termodynamic modeling for co2

Thermodynamic Modeling for CO2 Absorption in Aqueous MDEA Solution withElectrolyte NRTL Model

Ying Zhang

AspenTech, Limited, Pudong, Shanghai 201203, People’s Republic of China

Chau-Chyun Chen*

Aspen Technology, Inc., Burlington, Massachusetts 01803

Accurate modeling of thermodynamic properties for CO2 absorption in aqueous alkanolamine solutions isessential for the simulation and design of such CO2 capture processes. In this study, we use the ElectrolyteNonrandom Two-Liquid activity coefficient model to develop a rigorous and thermodynamically consistentrepresentation for the MDEA-H2O-CO2 system. The vapor-liquid equilibrium (VLE), heat capacity, andexcess enthalpy data for the binary aqueous amine system are used to determine the NRTL interactionparameters for the MDEA-H2O binary. The VLE, heat of absorption, heat capacity, and NMR spectroscopicdata for the MDEA-H2O-CO2 ternary system are used to identify the NRTL interaction parameters for themolecule-electrolyte binaries and the previously unavailable standard-state properties of the amine ion, MDEAprotonate. The calculated VLE, heat of absorption, heat capacity, and the species concentrations for theMDEA-H2O-CO2 system are compared favorably to experimental data.

1. Introduction

CO2 capture by absorption with aqueous alkanolamines isconsidered an important technology to reduce CO2 emissionsfrom fossil-fuel-fired power plants and to help alleviate globalclimate change.1 Methyldiethanolamine (MDEA), which is analternative to monoethanolamine (MEA) for bulk CO2 removal,has the advantage of relatively low heat of reaction of CO2 withMDEA.2 To properly simulate and design the absorption/stripping processes with MDEA-based aqueous solvents, it isessential to develop a sound process understanding of thetransfer phenomena3 and accurate thermodynamic models4 tocalculate the driving forces for heat and mass transfer. In otherwords, scalable simulation, design, and optimization of the CO2

capture processes start with modeling of the thermodynamicproperties, specifically vapor-liquid equilibrium (VLE) andchemical reaction equilibrium, as well as calorimetric properties.

Accurate modeling of thermodynamic properties requiresavailability of reliable experimental data. Earlier literaturereviews5,6 suggested that, while there are extensive sets ofexperimental data available for the MDEA system, some of thepublished CO2 solubility data for the aqueous MDEA systemmay be questionable. The use of a thermodynamically consistentframework makes it possible to correlate available experimentaldata, to screen out questionable data, and to morph these diverseand disparate data into a useful and thermodynamically con-sistent form for process modeling and simulation.

Excess Gibbs energy-based activity coefficient models pro-vide a practical and rigorous thermodynamic framework tomodel thermodynamic properties of aqueous electrolyte systems,including aqueous alkanolamine systems for CO2 capture.4,7 Forexample, Austgen et al.8 and Posey9 applied the electrolyteNRTL model10-12 to correlate CO2 solubility in aqueous MDEAsolution and other aqueous alkanolamines. Kuranov et al.,5

Kamps et al.,6 and Ermatchkov et al.13 used Pitzer’s equation14

to correlate the VLE data of the MDEA-H2O-CO2 system.

Arcis et al.15 also fitted the VLE data with Pitzer’s equationand used the thermodynamic model to estimate the enthalpy ofsolution of CO2 in aqueous MDEA. Faramarzi et al.16 used theextended UNIQUAC model17 to represent VLE for CO2

absorption in aqueous MDEA, MEA, and mixtures of the twoalkanolamines. Furthermore, they predicted the concentrationsof the species in both MDEA and MEA solutions containingCO2 and in the case of MEA, compared to NMR spectroscopicmeasurements.18,19

In the present work, we expand the scope of the work ofAustgen et al.8 and Posey9 to cover all thermodynamic proper-ties. We use the 2009 version10 of the electrolyte NRTLmodel10-12 as the thermodynamic framework to correlaterecently available experimental data for CO2 absorption inaqueous MDEA solution. Much new data for thermodynamicproperties and calorimetric properties have become availablein recent years, and they cover wider ranges of temperature,pressure, MDEA concentration, and CO2 loading. The binaryNRTL parameters for MDEA-water binary are regressed fromthe binary VLE, excess enthalpy, and heat capacity data. Thebinary NRTL parameters for water-electrolyte pairs andMDEA-electrolyte pairs and the standard-state properties ofprotonated MDEA ion are obtained by fitting to the ternary VLE,heat of absorption, heat capacity, and NMR spectroscopic data.This expanded model should provide a comprehensive thermo-dynamic representation for the MDEA-H2O-CO2 system overa broader range of conditions and give more reliable predictionsover previous works.

In conjunction with the use of the electrolyte NRTL modelfor the liquid-phase activity coefficients, we use the PC-SAFT20,21

equation of state (EOS) for the vapor-phase fugacity coefficients.While both PC-SAFT EOS and typical cubic EOS would givereliable fugacity calculations at low to medium pressures, wechoose PC-SAFT for its ability to model vapor-phase fugacitycoefficients at high pressures, which is an important consider-ation for modeling CO2 compression. The PC-SAFT parametersused in this model are given in Table 1. The parameters forwater and CO2 are taken from the literature21 and the Aspen

* To whom correspondence should be addressed. Tel.: 781-221-6420.Fax: 781-221-6410. E-mail: [email protected].

Ind. Eng. Chem. Res. XXXX, xxx, 000 A

10.1021/ie1006855 XXXX American Chemical Society

Databank.22 The parameters for MDEA are obtained from theregression of experimental data on vapor pressure, liquid density,and liquid heat capacity.

2. Thermodynamic Framework

2.1. Chemical and Phase Equilibrium. CO2 solubility inaqueous amine solutions is determined by both its physicalsolubility and the chemical equilibrium for the aqueous phasereactions among CO2, water, and amines.

2.1.1. Physical Solubility. Physical solubility is the equi-librium between gaseous CO2 molecules and CO2 molecules inthe aqueous amine solutions:

It can be expressed by Henry’s law:

where P is the system pressure, yCO2 the mole fraction of CO2

in the vapor phase, φCO2 the CO2 fugacity coefficient in the vaporphase, HCO2 the Henry’s law constant of CO2 in the mixedsolvent of water and amine, xCO2 the equilibrium CO2 molefraction in the liquid phase, and γCO2

* the unsymmetric activitycoefficient of CO2 in the mixed solvent of water and amine.

