 0 x — — ††
CPLXPn/6 dn,il 0 x — — ††
CPLXPn/7 en,il 0 x — — ††
CPLXPn/8 fn,il 0 x — — ††
CPLXPn/9 gn,il 0 x — — ††
CPLXPn/10 hn,il 0 x — — ††
† n is 1 through 2. CPLXP1 stores liquid parameters for the first temperaturerange. CPLXP2 stores liquid parameters for the second temperature range.
†† TEMPERATURE, ENTHALPY, ENTROPY
Ideal Gas Phase
The parameters in range n are valid for temperature: Tn,lig < T < Tn,h
ig
When you specify this parameter, be sure to specify at least elements 1through 3.Parameter Name †/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPIXPn/1 Tn,lig — x — — TEMPERATURE
CPIXPn/2 Tn,hig — x — — TEMPERATURE
CPIXPn/3 an,iig — x — — ††
CPIXPn/4 bn,iig 0 x — — ††
CPIXPn/5 cn,iig 0 x — — ††
CPIXPn/6 dn,iig 0 x — — ††
CPIXPn/7 en,iig 0 x — — ††
CPIXPn/8 fn,iig 0 x — — ††
CPIXPn/9 gn,iig 0 x — — ††
CPIXPn/10 hn,iig 0 x — — ††
† n is 1 through 3. CPIXP1 vector stores ideal gas parameters for the firsttemperature range. CPIXP2 vector stores ideal gas parameters for the secondtemperature range, and so on.
†† TEMPERATURE, ENTHALPY, ENTROPY
Pure-Component Solid Enthalpy PolynomialThis model calculates pure-component solid enthalpy from heat of fusion andheat capacity:
240 2 Thermodynamic Property Models
Where Cps is calculated from DIPPR equation 100 as in the General Pure
Component Solid Heat Capacity equation, but using parameter CPSPOL ratherthan CPSDIP:
Linear extrapolation occurs for Cp,i*,s versus T outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
CPSPOL/1 C1i — x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPSPOL/2,...,5 C2i, ..., C5i 0 x — — MOLE-HEAT-CAPACITY,TEMPERATURE
CPSPOL/6 C6i 0 x — — TEMPERATURE
CPSPOL/7 C7i 1000 x — — TEMPERATURE
DHSFRM Hfs — — — — MOLE ENTHALPY
Electrolyte NRTL Enthalpy Model(HMXENRTL)The equation for the electrolyte NRTL enthalpy model (HMXENRTL) is:
The molar enthalpy Hm* and the molar excess enthalpy Hm
*E are defined withthe asymmetrical reference state: the pure solvent water and infinite dilutionof molecular solutes and ions. (here * refers to the asymmetrical referencestate.)
Hw* is the pure water molar enthalpy, calculated from the Ideal Gas modeland the ASME Steam Table equation-of-state. (here * refers to purecomponent.)
Hs*,l is the enthalpy contribution from a non-water solvent. It is calculated as
usual for components in activity coefficient models:
Hs*,l(T) = Hs
*,ig + DHVs(T,p) - Hs,vap(T).
The term DHVs(T,p) = Hs*,v - Hs
*,ig is the vapor enthalpy departurecontribution to liquid enthalpy; option code 5 determines how this iscalculated.
The aqueous infinite dilution thermodynamic enthalpy Hk
is calculated from
the infinite dilution aqueous phase heat capacity as follows:
2 Thermodynamic Property Models 241
where the subscript k refers to any ion or molecular solute. By default,is calculated from the aqueous infinite dilution heat capacity polynomial. If
the polynomial model parameters are not available, is calculated fromthe Criss-Cobble correlation for ionic solutes.
For molecular solutes (e.g. Henry components), if the aqueous infinite dilution
heat capacity polynomial model parameters are not available, Hk
is
calculated from Henry's law:
Hm*E is calculated from the electrolyte NRTL activity coefficient model.
See Criss-Cobble correlation model and Henry's law model for moreinformation.ParameterName
ApplicableComponents
Symbol Default Units
IONTYP Ions † Ion 0 —
SO25C Cations Sc,aq (T=298) — MOLE-ENTROPY
Anions Sa,aq (T=298) — MOLE-ENTROPY
DHAQFM Ions, Molecular Solutes††
f Hk,aq — MOLE-ENTHALPY
CPAQ0 Ions, Molecular Solutes††
Cp,k,aq — HEAT-CAPACITY
DHFORM Molecular Solutes †† f Hi*,ig — MOLE-ENTHALPY
Water, Solvents f Hw*,ig — MOLE-ENTHALPY
CPIG Molecular Solutes Cp,i*,ig — †††
Water, Solvents Cp,w*,ig — †††
† IONTYP is not needed if CPAQ0 is given for ions.
†† DHFORM is not used if DHAQFM and CPAQ0 are given for molecular solutes(components declared as Henry's components). If CPAQ0 is missing, DHFORMand Henry's constants are used to calculate infinite dilution enthalpy forsolutes.
††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. IfCPIG/10 or CPIG/11 is non-zero, then absolute temperature units areassumed for CPIG/9 through CPIG/11. Otherwise, user input temperatureunits are used for all elements of CPIG. User input temperature units arealways used for other elements of CPIG.
242 2 Thermodynamic Property Models
Option Codes for Electrolyte NRTL Enthalpy Model(HMXENRTL)
The electrolyte NRTL enthalpy model (HMXENRTL) has seven option codesand the option codes can affect the performance of this model.
Option code 1. Use this option code to specify the default values of pairparameters for water/solute and solvent/solute; the solute represents acation/anion pair. The value (1) sets the default values to zero and the value(3) sets the default values for water/solute to (8,-4) and for solvent/solute to(10,-2). The value (3) is the default choice of the option code.
Option code 2. Use this option code to specify the vapor phase equation-of-state (EOS) model used for the liquid enthalpy calculation. The value (0) setsthe ideal gas EOS model and the value (1) sets the HF EOS model. The value(0) is the default.
Option code 3. Always leave this option code set to the value (1) to use thesolvent/solvent binary parameters obtained from NRTL parameters.
Option code 4. Not used.
Option code 5. Use this option code to specify how the vapor phase enthalpydeparture (DHV) is calculated. The value (0) sets DHV = 0, the value (1)specifies using Redlich-Kwong equation of state, and the value (3) specifiesusing Hayden-O’Connell equation of state. The value (0) is the default.
Option code 6. Not used.
Option code 7. Use this option code to specify the method for handlingHenry components and multiple solvents. The value (0) sets the pure liquidenthalpy to that calculated by aqueous infinite dilution heat capacity (onlywater as solvent) and the value (1) sets the pure liquid enthalpy for Henrycomponents using Henry’s law. Use value (1) when there are multiplesolvents. The value (0) is the default.
Electrolyte NRTL Gibbs Free Energy Model(GMXENRTL)The equation for the NRTL Gibbs free energy model (GMXENRTL) is:
The molar Gibbs free energy and the molar excess Gibbs free energy Gm* and
Gm*E are defined with the asymmetrical reference state: as pure water and
infinite dilution of molecular solutes and ions. (* refers to the asymmetricalreference state.) The ideal mixing term is calculated normally, where j refersto any component. The molar Gibbs free energy of pure water (or
thermodynamic potential) w* is calculated from the ideal gas contribution.
This is a function of the ideal gas heat capacity and the departure function.(here * refers to the pure component.)
The departure function is obtained from the ASME steam tables.
2 Thermodynamic Property Models 243
s*,l is the Gibbs free energy contribution from a non-water solvent. It is
calculated as usual for components in activity coefficient models.
The aqueous infinite dilution thermodynamic potential k
is calculated from
the infinite dilution aqueous phase heat capacity polynomial model, bydefault. Subscript k refers to any ion or molecular solute. If polynomial modelparameters are not available, it is calculated from the Criss-Cobble model forionic solutes:
where the subscript k refers to any ion or molecular solute and the term RT
ln(1000/Mw) is added because f Hk,aq and f Gk
,aq are based on a molality
scale, while k
is based on mole fraction scale.
By default, is calculated from the aqueous infinite dilution heat capacity
polynomial. If the polynomial model parameters are not available, iscalculated from the Criss-Cobble correlation for ionic solutes.
For molecular solutes (e.g. Henry components), if the aqueous infinite dilution
heat capacity polynomial model parameters are not available, k
is
calculated from Henry's law:
Gm*E is calculated from the electrolyte NRTL activity coefficient model.
See the Criss-Cobble correlation model and Henry's law model for moreinformation.ParameterName
ApplicableComponents
Symbol Default Units
IONTYP Ions † Ion 0 —
SO25C Cations † Sc,aq (T=298) — MOLE-ENTROPY
Anions † Sa,aq (T=298) — MOLE-ENTROPY
DGAQFM Ions, Molecular Solutes††
f Gk,aq — MOLE-ENTHALPY
CPAQ0 Ions, Molecular Solutes††
Cp,k,aq — HEAT-CAPACITY
DGFORM Molecular Solutes †† f Gi— MOLE-ENTHALPY
Water, Solvents f Gw— MOLE-ENTHALPY
244 2 Thermodynamic Property Models
ParameterName
ApplicableComponents
Symbol Default Units
CPIG Molecular Solutes Cp,i*,ig — †††
Water, Solvents Cp,w*,ig — †††
† IONTYP and SO25C are not needed if CPAQ0 is given for ions.
†† DGFORM is not needed if DHAQFM and CPAQ0 are given for molecularsolutes.
††† The unit keywords for CPIG are TEMPERATURE and HEAT-CAPACITY. IfCPIG/10 or CPIG/11 is non-zero, then absolute temperature units areassumed for CPIG/9 through CPIG/11. Otherwise, user input temperatureunits are used for all elements of CPIG. User input temperature units arealways used for other elements of CPIG.
Option Codes for Electrolyte NRTL Gibbs Free EnergyModel (GMXENRTL)
The electrolyte NRTL Gibbs free energy model (GMXENRTL) has six optioncodes and the option codes can affect the performance of this model.
Option code 1. Use this option code to specify the default values of pairparameters for water/solute and solvent/solute; the solute represents acation/anion pair. The value (1) sets the default values to zero and the value(3) sets the default values for water/solute to (8,-4) and for solvent/solute to(10,-2). The value (3) is the default choice of the option code.
Option code 2. Use this option code to specify the vapor phase equation-of-state (EOS) model used for the liquid Gibbs free energy calculation. The value(0) sets the ideal gas EOS model and the value (1) sets the HF EOS model.The value (0) is the default.
Option code 3. Always leave this option code set to the value (1) to use thesolvent/solvent binary parameters obtained from NRTL parameters.
Option code 4. Not used.
Option code 5. Use this option code to specify how the pure vapor phasefugacity coefficient (PHIV) is calculated. The value (0) sets PHIV = 1 (idealgas law), the value (1) specifies using Redlich-Kwong equation of state, andthe value (3) specifies using Hayden-O’Connell equation of state. The value(0) is the default.
Option code 6. Use this option code to specify the method for handlingHenry components and multiple solvents. The value (0) sets the pure liquidGibbs free energy to that calculated by aqueous infinite dilution heat capacity(only water as solvent) and the value (1) sets the pure liquid Gibbs freeenergy for Henry components using Henry’s law. Use value (1) when thereare multiple solvents. The value (0) is the default.
Liquid Enthalpy from Liquid Heat CapacityCorrelationLiquid enthalpy is directly calculated by integration of liquid heat capacity:
2 Thermodynamic Property Models 245
The reference enthalpy is calculated at Tref as:
Where:
Hi*,ig = Ideal gas enthalpy
Hi*,v - Hi
*,ig = Vapor enthalpy departure from equation of state
vapHi*,l = Heat of vaporization from General model
Tref = Reference temperature, specified by user. Defaults to298.15 K
See General Pure Component Heat of Vaporization for parameter requirementand additional details.
Enthalpies Based on Different ReferenceStatesTwo property methods, WILS-LR and WILS-GLR, are available to calculateenthalpies based on different reference states. The WILS-LR property methodis based on saturated liquid reference state for all components. The WILS-GLRproperty method allows both ideal gas and saturated liquid reference statesfor different components.
These property methods use an enthalpy method that optimizes the accuracytradeoff between liquid heat capacity, heat of vaporization, and vapor heatcapacity at actual process conditions. This highly recommended methodeliminates many of the problems associated with accurate thermal propertiesfor both phases, especially the liquid phase.
The liquid enthalpy of mixture is calculated by the following equation (see thetable labeled Liquid Enthalpy Methods):
Where:
Hmig = Enthalpy of ideal gas mixture
=
Hi*,ig = Ideal gas enthalpy of pure component i
(Hml-Hm
ig) = Enthalpy departure of mixture
For supercritical components, declared as Henry's components, the enthalpydeparture is calculated as follows:
246 2 Thermodynamic Property Models
For subcritical components:
Hml-Hm
ig =
HmE,l =
HA*,l-HA
*,ig = Enthalpy departure of pure component A
H*,ig and H*,l can be calculated based on either saturated liquid or ideal gas asreference state as described in the sections that follow.
For the WILS-LR property method, H*,ig and H*,l are calculated based on thesaturated liquid reference state for all components.
For the WILS-GLR property method, H*,ig and H*,l can be calculated based onthe saturated liquid reference state for some components and the ideal gasreference state for other components. You can set the value of a purecomponent parameter called RSTATE to specify the reference state for eachcomponent. RSTATE = 1 denotes ideal gas reference state. RSTATE = 2denotes saturated liquid reference state. If it is not set, the following defaultrules apply based on the normal boiling point of the component, i, TB(i):
If TB(i) <= 298.15 K, ideal gas reference state is used
If TB(i) > 298.15 K, saturated liquid reference state is used.
Note: When H*,ig (HIG) is calculated based on saturated liquid referencestate, ideal gas Gibbs free energy and entropy (GIG and SIG) are alsocalculated based on saturated liquid reference state to maintainthermodynamic consistency, and liquid Gibbs free energy and entropy arealso calculated based on saturated liquid reference state since they arecalculated based on departure from the ideal gas values.
Saturated Liquid as Reference State
The saturated liquid enthalpy at temperature T is calculated as follows:
Where:
Hiref,l = Reference enthalpy for liquid state at Ti
ref,l
Cp,i*,l = Liquid heat capacity of component i
The saturated liquid Gibbs free energy is calculated as follows:
Where:
Giref,l = Reference Gibbs free energy for liquid state at Ti
ref,l
i*,l = Liquid fugacity coefficient of component i
p = System pressure
2 Thermodynamic Property Models 247
pref = Reference pressure (=101325 N/m2)
For the WILS-LR property method, Hiref,l and Gi
ref,l default to zero (0). Thereference temperature Ti
ref,l defaults to 273.15K.
For the WILS-GLR property method, the reference temperature Tiref,l defaults
to 298.15K and Hiref,l defaults to:
And Giref,l defaults to:
Where:
Hiref,ig = Ideal gas enthalpy of formation for liquid state at
298.15K
Giref,ig = Ideal gas Gibbs free energy of formation for liquid
state at 298.15K
Hi*,v = Vapor enthalpy departure of component i
Gi*,v = Vapor Gibbs free energy departure of component i
vapHi* = Enthalpy of vaporization of component i
Note that we cannot default the liquid reference enthalpy and Gibbs freeenergy to zero, as is the case for WILS-LR, because it will cause inconsistencywith the enthalpy of components that use ideal-gas reference state. Thedefault values used result in the enthalpies of all components being on thesame basis. In fact, if you enter values for Hi
ref,l and Giref,l for a liquid-
reference state component you must make sure that they are consistent witheach other and are consistent with the enthalpy basis of the remainingcomponents in the mixture. If you enter a value for Hi
ref,l, you should alsoenter a value for Gi
ref,l to ensure consistency.
When the liquid-reference state is used, the ideal gas enthalpy attemperature T is not calculated from the integration of the ideal gas heatcapacity equation (see Ideal Gas as Reference State section below). Forconsistency, it is calculated from liquid enthalpy as follows:
Where:
Ticon,l = Temperature of conversion from liquid to vapor
enthalpy for component i
vapHi*(Ti
con,l) = Heat of vaporization of component i attemperature of Tcon,l
Hi*,v(Ti
con,l, pi*,l) = Vapor enthalpy departure of component i at the
conversion temperature and vapor pressure pi*,l
pi*,l = Liquid vapor pressure of component i
248 2 Thermodynamic Property Models
= Ideal gas heat capacity of component i
Ticon,l is the temperature at which one crosses from liquid state to the vapor
state. This is a user defined temperature that defaults to the systemtemperature T. Ti
con,l may be selected such that heat of vaporization forcomponent i at the temperature is most accurate.
The liquid heat capacity and the ideal gas heat capacity can be calculatedfrom the General Pure Component Liquid Heat Capacity and General PureComponent Ideal Gas Heat Capacity, or other available models. The heat ofvaporization can be calculated from the General Pure Component Heat ofVaporization, or other available models.
The ideal gas heat capacity at temperature T can be obtained bydifferentiating the ideal gas enthalpy equation above with respect totemperature. If the conversion temperature Ti
con,l is specified and not equal toT, then only the last term depends on T and the calculated ideal gas heat
capacity is obtained from the general pure component idealgas heat capacity or other models.