The Henry’s constant in the mixed solvent can be calculatedfrom those in the pure solvents:23

where Hi is the Henry’s constant of supercritical component iin the mixed solvent, HiA the Henry’s constant of supercriticalcomponent i in pure solvent A, γi

∞ the infinite dilution activitycoefficient of supercritical component i in the mixed solvent,γiA

∞ the infinite dilution activity coefficient of supercriticalcomponent i in pure solvent A, and xA the mole fraction ofsolvent A.

We use wA in lieu of xA in eq 3 to weigh the contributionsfrom different solvents.22 The parameter wA is calculated usingeq 4:

Here, ViA∞ represents the partial molar volume of supercritical

component i at infinite dilution in pure solvent A. ViA∞ is

calculated from the Brelvi-O’Connell model24 with the char-acteristic volume for the solute (VCO2

BO ) and solvent (VsBO), which

are listed in Table 2.

Henry’s law constants for CO2 with water and for CO2 withMDEA are required. The former has been extensively studied,25

although knowledge about the latter is relatively limited.Because it is not feasible to directly measure CO2 physicalsolubility in pure amines, because of the reactions between them,the common practice is to derive the CO2 physical solubility inamines from that of N2O for their analogy in molecular structureand, thus, in physical solubility as believed:26

In 1992, Wang et al.27 reported the solubility of N2O in pureMDEA solvent as follows:

Based on the work of Versteef and van Swaaij,28 we obtainedthe following two equations for the solubilities of N2O and CO2

in water:

We use eqs 5-8 to determine HCO2,MDEA and the parametersare summarized in Table 3.

The Henry’s constant of CO2 in pure solvent A is correctedwith the Poynting term for pressure:25

where HCO2,A(T,P) is the Henry’s constant of CO2 in pure solventA at system temperature and pressure, HCO2,A(T,pA

°,l) the Henry’sconstant of CO2 in pure solvent A at system temperature andthe solvent vapor pressure, and VCO2,A

∞ the partial molar volume

Table 1. Parameters for PC-SAFT Equation of State

MDEA H2O CO2

source this work Gross andSadowski 21

AspenDatabank22

segment numberparameter, m

3.3044 1.0656 2.5692

segment energyparameter, ε

237.44 K 366.51 K 152.10 K

segment sizeparameter, σ

3.5975 Å 3.0007 Å 2.5637 Å

association energyparameter, εAB

3709.9 K 2500.7 K 0 K

kAB 0.066454 Å3 0.034868 Å3 0 Å3

CO2(V) T CO2(l) (1)

PyCO2φCO2

) HCO2xCO2

γCO2* (2)

ln(Hi

γi∞) ) ∑

A

xA ln(HiA

γiA∞ ) (3)

wA )xA(ViA

∞ )2/3

∑B

xB(ViB∞ )2/3

(4)

Table 2. Parameters of the Characteristic Volume for theBrelvi-O’Connell Modela

Characteristic Volume (m3/kmol)

parameter MDEA H2O CO2

source this work Brelvi and O’Connell 24 Yan and Chen25

V1,i 0.369b 0.0464 0.175V2,i 0 0 -3.38 × 10-4

a The Brelvi-O’Connell model has been described in ref 24. Thecorrelation of the characteristic volume for the Brelvi-O’Connell model(Vi

BO) is given as follows: ViBO ) V1,i + V2,iT, where T is the

temperature (given in Kelvin). b Here, the critical volume was used asthe characteristic volume for MDEA.

Table 3. Parameters for Henry’s Constant (Expressed in Units of Pa)a

solute i CO2 CO2

solvent j H2O MDEAsource Yan and Chen25 this workaij 91.344 19.8933bij -5876.0 -1072.7cij -8.598 0.0dij -0.012 0.0

a The correlation for Henry’s constant is given as follows: ln Hij ) aij

+ bij/T + cij ln T + dijT, where T is the temperature (given in Kelvin).

HCO2,MDEA

HN2O,MDEA)

HCO2,water

HN2O,water(5)

HN2O,MDEA (kPa m3 kmol-1) ) (1.524 × 105) exp(-1312.7T )

(6)

HN2O,water (kPa m3 kmol-1) ) (8.5470 × 106) exp(-2284T )

(7)

HCO2,water (kPa m3 kmol-1) ) (2.8249 × 106) exp(-2044T )

(8)

HCO2,A(T, P) ) HCO2,A(T, pAo,l) exp( 1

RT ∫pA◦,l

PVCO2,A

∞ dp) (9)

B Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX

of CO2 at infinite dilution in pure solvent A calculated fromthe Brelvi-O’Connell model.

At low pressures, the Poynting correction is almost unity andcan be ignored.

2.1.2. Aqueous-Phase Chemical Equilibrium. The aqueous-phase chemical reactions involved in the MDEA-water-CO2

system can be expressed as

We calculate the equilibrium constants of the reaction fromthe reference-state Gibbs free energies of the participatingcomponents:

where Kj is the equilibrium constant of reaction j, ∆Gj°(T) thereference-state Gibbs free energy change for reaction j attemperature T, R the universal gas constant, and T the systemtemperature.

For the aqueous phase reactions, the reference states chosenare pure liquid for the solvents (water and MDEA), and aqueousphase infinite dilution for the solutes (ionic and molecular).

The Gibbs free energy of solvents is calculated from that ofideal gas and the departure function:

where Gs(T) is the Gibbs free energy of solvent s at temperatureT, Gs

ig(T) the ideal gas Gibbs free energy of solvent s attemperature T, and ∆Gs

igfl(T) the Gibbs free energy departurefrom ideal gas to liquid at temperature T.

The Gibbs free energy of an ideal gas is calculated from theGibbs free energy of formation of an ideal gas at 298.15 K, theenthalpy of formation of an ideal gas at 298.15 K, and the idealgas heat capacity.

where Gsig(T) is the ideal gas Gibbs free energy of solvent s at

temperature T, ∆fGs,298.15ig the ideal gas Gibbs free energy of

formation of solvent s at 298.15 K, ∆fHs,298.15ig the ideal gas

enthalpy of formation of solvent s at 298.15 K, and Cp,sig the

ideal gas heat capacity of solvent s.

The reference-state properties, ∆fGs,298.15ig and ∆fHs,298.15

ig , areshown in Table 4. The ideal gas heat capacities are shown inTable 5. For water, the Gibbs free energy departure function isobtained from the ASME steam tables. For MDEA, thedeparture function is calculated from the PC-SAFT equationof state.

For molecular solute CO2, the Gibbs free energy in aqueousphase infinite dilution is calculated from Henry’s law:

where Gi∞,aq(T) is the mole fraction scale aqueous-phase infinite

dilution Gibbs free energy of solute i at temperature T, ∆fGiig(T)

the ideal gas Gibbs free energy of formation of solute i attemperature T, Hi,w the Henry’s constant of solute i in water,and Pref the reference pressure.

For ionic species, the Gibbs free energy in aqueous-phaseinfinite dilution is calculated from the Gibbs free energy offormation in aqueous-phase infinite dilution at 298.15 K, theenthalpy of formation in aqueous-phase infinite dilution at298.15 K, and the heat capacity in aqueous-phase infinitedilution:

Here, Gi∞,aq(T) is the mole fraction scale aqueous-phase infinite

dilution Gibbs free energy of solute i at temperature T, ∆fGi,298.15∞,aq

the molality scale aqueous-phase infinite dilution Gibbs freeenergy of formation of solute i at 298.15 K, ∆fHi,298.15

∞,aq theaqueous phase infinite dilution enthalpy of formation of solutei at 298.15 K, and Cp,i

∞,aq the aqueous-phase infinite dilution heatcapacity of solute i. The term RT ln (1000/Mw) is added because

Table 4. Parameters for the Reference States Properties

property ∆fG298.15ig (J/kmol) ∆fH298.15

ig (J/kmol) ∆fG298.15∞,aq (J/kmol) ∆fH298.15

∞,aq (J/kmol) source

MDEA -1.6900 × 108 -3.8000 × 108 Aspen Databank22

H2O -2.2877 × 108 -2.4200 × 108 Aspen Databank22

CO2 -3.9437 × 108 -3.9351 × 108 Aspen Databank22

H3O+ -2.3713 × 108 -2.8583 × 108 Aspen Databank22

OH- -1.5724 × 108 -2.2999 × 108 Wagman et al.29

HCO3- -5.8677 × 108 -6.9199 × 108 Wagman et al.29

CO32- -5.2781 × 108 -6.7714 × 108 Wagman et al.29

MDEAH+ -2.5989 × 108 a -5.1422 × 108 a this work

a The values of MDEAH+ are calculated from the chemical equilibrium constant in Kamps and Maurer,30 which are used as the initial guess to fitexperimental data.

2H2O T H3O+ + OH- (10)

CO2 + 2H2O T H3O+ + HCO3

- (11)

HCO3- + H2O T H3O

+ + CO32- (12)

MDEAH+ + H2O T H3O+ + MDEA (13)

-RT ln Kj ) ∆Gjo(T) (14)

Gs(T) ) Gsig(T) + ∆Gs

igfl(T) (15)

Gsig(T) ) ∆fHs,298.15

ig + ∫298.15

TCp,s

ig dT - T ×

(∆fHs,298.15ig - ∆fGs,298.15

ig

298.15+ ∫298.15

T Cp,sig

TdT) (16)

Table 5. Parameters for Ideal Gas Heat Capacity

Heat Capacity (J/(kmol K))

parameter MDEA H2O CO2

source this work Aspen Databank22 Aspen Databank22

C1i 2.7303 × 104 3.3738 × 104 1.9795 × 104

C2i 5.4087 × 102 -7.0176 7.3437 × 10C3i 0 2.7296 × 10-2 -5.6019 × 10-2

C4i 0 -1.6647 × 10-5 1.7153 × 10-5

C5i 0 4.2976 × 10-9 0C6i 0 -4.1696 × 10-13 0C7i 278 200 300C8i 397 3000 1088.6

a The correlation for the ideal gas heat capacity is given as follows:Cp

ig ) C1i + C2iT + C3iT2 + C4iT3 + C5iT4 + C6iT5, C7i < T < C8i,where T is the temperature (given in Kelvin).

Gi∞,aq(T) ) ∆fGi

ig(T) + RT ln(Hi,w

Pref ) (17)

Gi∞,aq(T) ) ∆fHi,298.15

∞,aq + ∫298.15

TCp,i

∞,aq dT - T ×

(∆fHi,298.15∞,aq - ∆fGi,298.15

∞,aq

298.15+ ∫298.15

T Cp,i∞,aq

TdT) + RT ln(1000

Mw)

(18)

Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX C

∆fGi,298.15∞,aq , as reported in the literature, is based on molality

concentration scale while Gi∞,aq is based on mole fraction scale.

The standard-state properties ∆fGi,298.15∞,aq , ∆fHi,298.15

∞,aq , and Cp,i∞,aq

are available in the literature for most ionic species, except thoseof MDEAH+. (See Tables 4 and 6.) We calculate the reference-state properties of the MDEAH+ ion from the experimentalequilibrium constant of eq 13, as reported in 1996 by Kampsand Maurer.30 The calculated ∆fGi,298.15

∞,aq and ∆fHi,298.15∞,aq values

are given in Table 4, and the calculated Cp,i∞,aq values are given

in Table 6. As will be shown later, we use these calculatedreference-state properties for MDEAH+ as part of the adjustableparameters in the fitting experimental data of thermodynamicproperties, including VLE, heat of solution, heat capacity, andspecies concentration from NMR spectra. Also given in Table6 are estimated values of Cp,i

∞,aq for HCO3- and CO3

2-. They havebeen taken from the 1964 work of Criss and Cobble.31

2.2. Heat of Absorption and Heat Capacity. The CO2 heatof absorption in aqueous MDEA solutions can be derived froman enthalpy balance of the absorption process:

where ∆Habs is the heat of absorption per mole of CO2, HFinall

the molar enthalpy of the final solution, HInitiall the molar enthalpy

of the initial solution, HCO2

gthe molar enthalpy of gaseous CO2

absorbed, nFinal the number of moles of the final solution, nInitial

the number of moles of the initial solution, and nCO2 the numberof moles of CO2 absorbed.