However, if the conversion temperature is not specified, it defaults to T, andthe ideal gas enthalpy equation becomes:
And then the ideal gas heat capacity, calculated by differentiating thisequation, is:
The vapor enthalpy is calculated from ideal gas enthalpy as follows:
Where:
Hi*,v(T, P) = Vapor enthalpy departure of pure component i at the
system temperature and pressure
The enthalpy departure is obtained from an equation-of-state that is beingused in the property method. For WILS-LR and WILS-GLR, the ideal gasequation of state is used.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
RSTATE † — 2 — — — —
TREFHL Tiref,l †† — — — TEMPERATURE
DHLFRM Hiref,l ††† — — — MOLE ENTHALPY
DGLFRM Giref,l †††† — — — MOLE ENTHALPY
TCONHL Ticon,l T — — — TEMPERATURE
† Enthalpy reference state given by RSTATE. 2 denotes saturated liquid asreference state.
2 Thermodynamic Property Models 249
†† For WILS-LR property method TREFHL defaults to 273.15K. For WILS-GLRproperty method, TREFHL defaults to 298.15 K.
††† For WILS-LR property method, DHLFRM defaults to zero (0). For WILS-GLR property method, DHLFRM defaults to the equation above.
†††† For WILS-LR property method, DGLFRM defaults to zero (0). For WILS-GLR property method, DGLFRM defaults to the equation above.
Liquid heat capacity equation is required for all components.
Ideal Gas as Reference State
The saturated liquid enthalpy is calculated as follows:
Where:
Hiref,ig = Reference state enthalpy for ideal gas at Ti
ref,ig
= Heat of formation of ideal gas at 298.15 K by default
Tiref,ig = Reference temperature corresponding to Hi
ref,ig.Defaults to 298.15 K
Ticon,ig = The temperature at which one crosses from vapor
state to liquid state. This is a user definedtemperature that defaults to the system temperatureT. Ti
con,igmay be selected such that heat ofvaporization of component i at the temperature ismost accurate.
The ideal gas enthalpy is calculated as follows:
The vapor enthalpy is calculated as follows:
The liquid heat capacity and the ideal gas heat capacity can be calculatedfrom the General Pure Component Liquid Heat Capacity and General PureComponent Ideal Gas Heat Capacity, or other available models. The heat ofvaporization can be calculated from the General Pure Component Heat ofVaporization, or other available models. The enthalpy departure is obtainedfrom an equation of state that is being used in the property method. ForWILS-LR and WILS-GLR, the ideal gas equation of state is used.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
RSTATE — 1 † — — — —
TREFHI Tiref,ig †† — — — TEMPERATURE
DHFORM Hiref,ig — — — — MOLE ENTHALPY
TCONHI Ticon,ig T — — — TEMPERATURE
250 2 Thermodynamic Property Models
† Enthalpy reference state RSTATE for a component. Value of 1 denotes idealgas.
††For components with TB 298.15 K, RSTATE defaults to 1 (ideal gas).
TREFHI defaults to 298.15 K. For components with TB > 298.15 K, RSTATEdefaults to 2 (liquid) and TREFHI does not apply to these components. Seethe Saturated Liquid as Reference State section for more details.
Helgeson Equations of State
The Helgeson equations of state for standard volume , heat capacity ,
entropy , enthalpy of formation , and Gibbs energy of formationat infinite dilution in aqueous phase are:
2 Thermodynamic Property Models 251
Where:
252 2 Thermodynamic Property Models
Where:
= Pressure constant for a solvent (2600 bar for water)
= Temperature constant for a solvent (228 K forwater)
= Born coefficient
= Dielectric constant of a solvent
Tr = Reference temperature (298.15 K)
Pr = Reference pressure (1 bar)
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
AHGPAR/1, ... ,4
a1, ..., a4 0 — — — †
CHGPAR/1, ... ,2
c1, c2 x — — — —
DHAQHG 0 — -0.5x1010 0.5x1010 MOLE-ENTHALPY
DGAQHG 0 — -0.5x1010 0.5x1010 MOLE-ENTHALPY
S25HG 0 — -0.5x1010 0.5x1010 MOLE-ENTROPY
OMEGHG 0 — -0.5x1010 0.5x1010 MOLE-ENTHALPY
† Units for AHGPAR are complex, and involve temperature, pressure, andmole-enthalpy. If pressure is under 200 bar, AHGPAR may not be required.
References
Tanger, J.C. IV and H.C. Helgeson, "Calculation of the thermodynamic andtransport properties of aqueous species at high pressures and temperatures:Revised equation of state for the standard partial properties of ions andelectrolytes," American Journal of Science, Vol. 288, (1988), p. 19-98.
Shock, E.L. and H.C. Helgeson, "Calculation of the thermodynamic andtransport properties of aqueous species at high pressures and temperatures:
2 Thermodynamic Property Models 253
Correlation algorithms for ionic species and equation of state predictions to 5kb and 1000 C," Geochimica et Cosmochimica Acta, Vol. 52, p. 2009-2036.
Shock, E.L., H.C. Helgeson, and D.A. Sverjensky, "Calculation of thethermodynamic and transport properties of aqueous species at high pressuresand temperatures: Standard partial molal properties of inorganic neutralspecies," Geochimica et Cosmochimica Acta, Vol. 53, p. 2157-2183.
Quadratic Mixing RuleThe quadratic mixing rule is a general-purpose mixing rule which can beapplied to various properties. For a given property Q, with i and j beingcomponents, the rule is:
The pure component properties Qi and Qj are calculated by the default modelfor that property, unless modified by option codes. Composition xi and xj is inmole fraction unless modified by option codes. Kij is a binary parameterspecific to the mixing rule for each property. A variation on the equation usingthe logarithm of the property is used for viscosity.
When the binary parameters are all zero, the quadratic mixing rule reduces tothe ideal mixing rule.
Ideal Mixing RuleThe ideal mixing rule, sometimes called mole-fraction weighted averaging, isa general-purpose mixing rule which can be applied to various properties. Fora given property Q, where i is any component, the rule is:
The pure component property Qi is calculated by the default model for thatproperty, unless modified by option codes. Composition xi is usually in molefraction unless modified by option codes. These option codes may varydepending on the specific model implementing ideal mixing.
254 2 Thermodynamic Property Models
3 Transport Property Models 255
3 Transport Property Models
This section describes the transport property models available in the AspenPhysical Property System. The following table provides an overview of theavailable models. This table lists the Aspen Physical Property System modelnames, and their possible use in different phase types, for pure componentsand mixtures.
Viscosity models
These models calculate MUL (pure) and/or MULMX (mixture) for the liquidphase, and MUV (pure) and/or MUVMX (mixture) for the vapor phase, exceptmodels marked with * calculate MUVLP (pure) and/or MUVMXLP (mixture) forthe vapor phase, and models marked with ** calculate MUVPC (pure) andMUVMXPC (mixture).Model Model name Phase(s) Pure Mixture
Andrade Liquid MixtureViscosity
MUL2ANDR L — X
General Pure ComponentLiquid Viscosity
MUL0ANDR L X —
API Liquid Viscosity MUL2API L — X
API 1997 Liquid Viscosity MULAPI97 L — X
Aspen Liquid Mixture Viscosity MUASPEN L — X
ASTM Liquid Mixture Viscosity MUL2ASTM L — X
General Pure ComponentVapor Viscosity *
MUV0CEB V X —
Chapman-Enskog-Brokaw-Wilke Mixing Rule *
MUV2BROK,MUV2WILK
V — X
Chung-Lee-Starling LowPressure *
MUV0CLSL,MUV2CLSL
V X X
Chung-Lee-Starling MUV0CLS2,MUV2CLS2,MUL0CLS2,MUL2CLS2
V L X X
Dean-Stiel Pressure Correction**
MUV0DSPC,MUV2DSPC
V X X
IAPS Viscosity MUV0H2O,MUL0H2O
V L X —
Jones-Dole ElectrolyteCorrection
MUL2JONS L — X
256 3 Transport Property Models
Model Model name Phase(s) Pure Mixture
Letsou-Stiel MUL0LEST,MUL2LEST
L X X
Lucas MUV0LUC,MUV2LUC
V X X
TRAPP viscosity MUL0TRAP,MUL2TRAP,MUV0TRAP,MUV2TRAP
V L X X
Twu liquid viscosity MUL2TWU L — X
Viscosity quadratic mixing rule MUL2QUAD L — X
Thermal conductivity models
These models calculate KL (pure) and/or KLMX (mixture) for the liquid phase,and KV (pure) and/or KVMX (mixture) for the vapor phase, except modelsmarked with * calculate KVLP (pure) and/or KVMXLP (mixture) for the vaporphase, and models marked with ** calculate KVPC (pure) and KVMXPC(mixture) for the vapor phase.Model Model name Phase(s) Pure Mixture
Chung-Lee-Starling ThermalConductivtity
KV0CLS2,KV2CLS2,KL0CLS2,KL2CLS2
V L X X
IAPS Thermal Conductivity forWater
KV0H2OKL0H2O
VL
XX
——
Li Mixing Rule KL2LI L X X
Riedel Electrolyte Correction KL2RDL L — X
General Pure ComponentLiquid Thermal Conductivity
KL0SR,KL2SRVR
L X X
General Pure ComponentVapor Thermal Conductivity *
KV0STLP V X —
Stiel-Thodos PressureCorrection **
KV0STPC,KV2STPC
V X X
TRAPP Thermal Conductivity KV0TRAP,KV2TRAP,KL0TRAP,KL2TRAP
V L X X
Vredeveld Mixing Rule KL2SRVR L X X
Wassiljewa-Mason-Saxenamixing rule *
KV2WMSM V X X
Diffusivity models
These models calculate DL (binary) and/or DLMX (mixture) for the liquidphase, and DV (binary) and/or DVMX (mixture) for the vapor phase.Model Model name Phase(s) BinaryMixture
Chapman-Enskog-Wilke-LeeBinary
DV0CEWL V X —
Chapman-Enskog-Wilke-LeeMixture
DV1CEWL V — X
3 Transport Property Models 257
Model Model name Phase(s) BinaryMixture
Dawson-Khoury-KobayashiBinary
DV1DKK V X —
Dawson-Khoury-KobayashiMixture
DV1DKK V — X
Nernst-Hartley Electrolytes DL0NST,DL1NST
L X X
Wilke-Chang Binary DL0WC2 L X —
Wilke-Chang Mixture DL1WC L — X
Surface tension models
These models calculate SIGL (pure) and/or SIGLMX (mixture).Model Model name Phase(s) Pure Mixture
Liquid Mixture Surface Tension SIG2IDL L — X
API Surface Tension SIG2API L — X
General Pure ComponentLiquid Surface Tension
SIG0HSS,SIG2HSS
L X —
IAPS surface tension SIG0H2O L X —
Onsager-Samaras ElectrolyteCorrection
SIG2ONSG L — X
Modified MacLeod-Sugden SIG2MS L — X
Viscosity ModelsThe Aspen Physical Property System has the following built-in viscositymodels:Model Type
Andrade Liquid Mixture Viscosity Liquid
General Pure Component Liquid Viscosity Pure component liquid
API liquid viscosity Liquid
API 1997 liquid viscosity Liquid
General Pure Component Vapor Viscosity Low pressure vapor,pure components
Chapman-Enskog-Brokaw-Wilke Mixing Rule Low pressure vapor,mixture
Chung-Lee-Starling Low Pressure Low pressure vapor
Chung-Lee-Starling Liquid or vapor
Dean-Stiel Pressure correction Vapor
IAPS viscosity Water or steam
Jones-Dole Electrolyte Correction Electrolyte
Letsou-Stiel High temperature liquid
Lucas Vapor
TRAPP viscosity Vapor or liquid
Aspen Liquid Mixture Viscosity Liquid
ASTM Liquid Mixture Viscosity Liquid
258 3 Transport Property Models
Model Type
Twu liquid viscosity Liquid
Viscosity quadratic mixing rule Liquid
Andrade Liquid Mixture ViscosityThe liquid mixture viscosity is calculated by the modified Andrade equation:
Where:
kij =
mij =
fi depends on the option code for the model MUL2ANDR.If first option code ofMUL2ANDR is
Then fi is
0 (Default) Mole fraction of component i
1 Mass fraction of component i
Note that the Andrade liquid mixture viscosity model is called from othermodels. The first option codes of these models cause fi to be mole or massfraction when Andrade is used in the respective models. To maintainconsistency across models, if you set the first option code for MUL2ANDR to1, you should also the set the first option code of the other models to 1, ifthey are used in your simulation.Model Model Name
MUL2JONS Jones-Dole Electrolyte Viscosity model
DL0WCA Wilke-Chang Diffusivity model (binary)
DL1WCA Wilke-Chang Diffusivity model (mixture)
DL0NST Nernst-Hartley Electrolyte Diffusivity model (binary)
DL1NST Nernst-Hartley Electrolyte Diffusivity model (mixture)
The binary parameters kij and mij allow accurate representation of complexliquid mixture viscosity. Both binary parameters default to zero.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
ANDKIJ/1 aij 0 — — — —
ANDKIJ/2 bij 0 — — — —
ANDMIJ/1 cij 0 — — — —
ANDMIJ/2 dij 0 — — — —
The pure component liquid viscosity i*,l is calculated by the General Pure
Component Liquid Viscosity model.
3 Transport Property Models 259
General Pure Component Liquid ViscosityThe Aspen Physical Property System has several submodels for calculatingpure component liquid viscosity. It uses parameter TRNSWT/1 to determinewhich submodel is used. See Pure Component Temperature-DependentProperties for details.If TRNSWT/1 is This equation is used And this parameter is used
0 Andrade MULAND
101, 115 DIPPR 101 or 115 MULDIP
301 PPDS MULPDS
401 IK-CAPE polynomial equation MULPO
404 IK-CAPE exponential equationMULIKC
508 NIST TDE equation MULNVE
509 NIST PPDS9 MULPPDS9
Andrade Liquid Viscosity
The Andrade equation is:
Linear extrapolation of ln(viscosity) versus 1/T occurs for temperaturesoutside bounds.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULAND/1 Ai — X — — VISCOSITY,TEMPERATURE †
MULAND/2 Bi — X — — TEMPERATURE †
MULAND/3 Ci — X — — TEMPERATURE †
MULAND/4 Tl 0.0 X — — TEMPERATURE
MULAND/5 Th 500.0 X — — TEMPERATURE
† If Bi or Ci is non-zero, absolute temperature units are assumed for Ai, Bi,and Ci. Otherwise, all coefficients are interpreted in user input temperatureunits. The temperature limits are always interpreted in user input units.
DIPPR Liquid Viscosity
There are two DIPPR equations for liquid viscosity. The value of TRNSWT/1determines which one is used.
Equation 101 for the DIPPR liquid viscosity model is:
Equation 115 for the DIPPR liquid viscosity model is:
Linear extrapolation of ln(viscosity) versus 1/T occurs for temperaturesoutside bounds.
260 3 Transport Property Models
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULDIP/1 C1i — X — — VISCOSITY,TEMPERATURE ††
MULDIP/2, ..., 5 C2i, ..., C5i 0 X — — TEMPERATURE ††
MULDIP/6 C6i 0 X — — TEMPERATURE
MULDIP/7 C7i 1000 X — — TEMPERATURE
†† If any of C3i through C5i are non-zero, absolute temperature units areassumed for C3i through C5i. Otherwise, all coefficients are interpreted in userinput temperature units. The temperature limits are always interpreted inuser input units.
PPDS
The PPDS equation is:
Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULPDS/1 C1i — — — — —
MULPDS/2 C2i — — — —
MULPDS/3 C3i — — — TEMPERATURE
MULPDS/4 C4i — — — TEMPERATURE
MULPDS/5 C5i — — — — VISCOSITY
MULPDS/6 C6i — — — TEMPERATURE
MULPDS/7 C7i — — — TEMPERATURE
NIST PPDS9 Equation
This is the same as the PPDS equation above, but it uses parameterMULPPDS9. Note that the parameters are in a different order.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULPPDS9/1 C5i — — — — VISCOSITY
MULPPDS9/2 C1i — — — —
MULPPDS9/3 C2i — — — —
MULPPDS9/4 C3i — — — TEMPERATURE
MULPPDS9/5 C4i — — — — TEMPERATURE
MULPPDS9/6 C6i — — — TEMPERATURE
MULPPDS9/7 C7i — — — TEMPERATURE
3 Transport Property Models 261
IK-CAPE Liquid Viscosity Model
The IK-CAPE liquid viscosity model includes both exponential and polynomialequations.
Exponential
Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.ParameterName/Element
SymbolDefault MDS LowerLimit
UpperLimit
Units
MULIKC/1 C1i — X — — VISCOSITY
MULIKC/2 C2i 0 X — — TEMPERATURE †††
MULIKC/3 C3i 0 X — — VISCOSITY
MULIKC/4 C4i 0 X — — TEMPERATURE
MULIKC/5 C5i 1000 X — — TEMPERATURE
††† Absolute temperature units are assumed for C2i. The temperature limitsare always interpreted in user input units.
Polynomial
Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULPO/1 C1i — X — — VISCOSITY
MULPO/2, ..., 10 C2i, ..., C10i 0 X — — VISCOSITY,TEMPERATURE
MULPO/11 C11i 0 X — — TEMPERATURE
MULPO/12 C12i 1000 X — — TEMPERATURE
NIST TDE Equation
Linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.
Absolute temperature units are assumed for C2i, C3i, and C4i. The temperaturelimits are always interpreted in user input units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULNVE/1 C1i — X — — —
262 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULNVE/2, 3, 4 C2i, C3i, C4i 0 X — — TEMPERATURE
MULNVE/5 C5i 0 X — — TEMPERATURE
MULNVE/6 C6i 1000 X — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 439.