There are two types of heat of absorption: integral heat ofabsorption and differential heat of absorption. The integral heatof absorption for a certain amine-H2O-CO2 system refers tothe heat effect per mole of CO2 during the CO2 loading of theamine solution increasing from zero to the final CO2 loadingvalue of that amine-H2O-CO2 system. The differential heatof absorption for an amine-H2O-CO2 system refers to the heateffect per mole of CO2 if a very small amount of CO2 is addedinto this amine-H2O-CO2 system.

For calculation of both types of heat of absorption, enthalpycalculations for the initial and final amine-H2O-CO2 systemsand for gaseous CO2 are required. The heat capacity of theMDEA-H2O-CO2 system can be calculated from the temper-ature derivative of enthalpy.

We use the following equation for liquid enthalpy:

Here, Hl is the molar enthalpy of the liquid mixture, Hwl the

molar enthalpy of liquid water, Hsl the molar enthalpy of liquid

nonaqueous solvent s, Hi∞,aq the molar enthalpy of solute i

(molecular or ionic) in aqueous-phase infinite dilution, and Hex

the molar excess enthalpy. The terms xw, xs, and xi representthe mole fractions of water, nonaqueous solvent s, and solute i,respectively.

The liquid enthalpy of pure water is calculated from the idealgas model and the ASME Steam Tables EOS for enthalpydeparture:

where Hwl (T) is the liquid enthalpy of water at temperature T,

∆fHw,298.15ig the ideal gas enthalpy of formation of water at 298.15

K, Cp,wig the ideal-gas heat capacity of water, and ∆Hw

igfl(T,p)the enthalpy departure calculated from the ASME Steam TablesEOS.

Liquid enthalpy of the nonaqueous solvent s is calculatedfrom the ideal-gas enthalpy of formation at 298.15 K, the ideal-gas heat capacity, the vapor enthalpy departure, and the heat ofvaporization:

Here, Hsl(T) is the liquid enthalpy of solvent s at temperature T,

∆fHs,298.15ig the ideal-gas enthalpy of formation of solvent s at

298.15 K, Cp,sig the ideal-gas heat capacity of solvent s, ∆Hs

V(T,p)the vapor enthalpy departure of solvent s, and ∆vapHs(T) theheat of vaporization of solvent s.

The PC-SAFT EOS is used for the vapor enthalpy departureand the DIPPR heat of vaporization correlation is used for theheat of vaporization. Table 7 shows the DIPPR equation andthe correlation parameters for the heat of vaporization.

The enthalpies of ionic solutes in aqueous phase infinitedilution are calculated from the enthalpy of formation at 298.15K in aqueous-phase infinite dilution and the heat capacity inaqueous-phase infinite dilution:

where Hi∞,aq(T) is the enthalpy of solute i in aqueous-phase

infinite dilution at temperature T, ∆fHi,298.15∞,aq the enthalpy of

formation of solute i in aqueous-phase infinite dilution at 298.15K, and Cp,i

∞,aq the heat capacity of solute i in aqueous-phaseinfinite dilution.

Table 6. Parameters for Aqueous-Phase Infinite Dilution Heat Capacitya

Heat Capacity (J/(kmol K))

parameter H3O+ OH- HCO3- CO3

2- MDEAH+

source Aspen Databank22 Aspen Databank22 Criss and Cobble31 Criss and Cobble31 this workC1 7.5291 × 104 -1.4845 × 105 -2.9260 × 104 b -3.9710 × 105 b 2.9900 × 105 b

a The aqueous-phase infinite dilution heat capacity is assumed to be constant (Cp,i∞,aq ) C1). b The Cp,i

∞,aq value of MDEAH+ is calculated from thechemical equilibrium constant in Kamps and Maurer,30 which is used as the initial guess to fit experimental data. The Cp,i

∞,aq values of HCO3- and CO3

2-

are the average values of heat capacity between 298 K and 473 K (taken from Criss and Cobble31).

∆Habs )nFinalHFinal

l - nInitialHInitiall - nCO2

HCO2

g

nCO2

(19)

Hl ) xwHwl + xsHs

l + ∑i

xiHi∞,aq + Hex (20)

Table 7. Parameters for Heat of Vaporization (Expressed in Unitsof J/kmol)a

component i MDEAsource this workC1i 9.7381 × 107

C2i 4.6391 × 10-1

C3i 0C4i 0C5i 0Tci 741.9b

a The DIPPR equation for the heat of vaporization is given as follows:∆vapHi ) C1i(1 - Tri)Z, where Z ) C2i + C3iTri + C4iTri

2 + C5iTri3 and

Tri ) T/Tci (here, Tci is the critical temperature of component i). Thetemperatures are given in Kelvin. b The Tci value for MDEA is obtainedfrom Von Niederhausern et al.32

Hwl (T) ) ∆fHw,298.15

ig + ∫298.15

TCp,w

ig dT + ∆Hwigfl(T, p) (21)

Hsl(T) ) ∆fHs,298.15

ig + ∫298.15

TCp,s

ig dT + ∆HsV(T, p) - ∆vapHs(T)

(22)

Hi∞,aq(T) ) ∆fHi,298.15

∞,aq + ∫298.15

TCp,i

∞,aq dT (23)

D Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX

Both ∆fHi,298.15∞,aq and Cp,i

∞,aq are also used in the calculation ofGibbs free energy of the solutes, thus impacting chemicalequilibrium calculations. In this study, ∆fHi,298.15

∞,aq and Cp,i∞,aq for

MDEAH+ are determined by fitting to the experimental phaseequilibrium data, the heat of solution data, and the speciationdata, together with molality scale Gibbs free energy of formationat 298.15 K, ∆fGi,298.15

∞,aq , and NRTL interaction parameters.The enthalpies of molecular solutes in aqueous phase infinite

dilution are calculated from Henry’s law:

Hi∞,aq(T) ) ∆fHi

ig(T) - RT 2(∂ ln Hi,w

∂T ) (24)

where ∆fHiig(T) is the ideal gas enthalpy of formation of solute

i at temperature T, and Hi,w Henry’s constant of solute i in water.Excess enthalpy (Hex) is calculated from the activity coef-

ficient model (i.e., the electrolyte NRTL model).2.3. Activity Coefficients. Activity coefficients are required

in phase equilibrium calculations, aqueous-phase chemicalequilibrium calculations, heat of absorption, liquid heat capacity,and liquid enthalpy calculations. The activity coefficient of acomponent in a liquid mixture is a function of temperature,pressure, mixture composition, and choice of reference state.In VLE calculations, we use the asymmetric mixed-solventreference state for the molecular solute CO2, and in aqueous-

phase chemical equilibrium calculations, we choose the aqueous-phase infinite dilution reference state for molecular solute CO2

and all ionic species.In applying the electrolyte NRTL model for liquid-phase

activity coefficient calculations, the binary NRTL interactionparameters for molecule-molecule binary, molecule-electrolytebinary, and electrolyte-electrolyte binary systems are required.Here, electrolytes are defined as cation and anion pairs. Inaddition, solvent dielectric constants are needed to facilitatecalculations of long-range ion-ion interaction contribution toactivity coefficients. Table 8 shows the dielectric constantcorrelation used in this work for MDEA.

Unless specified otherwise, all molecule-molecule binaryparameters and electrolyte-electrolyte binary parameters aredefaulted to zero. All molecule-electrolyte binary parameters aredefaulted to (8,-4), average values of the parameters as reportedfor the electrolyte NRTL model.12 The nonrandomness factor (R)is fixed at 0.2. The calculated thermodynamic properties of theelectrolyte solution are dominated by the binary NRTL parametersassociated with the major species in the system. In otherwords, the binary parameters for the water-MDEA binary, thewater-(MDEAH+, HCO3

-) binary, the water-(MDEAH+, CO32-)

binary, and the MDEA-(MDEAH+, HCO3-) binary systems

determine the calculated thermodynamic properties. These binaryparameters, in turn, are identified from fitting to available experi-mental data.

3. Modelling Results

Table 9 summarizes the model parameters and sources ofthe parameters used in the thermodynamic model. Most of theparameters can be obtained from the literature. The remainingparameters are determined by fitting to the experimental data.

Table 8. Parameters for Dielectric Constanta

component i MDEAsource Aspen Databank22

Ai 21.9957Bi 8992.68Ci 298.15

a The correlation for the dielectric constant is given as follows: εi(T)) Ai + Bi[(1/T) - (1/Ci)], where T is the temperature (given in Kelvin).

Table 9. Parameters Estimated in Modeling

parameter component source data used for regression

Antoine equation MDEA regression vapor pressure of MDEA∆vapH MDEA regression heat of vaporization of MDEA, calculated from the vapor

pressure using the Clausius-Clapeyron equationdielectric constant MDEA Aspen Databank22

Henry’s constant CO2 in H2O Yan and Chen25

CO2 in MDEA this workNRTL binary parameters CO2-H2O binary Yan and Chen25

MDEA-H2O binary regression VLE, excess enthalpy, and heat capacity for the MDEA-H2O binarymolecule-electrolyte binaries regression VLE, excess enthalpy, heat capacity, and species concentration from

NMR spectra for the MDEA-H2O-CO2 system∆fG298.15

ig H2O, MDEA, CO2 Aspen Databank22

∆fH298.15ig H2O, MDEA, CO2 Aspen Databank22

Cpig H2O, CO2 Aspen Databank22

MDEA regression liquid heat capacity of MDEA∆fG298.15

∞,aq H3O+, OH-, HCO3-, CO3

2- Aspen Databank22

MDEAH+ regression VLE, excess enthalpy, heat capacity, and species concentration fromNMR spectra for the MDEA-H2O-CO2 system

∆fH298.15∞,aq H3O+, OH-, HCO3

-, CO32- Aspen Databank22


Cp∞,aq H3O+, OH- Aspen Databank22

HCO3-, CO3

2- Criss and Cobble31


Table 10. Experimental Data Used in the Regression for Pure MDEA

data type temperature, T (K) pressure, P (kPa) data points average relative deviation, |∆Y/Y| (%) reference

vapor pressure 293-401 0.0006-1.48 26 1.5 Daubert et al.33

vapor pressure 420-513 3.69-90.4 14 4.0 Noll et al.34

vapor pressure 420-738 3.69-3985 23 2.9 VonNiederhausern et al.32

liquid heat capacity 299-397 5 0.5 Maham et al.35

liquid heat capacity 303-353 11 0.4 Chen et al.36

liquid heat capacity 278-368 19 0.3 Zhang et al.37

Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX E

3.1. MDEA. Extensive experimental vapor pressure data andliquid heat capacity data are available for MDEA. The data usedin the regression for MDEA and the correlation results aresummarized in Table 10.

Table 11 shows the Antoine equation parameters regressed fromthe recently available vapor pressure data.32-34 The heat ofvaporization (from 293 K to 473 K) generated with the regressedAntoine equation parameters through the Clausius-Clapeyronequation are used to determine the DIPPR heat of vaporizationequation parameters (shown in Table 7). The ideal-gas heat capacitycorrelation parameters are obtained by fitting to the liquid heatcapacity data35-37 (shown in Table 5). Table 10 shows the excellentcorrelation of the experimental data for vapor pressure, with anaverage relative deviation of <4%, and liquid heat capacity, withan average relative deviation of <0.5%.

The PC-SAFT parameters of MDEA (shown in Table 1) areregressed from the vapor pressure data32-34 (with an averagerelative deviation of 13.1%), the liquid heat capacity data35-37

(with an average relative deviation of 22.6%), and the liquiddensity data38,39 (with an average relative deviation of 2.7%).

3.2. MDEA-H2O System. Extensive literature data onVLE,40-42 excess enthalpy,9,35,43 and heat capacity36,37,44 of theMDEA-H2O binary system are available (see Table 12). Thesedata cover the complete MDEA-H2O binary concentrationrange from room temperature to 458 K. Together, all of thesedata are used to identify the NRTL binary parameters, includingtheir temperature dependencies for the MDEA-H2O binarysystem.