API Liquid ViscosityThe liquid mixture viscosity is calculated using a combination of the API andGeneral equations. This model is recommended for petroleum andpetrochemical applications. It is used in the CHAO-SEA, GRAYSON, LK-PLOCK,PENG-ROB, and RK-SOAVE option sets.
For pseudocomponents, the API model is used:
Where:
fcn = A correlation based on API Procedures and Figures 11A4.1, 11A4.2,and 11A4.3 (API Technical Data Book, Petroleum Refining, 4thedition)
Vml is obtained from the API liquid volume model.
For real components, the General model is used.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TB Tbi — — 4.0 2000.0 TEMPERATURE
API APIi — — -60.0 500.0 —
API 1997 Liquid ViscosityThe liquid mixture viscosity is calculated using a combination of the API andGeneral equations. This model is recommended over the earlier API viscositymodel.
This model is applicable to petroleum fractions with normal boiling points from150 F to 1200 F and API gravities between 0 and 75. Testing by AspenTechindicates that this model is slightly more accurate than the Twu model forlight and medium boiling petroleum components, while the Twu model issuperior for heavy fractions.
For pseudocomponents, the API model is used:
Where:
3 Transport Property Models 263
fcn = A correlation based on API Procedures and Figures 11A4.2, 11A4.3,and 11A4.4 (API Technical Data Book, Petroleum Refining, 1997edition)
Vml is obtained from the API liquid volume model.
For real components, the General model is used.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TB Tbi — — 4.0 2000.0 TEMPERATURE
API APIi — — -60.0 500.0 —
Aspen Liquid Mixture ViscosityThe liquid mixture viscosity is calculated by the equation:
Where:
Xi = Mole fraction or weight fraction of component i
kij = Symmetric binary parameter (kij = kji)
lij = Antisymmetric binary parameter (lij = -lji)
The pure component liquid viscosity i*,l is calculated by the General Pure
Component Liquid Viscosity model.
The binary parameters kij and lij allow accurate representation of complexliquid mixture viscosity temperature dependence. Both binary parametersdefault to zero. Both binary parameters, kij and lij, have to be specified foreach component-component pair.
with
Where:
Tref = Reference temperature and the default value = 298.15 K
One option code is used with this model. It determines whether Xi is molefraction (default, option value 0) or weight fraction (option value 1).
264 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MUKIJ/1 aij 0 X --- --- ---
MUKIJ/2 bij 0 X --- --- ---
MUKIJ/3 cij 0 X --- --- ---
MUKIJ/4 dij 0 X --- --- ---
MUKIJ/5 eij 0 X --- --- ---
MUKIJ/6 Tref 298.15 X --- --- ---
MULIJ/1 a'ij 0 X --- --- ---
MULIJ/2 b'ij 0 X --- --- ---
MULIJ/3 c'ij 0 X --- --- ---
MULIJ/4 d'ij 0 X --- --- ---
MULIJ/5 e'ij 0 X --- --- ---
MULIJ/6 Tref 298.15 X --- --- ---
Aspen Liquid Mixture Viscosity Model (MUASPEN) is a correlative model and itis essentially a new mixing rule for calculating the mixture viscosity from thepure component viscosities. It requires the pure component liquid viscositiesbeing calculated by another model before the mixture liquid viscosity can becalculated. To ensure this prerequisite, the route MULMX14 was createdparticularly for this model. To use this model in a property method youcreate, you should specify or change the route for MULMX to MULMX14 ratherthan changing the mixture liquid viscosity model to MUASPEN directly.
ASTM Liquid Mixture ViscosityIt is generally difficult to predict the viscosity of a mixture of viscouscomponents. For hydrocarbons, the following weighting method (ASTM †) isknown to give satisfactory results:
Where:
wi = Weight fraction of component i
m= Absolute viscosity of the mixture (N-sec/m2)
i= Absolute viscosity of component i (N-sec/m2)
log = Common logarithm (base 10)
f = An adjustable parameter, typically in therange of 0.5 to 1.0
There are two significant differences in this implementation as compared withthe version from the book †. The book uses kinematic viscosity in mm2/swhile the Aspen Physical Property System uses absolute viscosity in cP (=0.001 N-sec/m2) with an equation in the same form. And f is treated as anadjustable parameter in this model, while the book makes it a function of thepure component kinematic viscosity.
3 Transport Property Models 265
The individual component viscosities are calculated by the General PureComponent Liquid Viscosity model. The parameter f can be specified bysetting the value for MULOGF for the first component in the component list(as defined on the Components | Specifications | Selection sheet).ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MULOGF f 1.0 — 0.0 2.0 —
† "Petroleum Refining, 1 Crude Oil, Petroleum Products, Process Flowsheets",Institut Francais du Petrole Publications, 1995, p. 130.
General Pure Component Vapor ViscosityThe Aspen Physical Property System has several submodels for calculatingpure component low pressure vapor viscosity. It uses parameter TRNSWT/2to determine which submodel is used. See Pure Component Temperature-Dependent Properties for details.If TRNSWT/2 is This equation is used And this parameter is
used
0 Chapman-Enskog-Brokaw
STKPAR, LJPAR
102 DIPPR MUVDIP
301 PPDS MUVPDS
302 PPDS kinetic theory MUVCEB
401 IK-CAPE polynomialequation
MUVPO
402 IK-CAPE Sutherlandequation
MUVSUT
503 NIST ThermoMLpolynomial
MUVTMLPO
Chapman-Enskog-Brokaw
The equation for the Chapman-Enskog model is:
Where:
=
A parameter is used to determine whether to use the Stockmayer or
Lennard-Jones potential parameters for /k (energy parameter) and (collision diameter). To calculate , the dipole moment p and either the
Stockmayer parameters or Tb and Vb are needed. The polarity correction isfrom Brokaw.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
266 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) — X — TEMPERATURE
STKPAR/2 iST fcn(Tbi, Vbi, pi) X — — LENGTH
LJPAR/1 (i/k)LJ fcn(Tci, i) X — — TEMPERATURE
LJPAR/2 iLJ fcn(Tci, pci, i) X — — LENGTH
DIPPR Vapor Viscosity
The equation for the DIPPR vapor viscosity model is:
When necessary, the vapor viscosity is extrapolated beyond this temperaturerange linearly with respect to T, using the slope at the temperature limits.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
PCES uses the DIPPR equation in estimating vapor viscosity.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MUVDIP/1 C1i — X — — VISCOSITY
MUVDIP/2 C2i 0 X — — —
MUVDIP/3, 4 C3i, C4i 0 X — — TEMPERATURE †
MUVDIP/5 †† 0 X — — —
MUVDIP/6 C6i 0 X — — TEMPERATURE
MUVDIP/7 C7i 1000 X — — TEMPERATURE
† If any of C2i through C4i are non-zero, absolute temperature units areassumed for C1i through C4i. Otherwise, all coefficients are interpreted in userinput temperature units. The temperature limits are always interpreted inuser input units.
†† MUVDIP/5 is not used in this equation. It is normally set to zero. Theparameter is provided for consistency with other DIPPR equations.
PPDS
The PPDS submodel includes both the basic PPDS vapor viscosity equationand the PPDS kinetic theory vapor viscosity equation. For either equation,linear extrapolation of viscosity versus T occurs for temperatures outsidebounds.
PPDS Vapor Viscosity
The equation is:
3 Transport Property Models 267
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
MUVPDS/1 C1i — — — — VISCOSITY
MUVPDS/2 C2i 0 — — — —
MUVPDS/3 C3i 0 — — — —
MUVPDS/4 C4i 0 — — — TEMPERATURE
MUVPDS/5 C5i 1000 — — — TEMPERATURE
PPDS Kinetic Theory Vapor Viscosity
The equation is:
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
MUVCEB/1 C1i — — — — LENGTH
MUVCEB/2 C2i — — — — TEMPERATURE †
MUVCEB/3 C3i 0 — — — —
MUVCEB/4 C4i 0 — — — TEMPERATURE
MUVCEB/5 C5i 1000 — — — TEMPERATURE
† Absolute temperature units are assumed for C2i . The temperature limits arealways interpreted in user input units.
IK-CAPE Vapor Viscosity
The IK-CAPE vapor viscosity model includes both the Sutherland equation andthe polynomial equation. For either equation, linear extrapolation of viscosityversus T occurs for temperatures outside bounds.
Sutherland Equation
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
MUVSUT/1 C1i — X — — VISCOSITY
MUVSUT/2 C2i 0 X — — TEMPERATURE ††
MUVSUT/3 C3i 0 X — — TEMPERATURE
268 3 Transport Property Models
ParameterName/Element
Symbol DefaultMDS LowerLimit
UpperLimit
Units
MUVSUT/4 C4i 1000 X — — TEMPERATURE
†† If C2i is non-zero, absolute temperature units are assumed for C1i and C2i.Otherwise, all coefficients are interpreted in user input temperature units. Thetemperature limits are always interpreted in user input units.
Polynomial
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MUVPO/1 C1i — X — — VISCOSITY
MUVPO/2, ..., 10 C2i, ..., C10i 0 X — — VISCOSITY,TEMPERATURE
MUVPO/11 C11i 0 X — — TEMPERATURE
MUVPO/12 C12i 1000 X — — TEMPERATURE
NIST ThermoML Polynomial
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MUVTMLPO/1 C1i — X — — Pa*s/T
MUVTMLPO/2, ..., 4 C2i , ..., C4i 0 X — — Pa*s/T
MUVTMLPO/5 nTerms 4 X — — —
MUVTMLPO/6 Tlower 0 X — — TEMPERATURE
MUVTMLPO/7 Tupper 1000 X — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling. The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 392.
Chapman-Enskog-Brokaw-Wilke MixingRuleThe low pressure vapor mixture viscosity is calculated by the Wilkeapproximation of the Chapman-Enskog equation:
For ij,the formulation by Brokaw is used:
3 Transport Property Models 269
Where:
The Stockmayer or Lennard-Jones potential parameters /k (energy
parameter) and (collision diameter) and the dipole moment p are used to
calculate The k represents Boltzmann's constant 1.38065 x 10-23 J/K. If the
Stockmayer parameters are not available, is estimated from Tb and Vb:
Where p is in debye.
The pure component vapor viscosity i*,v (p = 0) can be calculated using the
General Pure Component Vapor Viscosity (or another low pressure vaporviscosity model).
Ensure that you supply parameters for i*,v (p = 0).
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) — X — TEMPERATURE
270 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
STKPAR/2 iST fcn(Tbi, Vbi, pi) X — — LENGTH
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases andLiquids, 3rd ed., (New York: McGraw-Hill, 1977), pp. 410–416.
Chung-Lee-Starling Low-Pressure VaporViscosityThe low-pressure vapor viscosity by Chung, Lee, and Starling is:
Where the viscosity collision integral is:
The shape and polarity correction is:
The parameter pr is the reduced dipolemoment:
C1 is a constant of correlation.
The polar parameter is tabulated for certain alcohols and carboxylic acids.
The previous equations can be used for mixtures when applying these mixingrules:
3 Transport Property Models 271
Where:
Vcij =
ij= 0 (in almost all cases)
Tcij =
ij= 0 (in almost all cases)
ij=
Mij =
ij=
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCCLS Tci TC x 5.0 2000.0 TEMPERATURE
VCCLS Vci VC x 0.001 3.5 MOLE-VOLUME
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
OMGCLS iOMEGA x -0.5 2.0 —
CLSK i0.0 x 0.0 0.5 —
CLSKV ij0.0 x -0.5 -0.5 —
CLSKT ij0.0 x -0.5 0.5 —
The model specific parameters also affect the Chung-Lee-Starling Viscosityand the Chung-Lee-Starling Thermal Conductivity models.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 396, p. 413.
272 3 Transport Property Models
Chung-Lee-Starling ViscosityThe Chung-Lee-Starling viscosity equation for vapor and liquid, high and lowpressure is:
With:
f1 =
f2 =
FC =
The molar density can be calculated using an equation-of-state model (forexample, the Benedict-Webb-Rubin). The parameter pr is the reduceddipolemoment:
C1 and C2 are constants of correlation.
The polar parameter is tabulated for certain alcohols and carboxylic acids.
For low pressures, f1 is reduced to 1.0 and f2 becomes negligible. Theequation reduces to the low pressure vapor viscosity model by Chung-Lee andStarling.
The previous equations can be used for mixtures when applying these mixingrules:
3 Transport Property Models 273
Where:
Vcij =
ij= 0 (in almost all cases)
Tcij =
ij= 0 (in almost all cases)
ij=
Mij =
ij=
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCCLS Tci TC x 5.0 2000.0 TEMPERATURE
VCCLS Vci VC x 0.001 3.5 MOLE-VOLUME
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
OMGCLS iOMEGA x -0.5 2.0 —
CLSK i0.0 x 0.0 0.5 —
CLSKV ij0.0 x -0.5 -0.5 —
CLSKT ij0.0 x -0.5 0.5 —
The model specific parameters affect the results of the Chung-Lee-StarlingThermal Conductivity and Low Pressure Viscosity models as well.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 427.
274 3 Transport Property Models
Dean-Stiel Pressure CorrectionThe residual vapor viscosity or the pressure correction to low pressure vaporviscosity by Dean and Stiel is:
Where v (p = 0) is obtained from a low pressure viscosity model (for
example, General Pure Component Vapor Viscosity). The dimensionless-
making factor is:
=
Tc =
M =
pc =
Vcm =
Zcm =
rm= Vcm / Vm
v
The parameter Vmv is obtained from Redlich-Kwong equation-of-state.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
VC Vci — — 0.001 3.5 MOLE-VOLUME
IAPS Viscosity for WaterThe IAPS viscosity models, developed by the International Association forProperties of Steam, calculate vapor and liquid viscosity for water and steam.These models are used in option sets STEAMNBS and STEAM-TA.
The general form of the equation for the IAPS viscosity models is:
w=fcn(T, p)
Where:
fcn = Correlation developed by IAPS
The models are only applicable to water. There are no parameters requiredfor the models.
3 Transport Property Models 275
Jones-Dole Electrolyte CorrectionThe Jones-Dole model calculates the correction to the liquid mixture viscosityof a solvent mixture, due to the presence of electrolytes:
Where:
solv= Viscosity of the liquid solvent mixture, by default
calculated by the Andrade model
cal = Contribution to the viscosity correction due to
apparent electrolyte ca
The parameter solv can be calculated by different models depending on
option code 3 for MUL2JONS:Option CodeValue
Solvent liquid mixture viscositymodel
0Andrade liquid mixture viscositymodel (default)
1 Viscosity quadratic mixing rule
2 Aspen liquid mixture viscositymodel
The parameter cal can be calculated by three different equations.
If these parameters are available Use this equation
IONMOB and IONMUB Jones-Dole †
IONMUB Breslau-Miller
— Carbonell
† When the concentration of apparent electrolyte exceeds 0.1 M, the Breslau-Miller equation is used instead.
Jones-Dole
The Jones-Dole equation is:
(1)
Where:
= Concentration of apparent electrolyte ca (2)
xcaa = Mole fraction of apparent electrolyte ca (3)
Aca = (4)
La = (5)
276 3 Transport Property Models
Lc = (6)
Bca = (7)
When the electrolyte concentration exceeds 0.1 M, the Breslau-Miller equationis used instead. This behavior can be disabled by setting the second optioncode for MUL2JONS to 1.
Breslau-Miller
The Breslau-Miller equation is:
(8)
Where the effective volume Vc is given by:
for salts involving univalent ions
(9)
for other salts
(9a)
Carbonell
The Carbonell equation is:
(10)
Where:
Mk = Molecular weight of an apparent electrolytecomponent k
You must provide parameters for the model used for the calculation of theliquid mixture viscosity of the solvent mixture.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
CHARGE z 0.0 — — —
MW M — 1.0 5000.0 —
IONMOB/1 l1 — † — — AREA, MOLES
IONMOB/2 l2 0.0 — — AREA, MOLES,TEMPERATURE
IONMUB/1 b1 — † — — MOLE-VOLUME
IONMUB/2 b2 0,0 — — MOLE-VOLUME,TEMPERATURE
†When IONMOB/1 is missing, the Jones-Dole model uses a nominal value of5.0 and issues a warning. This parameter should be specified for ions, and notallowed to default to this value.
3 Transport Property Models 277
References
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: EllisHorwood, 1985).
Letsou-StielThe Letsou-Stiel model calculates liquid viscosity at high temperatures for
0.76 Tr 0.98. This model is used in PCES.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
The general form for the model is:
l = (l)0 + (l)1
Where:
(l)0 =
(l)1 =
=
=
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
TC Tci — — 5.0 2000.0 TEMPERATURE
PC pci — — 105 108 PRESSURE
OMEGA i— — -0.5 2.0 —
References
R.C. Reid, J.M. Pransnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 471.
Lucas Vapor ViscosityThe equation for the Lucas vapor viscosity model is:
Where the dimensionless low pressure viscosity is given by:
The dimensionless-making group is:
278 3 Transport Property Models
The pressure correction factor Y is:
The polar and quantum correction factors at high and low pressure are:
FP =
FQ =
FPi (p = 0) =
FQi (p = 0) = fcn(Tri), but is only nonunity for the quantumgates i = H2, D2, and He.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.
The Lucas mixing rules are:
Tc =
pc =
M =
FP (p = 0) =
FQ (p = 0) =
Where A differs from unity only for certain mixtures.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCLUC Tci TC x 5.0 2000.0 TEMPERATURE
PCLUC pci PC x 105 108 PRESSURE
ZCLUC Zci ZC x 0.1 0.5 —
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 421, 431.
3 Transport Property Models 279
TRAPP Viscosity ModelThe general form for the TRAPP viscosity model is:
Where:
The parameter is the mole fraction vector; fcn is a corresponding statescorrelation based on the model for vapor and liquid viscosity TRAPP, by theNational Bureau of Standards (NBS, currently NIST) . The model can be usedfor both pure components and mixtures. The model should be used fornonpolar components only.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
TCTRAP Tci TC x 5.0 2000.0 TEMPERATURE
PCTRAP pci PC x 105 108 PRESSURE
VCTRAP Vci VC x 0.001 3.5 MOLE-VOLUME
ZCTRAP Zci ZC x 0.1 1.0 —
OMGRAP iOMEGA x -0.5 3.0 —
References
J.F. Ely and H.J.M. Hanley, "Prediction of Transport Properties. 1. Viscositiesof Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 20, (1981), pp. 323–332.
Twu Liquid ViscosityThe Twu liquid viscosity model is based upon the work of C.H. Twu (1985).The correlation uses n-alkanes as a reference fluid and is capable ofpredicting liquid viscosity for petroleum fractions with normal boiling points upto 1340 F and API gravity up to -30.
Given the normal boiling point Tb and the specific gravity SG of the system tobe modeled, the Twu model estimates the viscosity of the n-alkane referencefluid of the same normal boiling point at 100 F and 210 F, and its specificgravity. These are used to estimates the viscosity of the system to bemodeled at 100 F and at 210 F, and these viscosities are used to estimate theviscosity at the temperature of interest.
280 3 Transport Property Models
Where:
SG = Specific gravity of petroleum fraction
Tb = Normal boiling point of petroleum fraction, Rankine
SG° = Specific gravity of reference fluid with normalboiling point Tb
T = Temperature of petroleum fraction, Rankine
= Kinematic viscosity of petroleum fraction at T, cSt
i= Kinematic viscosity of petroleum fraction at 100 F
(i=1) and 210 F (i=2), cSt
1°, 2° = Kinematic viscosity of reference fluid at 100 F and210 F, cSt
Tc° = Critical temperature of reference fluid, Rankine
3 Transport Property Models 281
Reference
C.H. Twu, "Internally Consistent Correlation for Predicting Liquid Viscosities ofPetroleum Fractions," Ind. Eng. Chem. Process Des. Dev., Vol. 24 (1985), pp.1287-1293
Viscosity Quadratic Mixing RuleWith i and j being components, the viscosity quadratic mixing rule is:
The pure component viscosity is calculated by the General Pure ComponentLiquid Viscosity model.
Option CodesOption Code Value Descriptions
1 0 Use mole basis composition (default)
1 Use mass basis composition
ParameterParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MLQKIJ Kij - x - - —
Thermal Conductivity ModelsThe Aspen Physical Property System has eight built-in thermal conductivitymodels. This section describes the thermal conductivity models available.Model Type
Chung-Lee-Starling Vapor or liquid
IAPS Water or steam
Li Mixing Rule Liquid mixture
Riedel Electrolyte Correction Electrolyte
General Pure Component Liquid ThermalConductivity
Liquid
Solid Thermal Conductivity Polynomial Solid
General Pure Component Vapor ThermalConductivity
Low pressure vapor
Stiel-Thodos Pressure Correction Vapor
TRAPP Thermal Conductivity Vapor or liquid
Vredeveld Mixing Rule Liquid mixture
Wassiljewa-Mason-Saxena Mixing Rule Low pressure vapor
282 3 Transport Property Models
Chung-Lee-Starling Thermal ConductivityThe main equation for the Chung-Lee-Starling thermal conductivity model is:
Where:
f1 =
f2 =
=
(p = 0) can be calculated by the low pressure Chung-Lee-Starling model.
The molar density can be calculated using an equation-of-state model (forexample, the Benedict-Webb-Rubin equation-of-state). The parameter pr isthe reduced dipolemoment:
The polar parameter is tabulated for certain alcohols and carboxylic acids.
For low pressures, f1 is reduced to 1.0 and f2 is reduced to zero. This givesthe Chung-Lee-Starling expression for thermal conductivity of low pressuregases.
The same expressions are used for mixtures. The mixture expression for (p= 0) must be used. (See Chung-Lee-Starling Low-Pressure Vapor Viscosity.)
Where:
3 Transport Property Models 283
Vcij =
ij= 0 (in almost all cases)
Tcij =
ij= 0 (in almost all cases)
ij=
Mij =
ij=
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TCCLS Tci TC x 5.0 2000.0 TEMPERATURE
VCCLS Vci VC x 0.001 3.5 MOLE-VOLUME
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
OMGCLS iOMEGA x -0.5 2.0 —
CLSK i0.0 x 0.0 0.5 —
CLSKV ij0.0 x -0.5 -0.5 —
CLSKT ij0.0 x -0.5 0.5 —
The model-specific parameters also affect the results of the Chung-Lee-Starling Viscosity models.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 505, 523.
IAPS Thermal Conductivity for WaterThe IAPS thermal conductivity models were developed by the InternationalAssociation for Properties of Steam. These models can calculate vapor andliquid thermal conductivity for water and steam. They are used in option setsSTEAMNBS and STEAM-TA.
The general form of the equation for the IAPS thermal conductivity models is:
w=fcn(T, p)
Where:
284 3 Transport Property Models
fcn = Correlation developed by IAPS
The models are only applicable to water. No parameters are required.
Li Mixing RuleLiquid mixture thermal conductivity is calculated using Li equation (Reidet.al., 1987):
Where:
The pure component liquid molar volume Vi*,l is calculated from the Rackett
model.
The pure component liquid thermal conductivity i*,l is calculated by the
General Pure Component Liquid Thermal Conductivity model.
Reference: R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gasesand Liquids, 4th ed., (New York: McGraw-Hill, 1987), p. 550.
Riedel Electrolyte CorrectionThe Riedel model can calculate the correction to the liquid mixture thermalconductivity of a solvent mixture, due to the presence of electrolytes:
Where:
lsolv
= Thermal conductivity of the liquid solvent mixture,calculated by the General Pure Component LiquidThermal Conductivity model using the Vredeveldmixing rule
xcaa = Mole fraction of the apparent electrolyte ca
ac, aa = Riedel ionic coefficient
Vml = Apparent molar volume computed by the Clarke
density model
Apparent electrolyte mole fractions are computed from the true ion mole-fractions and ionic charge number. They can also be computed if you use theapparent component approach. A more detailed discussion of this method isfound in Electrolyte Calculation.
3 Transport Property Models 285
You must provide parameters for the Sato-Riedel model. This model is usedfor the calculation of the thermal conductivity of solvent mixtures.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
CHARGE z 0.0 — — —
IONRDL a 0.0 — — †
† THERMAL CONDUCTIVITY, MOLE-VOLUME
The behavior of this model can be changed using option codes (these codesapply to the Vredeveld mixing rule).OptionCode
OptionValue
Description
1 0 Do not check ratio of KL max / KL min
1 Check ratio. If KL max / KL min > 2, set exponent to 1,overriding option code 2.
2 0 Exponent is -2
1 Exponent is 0.4
2 Exponent is 1. This uses a weighted average of liquid thermalconductivities.
General Pure Component Liquid ThermalConductivityThe Aspen Physical Property System has several submodels for calculatingpure component liquid thermal conductivity. It uses parameter TRNSWT/3 todetermine which submodel is used. See Pure Component Temperature-Dependent Properties for details.If TRNSWT/3 is This equation is used And this parameter is used
0 Sato-Riedel —
100 DIPPR KLDIP
301 PPDS KLPDS
401 IK-CAPE KLPO
503 NIST ThermoMLpolynomial
KLTMLPO
510 NIST PPDS8 equation KLPPDS8
Sato-Riedel
The Sato-Riedel equation is (Reid et al., 1987):
Where:
Tbri = Tbi / Tci
Tri = T / Tci
286 3 Transport Property Models
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
TC Tci — — 5.0 2000.0 TEMPERATURE
TB Tbi — — 4.0 2000.0 TEMPERATURE
PPDS
The equation is:
Linear extrapolation of *,l versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLPDS/1 C1i — — — — THERMAL-CONDUCTIVITY
KLPDS/2 C2i 0 — — — —
KLPDS/3 C3i 0 — — — —
KLPDS/4 C4i 0 — — — —
KLPDS/5 C5i 0 — — — TEMPERATURE
KLPDS/6 C6i 1000 — — — TEMPERATURE
NIST PPDS8 Equation
The equation is
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLPPDS8/1 C1i — — — — THERMAL-CONDUCTIVITY
KLPPDS8/2, ..., 7 C2i , ..., C7i 0 — — — —
KLPPDS8/8 TCi — — — — TEMPERATURE
KLPPDS8/9 nTerms 7 — — — —
KLPPDS8/10 Tlower 0 — — — TEMPERATURE
KLPPDS8/11 Tupper 1000 — — — TEMPERATURE
DIPPR Liquid Thermal Conductivity
The DIPPR equation is:
3 Transport Property Models 287
Linear extrapolation of *,l versus T occurs outside of bounds.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
The DIPPR equation is used by PCES when estimating liquid thermalconductivity.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLDIP/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KLDIP/2, ... , 5 C2i , ..., C5i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KLDIP/6 C6i 0 x — — TEMPERATURE
KLDIP/7 C7i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
The equation is:
Linear extrapolation of *,l versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLTMLPO/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KLTMLPO/2, ... ,4
C2i , ..., C4i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KLTMLPO/5 nTerms 4 x — — —
KLTMLPO/6 Tlower 0 x — — TEMPERATURE
KLTMLPO/7 Tupper 1000 x — — TEMPERATURE
IK-CAPE
The IK-CAPE equation is:
Linear extrapolation of *,l versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLPO/1 C1i — x — — THERMAL-CONDUCTIVITY
288 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KLPO/2, ... , 10 C2i , ..., C10i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KLPO/11 C11i 0 x — — TEMPERATURE
KLPO/12 C12i 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 550.
Solid Thermal Conductivity PolynomialThermal conductivity for solid pure components is calculated using the solidthermal conductivity polynomial. For mixtures, the mole-fraction weightedaverage is used.
For pure solids, thermal conductivity is calculated by:
For mixtures:
Linear extrapolation of i*,s versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KSPOLY/1 a — — — — THERMALCONDUCTIVITY
KSPOLY/2, 3, 4, 5 b, c, d, e 0 — — — THERMALCONDUCTIVITY,TEMPERATURE
KSPOLY/6 0 x — — TEMPERATURE
KSPOLY/7 1000 x — — TEMPERATURE
General Pure Component Vapor ThermalConductivityThe Aspen Physical Property System has several submodels for calculatingpure component low pressure vapor thermal conductivity. It uses parameterTRNSWT/4 to determine which submodel is used. See Pure ComponentTemperature-Dependent Properties for details.
3 Transport Property Models 289
If TRNSWT/4 is This equation is used And this parameter isused
0 Stiel-Thodos —
102 DIPPR KVDIP
301 PPDS KVPDS
401 IK-CAPE KVPO
503 NIST ThermoMLpolynomial
KVTMLPO
Stiel-Thodos
The Stiel-Thodos equation is:
Where:
i*,v(p = 0) can be obtained from the General Pure Component Vapor
Viscosity model.
Cpi*,ig is obtained from the General Pure Component Ideal Gas Heat Capacity
model.
R is the universal gas constant.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
DIPPR Vapor Thermal Conductivity
The DIPPR equation for vapor thermal conductivity is:
Linear extrapolation of i*,v versus T occurs outside of bounds.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
The DIPPR equation is used in PCES when estimating vapor thermalconductivity.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KVDIP/1 C1i — x — — THERMALCONDUCTIVITY
KVDIP/2 C2i 0 x — — —
KVDIP/3, 4 C3i, C4i 0 x — — TEMPERATURE †
KVDIP/5 — 0 x — — —
KVDIP/6 C6i 0 x — — TEMPERATURE
KVDIP/7 C7i 1000 x — — TEMPERATURE
† If any of C2i through C4i are non-zero, absolute temperature units areassumed for C1i through C4i. Otherwise, all coefficients are interpreted in user
290 3 Transport Property Models
input temperature units. The temperature limits are always interpreted inuser input units.
PPDS
The equation is:
Linear extrapolation of i*,v versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KVPDS/1 C1i — — — — THERMAL-CONDUCTIVITY
KVPDS/2 C2i 0 — — — THERMAL-CONDUCTIVITY
KVPDS/3 C3i 0 — — — THERMAL-CONDUCTIVITY
KVPDS/4 C4i 0 — — — THERMAL-CONDUCTIVITY
KVPDS/5 C5i 0 — — — TEMPERATURE
KVPDS/6 C6i 1000 — — — TEMPERATURE
IK-CAPE Polynomial
Linear extrapolation of i*,v versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KVPO/1 C1i — x — — THERMAL-CONDUCTIVITY
KVPO/2, ... , 10 C2i, ..., C10i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KVPO/11 C11i 0 x — — TEMPERATURE
KVPO/12 C12i 1000 x — — TEMPERATURE
NIST ThermoML Polynomial
Linear extrapolation of i*,v versus T occurs outside of bounds.
3 Transport Property Models 291
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
KVTMLPO/1 C1i — x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KVTMLPO/2, ... ,4
C2i, ..., C4i 0 x — — THERMAL-CONDUCTIVITY,TEMPERATURE
KVTMLPO/5 nTerms 4 x — — —
KVTMLPO/6 Tlower 0 x — — TEMPERATURE
KVTMLPO/7 Tupper 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquid,4th ed., (New York: McGraw-Hill, 1987), p. 494.
Stiel-Thodos Pressure Correction ModelThe pressure correction to a pure component or mixture thermal conductivityat low pressure is given by:
Where:
rm=
The parameter Vmv can be obtained from Redlich-Kwong.
v(p = 0) can be obtained from the low pressure General Pure Component
Vapor Thermal Conductivity.
This model should not be used for polar substances, hydrogen, or helium.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
TC Tci — — 5.0 2000.0 TEMPERATURE
PC — — — 105 108 PRESSURE
VC Vci — — 0.001 3.5 MOLE-VOLUME
ZC Zci — — 0.1 0.5 —
References
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquids,4th ed., (New York: McGraw-Hill, 1987), p. 521.
Vredeveld Mixing RuleLiquid mixture thermal conductivity is calculated using the Vredeveld equation(Reid et al., 1977):
292 3 Transport Property Models
Where:
wi = Liquid phase weight fraction of component i
i*,l = Pure component liquid thermal conductivity of component i
Where n is determined from two option codes on model KL2VR:If option code 1 is Then n is determined by
0 (default) Option code 2, always
1Option code 2, unless . In this case n isset to 1.
If option code 2 is Then n is
0 (default) -2
1 0.4
2 1 (This uses a weighted average of liquid thermalconductivities.)
For most systems, the ratio of maximum to minimum pure component liquidthermal conductivity is between 1 and 2, where the exponent -2 isrecommended, and is the default value used.
Pure component liquid thermal conductivity i*,l is calculated by the General
Pure Component Liquid Thermal Conductivity model.
Reference: R.C. Reid, J.M. Prausnitz, and T.K. Sherwood, The Properties ofGases and Liquids, 4th ed., (New York: McGraw-Hill, 1977), p. 533.
TRAPP Thermal Conductivity ModelThe general form for the TRAPP thermal conductivity model is:
Where:
= Mole fraction vector
Cpi*,ig = Ideal gas heat capacity calculated using the
General pure component ideal gas heat capacitymodel
fcn = Corresponding states correlation based on themodel for vapor and liquid thermal conductivitymade by the National Bureau of standards (NBS,currently NIST)
The model can be used for both pure components and mixtures. The modelshould be used for nonpolar components only.
3 Transport Property Models 293
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
TCTRAP Tci TC x 5.0 2000.0 TEMPERATURE
PCTRAP pci PC x 105 108 PRESSURE
VCTRAP Vci VC x 0.001 3.5 MOLE-VOLUME
ZCTRAP Zci ZC x 0.1 1.0 —
OMGRAP iOMEGA x -0.5 3.0 —
References
J.F. Ely and H.J. M. Hanley, "Prediction of Transport Properties. 2. ThermalConductivity of Pure Fluids and Mixtures," Ind. Eng. Chem. Fundam., Vol. 22,(1983), pp. 90–97.
Wassiljewa-Mason-Saxena Mixing RuleThe vapor mixture thermal conductivity at low pressures is calculated fromthe pure component values, using the Wassiljewa-Mason-Saxena equation:
Where:
i*,v = Calculated by the General Pure Component Vapor
Thermal Conductivity model
i*,v(p = 0) = Obtained from the General Pure Component Vapor
Viscosity model
You must supply parameters for i*,v(p = 0) and i
*,v.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), pp. 530–531.
Diffusivity ModelsThe Aspen Physical Property System has seven built-in diffusivity models. Thissection describes the diffusivity models available.