The regressed NRTL parameters are summarized in Table13. The experimental data for the binary MDEA-H2O systemare well-represented. The average relative deviations betweenthe calculated values and the experimental data are summarizedin Table 12. Figure 1 shows the parity plot, while Figure 2 showsthe comparison for the experimental total pressure data and thecalculated results from the model. Figure 3 shows the compari-son results for the MDEA vapor composition. The excessenthalpy fit is given in Figure 4. Both the experimental excessenthalpy data from Posey9 and those of Maham et al.35,43 arerepresented very well. Figure 5 shows the model also providessatisfactory representation of the heat capacity data.

Figure 6 shows the model predictions for water and MDEAactivity coefficients at 313, 353, and 393 K. While the water

activity coefficient remains relatively constant, the modelsuggests that the MDEA activity coefficient varies strongly withMDEA concentration and temperature, especially in diluteaqueous MDEA solutions.

Table 13. Regressed NRTL Parameters for the MDEA-H2O BinarySystem with r ) 0.2a

parameter component i component j value standard deviation

aij H2O MDEA 8.5092 0.1641aij MDEA H2O -1.7141 0.0566bij H2O MDEA -1573.9 45.70bij MDEA H2O -261.85 22.97

a Correlation for the NRTL parameters: τij ) aij + bij/T, where T isthe temperature (given in Kelvin).

Figure 1. Parity plot for the MDEA-H2O system total pressure, experimentversus model: (4) Xu et al.,40 (O) Voutsas et al.,41 and (0) Kim et al.42

Figure 2. Comparison of the experimental data from Kim et al.42

(represented by symbols: (O) T ) 373 K, (4) T ) 353 K, (0) T ) 333 K,and (×) T ) 313 K) for total pressure of the MDEA-H2O binary solutionand the model results (represented by lines).

Table 11. Antoine Equation Parameters for Pure MDEAa

parameter component i value

C1i MDEA 1.2276 × 102

C2i MDEA -1.3253 × 104

C3i MDEA -1.3839 × 10C4i MDEA 3.20 × 10-6

a The correlation for the Antoine equation is given as follows: ln Pi*,l

) C1i + C2i/T + C3i ln T + C4iT2, where T is the temperature (given inKelvin).

Table 12. Experimental Data Used in the Regression for the MDEA-H2O System

data type temperature, T (K) pressure, P (kPa) MDEA mole fractiondata

pointsaverage relative

deviation, |∆Y/Y| (%) reference

VLE (isoconcentration), TP 326-381 13-101 0.016-0.26 34 3.4a Xu et al.40

VLE (isobaric), Tx 349-458 40.0-66.7 0-0.93 30 3.3a Voutsas et al.41

VLE (isothermal), TPxy 313-373 6-100 0-0.36 61 3.0a Kim et al.42

excess enthalpy (isothermal) 298, 342 0.02-0.74 19 6.3 Posey9

excess enthalpy (isothermal) 298, 303 0.03-0.93 26 5.4 Maham et al.35

excess enthalpy (isothermal) 338 0.10-0.90 9 11.2 Maham et al.43

heat capacity (isobaric) 303-353 100 0.13-0.80 44 2.2 Chiu and Li44

heat capacity (isobaric) 303-353 100 0.20-0.80 44 2.2 Chen et al.36

heat capacity (isobaric) 278-368 100 0-1.0 228 2.8 Zhang et al.37

a The average relative deviation is that of total pressure.

F Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX

3.3. MDEA-H2O-CO2 System. Extensive VLE,5,6,8,13,45-64

heat of absorption,65,66 heat capacity,67 and NMR spectro-scopic68 data of the ternary MDEA-H2O-CO2 system areavailable.

The terms ∆fG298.15∞,aq , ∆fH298.15

∞,aq , and Cp∞,aq of MDEAH+ and

the binary NRTL parameters for major molecule-electrolytepairs are regressed from selected experimental data of theMDEA-H2O-CO2 system. Table 14 summarizes the VLE,5,6,13

heat of absorption,65,66 heat capacity,67 and species concentra-tion68 data used to obtain these parameters.

Species concentration data from NMR spectra are very usefulto validate the model predictions for the species distribution inthe ternary system. Calculated heat of absorption of CO2 bythe MDEA solution also strongly depends on the speciesdistribution.

For VLE data, we choose the total pressure data of Kuranovet al.,5 Kamps et al.,6 and the CO2 partial pressure data ofErmatchkov et al.13 in the regression. Together, these data covertemperatures from 313 K to 413 K, pressures from 0.1 kPa to6000 kPa, MDEA mole fractions from 0.03 to 0.13, and CO2

loadings from 0.003 to 1.32. The CO2 partial pressure data ofJou et al.45 also cover wide ranges for temperature, pressure,MDEA concentration, and CO2 loading. However, consideringthe reported inconsistency5,6,13 between these data45 and thoseof Kuranov et al.,5 Kamps et al.,6 and Ermatchkov et al.,13 wechoose to exclude the data of Jou et al.45 from the regression.The Jou et al. data45 and all other available literature VLEdata8,46-64 are used only for model validation.

The average relative deviations between the correlation resultsand the various experimental data are shown in Table 14. Theregressed parameters for the MDEA-H2O-CO2 system aresummarized in Table 15. As expected, the regressed values of∆fG298.15

∞,aq , ∆fH298.15∞,aq , and Cp

∞,aq for MDEAH+ in Table 15 arecomparably close to the estimated values reported in Tables 4and 6.

Figures 7 and 8 show that most of the total pressure data ofKuranov et al.5 and Kamps et al.6 are fitted within (20%.Figures 9-11 show the excellent correlation results for the totalpressure data for MDEA concentration from 2 m to 8 m, CO2

loading from 0.11 to 1.32, temperature from 313 K to 413 K,and pressure up to 6000 kPa. Figures 12 and 13 show that mostof the CO2 partial pressure data of Ermatchkov et al.13 are fittedwithin (30%. Figure 12 suggests that there is a slight systematicdeviation that changes from negative to positive as the CO2

loading increases. Figures 14-16 show the satisfactory cor-relation results for the CO2 partial pressure data for MDEAconcentration from 2 m to 8 m, CO2 loading from 0.003 to 0.78,temperature from 313 K to 393 K, and pressure from 0.1 kPa

Figure 3. Comparison of the experimental data from Kim et al.42

(represented by symbols: (O) T ) 373 K, (4) T ) 353 K, (0) T ) 333 K,and (×) T ) 313 K) for the vapor composition of the MDEA-H2O binarysolution and the model results (represented by lines).

Figure 4. Comparison of the experimental data from Posey9 (representedby full symbols: (b) T ) 298 K, ([) T ) 342 K) and Maham et al.35,43

(represented by empty symbols: (O) T ) 298 K, (4) T ) 313 K, (0) T )338 K) for excess enthalpy of the MDEA-H2O binary solution and themodel results (represented by lines).

Figure 5. Comparison of the experimental data from Chen et al.36

(represented by symbols: (O) MDEA mole fraction ) 0.8, (4) MDEA molefraction ) 0.6, (0) MDEA mole fraction ) 0.4, and (×) MDEA molefraction ) 0.2) for heat capacity of the MDEA-H2O binary solution andthe model results (represented by lines).

Figure 6. Model predictions of water and MDEA activity coefficients at313, 353, and 393 K over the entire mole fraction range; solid lines representwater activity coefficients and dashed lines represent MDEA activitycoefficients.

Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX G

to 70 kPa. The correlation results match the experimental datawell, except that the calculated CO2 pressure at 313 K is slighterhigher than the measured values for the 8 m MDEA solution athigh CO2 loading (see Figure 16). Upon further examination,we find that, under the same conditions, the predicted totalpressure matches the experimental data of Sidi-Boumedine etal.62 well.

Table 16 shows a comparison of model predictions andexperimental VLE data from numerous other sources notincluded in the regression. The results highlight the fact thatwe cannot match all the VLE data because the experimental

Table 14. Experimental Data Used in the Regression for the MDEA-H2O-CO2 System

data typetemperature,

T (K)pressure,P (kPa)

MDEAmole fraction CO2 loading

datapoints

average relativedeviation, |∆Y/Y| (%) reference

VLE, TPx, total pressure 313-413 70-5000 0.035-0.067 0-1.32 82 6.8 Kuranov et al.5

VLE, TPx, total pressure 313-393 200-6000 0.126 0.13-1.15 23 10.5 Kamps et al.6

VLE, TPx, CO2 pressure 313-393 0.1-70 0.033-0.132 0.003-0.78 101 17.7 Ermatchkov et al.13

heat of solution 313-393 0.06 0.1-1.4 112 6.8 Mathonat65

heat of solution 298 0.017-0.061 0.02-0.25 40 2.1 Carson et al.66

heat capacity (isobaric) 298 0.061-0.185 0-0.64 39 3.0 Weiland et al.67

species concentration 293-313 0.04 0.1-0.7 8 47.5 Jakobsen et al.68

Table 15. Regressed Parameters for the MDEA-H2O-CO2 System with r ) 0.2

parameter component i component j value standard deviation

∆fG298.15∞,aq (J/kmol) MDEAH+ -2.5951 × 108 2.1986 × 105

∆fH298.15∞,aq (J/kmol) MDEAH+ -5.1093 × 108 5.8718 × 105

Cp∞,aq (J/(kmol K)) MDEAH+ 3.3206 × 105 1.2799 × 104

τij H2O (MDEAH+, HCO3-) 8.7170 0.2246

τij (MDEAH+, HCO3-) H2O -4.2995 0.0836

τij H2O (MDEAH+, CO32-) 10.4032 0.3676

τij (MDEAH+, CO32-) H2O -4.9252 0.1248

τij MDEA (MDEAH+, HCO3-) 5.2964 0.2746

τij (MDEAH+, HCO3-) MDEA -0.8253 0.0685

Figure 7. Ratio of experimental total pressure to calculated total pressure,as a function of CO2 loading ((4) data from Kuranov et al.5 and (O) datafrom Kamps et al.6).

Figure 8. Parity plot for the MDEA-H2O-CO2 system total pressure:experiment versus model ((4) Kuranov et al.5 and (O) Kamps et al.6).

Figure 9. Comparison of the experimental data from Kuranov et al.5

(represented by symbols: (O) T ) 413 K, (4) T ) 393 K, (×) T ) 373 K,(0) T ) 353 K, and (]) T ) 313 K) for total pressure of theMDEA-H2O-CO2 system and the model results (represented by lines);the MDEA concentration is ∼2 m.

Figure 10. Comparison of the experimental data from Kuranov et al.5

(represented by symbols: (O) T ) 413 K, (4) T ) 393 K, (×) T ) 373 K,(0) T ) 353 K, and (]) T ) 313 K) for total pressure of theMDEA-H2O-CO2 system and the model results (represented by lines);the MDEA concentration is ∼4 m.

H Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX

data from different sources can be inconsistent. With theexception of the data from Jou et al.,45 Silkenbaeumer et al.,56

and Ali and Aroua,61 the model predictions are very satisfactory,with the average relative deviation on pressure (either totalpressure or CO2 partial pressure) in the range of 7%-80%. Itis particularly significant that the model predictions give anexcellent match with the recent data of Kamps et al.,60 Sidi-Boumedine et al.,62 and Ma’mum et al.63

Figure 17 shows the species distribution as a function of CO2

loading for a 23 wt % MDEA solution at 293 K. The calculated

Figure 11. Comparison of the experimental data from Kamps et al.6

(represented by symbols: (O) T ) 393 K, (0) T ) 353 K, and (]) T ) 313K) for total pressure of the MDEA-H2O-CO2 system and the model results(represented by lines); the MDEA concentration is ∼8 m.

Figure 12. Rato of experimental CO2 partial pressure ((O) Ermatchkov etal.13) to calculated CO2 partial pressure (line), as a function of CO2 loading.

Figure 13. Parity plot for CO2 partial pressure of the MDEA-H2O-CO2

system: experiment ((O) Ermatchkov et al.13) versus model (line).

Figure 14. Comparison of the experimental data for CO2 partial pressureof the MDEA-H2O-CO2 system and the model results; the MDEAconcentration is ∼2 m. Empty symbols are data from Ermatchkov et al.13

((O) T ) 393 K, (0) T ) 353 K, (]) T ) 313 K), solid lines represent the2009 eNRTL model results, and dashed lines represent the 1986 eNRTLmodel results.





Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX I

concentrations of the species are consistent with the experimentalNMR measurements from Jakobsen et al.68

Figures 18-20 show comparisons of the model correlationsand the experimental data of Mathonat65 for the integral heatof CO2 absorption in aqueous MDEA solution at 313, 353, and393 K, respectively. The calculated values are in reasonableagreement with the experimental data. Also shown in Figures18-20 are the predicted differential heats of CO2 absorption.The integral heat and the differential heat overlap at low CO2

loadings, and then diverge much at high CO2 loadings (i.e.,>0.8), where the differential heat decreases by >50%. We furthershow the computed integral heat of absorption as the sum ofthe various contributions from reactions 10-13, CO2 dissolution,and excess enthalpy.

where ∆Habs is the integral heat of absorption per mole of CO2,∆Hi° the standard heat of reaction for reaction i per mole of

key component reacted, and ∆ni the reaction extent of thereaction key component for reaction i when 1 mol CO2 isabsorbed.

The heat of CO2 dissolution (∆Hdissolution) is calculated as theenthalpy difference between 1 mol of CO2 in the vapor phaseand 1 mol of CO2 in aqueous-phase infinite dilution. Thecontribution of excess enthalpies (∆Hex) is computed as theexcess enthalpy difference between the final and initial com-positions of the solution per mole of CO2 absorbed.

The results in Figures 18-20 show that the heat of absorptionis dominated by MDEAH+ dissociation and excess enthalpy.In addition, CO2 dissolution is important near room temperature,whereas CO2 dissociation becomes more important at highertemperatures.

Figure 21 shows a comparison of the model correlations andthe experimental data of Weiland et al.67 for heat capacity ofthe MDEA-H2O-CO2 system. The model results are consistentwith the data.

To show the impact of the different versions of theelectrolyte NRTL model to the model results, we perform

Table 16. Comparison between Experimental Data and Model Predictions for Total Pressure or CO2 Partial Pressure of the MDEA-H2O-CO2

System

source data points temperature, T (K) pressure, P (kPa) MDEA concentration CO2 loading |∆P/P|a (%)

Jou et al.45 118 298-393 0.001-6000 0.044-0.128 0.0004-1.68 204Chakma and Meisen46 76 373-473 100-5000 0.03-0.12 0.01-0.95 31.5Maddox et al.47 99 310-388 20-6000 0.02-0.04 0.17-1.51 21.1Austgen et al.8 14 313 0.005-100 0.045-0.13 0.003-0.67 32.2MacGregor and Mather48 5 313 1-4000 0.04 0.12-1.2 22.1Jou et al.49 37 313-373 0.004-260 0.07 0.002-0.80 37.5Dawodu and Meisen50 12 373-393 160-4000 0.12 0.09-0.8 13.3Liu et al.51 16 303-363 20-350 0.09 0.09-0.85 28.5Mathonat et al.52 9 313-393 2000-10000 0.06 0.5-1.3 57.4Rho et al.53 103 323-373 0.1-268 0.008-0.31 0.006-0.68 78.7Baek and Yoon54 12 313 1-2000 0.06 0.12-1.13 53.6Rogers et al.55 34 313-323 0.00007-1 0.04-0.13 0.0002-0.12 27.1Silkenbaeumer et al.56 11 313 12-4000 0.07 0.2-1.3 135Xu et al.57 65 328-363 4-800 0.07-0.13 0.04-0.9 20.2Lemoine et al.58 13 298 0.02-1.64 0.04 0.02-0.26 11.9Bishnoi and Rochelle59 3 313 0.1-0.7 0.13 0.01-0.03 17.9Kamps et al.60 5 313 80-5000 0.03 1.06-1.41 8.9Ali and Aroua61 15 313-353 0.08-100 0.04 0.05-0.8 495Sidi-Boumedine et al.62 103 298-348 2.7-4500 0.05-0.11 0.008-1.30 7.7Ma’mun et al.63 34 328-358 66-813 0.12 0.17-0.81 6.5Dicko et al.64 5 323 6-434 0.12 0.1-0.9 48.5

a Experimental pressure expressed either as total pressure or CO2 partial pressure.

Figure 17. Comparison of the experimental data for species concentrationin MDEA-H2O-CO2 and the model results at T ) 293 K. MDEAconcentration is 23 wt %. Symbols represent experimental data fromJakobsen et al.68 ((O) MDEA, (4) HCO3

-, (0) MDEAH+, (×) CO32-, (])

CO2); lines represent model results ((s) MDEA, (- - -) HCO3-, (- · -)

MDEAH+, (- · · -) CO32-, and ( · · · ) CO2.

∆Habs ) ∑i)1

k

∆ni∆Hi° + ∆Hdissolution + ∆Hex (25)

Figure 18. Integral CO2 heat of absorption in 30 wt % MDEA aqueoussolution at 313 K. Symbols (0) represent experimental data from Matho-nat;65 lines represent model results ((s) integral heat of absorption,(- · · -) differential heat of absorption, ( · · · ) contribution of reactions,(- · -) contribution of CO2 dissolution, (- - -) contribution of excessenthalpies).

J Ind. Eng. Chem. Res., Vol. xxx, No. xx, XXXX

VLE predictions with the same model parameter values givenin Table 15 with the 1986 version of the electrolyte NRTL

model.11 Figures 14-16 show that the two versions of themodel yield practically identical results at low MDEAconcentrations. The difference increases slightly with increas-ing MDEA concentration.

4. Conclusion

To support process modeling and simulation of the CO2

capture process with MDEA, the electrolyte NRTL model hasbeen successfully applied to correlate the available experimentaldata on thermodynamic properties of the MDEA-H2O-CO2

system. The model has been validated for predictions of vapor-liquid equilibrium (VLE), heat capacity, and CO2 heat ofabsorption of the MDEA-H2O-CO2 system with temperaturesfrom 313 K to 393 K, MDEA concentrations up to 8 m (∼50wt %), and CO2 loadings up to 1.32. This model should providea comprehensive thermodynamic property representation for theMDEA-H2O-CO2 system over a broader range of conditionsand give more-reliable predictions than those from previousworks.

Acknowledgment

The authors thank Huiling Que and Joseph DeVincentis fortheir support in preparing the manuscript.

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ReceiVed for reView March 19, 2010ReVised manuscript receiVed June 25, 2010

Accepted July 12, 2010

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termodynamic modeling for co2

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