294 3 Transport Property Models
Model Type
Chapman-Enskog-Wilke-Lee (Binary) Low pressure vapor
Chapman-Enskog-Wilke-Lee (Mixture) Low pressure vapor
Dawson-Khoury-Kobayashi (Binary) Vapor
Dawson-Khoury-Kobayashi (Mixture) Vapor
Nernst-Hartley Electrolyte
Wilke-Chang (Binary) Liquid
Wilke-Chang (Mixture) Liquid
Chapman-Enskog-Wilke-Lee (Binary)
The binary diffusion coefficient at low pressures is calculated usingthe Chapman-Enskog-Wilke-Lee model:
Dijv=Dji
v
Where:
The collision integral for diffusion is:
D=
The binary size and energy parameters are defined as:
ij=
ij=
A parameter is used to determine whether to use the Stockmayer or
Lennard-Jones potential parameters for /k (energy parameter ) and (collision diameter). To calculate , the dipole moment p, and either the
Stockmayer parameters or Tb and Vb are needed.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
MW Mi — — 1.0 5000.0 —
MUP pi — — 0.0 5x10-24 DIPOLEMOMENT
TB Tbi — — 4.0 2000.0 TEMPERATURE
VB Vb — — 0.001 3.5 MOLE-VOLUME
OMEGA i— — -0.5 2.0 —
STKPAR/1 (i/k)ST fcn(Tbi, Vbi, pi) x — — TEMPERATURE
3 Transport Property Models 295
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
STKPAR/2 iST fcn(Tbi, Vbi, pi) x — — LENGTH
LJPAR/1 (i/k)LJ fcn(Tci, i) x — — TEMPERATURE
LJPAR/2 iLJ fcn(Tci, pci, i) x — — LENGTH
References
R.C. Reid, J.M. Praunitz, and B.E. Poling, The Properties of Gases and Liquids,4th ed., (New York: McGraw-Hill, 1987), p. 587.
Chapman-Enskog-Wilke-Lee (Mixture)The diffusion coefficient of a gas into a gas mixture at low pressures iscalculated using an equation of Bird, Stewart, and Lightfoot by default (optioncode 0):
If the first option code is set to 1, Blanc's law is used instead:
The binary diffusion coefficient Dijv(p = 0) at low pressures is calculated using
the Chapman-Enskog-Wilke-Lee model. (See Chapman-Enskog-Wilke-Lee(Binary).)
You must provide parameters for this model.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DVBLNC — 1 x — — —
DVBLNC is set to 1 for a diffusing component and 0 for a non-diffusingcomponent.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 597.
Dawson-Khoury-Kobayashi (Binary)The binary diffusion coefficient Dij
v at high pressures is calculated from theDawson-Khoury-Kobayashi model:
296 3 Transport Property Models
Dijv=Dji
v
Dijv(p = 0) is the low-pressure binary diffusion coefficient obtained from the
Chapman-Enskog-Wilke-Lee model.
The parameters mv and Vm
v are obtained from the Redlich-Kwong equation-
of-state model.
You must supply parameters for these two models.
Subscript i denotes a diffusing component. j denotes a solvent.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
VC Vci — x 0.001 3.5 MOLE-VOLUME
References
R.C. Reid, J.M. Prausnitz, and T.K. Sherwood. The Properties of Gases andLiquids, 3rd ed., (New York: McGraw-Hill, 1977), pp. 560-565.
Dawson-Khoury-Kobayashi (Mixture)The diffusion coefficient of a gas into a gas mixture at high pressure iscalculated using an equation of Bird, Stewart, and Lightfoot by default (optioncode 0):
If the first option code is set to 1, Blanc's law is used instead:
The binary diffusion coefficient Dijv at high pressures is calculated from the
Dawson-Khoury-Kobayashi model. (See Dawson-Khoury-Kobayashi (Binary).)At low pressures (up to 1 atm) the binary diffusion coefficient is insteadcalculated by the Chapman-Enskog-Wilke-Lee (Binary) model.
You must provide parameters for this model.
3 Transport Property Models 297
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
DVBLNC — 1 — — — —
DVBLNC is set to 1 for a diffusing component and 0 for a nondiffusingcomponent.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 597.
Nernst-HartleyThe effective diffusivity of an ion i in a liquid mixture with electrolytes can becalculated using the Nernst-Hartley model:
(1)
Where:
F = 9.65x107C/kmole (Faraday's number)
xk = Mole fraction of any molecular species k
zi = Charge number of species i
The binary diffusion coefficient of the ion with respect to a molecular speciesis set equal to the effective diffusivity of the ion in the liquid mixture:
(2)
The binary diffusion coefficient of an ion i with respect to an ion j is set to themean of the effective diffusivities of the two ions:
The diffusivity for molecular species is calculated by the Wilke-Chang(Mixture) model.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
CHARGE z 0.0 — — —
IONMOB/1 l1 — † — — AREA, MOLES
IONMOB/2 l2 0.0 — — AREA, MOLES,TEMPERATURE
†When IONMOB/1 is missing, the Nernst-Hartley model uses a nominal valueof 5.0 and issues a warning. This parameter should be specified for ions, andnot allowed to default to this value.
298 3 Transport Property Models
References
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: EllisHorwood, Ltd, 1985).
Wilke-Chang (Binary)The Wilke-Chang model calculates the liquid diffusion coefficient ofcomponent i in a mixture at finite concentrations:
Dijl = Dji
l
The equation for the Wilke-Chang model at infinite dilution is:
Where i is the diffusing solute and j the solvent, and:
j= Association factor of solvent. 2.26 for water, 1.90
for methanol, 1.50 for ethanol, 1.20 for propylalchohols and n-butanol, and 1.00 for all othersolvents.
Vbi = Liquid molar volume at Tb of solvent i
jl = Liquid viscosity of the solvent. This can be obtained
from the General Pure Component Liquid Viscositymodel. You must provide parameters for one ofthese models.
l = Liquid viscosity of the complete mixture of ncomponents
xi, xj = Apparent binary mole fractions. If the actual mole
fractions are then
ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
MW Mj — 1.0 5000.0 —
VB Vbi*,l — 0.001 3.5 MOLE-VOLUME
3 Transport Property Models 299
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 598–600.
Wilke-Chang (Mixture)The Wilke-Chang model calculates the infinite-dilution liquid diffusioncoefficient of component i in a mixture.
The equation for the Wilke-Chang model is:
With:
Where:
j= Association factor of solvent. 2.26 for water, 1.90 for
methanol, 1.50 for ethanol, 1.20 for propyl alchoholsand n-butanol, and 1.00 for all other solvents.
nl = Mixture liquid viscosity of all nondiffusingcomponents. This can be obtained from severalmodels, all of which in turn use pure componentviscosity from the General Pure Component LiquidViscosity model. You must provide parameters forone its submodels.
The parameter DLWC specifies which components diffuse. It is set to 1 for adiffusing component and 0 for a non-diffusing component.
Wilke-Chang (Mixture) has two option codes. The first option code is used inthe liquid mixture viscosity model to determine weighting of pure-componentliquid viscosities in computing the mixture viscosity: by mole (default) for 0 orby mass for 1. The second option code determines which liquid mixtureviscosity model is used: Andrade (0, default), quadratic mixing rule (1), orAspen (2).ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
MW Mj — 1.0 5000.0 —
VB Vbi*,l — 0.001 3.5 MOLE-VOLUME
DLWC — 1 — — —
References
R.C. Reid, J.M. Praunsnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th ed., (New York: McGraw-Hill, 1987), p. 618.
300 3 Transport Property Models
Surface Tension ModelsThe Aspen Physical Property System has the following built-in surface tensionmodels.This section describes the surface tension models available.Model Type
Liquid Mixture Surface Tension Liquid-vapor
API Liquid-vapor
IAPS Water-stream
General Pure Component Liquid SurfaceTension
Liquid-vapor
Onsager-Samaras Electrolyte Correction Electrolyte liquid-vapor
Modified MacLeod-Sugden Liquid-vapor
Liquid Mixture Surface Tension
The liquid mixture surface tension is calculated using a general weightedaverage expression (R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Propertiesof Gases and Liquids, 4th. ed., New York: McGraw-Hill, 1987, p. 643):
Where:
x = Mole fraction
r = Exponent (specified by the option code)
Hadden (S. T. Hadden, Hydrocarbon Process Petrol Refiner, 45(10), 1966, p.161) suggested that the exponent value r =1 should be used for mosthydrocarbon mixtures. However, Reid recommended the value of r in therange of -1 to -3. The exponent value r can be specified using the model’sOption Code (option code = 1, -1, -2, ..., -9 corresponding to the value of r).The default value of r for this model is 1.
The pure component liquid surface tension i*,l is calculated by the General
Pure Component Liquid Surface Tension model.
API Surface TensionThe liquid mixture surface tension for hydrocarbons is calculated using theAPI model. This model is recommended for petroleum and petrochemicalapplications. It is used in the CHAO-SEA, GRAYSON, LK-PLOCK, PENG-ROB,and RK-SOAVE property models. The general form of the model is:
Where:
fcn = A correlation based on API Procedure 10A32 (API Technical Data Book,Petroleum Refining, 4th edition)
3 Transport Property Models 301
The original form of this model is only designed for petroleum, and treats allcomponents as pseudocomponents (estimating surface tension from boilingpoint, critical temperature, and specific gravity). If option code 1 is set to 0(the default), it behaves this way. Set option code 1 to 1 for the model to usethe General Pure Component Liquid Surface Tension model to calculate thesurface tension of real components and the API model for pseudocomponents.The mixture surface tension is then calculated as a mole-fraction-weightedaverage of these surface tensions.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
TB Tbi — — 4.0 2000.0 TEMPERATURE
SG SG — — 0.1 2.0 —
TC Tci — — 5.0 2000 TEMPERATURE
IAPS Surface Tension for WaterThe IAPS surface tension model was developed by the InternationalAssociation for Properties of Steam. It calculates liquid surface tension forwater and steam. This model is used in option sets STEAMNBS and STEAM-TA.
The general form of the equation for the IAPS surface tension model is:
w=fcn(T, p)
Where:
fcn = Correlation developed by IAPS
The model is only applicable to water. No parameters are required.
General Pure Component Liquid SurfaceTensionThe Aspen Physical Property System has several submodels for calculatingliquid surface tension. It uses parameter TRNSWT/5 to determine whichsubmodel is used. See Pure Component Temperature-Dependent Propertiesfor details.If TRNSWT/5 is This equation is used And this parameter is
used
0 Hakim-Steinberg-Stiel —
106 DIPPR SIGDIP
301 PPDS SIGPDS
401 IK-CAPE polynomialequation
SIGPO
505 NIST TDE Watsonequation
SIGTDEW
511 NIST TDE expansion SIGISTE
512 NIST PPDS14 Equation SIGPDS14
302 3 Transport Property Models
Hakim-Steinberg-Stiel
The Hakim-Steinberg-Stiel equation is:
Where:
Qpi =
mi =
The parameter i is the Stiel polar factor.
ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
TC Tci — 5.0 2000.0 TEMPERATURE
PC pci — PRESSURE
OMEGA i— -0.5 2.0 —
CHI i0 — — —
DIPPR Liquid Surface Tension
The DIPPR equation for liquid surface tension is:
Where:
Tri = T / Tci
Linear extrapolation of i*,l versus T occurs outside of bounds.
(Other DIPPR equations may sometimes be used. See Pure ComponentTemperature-Dependent Properties for details.)
The DIPPR model is used by PCES when estimating liquid surface tension.
Note: Reduced temperature Tr is always calculated using absolutetemperature units.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
SIGDIP/1 C1i — — — SURFACE-TENSION
SIGDIP/2, ..., 5 C2i, ..., C5i 0 — — —
SIGDIP/6 C6i 0 — — TEMPERATURE
SIGDIP/7 C7i 1000 — — TEMPERATURE
PPDS
The equation is:
3 Transport Property Models 303
Linear extrapolation of i*,l versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SIGPDS/1 C1i — — — — SURFACE-TENSION
SIGPDS/2 C2i 0 — — — —
SIGPDS/3 C3i 0 — — — —
SIGPDS/4 C4i 0 — — — TEMPERATURE
SIGPDS/5 C5i 1000 — — — TEMPERATURE
NIST PPDS14 Equation
This equation is the same as the PPDS equation above, but it uses its ownparameter set which includes critical temperature.ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SIGPDS14/1 C1i — x — — N/m
SIGPDS14/2 C2i 0 x — — —
SIGPDS14/3 C3i 0 x — — —
SIGPDS14/4 Tci — x — — TEMPERATURE
SIGPDS14/5 C4i 0 x — — TEMPERATURE
SIGPDS14/6 C5i 1000 x — — TEMPERATURE
IK-CAPE Polynomial
The IK-CAPE equation is:
Linear extrapolation of i*,l versus T occurs outside of bounds.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SIGPO/1 C1i — x — — SURFACE-TENSION
SIGPO/2, ..., 10 C2i, ..., C10i 0 x — — SURFACE-TENSIONTEMPERATURE
SIGPO/11 C11i 0 x — — TEMPERATURE
SIGPO/12 C12i 1000 x — — TEMPERATURE
NIST TDE Watson Equation
This equation can be used when parameter SIGTDEW is available.
304 3 Transport Property Models
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SIGTDEW/1 C1i — x — — —
SIGTDEW/2, 3, 4 C2i, C3i, C4i 0 x — — —
SIGTDEW/5 Tc — x — — TEMPERATURE
SIGTDEW/6 nTerms 4 x — — —
SIGTDEW/7 Tlower 0 x — — TEMPERATURE
SIGTDEW/8 Tupper 1000 x — — TEMPERATURE
NIST TDE Expansion
This equation can be used when parameter SIGISTE is available.
ParameterName/Element
Symbol Default MDS LowerLimit
UpperLimit
Units
SIGISTE/1 C1i — x — — N/m
SIGISTE/2, 3, 4 C2i, C3i, C4i 0 x — — N/m
SIGISTE/5 Tci — x — — TEMPERATURE
SIGISTE/6 nTerms 4 x — — —
SIGISTE/7 Tlower 0 x — — TEMPERATURE
SIGISTE/8 Tupper 1000 x — — TEMPERATURE
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 4th. ed., (New York: McGraw-Hill, 1987), p. 638.
Onsager-SamarasThe Onsager-Samaras model calculates the correction to the liquid mixturesurface tension of a solvent mixture, due to the presence of electrolytes:
for salt concentration < 0.03M
(1)
Where:
solv= Surface tension of the solvent mixture
xcaa = Mole fraction of the apparent electrolyte ca
ca= Contribution to the surface tension correction due
to apparent electrolyte ca
3 Transport Property Models 305
solv is calculated using a general weighted average expression:
where
r =Exponent specified by the first option code
m=Number of molecular components specified the secondoption code
The pure component liquid surface tension i*,l is calculated by the General
Pure Component Liquid Surface Tension model. The exponent r andparameter m are specified by option codes to SIG2ONSG:
Optioncode 1
1, -1, -2, ..., -9 Exponent in mixing rule (default 1)
Optioncode 2
0 m includes contributions from bothsolvents and Henry components (default).
1 m includes only contributions fromsolvents.
For each apparent electrolyte ca, the contribution to the surface tensioncorrection is calculated as:
(2)
Where:
solv= Dielectric constant of the solvent mixture
ccaa =
Vml = Liquid molar volume calculated by the Clarke
model
Apparent electrolyte mole fractions are computed from the true ion mole-fractions and ionic charge number. They are also computed if you use theapparent component approach. See Apparent Component and TrueComponent Approaches in the Electrolyte Calculation chapter for a moredetailed discussion of this method.
Above salt concentration 0.03 M, the slope of surface tension vs. molefraction is taken to be constant at the value from 0.03 M.
You must provide parameters for the General Pure Component Liquid SurfaceTension model, used for the calculation of the surface tension of the solventmixture.ParameterName/Element
Symbol Default LowerLimit
UpperLimit
Units
CHARGE z 0.0 — — —
306 3 Transport Property Models
References
A. L. Horvath, Handbook of Aqueous Electrolyte Solutions, (Chichester: Ellis,Ltd. 1985).
Modified MacLeod-SugdenThe modified MacLeod-Sugden equation for mixture liquid surface tension canbe derived from the standard MacLeod-Sugden equation by assuming that thedensity of the vapor phase is zero. The modified MacLeod-Sugden equation is:
Where:
i*,l = Surface tension for pure component i, calculated using
the General Pure Component Liquid Surface Tensionmodel.
Vi*,l = Liquid molar volume for pure component i, calculated
using the General Pure Component Liquid Molar Volumemodel.
V l = Mixture liquid molar volume, calculated using theRackett model.
References
R.C. Reid, J.M. Prausnitz, and B.E. Poling, The Properties of Gases andLiquids, 3rd. ed., (New York: McGraw-Hill, 1977).
4 Nonconventional Solid Property Models 307
4 Nonconventional SolidProperty Models
This section describes the nonconventional solid density and enthalpy modelsavailable in the Aspen Physical Property System. The following table lists theavailable models and their model names. Nonconventional components aresolid components that cannot be characterized by a molecular formula. Thesecomponents are treated as pure components, though they are complexmixtures.
Nonconventional Solid Property ModelsGeneral Enthalpy andDensity Models
Model name Phase(s)
General density polynomial DNSTYGEN S
General heat capacitypolynomial
ENTHGEN S
Enthalpy and DensityModels for Coal and Char
Model name Phase(s)
General coal enthalpy model HCOALGEN S
IGT coal density model DCOALIGT S
IGT char density model DCHARIGT S
General Enthalpy and DensityModelsThe Aspen Physical Property System has two built-in general enthalpy anddensity models. This section describes the general enthalpy and densitymodels available:
General Density PolynomialDNSTYGEN is a general model that gives the density of any nonconventionalsolid component. It uses a simple mass fraction weighted average for thereciprocal temperature-dependent specific densities of its individualconstituents. There may be up to twenty constituents with mass percentages.
308 4 Nonconventional Solid Property Models
You must define these constituents, using the general component attributeGENANAL. The equations are:
Where:
wij = Mass fraction of the jth constituent in component i
ijs = Density of the jth consituent in component i
ParameterName/Element
Symbol MDS Default LowerLimit
UpperLimit
Units
DENGEN/1, 5, 9, …, 77 ai,j1 x — — — MASS-ENTHALPYand TEMPERATURE
DENGEN/2, 6, 10, …,78
ai,j2 x 0 — — MASS-ENTHALPYand TEMPERATURE
DENGEN/3, 7, 11, …,79
ai,j3 x 0 — — MASS-ENTHALPYand TEMPERATURE
DENGEN/4, 8, 12, …,80
ai,j4 x 0 — — MASS-ENTHALPYand TEMPERATURE
Use the elements of GENANAL to input the mass percentages of theconstituents. The structure of DENGEN is: Elements 1 to 4 are the fourcoefficients for the first constituent, elements 5 to 8 are the coefficients forthe second constitutent, and so on, for up to 20 constituents.
General Heat Capacity PolynomialENTHGEN is a general model that gives the specific enthalpy of anynonconventional component as a simple mass-fraction-weighted-average forthe enthalpies of its individual constituents. You may define up to twentyconstituents with mass percentages, using the general component attributeGENANAL. The specific enthalpy of each constituent at any temperature iscalculated by combining specific enthalpy of formation of the solid with asensible heat change. (See Nonconventional Component Enthalpy Calculationin Physical Property Methods.)
The equations are:
Where:
4 Nonconventional Solid Property Models 309
wij = Mass fraction of the jth constituent incomponent i
his = Specific enthalpy of solid component i
fhjs = Specific enthalpy of formation of constituent j
Cps = Heat capacity of the jth constituent in
component i
ParameterName/Element
Symbol MDS Default LowerLimit
UpperLimit
Units
DHFGEN/J fhjs x 0 — — MASS-ENTHALPY
HCGEN/1, 5, 9, …, 77 ai,j1 x — — — MASS-ENTHALPYandTEMPERATURE
HCGEN/2, 6, 10, …, 78 ai,j2 x 0 — — MASS-ENTHALPYandTEMPERATURE
HCGEN/3, 7, 11, …, 79 ai,j3 x 0 — — MASS-ENTHALPYandTEMPERATURE
HCGEN/4, 8, 12, …, 80 ai,j4 x 0 — — MASS-ENTHALPYandTEMPERATURE
The elements of GENANAL are used to input the mass percentages of theconstituents. The structure for HCGEN is: Elements 1 to 4 are the fourcoefficients for the first constituent, elements 5 to 8 are the coefficients forthe second constitutent, and so on, for up to 20 constituents.
Enthalpy and Density Modelsfor Coal and CharCoal is modeled in the Aspen Physical Property System as a nonconventionalsolid. Coal models are empirical correlations, which require solid materialcharacterization information. Component attributes are derived fromconstituent analyses. Definitions of coal component attributes are given in theAspen Plus User Guide, Chapter 6.
Enthalpy and density are the only properties calculated for nonconventionalsolids. This section describes the special models available in the AspenPhysical Property System for the enthalpy and density of coal and char. Thecomponent attributes required by each model are included. The coal modelsare:
General coal enthalpy
IGT Coal Density
IGT Char Density
310 4 Nonconventional Solid Property Models
User models for density and enthalpy. See User Models forNonconventional Properties in Chapter 6 of Aspen Plus User Models, fordetails on writing the subroutines for these user models.
Notation
Most correlations for the calculation of coal properties require proximate,ultimate, and other analyses. These are converted to a dry, mineral-matter-free basis. Only the organic portion of the coal is considered.
Moisture corrections are made for all analyses except hydrogen, according tothe formula:
Where:
w = The value determined for weight fraction
wd = The value on a dry basis
= The moisture weight fraction
For hydrogen, the formula includes a correction for free-moisture hydrogen:
The mineral matter content is calculated using the modified Parr formula:
The ash term corrects for water lost by decomposition of clays in the ashdetermination. The average water constitution of clays is assumed to be 11.2percent. The sulfur term allows for loss in weight of pyritic sulfur when pyriteis burned to ferric oxide. The original Parr formula assumed that all sulfur ispyritic sulfur. This formula included sulfatic and organic sulfur in the mineral-matter calculation. When information regarding the forms of sulfur isavailable, use the modified Parr formula to give a better approximation of thepercent of inorganic material present. Because chlorine is usually small forUnited States coals, you can omit chlorine from the calculation.
Correct analyses from a dry basis to a dry, mineral-matter-free basis, usingthe formula:
Where:
wd = Correction factor for other losses, such as the lossof carbon in carbonates and the loss of hydrogenpresent in the water constitution of clays
4 Nonconventional Solid Property Models 311
The oxygen and organic sulfur contents are usually calculated by differenceas:
Where:
Cp = Heat capacity / (J/kgK)
cp = Heat capacity / (cal/gC)
h = Specific enthalpy
ch = Specific heat of combustion
fh = Specific heat of formation
Ro = Mean-maximum relectance in oil
T = Temperature/K
t = Temperature/C
w = Weight fraction
= Specific density
Subscripts:
A = Ash
C = Carbon
Cl = Chlorine
FC = Fixed carbon
H = Hydrogen
H2O = Moisture
MM = Mineral matter
N = Nitrogen
O = Oxygen
So = Organic sulfur
Sp = Pyritic sulfur
St = Total sulfur
S = Other sulfur
VM = Volatile matter
Superscripts:
d = Dry basis
312 4 Nonconventional Solid Property Models
m = Mineral-matter-free basis
General Coal Enthalpy ModelThe general coal model for computing enthalpy in the Aspen Physical PropertySystem is HCOALGEN. This model includes a number of different correlationsfor the following:
Heat of combustion
Heat of formation
Heat capacity
You can select one of these correlations using an option code in the Methods| NC-Props form. (See the Aspen Plus User Guide, Chapter 6). Use optioncodes to specify a calculation method for properties. Each element in theoption code vector is used in the calculation of a different property.
The table labeled HCOALGEN Option Codes (below) lists model option codesfor HCOALGEN. The table is followed by a detailed description of thecalculations used for each correlation.
The correlations are described in the following section. The componentattributes are defined in Aspen Plus User Guide, Chapter 6.
Note: The correlations used here may generate slightly different enthalpy forwater are compared with steam tables or other methods typically used whenwater is in the MIXED substream. Small temperature differences may resultwhen water is extracted from coal.
Heat of Combustion Correlations
The heat of combustion of coal in the HCOALGEN model is a gross calorificvalue. It is expressed in Btu/lb of coal on a dry mineral-matter-free basis.ASTM Standard D5865-07a defines standard conditions for measuring grosscalorific value. (Earlier ASTM Standard D-2015 used the same conditions.)Initial oxygen pressure is 20 to 40 atmospheres. Products are in the form ofash; liquid water; and gaseous CO2, SO2, and NO2.
You can calculate net calorific value from gross calorific value by making adeduction for the latent heat of vaporization of water.
Heat of combustion values are converted back to a dry, mineral-matter-containing basis with a correction for the heat of combustion of pyrite. Theformula is:
The heat of combustion correlations were evaluated by the Institute of GasTechnology (IGT). They used data for 121 samples of coal from the PennState Data Base (IGT, 1976) and 457 samples from a USGS report (Swanson,et al., 1976). These samples included a wide range of United States coalfields. The constant terms in the HCOALGEN correlations are bias correctionsobtained from the IGT study.
4 Nonconventional Solid Property Models 313
Boie Correlation:
Parameter Name/Element Symbol Default
BOIEC/1 a1i 151.2
BOIEC/2 a2i 499.77
BOIEC/3 a3i 45.0
BOIEC/4 a4i -47.7
BOIEC/5 a5i 27.0
BOIEC/6 a6i -189.0
Dulong Correlation:
Parameter Name/Element Symbol Default
DLNGC/1 a1i 145.44
DLNGC/2 a2i 620.28
DLNGC/3 a3i 40.5
DLNGC/4 a4i -77.54
DLNGC/5 a5i -16.0
Grummel and Davis Correlation:
Parameter Name/Element Symbol Default
GMLDC/1 a1i 0.3333
GMLDC/2 a2i 654.3
GMLDC/3 a3i 0.125
GMLDC/4 a4i 0.125
GMLDC/5 a5i 424.62
GMLDC/6 a6i -2.0
Mott and Spooner Correlation:
Parameter Name/Element Symbol Default
MTSPC/1 a1i 144.54
MTSPC/2 a2i 610.2
MTSPC/3 a3i 40.3
MTSPC/4 a4i 62.45
MTSPC/5 a5i 30.96
MTSPC/6 a6i 65.88
314 4 Nonconventional Solid Property Models
Parameter Name/Element Symbol Default
MTSPC/7 a7i -47.0
IGT Correlation:
Parameter Name/Element Symbol Default
CIGTC/1 a1i 178.11
CIGTC/2 a2i 620.31
CIGTC/3 a3i 80.93
CIGTC/4 a4i 44.95
CIGTC/5 a5i -5153.0
Revised IGT Correlation (Perry's, 7th ed., equation 27-7):
Parameter Name/Element Symbol Default
CIGT2/1 a1i 146.58
CIGT2/2 a2i 568.78
CIGT2/3 a3i 29.4
CIGT2/4 a4i -6.58
CIGT2/5 a5i -51.53
User Input Value of Heat CombustionParameter Name/Element Symbol Default
HCOMB chid 0
Standard Heat of Formation Correlations
There are two standard heat of formation correlations for the HCOALGENmodel:
Heat of combustion-based
Direct
Heat of Combustion-Based Correlation: This is based on the assumption thatcombustion results in complete oxidation of all elements except sulfatic sulfurand ash, which are considered inert. The numerical coefficients arecombinations of stoichiometric coefficients and heat of formation for CO2,H2O, HCl, and NO2 at 298.15K:
For example, the complete oxidation of hydrogen is based on the reaction
, since the stable phase of water at 298.15 K isliquid, the heat of vaporization at 298.15 K is needed in the conversion. The
4 Nonconventional Solid Property Models 315
numerical coefficient of is calculated by:
The complete oxidation of carbon is based on the reaction
, and the numerical coefficient of is calculated by:
The complete oxidation of sulfur (pyritic and organic sulfur) is based on the
reaction , and the numerical coefficient of is
calculated by:
The complete oxidation of nitrogen is based on the reaction
, and the numerical coefficient of is calculated by:
The complete oxidation of chlorine is based on the reaction
, and the numerical coefficient of
is calculated by:
Direct Correlation: The heat of formation of coal is normally small, relative to
its heat of combustion. An error of 1% in the heat of combustion produces about
a 50% error when it is used to calculate the heat of formation. For this reason,the following direct correlation was developed, using data from the Penn StateData Base. It has a standard deviation of 112.5 Btu/lb, which is close to thelimit, due to measurement in the heat of combustion:
Where Ro,i is reflectance, specified as element 1 of component attribute COALMISC, and: Parameter Name/Element Symbol Default
HFC/1 a1i 1810.123
316 4 Nonconventional Solid Property Models
Parameter Name/Element Symbol Default
HFC/2 a2i -502.222
HFC/3 a3i 329.1087
HFC/4 a4i 121.766
HFC/5 a5i -542.393
HFC/6 a6i 1601.573
HFC/7 a7i 424.25
HFC/8 a8i -525.199
HFC/9 a9i -11.4805
HFC/10 a10i 31.585
HFC/11 a11i 13.5256
HFC/12 a12i 11.5
HFC/13 a13i -685.846
HFC/14 a14i -22.494
HFC/15 a15i -64836.19
Heat Capacity Kirov Correlations
The Kirov correlation (1965) considered coal to be a mixture of moisture, ash,fixed carbon, and primary and secondary volatile matter. Secondary volatilematter is any volatile matter up to 10% on a dry, ash-free basis; theremaining volatile matter is primary. The correlation developed by Kirovtreats the heat capacity as a weighted sum of the heat capacities of theconstituents:
Where:
i = Component index
j = Constituent index j = 1, 2 , ... , ncn
Where the values of j represent:
1 Moisture
2 Fixed carbon
3 Primary volatile matter
4 Secondary volatile matter
5 Ash
wj = Mass fraction of jth constituent on dry basis
This correlation calculates heat capacity in cal/gram-C using temperature inC. The parameters must be specified in appropriate units for this conversion.Parameter Name/Element Symbol Default
CP1C/1 ai,11 1.0
4 Nonconventional Solid Property Models 317
Parameter Name/Element Symbol Default
CP1C/2 ai,12 0
CP1C/3 ai,13 0
CP1C/4 ai,14 0
CP1C/5 ai,21 0.165
CP1C/6 ai,22
CP1C/7 ai,23
CP1C/8 ai,24 0
CP1C/9 ai,31 0.395
CP1C/10 ai,32
CP1C/11 ai,33 0
CP1C/12 ai,34 0
CP1C/13 ai,41 0.71
CP1C/14 ai,42
CP1C/15 ai,43 0
CP1C/16 ai,44 0
CP1C/17 ai,51 0.18
CP1C/18 ai,52
CP1C/19 ai,53 0
CP1C/20 ai,54 0
Cubic Temperature Equation
The cubic temperature equation is:
Parameter Name/Element Symbol Default
CP2C/1 a1i 0.438
CP2C/2 a2i
CP2C/3 a3i
CP2C/4 a4i
The default values of the parameters were developed by Gomez, Gayle, andTaylor (1965). They used selected data from three lignites and asubbituminous B coal, over a temperature range from 32.7 to 176.8C. Thiscorrelation calculates heat capacity in cal/gram-C using temperature in C. Theparameters must be specified in appropriate units for this conversion.
HCOALGEN Option CodesOption CodeNumber
Option CodeValue†
CalculationMethod
ParameterNames
ComponentAttributes
1 Heat of Combustion
1 Boie correlation BOIEC ULTANALSULFANALPROXANAL
318 4 Nonconventional Solid Property Models
Option CodeNumber
Option CodeValue†
CalculationMethod
ParameterNames
ComponentAttributes
1 Heat of Combustion
2 Dulongcorrelation
DLNGC ULTANALSULFANALPROXANAL
3 Grummel andDavis correlation
GMLDC ULTANALSULFANALPROXANAL
4 Mott and Spoonercorrelation
MTSPC ULTANALSULFANALPROXANAL
5 IGT correlation CIGTC ULTANALPROXANAL
6 User input value HCOMB ULTANALPROXANAL
7 Revised IGTcorrelation
CIGT2 ULTANALPROXANAL
2 Standard Heat of Formation
1 Heat-of-combustion-based correlation
— ULTANALSULFANAL
2 Direct correlation HFC ULTANALSULFANALPROXANAL
COALMISC3 Heat Capacity
1 Kirov correlation CP1C PROXANAL
2 Cubictemperatureequation
CP2C —
4 Enthalpy Basis
1 Elements in theirstandard statesat 298.15K and 1atm
——
——
2 Component at298.15 K
— —
† Default = 1 for each option code
Older Enthalpy Models
Three other versions of the correlation also exist.
HCJ1BOIE is similar to HCOALGEN with the first, second, and fourth optioncodes set to 1. That is, it always uses the Boie correlation for heat ofcombustion, the heat-of-combustion-based heat of formation correlation, andelements as enthalpy basis. The option code of HCJ1BOIE is equivalent to thethird option code of HCOALGEN, selecting the heat capacity equation.
HCOAL-R8 and HBOIE-R8 are old versions of HCOALGEN and HCJ1BOIE,respectively. They do not perform the dry/wet basis conversions correctly.They are preserved for upward compatibility only and are not recommendedfor use in any new simulations.
4 Nonconventional Solid Property Models 319
References
Gomez, M., J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specific Heat ofCoals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.
IGT (Institute of Gas Technology), Coal Conversion Systems Technical DataBook, Section PMa. 44.1, 1976.
Kirov, N.Y., "Specific Heats and Total Heat Contents of Coals and RelatedMaterials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),pp. 29, 33.
Swanson, V.E. et al., Collection, Chemical Analysis and Evaluation of CoalSamples in 1975, U.S. Geological Survey, Open-File Report (1976), pp. 76–468.
R. H. Perry and D. W. Green, eds., Perry's Chemical Engineers' Handbook, 7thed., McGraw-Hill (1997), p. 27-5.
IGT Coal Density ModelThe DCOALIGT model gives the true (skeletal or solid-phase) density of coalon a dry basis. It uses ultimate and sulfur analyses. The model is based onequations from IGT (1976):
The equation for idm is good for a wide range of hydrogen contents, including
anthracities and high temperature cokes. The standard deviation of thiscorrelation for a set of 190 points collected by IGT from the literature was12x10-6 m3/kg. The points are essentially uniform over the whole range. Thisis equivalent to a standard deviation of about 1.6% for a coal having ahydrogen content of 5%. It increases to about 2.2% for a coke or anthracitehaving a hydrogen content of 1%.Parameter Name/Element Symbol Default
DENIGT/1 a1i 0.4397
DENIGT/2 a2i 0.1223
DENIGT/3 a3i -0.01715
DENIGT/4 a4i 0.001077
Reference
IGT (Institute of Gas Technology), Coal Conversion Systems Technical DataBook, Section PMa. 44.1, 1976.
320 4 Nonconventional Solid Property Models
IGT Char Density ModelThe DGHARIGT model gives the true (skeletal or solid-phase) density of charor coke on a dry basis. It uses ultimate and sulfur analyses. This model isbased on equations from IGT (1976):
Parameter Name/Element Symbol Default
DENIGT/1 a1i 0.4397
DENIGT/2 a2i 0.1223
DENIGT/3 a3i -0.01715
DENIGT/4 a4i 0.001077
The densities of graphitic high-temperature carbons (including cokes) rangefrom 2.2x103 to 2.26x103 kg/m3. Densities of nongraphitic high-temperaturecarbons (derived from chars) range from 2.0x103 to 2.2x103 kg/m3. Most ofthe data used in developing this correlation were for carbonized coking coals.Although data on a few chars (carbonized non-coking coals) were included,none has a hydrogen content less than 2%. The correlation is probably notaccurate for high temperature chars.
References
I.M. Chang, B.S. Thesis, Massachusetts Institute of Technology, 1979.
M. Gomez, J.B. Gayle, and A.R. Taylor, Jr., Heat Content and Specific Heat ofCoals and Related Products, U.S. Bureau of Mines, R.I. 6607, 1965.
IGT (Institute of Gas Technology), Coal Conversion Systems Technical DataBook, Section PMa. 44.1, 1976.
N.Y. Kirov, "Specific Heats and Total Heat Contents of Coals and RelatedMaterials are Elevated Temperatures," BCURA Monthly Bulletin, (1965),pp. 29, 33.
V.E. Swanson et al., Collection, Chemical Analysis and Evaluation of CoalSamples in 1975, U.S. Geological Survey, Open-File Report (1976), pp. 76–468.
5 Property Model Option Codes 321
5 Property Model OptionCodes
The following tables list the model option codes available:
Option Codes for Transport Property Models
Option Codes for Activity Coefficient Models
Option Codes for Equation of State Models
Option Codes for K-value Models
Option Codes for Enthalpy Models
Option Codes for Gibbs Energy Models
Option Codes for Molar Volume Models
Option Codes for TransportProperty ModelsModel Name Option Code Value Descriptions
SIG2HSS 1 1 Exponent in mixing rule (default)
-1,-2,..., -9
Exponent in mixing rule
SIG2ONSG 1 1 Exponent in mixing rule (default)
-1,-2,..., -9
Exponent in mixing rule
2 0 Includes contributions from bothsolvents and Henry components(default).
1 Includes only contributions fromsolvents.
SIG2API 1 0 Use original API model for allcomponents
1 Use API model forpseudocomponents, General PureComponent Liquid Surface Tensionfor real components, and take amole-fraction-weighted average ofthe results.
322 5 Property Model Option Codes
MUL2API, MULAPI92 1 0 Release 9 method. First, the API, SGof the mixture is calculated, then theAPI correlation is used (default)
1 Pre-release 9 method. Liquidviscosity is calculated for eachpseudocomponent using the APImethod. Then mixture viscosity iscalculated by mixing rules.
MUL2ANDR,DL0WCA, DL1WCA,DL0NST, DL1NST
1 0 Mixture viscosity weighted by molefraction (default)
1 Mixture viscosity weighted by massfraction
DL1WCA andDL1NST only
2 0 Mixture viscosity from Andrade liquidmixture viscosity model (default)
1 Mixture viscosity from Viscosityquadratic mixing rule
2 Mixture viscosity from Aspen liquidmixture viscosity model
MUASPEN 1 0 Mixture viscosity weighted by molefraction (default)
1 Mixture viscosity weighted by massfraction
MUL2JONS 1 0 Mixture viscosity weighted by molefraction (default)
1 Mixture viscosity weighted by massfraction
2 0 Use Breslau and Miller equationinstead of Jones and Dole equationwhen electrolyte concentrationexceeds 0.1 M.
1 Always use Jones and Dole equationwhen the parameters are available.
3 0 Solvent liquid mixture viscosity fromAndrade liquid mixture viscositymodel (default)
1 Solvent liquid mixture viscosity fromquadratic mixing rule
2 Solvent liquid mixture viscosity fromAspen liquid mixture viscosity model
MUL2CLS,MUL2CLS2
1 0 Original correlation
1 Modified UOP correlation
MUL2QUAD 1 0 Use mole basis composition (default)
1 Use mass basis composition
KL2VR, KL2RDL 1 0 Do not check ratio of KL max / KLmin
1 Check ratio. If KL max / KL min > 2,set exponent to 1, overriding optioncode 2.
5 Property Model Option Codes 323
2 0 Exponent is -2
1 Exponent is 0.4
2 Exponent is 1. This uses a weightedaverage of liquid thermalconductivities.
KL0GLY, KL2GLY,KL0HPR, KL2HPR,KL0HSRK, KL2HSRK
1 0 Use API 12A3.2-1 method for thermalconductivity for most components(default)
1 Use API 12A1.2-1 method for thermalconductivity for all components
Option Codes for ActivityCoefficient ModelsModel Name Option
CodeValue Descriptions
GMXSH 1 0 No volume term (default)
1 Includes volume term
WHENRY (Options used in calculating PHILMX)
1 1 Calculate WB with equal weighting (solutes)
2 Size - VC1/3
3 Area - VC2/3 (default)
4 Volume - VC
2 0 Calculate A for solvents
1 Set A = 1 (ln A = 0) for solvents
Electrolyte NRTL Activity Coefficient Model (GMELC and GMENRHG)
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for GMELC)
3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGMENRHG)
2 Not used
3 Solvent/solvent binary parameter values obtainedfrom
0 Scalar GMELCA, GMELCB and GMELCM (defaultfor GMELC)
1 Vector NRTL(8) (default for GMENRHG)
GMPT1, GMPT3 (Pitzer)
1 Defaults for pair mixing rule
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
324 5 Property Model Option Codes
Model Name OptionCode
Value Descriptions
Symmetric and Unsymmetric Electrolyte NRTL Activity Coefficient Model (GMENRTLS andGMENRTLQ)
1 PDH long-range term
0 Long-range term calculated (default)
1 Long-range term ignored
2 Water dielectric constant calculation
0 Calculated from Helgeson and Kirkham correlation(1974) (default)
1 Calculated from parameter CPDIEC (as inElectrolyte NRTL Activity Coefficient Model)
3 Water density calculation
0 Calculated from steam table (default)
1 Calculated from DIPPR correlation model
COSMOSAC
1 Model choice
1 COSMO-SAC model by Lin and Sandler (2002)(Default)
2 COSMO-RS model by Klamt and Eckert (2000)
3 Lin and Sandler model with modified exchangeenergy (Lin et al., 2002)
Additional option codes for COSMOSAC are for features under development, but currentlyinactive.
Hansen
1 0 Hansen volume input by user (default)
1 Hansen volume calculated by Aspen Plus
NRTLSAC (patent pending) for Segments/Oligomers, ENRTLSAC (patent pending)
1 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
NRTL-SAC (GMNRTLS)
1 0 Reference state for ions is unsymmetric: infinitedilution in aqueous solution (default)
2 Reference state for ions is symmetric: pure fusedsalts
2 0 Flory-Huggins term included (default)
1 Flory-Huggins term removed
3 0 Long-range interaction term included (default)
1 Long-range interaction term removed
4 Water dielectric constant calculation
0 Calculated from Helgeson and Kirkham correlation(1974) (default)
1 Calculated from parameter CPDIEC (as inElectrolyte NRTL Activity Coefficient Model)
5 Water density calculation
0 Calculated from steam table (default)
1 Calculated from DIPPR correlation model
5 Property Model Option Codes 325
Option Codes for Equation ofState ModelsModel Name Option
CodeValue Descriptions
ESBWRS, ESBWRS0 1 0 Do not use steam tables
1 Calculate properties (H, S, G, V) of water fromsteam table (default; see Note)
2 0 Original RT-Opt root search method (default)
1 VPROOT/LQROOT Aspen Plus root searchmethod. Use this if the equation-oriented AspenPlus solution fails to converge and some streamswith missing phases show the same propertiesfor the missing phase as for another phase.
ESHOC, ESHOC0,PHV0HOC
1 0 Hayden-O'Connell model. Use chemical theoryonly if one component has HOCETA=4.5 (default)
1 Always use the chemical theory regardless ofHOCETA values
2 Never use the chemical theory regardless ofHOCETA values
2 0 Check high-pressure limit. If exceeded, calculatevolume at cut-off pressure.
1 Ignore high-pressure limit. Calculate volumemodel T and P.
ESPR, ESPR0,ESPRSTD,ESPRSTD0
1 0 ASPEN Boston/Mathias alpha function when Tr
>1, original literature alpha function otherwise.(default for ESPR)
1 Original literature alpha function (default forESPRSTD)
2 Extended Gibbons-Laughton alpha function
3 Twu Generalized alpha function
4 Twu alpha function
5 HYSYS alpha function
6 Mathias-Copeman alpha function
7 Schwartzentruber-Renon-Watanasiri alphafunction
2 0 Standard Peng-Robinson mixing rules (default)
1 Asymmetric Kij mixing rule from Dow
3 0 Do not use steam tables (default)
1 Calculate water properties (H, S, G, V) fromsteam table (see Note)
4 0 Do not use Peneloux liquid volume correction(default)
1 Apply Peneloux liquid volume correction (SeeSRK)
326 5 Property Model Option Codes
Model Name OptionCode
Value Descriptions
2 Apply volume correction to both liquid and vaporphases
5 0 Use analytical method for root finding (default)
1 Use RTO numerical method for root finding
2 Use VPROOT/LQROOT numerical method for rootfinding
ESPRWS, ESPRWS0,ESPRV1, ESPRV10,ESPRV2, ESPRV20,
1 0 ASPEN Boston/Mathias alpha function
2 Mathias-Copeman alpha function
3 Schwartzentruber-Renon-Watanasiri alphafunction
ESPSAFT, ESPSAFT0 1 0 Random copolymer (default)
1 Alternative copolymer
2 Block copolymer
2 0 Do not use Sadowski's copolymer model
1 Use Sadowski's copolymer model in which acopolymer must be built only by two differenttypes of segments
3 0 Use association term (default)
1 Do not use association term
ESRKS, ESRKS0,ESRKSTD,ESRKSTD0, ESSRK,ESSRK0, ESRKSML,ESRKSML0
See Soave-Redlich-Kwong Option Codes
ESRKSW, ESRKSW0 1 0 ASPEN Boston/Mathias alpha function (default)
1 Original literature alpha function
2 Grabowski and Daubert alpha function for H2
above TC ( = 1.202 exp(-0.30228xTri))
6 Mathias-Copeman alpha function
7 Schwartzentruber-Renon-Watanasiri alphafunction
ESRKU, ESRKU0 1 Initial temperature for binary parameterestimation
0 At TREF=25 C (default)
1 The lower of TB(i) or TB(j)
2 (TB(i) + TB(j))/2
100-999Value entered used as temperature in K
2 VLE or LLE UNIFAC
0 VLE (default)
1 LLE
3 Property diagnostic level flag (-1 to 8)
5 Property Model Option Codes 327
Model Name OptionCode
Value Descriptions
4 Vapor phase EOS used in generation of TPxy datawith UNIFAC
0 Hayden-O'Connell (default)
1 Redlich-Kwong
5 Do/do not estimate binary parameters
0 Estimate (default)
1 Set to zero
ESHF, ESHF0 1 0 Equation form for Log(k) expression:
log(K) = A + B/T + C ln(T) + DT (default)
1 log(K) = A + B/T + CT + DT2 + E log(P)
1 Original literature alpha function
2 Mathias-Copeman alpha function
3 Schwartzentruber-Renon alpha function (default)
ESRKSWS,ESRKSWS0,ESRKSV1,ESRKSV10,ESRKSV2,ESRKSV20,
1 Equation form for alpha function
1 Original literature alpha function
2 Mathias-Copeman alpha function
3 Schwartzentruber-Renon alpha function (default)
ESSTEAM, ESSTEAM0 (STEAMNBS, STMNBS2)
1 0 ASME 1967 correlations
1 NBS 1984 equation of state (default)
2 NBS 1984 equation of state with alternate rootsearch method (STMNBS2)
2 0 Original fugacity and enthalpy calculations whenused with STMNBS2
1 Rigorous fugacity calculation from Gibbs energyand corrected enthalpy departure with STMNBS2root search method
2 Rigorous fugacity calculation from Gibbs energyand corrected enthalpy departure with AspenPlus root search method (default)
ESGLY, ESGLY0 1 0 Cubic EOS analytical solution method
1 Numerical solution method
ESHPR, ESHPR0 1 0 Cubic EOS analytical solution method
1 Numerical solution method
2 0 Use modified Tc, Pc for H2 and He
1 Use unmodified Tc, Pc for H2 and He
3 0 No liquid volume translation
1 Translation volume estimated by COSTALD
2 Translation volume estimated by Rackett
4 0 HYSYS alpha function
328 5 Property Model Option Codes
Model Name OptionCode
Value Descriptions
1 Standard alpha function
ESHSPR, ESHSPR0 1 0 Cubic EOS analytical solution method
1 Numerical solution method
2 0 Use modified Tc, Pc for H2 and He
1 Use unmodified Tc, Pc for H2 and He
ESHSRK, ESHSRK0 1 0 Cubic EOS analytical solution method
1 Numerical solution method
2 0 Use modified Tc, Pc for H2 and He
1 Use unmodified Tc, Pc for H2 and He
3 0 No liquid volume translation
1 Translation volume estimated by COSTALD
2 Translation volume estimated by Rackett
ESHSSRK,ESHSSRK0
1 0 Cubic EOS analytical solution method
1 Numerical solution method
2 0 Use modified Tc, Pc for H2 and He
1 Use unmodified Tc, Pc for H2 and He
ESH2O, ESH2O0 1 0 ASME 1967 correlations (default)
1 NBS 1984 equation of state
2 NBS 1984 equation of state with alternate rootsearch method (STMNBS2)
Note: The enthalpy, entropy, Gibbs energy, and molar volume of water arecalculated from the steam tables when the relevant option is enabled. Thetotal properties are mole-fraction averages of these values with the propertiescalculated by the equation of state for other components. Fugacity coefficientis not affected.
Soave-Redlich-Kwong OptionCodesThere are five related models all based on the Soave-Redlich-Kwong equationof state which are very flexible and have many options. These models are:
Standard Redlich-Kwong-Soave (ESRKSTD0, ESRKSTD)
Redlich-Kwong-Soave-Boston-Mathias (ESRKS0, ESRKS)
Soave-Redlich-Kwong (ESSRK, ESSRK0)
SRK-Kabadi-Danner (ESSRK, ESSRK0)
SRK-ML (ESRKSML, ESRKSML0)
The options for these models can be selected using the option codesdescribed in the following table:
5 Property Model Option Codes 329
OptionCode
Value Description
1 0 Standard SRK alpha function for Tr < 1, Boston-Mathias alphafunction for Tr > 1
1 Standard SRK alpha function for all
2 Grabovsky – Daubert alpha function for H2 and standard SRKalpha function for others (default)
3 Extended Gibbons-Laughton alpha function for all components(see notes 1, 2, 3)
4 Mathias alpha function
5 Twu generalized alpha function
8 Twu alpha function
2 0 Standard SRK mixing rules (default for other models)
1 Kabadi – Danner mixing rules (default for SRK-Kabadi-Danner(see notes 3, 4, 5)
2 Standard mixing rules with unsymmetric Kij and with Lij
calculated as Kij - Kji (default for SRK-ML)
3 0 Do not calculate water properties from steam table (Default)
1 Calculate properties (H, S, G, V) of water from steam table(see note 6)
4 0 Do not apply the Peneloux liquid volume correction (default forSRK-ML and both Redlich-Kwong-Soave models)
1 Apply the liquid volume correction (default for Soave-Redlich-Kwong and SRK-Kabadi-Danner, see Soave-Redlich-Kwong fordetails)
2 Apply volume correction to both liquid and vapor phases
5 0 Use analytical method for root finding (default)
1 Use RTO numerical method for root finding
2 Use VPROOT/LQROOT numerical method for root finding
6 0 Use true logarithm in calculating properties (default forRedlich-Kwong-Soave models)
1 Use smoothed logarithm in calculating properties (default forSRK models)
Notes
1 The standard alpha function is always used for Helium.
2 If extended Gibbons-Laughton alpha function parameters are missing, theBoston-Mathias extrapolation will be used if T > Tc, and the standardalpha function will be used if T < Tc.
3 The extended Gibbons-Laughton alpha function should not be used withthe Kabadi-Danner mixing rules.
4 The Kabadi-Danner mixing rules should not be used if Lij parameters areprovided for water with any other components.
5 It is recommended that you use the SRK-KD property method rather thanchange this option code.
6 The enthalpy, entropy, Gibbs energy, and molar volume of water arecalculated from the steam tables when this option is enabled. The totalproperties are mole-fraction averages of these values with the properties
330 5 Property Model Option Codes
calculated by the equation of state for other components. Fugacitycoefficient is not affected.
Option Codes for K-ValueModelsModelName
OptionCode
Value Descriptions
BK10 1 0 Treat pseudocomponents as paraffins (default)
1 Treat pseudocomponents as aromatics
Option Codes for EnthalpyModelsModel Name Option
CodeValue Descriptions
DHL0HREF 1 1 Use Liquid reference state for all components (Default)
2 Use liquid and gaseous reference states based on thestate of each component
Electrolyte NRTL Enthalpy (HAQELC, HMXELC, and HMXENRHG)
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters default tozero (default for ELC models)
3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forHMXENRHG)
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Ideal gas EOS (default)
1 HF EOS for hydrogen fluoride
3 Solvent/solvent binary parameter values obtainedfrom:
0 Scalar GMELCA, GMELCB and GMELCM (default for ELCmodels)
1 Vector NRTL(8) (default for HMXENRHG)
4 Enthalpy calculation method
0 Electrolyte NRTL Enthalpy (default for ELC models andELECNRTL property method)
1 Helgeson method (default for HMXENRHG)
5 Vapor phase enthalpy departure contribution to liquidenthalpy. Hliq = Hig + DHV - Hvap; this option indicateshow DHV is calculated.
0 Do not calculate (DHV=0) (default)
1 Calculate using Redlich-Kwong equation of state
5 Property Model Option Codes 331
Model Name OptionCode
Value Descriptions
2 Calculate using Hayden-O'Connell equation of state
6 Method for calculating corresponding states (forhandling solvents that exist in both subcritical andsupercritical conditions)
0 Original method (default)
1 Corresponding state method. Calculates a pseudo-critical temperature of the solvents and uses ittogether with the actual critical temperatures of thepure solvents to adjust the liquid enthalpy departure.This results in a smoother transition of the liquidenthalpy contribution when the component transformsfrom subcritical to supercritical.
7 Method for handling Henry components and multiplesolvents
0 Pure liquid enthalpy calculated by aqueous infinitedilution heat capacity; only water as solvent
1 Pure liquid enthalpy for Henry components calculatedusing Henry's law; use this option when there aremultiple solvents.
HLRELNRT and HLRELELC
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters default tozero (default for HLRELELC)
3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forHLRENRTL)
2 Solvent/solvent binary parameter values obtainedfrom:
0 Scalar GMELCA, GMELCB and GMELCM (default)
1 Vector NRTL(8)
3 Mixture density model
0 Rackett equation with Campbell-Thodos modification
1 Quadratic mixing rule for molecular components (molebasis)
HIG2ELC, HIG2HG
1 Enthalpy calculation method
0 Electrolyte NRTL Enthalpy (default for HIG2ELC)
1 Helgeson method (default for HIG2HG)
DHLELC
1 Steam table for liquid enthalpy of water
0 Use steam table for liquid enthalpy of water (default)
1 Use specified EOS model
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Use specified EOS model (default)
1 HF EOS for hydrogen fluoride
332 5 Property Model Option Codes
Model Name OptionCode
Value Descriptions
HAQPT1, HAQPT3 (Pitzer)
1 Defaults for pair mixing rule
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
2 Standard enthalpy calculation
0 Standard electrolytes method (Pre-release 10)
1 Helgeson method (Default)
3 Estimation of K-stoic temperature dependency
0 Use value at 298.15 K
1 Helgeson Method (default)
HS0POL1, GS0POL1, SS0POL1 (Solid pure component polynomials)
1 Reference temperature usage
0 Use standard reference temperature (default)
1 Use liquid reference temperature
PHILELC
1 Steam table for liquid enthalpy of water
0 Use steam table for liquid enthalpy of water (default)
1 Use specified EOS model
2 Vapor phase equation-of-state for liquid enthalpy of HF
0 Use specified EOS model (default)
1 HF EOS for hydrogen fluoride
Option Codes for Gibbs FreeEnergy ModelsModel Name Option
CodeValue Descriptions
Electrolyte NRTL Gibbs Energy (GAQELC, GMXELC, and GMXENRHG)
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for ELC models)
3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGMXENRHG)
2 Vapor phase equation-of-state for liquid Gibbsfree energy of HF
0 Ideal gas EOS (default)
1 HF EOS for hydrogen fluoride
3 Solvent/solvent binary parameter values obtainedfrom
5 Property Model Option Codes 333
Model Name OptionCode
Value Descriptions
0 Scalar GMELCA, GMELCB and GMELCM (defaultfor ELC models)
1 Vector NRTL(8) (default for GMXENRHG)
4 Gibbs free energy calculation method
0 Electrolyte NRTL Gibbs free energy (default forELC models)
1 Helgeson method (default for GMXENRHG)
5 Vapor phase fugacity coefficient (PHIV)calculation method.
0 Do not calculate (PHIV=1) (default)
1 Calculate using Redlich-Kwong equation of state
2 Calculate using Hayden-O'Connell equation ofstate
6 Method for handling Henry components andmultiple solvents
0 Pure liquid Gibbs free energy calculated byaqueous infinite dilution heat capacity; only wateras solvent
1 Pure liquid Gibbs free energy for Henrycomponents calculated using Henry's law; usethis option when there are multiple solvents.
GLRELNRT, GLRELELC
1 Defaults for pair parameters
1 Pair parameters default to zero
2 Solvent/solute pair parameters default to waterparameters. Water/solute pair parameters defaultto zero (default for GLRELELC)
3 Default water parameters to 8, -4. Defaultsolvent/solute parameters to 10, -2 (default forGLRENRTL)
2 Solvent/solvent binary parameter values obtainedfrom:
0 Scalar GMELCA, GMELCB and GMELCM (default)
1 Vector NRTL(8)
3 Mixture density model
0 Rackett equation with Campbell-Thodosmodification
1 Quadratic mixing rule for molecular components(mole basis)
GIG2ELC, GIG2HG
1 Gibbs free energy calculation method
0 Electrolyte NRTL Gibbs free energy (default forGIG2ELC)
1 Helgeson method (default for GIG2HG)
GAQPT1, GAQPT3 (Pitzer)
1 Defaults for pair mixing rule
334 5 Property Model Option Codes
Model Name OptionCode
Value Descriptions
-1 No unsymmetric mixing
0 Unsymmetric mixing polynomial (default)
1 Unsymmetric mixing integral
2 Standard Gibbs free energy calculation
0 Standard electrolytes method (Pre-release 10)
1 Helgeson method (Default)
3 Estimation of K-stoic temperature dependency
0 Use value at 298.15 K
1 Helgeson Method (default)
Option Codes for Liquid VolumeModelsModelName
OptionCode
Value Descriptions
VL2QUAD 1 0 Use normal pure component liquid volume model forall components (default)
1 Use steam tables for water
2 0 Use mole basis composition (default)
1 Use mass basis composition
VAQCLK 1 0 Use Clarke model
1 Use liquid volume quadratic mixing rule
COSTALD liquid volume model for Aspen HYSYS property methods: VL2GLYCT,VL0GLYCT (GLYCOL); VL2HPRCT, VL0HPRCT (HYSPR); VL2HSRKC, VL0HSRKC (HYSSRK)
1 0 Smoothly make liquid density change to equation ofstate when Tr > 0.95
1 No smoothing of liquid density
2 0 Chueh-Prausnitz equation for pressure correction
1 Tait equation for pressure correction
1 0 Cutoff between linear and quadratic forms ofequation for partial molar volume based on densityoccurs at reduced solvent density = 2.785 (original from BrelviO'Connell paper) (Default)
1 Cutoff occurs at reduced solvent density = 3.0784491983 (avoids discontinuity)
VL1BROC
Index 335
Index
A
activity coefficient models 91list of property models 91
alpha functions 72, 77Peng-Robinson 72Soave 77
Andrade liquid mixture viscositymodel 258
Andrade/DIPPR viscosity model259
Antoine/Wagner vapor pressuremodel 187
API model 201, 262, 300liquid molar volume 201liquid viscosity 262surface tension 300
API Sour model 192applications 96
metallurgical 96aqueous infinite dilution heat
capacity model 221ASME steam tables 16Aspen liquid mixture viscosity
model 263Aspen polynomial equation 219ASTM 264
liquid viscosity 264
B
Barin equations thermodynamicproperty model 237
Benedict-Webb-Rubin-Starlingproperty model 18
Braun K-10 model 192Brelvi-O'Connell model 202Bromley-Pitzer activity coefficient
model 91, 92, 94
about 91parameter conversion 94working equations 92
BWR-Lee-Starling property model16
C
Cavett thermodynamic propertymodel 236
Chao-Seader fugacity model 193Chapman-Enskog 265, 268, 294,
295Brokaw/DIPPR viscosity model
265Brokaw-Wilke mixing rule
viscosity model 268Wilke-Lee (binary) diffusion
model 294Wilke-Lee (mixture) diffusion
model 295Chien-Null activity coefficient
model 94Chueh-Prausnitz model 203Chung-Lee-Starling model 270,
272, 282low pressure vapor viscosity 270thermal conductivity 282viscosity 272
Clarke electrolyte liquid volumemodel 205
Clausius-Clapeyron equation 199heat of vaporization 199
coal 309property models 309
constant activity coefficient model96
336 Index
copolymer PC-SAFT EOS propertymodel 35, 36, 38, 41, 42, 45,46, 47
about 35association term 42chain connectivity 38dispersion term 41fundamental equations 36parameters 46, 47polar term 45
COSMO-SAC solvation model 96COSTALD liquid volume model 207Criss-Cobble aqueous infinite
dilution ionic heat capacitymodel 222
D
Dawson-Khoury-Kobayashidiffusion model 295, 296
binary 295mixture 296
DCOALIGT coal density model 319Dean-Stiel pressure correction
viscosity model 274Debye-Hückel volume model 208DGHARIGT char density model 320diffusivity models 293
list 293DIPPR equation 6, 224DIPPR model 196, 210, 222, 227,
259, 265, 285, 288, 301heat of vaporization 196ideal gas heat capacity 227liquid heat capacity 222liquid volume 210surface tension 301thermal conductivity 285, 288viscosity 259, 265
DNSTYGEN nonconventionalcomponent density model 307
E
electrolyte models 205, 240, 242,275, 284, 297, 304
Clarke liquid volume 205electrolyte NRTL enthalpy 240Gibbs energy 242Jones-Dole viscosity 275Nernst-Hartley diffusion 297Onsager-Samaras surface
tension 304
Riedel thermal conductivity 284electrolyte NRTL 99, 102, 240, 242
activity coefficient model 99, 102enthalpy thermodynamic
property model 240Gibbs energy thermodynamic
property model 242eNRTL-SAC activity coefficient
model 112ENTHGEN nonconventional
component heat capacitymodel 308
equation-of-state method 15property models 15
extrapolation 9temperature limits 9
G
Grayson-Streed fugacity model 193group contribution activity
coefficient models 177, 179,180
Dortmund-modified UNIFAC 179Lyngby-modified UNIFAC 180UNIFAC 177
H
Hakim-Steinberg-Stiel/DIPPRsurface tension 301
Hansen solubility parameter model117
Hayden-O'Connell 22property model 22
HCOALGEN 312general coal model for enthalpy
312heat of vaporization 196
models 196Helgeson thermodynamic property
model 250HF equation of state 25
property model 25Huron-Vidal mixing rules 84
I
IAPS models for water 274, 283,301
surface tension 301thermal conductivity 283viscosity 274
ideal gas heat capacity 227
Index 337
ideal gas law 29property model 29
ideal gas/DIPPR heat capacitymodel 227
ideal liquid activity coefficientmodel 119
ideal mixing 253IGT density model for 319, 320
char 320coal 319
IK-CAPE equation 198, 225heat of vaporization 198liquid heat capacity 225
J
Jones-Dole electrolyte correctionviscosity model 275
K
Kent-Eisenberg fugacity model 194
L
Lee-Kesler Plöcker property model31
Lee-Kesler property model 30Letsou-Stiel viscosity model 277Li mixing rule thermal conductivity
model 284liquid constant molar volume
model 210liquid enthalpy 244
thermodynamic property model244
liquid heat capacity 224DIPPR equation 224
liquid mixture 258, 284, 300surface tension 300thermal conductivity 284viscosity 258
liquid thermal conductivity 285general pure components 285
liquid viscosity 258, 259, 262, 263,264, 279
Andrade equation 258API 262API 1997 262Aspen 263ASTM 264pure components 259Twu 279
liquid volume quadratic mixing rule221
Lucas vapor viscosity model 277
M
Mathias alpha function 77Mathias-Copeman alpha function
72, 77Maxwell-Bonnell vapor pressure
model 195MHV2 mixing rules 85mixing rules 84, 85, 87, 89, 221,
253, 268, 281, 284, 291, 293Brokaw-Wilke viscosity model
268Huron-Vidal 84ideal 253Li 284liquid volume quadratic 221MHV2 85predictive Soave-Redlich-Kwong-
Gmehling 87quadratic 253viscosity quadratic 281Vredeveld 291Wassiljewa-Mason-Saxena 293Wong-Sandler 89
modified MacLeod-Sugden surfacetension model 306
N
Nernst-Hartley electrolyte diffusionmodel 297
NIST 226liquid heat capacity 226
NIST TDE Watson equation 198heat of vaporization 198
nonconventional components 307,308, 312
coal model for enthalpy 312density polynomial model 307enthalpy and density models list
307heat capacity polynomial model
308nonconventional solid property
models 307density 307enthalpy 307list of 307
Nothnagel 33
338 Index
property model 33NRTL 99, 119
electrolyte NRTL property model99
property model 119NRTL-SAC 120, 123, 135
for Segments/Oligomers 135model derivation 123property model 120Using 140
O
Onsager-Samaras electrolytesurface tension model 304
option codes 321, 323, 325, 328,330, 332, 334
activity coefficient models 323enthalpy models 330equation of state models 325Gibbs energy models 332K-value models 330liquid volume models 334list 321Soave-Redlich-Kwong models
328transport property models 321
P
PC-SAFT property method 35property model 35
Peng-Robinson 48, 50, 52, 53, 72alpha functions 72MHV2 property model 52property model 48standard 50Wong-Sandler property model 53
physical properties 11, 15models 11, 15
Pitzer activity coefficient model140, 142, 143, 145, 149
about 140activity coefficients 145aqueous strong electrolytes 143model development 142parameters 149
polynomial activity coefficientmodel 152
PPDS equation 197, 224heat of vaporization 197liquid heat capacity 224
predictive Soave-Redlich-Kwong-Gmehling mixing rules 87
predictive SRK property model(PSRK) 52
property models 5, 11, 15, 187,200, 221, 321
equation-of-state list 15fugacity models list 187heat capacity models list 221list of 5molar volume and density
models list 200option codes 321thermodynamic list 11vapor pressure model list 187
property parameters 6temperature-dependent
properties 6PSRK 52
property model 52pure component properties 6
temperature-dependent 6
Q
quadratic mixing rules 253
R
Rackett 215, 216, 217extrapolation method 217mixture liquid volume model 215modified model for molar volume
216Rackett pure component liquid
volume model 210Raoult's law 119Redlich-Kister activity coefficient
model 153Redlich-Kwong 53, 77
alpha function 77property model 53
Redlich-Kwong-Aspen propertymodel 54
Redlich-Kwong-Soave 55, 57, 59,62, 77
alpha function list 77Boston-Mathias property model
57MHV2 property model 59property model 55Soave-Redlich-Kwong property
model 62
Index 339
Wong-Sandler property model 59Riedel electrolyte correction
thermal conductivity model284
S
Sato-Riedel/DIPPR thermalconductivity model 285
Scatchard-Hildebrand activitycoefficient model 154
Schwartzentruber-Renon propertymodel 60
Soave-Redlich-Kwong 62property model 62
Soave-Redlich-Kwong models 328options codes 328
solid Antoine vapor pressuremodels 195
solid thermal conductivitypolynomial 288
solids polynomial heat capacitymodel 231
solubility correlation models 233,234, 235
Henry's constant 234hydrocarbon 235list 233water solubility model 235
SRK-Kabadi-Danner propertymodel 64
SRK-ML property model 67standard Peng-Robinson property
model 50standard Redlich-Kwong-Soave
property model 55steam tables 16, 33
NBS/NRC 33property models 16
STEAMNBS property method 33Stiel-Thodos pressure correction
thermal conductivity model291
Stiel-Thodos thermal conductivitymodel 288
surface tension 300, 306general pure components 301liquid mixtures 300models list 300modified MacLeod-Sugden 306
Symmetric and UnsymmetricElectrolyte NRTL activitycoefficient model 156, 159
about 156working equations 159
T
temperature 9extrapolating limits 9
temperature-dependent properties6
pure component 6units 6
thermal conductivity 281, 288models list 281solids 288
thermo switch 6thermodynamic property 11, 236
list of additional models 236models list 11
three-suffix Margules activitycoefficient model 155
THRSWT 6transport property 255
models list 255transport switch 6TRAPP 279, 292
thermal conductivity model 292viscosity model 279
TRNSWT 6Twu liquid viscosity model 279
U
UNIFAC 177, 179, 180activity coefficient model 177Dortmund modified activity
coefficient model 179Lyngby modified activity
coefficient model 180UNIQUAC 181
activity coefficient model 181
V
Van Laar activity coefficient model183
vapor thermal conductivity 288general pure components 288
vapor viscosity 265, 268, 270, 277Brokaw-Wilke mixing rule
viscosity model 268Chung-Lee-Starling 270Lucas 277pure components 265
viscosity 257
340 Index
models 257viscosity quadratic mixing rule 281VPA/IK-CAPE equation of state 67Vredeveld mixing rule 291
W
Wagner Interaction Parameteractivity coefficient model 184
Wagner vapor pressure model 187Wassiljewa-Mason-Saxena mixing
rule 293Watson equation 197
heat of vaporization 197Wilke-Chang diffusion model 298,
299binary 298mixture 299
WILS-GLR property method 245WILS-LR property method 245Wilson (liquid molar volume)
activity coefficient model 186Wilson activity coefficient model
185Wong-Sandler mixing rules 89