thermophysical properties useful equations

8/22/2019 Thermophysical Properties Useful Equations

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Session 2 - Useful Equations


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Vapor-liquid equilibria fundamental equations

n The K-values are defined as:

and

ii

i

=

i

i

n

i

i

n

= =

= =1 1


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Training

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Vapor-liquid equilibria fundamental equations

K-Value

Ki = yi / xi i = 1, .., n

Component material balance

li = fi / (1 + Ki L/V) i = 1, .., n

li= mols component i in liquid

fi = mols component i in feed

L = total mols liquid

V = total mols vapor


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Phase equilibria in ideal mixtures

Ideal mixtures - Raoults law

Ki = Pi* / P

Molecules are of samen Size

n Shape

n Molecular type


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Basic phase equilibria relations

n K-values can be calculated via the equation of stateapproach

or the activity coefficient approach

( )

K

y

x

Pv

RTP P

Pii

i

i

l

i

sat

i

sat i

l

i

sat

iv= =

-

g f

f

exp

K

y

xii

i

i

l

iv= =

f

f


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n Although most LTD technologies use the

equation of state (EOS) approach we will

focus on the activity coefficient approach

because it more readily demonstrates theeffect of non-idealities


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K-values - rigorous equation

-

F

Fg=

Li

*i

P,i

*iP,i*ii

i


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*iP,i

P,i

i

i

i

Li

i

y

x

V

T*P

P

K

F

F

g

Vapor-liquid equilibrium constant

Pressure

Vapor pressureAbsolute temperature

Liquid molar volume of component i

Liquid mole fraction of component i

Vapor mole fraction of component i

Liquid phase activity coefficient of component i

Fugacity coefficient of mixture at system pressure

Pure component fugacity coefficient at its vapor pressure


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K-values

Non-ideal mixtures

Ki = Pi* Eigi/ P

Ei = non-ideal gas correctionsgi = activity coefficient

Application: very low to moderate pressures

n Ei is close to unity for low pressures

n Ei becomes a significant correction at moderate

pressures


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10

VLE - effect of pressure

Very low P Vacuum

Low P 1 - 3 atm.

Moderate P 3 - 17 atm.High P 17- 70 atm.

Very high P >70 atm.


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K-values

:stateofequationangsinucalculatedareand

compoundpuretheofpropertiesareVandP

P,i*iP,i

Li

*i

FF

Calculation of non-ideal gas corrections

Redlich-Kwong (RK)

Soave-Redlich-Kwong (SRK)

Peng-Robinson (PR)


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Activity coefficient

giaccounts for differences inn molecular type

n molecular size

n molecular shape

gimodels:n Regular

n NRTL

n Wilson

n Uniquac

n van Laarn Margules

n

Unifac


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n Only Unifac is predictive (based on group

contributions)

n Parameters for all other methods must be determined

from experimental vapor-liquid equilibria data


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Group contribution estimation methods

CH3

CH3 - CH2 - C = OH

CH3

T - Amyl Alcohol

Method 1-CH3 3

-CH2- 1

- C - 1

-OH 1

Method 2C 4

H 9

-CH2- 1H in OH 1

Sec-Tert 1


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Margules:

A12 and A21 are adjustable parameters

( )[ ]2211221121 xxAA2A -+=g


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n Interaction parameters required for every pair of

compounds in the mixture.


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In LTD we use

Regular - hydrocarbon systems

NRTL - non-ideal systems

Uniquac - non-ideal systems

Unifac - fill in missing interaction parameters


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ACTIVITY COEFFICIENTS

1 ETHYLBENZENE

2 ETHYLCYCLOHEXANE

P = 1 ATM.


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n Activity coefficient of a component rises to its

highest value when the component is most dilute

n Infinite dilution

n If infinite dilution activity coefficient is 2.0 then that

component has volatility that is twice what its vapor

pressure would indicate.

n is unity when the composition approaches 100%


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Non-ideality has an effect on column design

n More difficult to keep heavy key component out ofoverhead product

n Easier to strip light key component out of bottoms

product

n Will change feed tray location

n Overall effect on column depends on factors such

as product specifications, etc.


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A t


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Azeotropes

n A result of non-idealities which boosts the volatilityof one component to match the other component

(binary mixture).

n If a third component is added it will have an effect

on the activity coefficients thus changing the

volatilities.

n Two components which form an azeotrope do not

necessarily stick together in a multi-component

mixture.

A t


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Azeotropes

A very specific result of the more general phenomena:

Compounds do not necessarily end up where theirvapor pressures say they will end up

A i i C f ti t


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Ammonia in C2 fractionator

Vapor IdealPressure Relative

NBP psia Volatility

Ethylene -154.7 390 1.77

Ethane -127.5 220 1.0

NH3 -28.0 30 0.14

NH3 in small amounts will distribute between ethylene

and ethane

n Reason: activity coefficient of NH3 (dilute) is in the

order of 7.5


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Relative volatility of 1,3 Butadiene to n-Butane

Comparison of relative volatilities of C4h d b t 1 3 B t di


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hydrocarbons to 1-3 Butadiene

with and without an 80-mol % acetonitrile 20-mol%

water solvent

No Solvent Solvent

1,3 Butadiene 1.00 1.00cis-2-Butadiene 0.72 1.35

Isobutylene 0.90 1.83

1-Butene 0.90 1.96

n-Butane 0.86 2.84

Isobutane 0.93 3.63

Azeotropes


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Azeotropes

n A solvent can be added specifically to break theazeotrope.

n Extractive distillation

Extractive distillation


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Extractive distillation

Liquid Liquid Equilibrium


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Liquid-Liquid Equilibrium

n In cases considered above the components aremiscible

n Highly non-ideal mixtures can lead to immiscibility -

a second liquid phase separates itself from the first.

Oil and water do not mix!

n Additional phase relationships are needed


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Water/hydrocarbon


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Water/hydrocarbon

Three phase equilibrian The point of three phase equilibrium is sometimes called an

azeotrope. The proper term is heterogeneous azeotrope.

n Temperature is a minimum.n Composition of phases are not equal.

Liquid-liquid equilibrium


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Liquid-liquid equilibrium

L-L equilibrium fundamental equation

applies to any two liquid phases in equilibrium, L-L or

V-L-L

L2i

xL2i

L1i

xL1i

=

Water - hydrocarbon systems


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Water hydrocarbon systems

n Non-ideality is high enough so that

n Hydrocarbon phase contains very little water

n Water phase contains very little hydrocarbon

Water - hydrocarbon systems


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Water hydrocarbon systems

For a water/hydrocarbon mixture we can assume

L1 = water phase

L2 = hydrocarbon phase

2Li

2Li

1Li

1Li g=g

11x

1Lw

1L

w

=g

=

*w

2Lw xx =


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n X*W = mole fraction solubility of water in thehydrocarbon phase when full L-L

equilibrium is attained

n SDB I/9.4-9.1


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V-L-L equilibrium - water/hydrocarbon


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q y

Therefore for the hydrocarbon phase in equilibriumwith the vapor

ow

*w

2Lw

*w

2Lw

=

=g

V-L-L equilibrium - water/hydrocarbon


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q y

and for the water phase in equilibrium with the vapor

ow1L

w=

V-L-L equilibrium - Water/Hydrocarbon


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q y

n Water K-values can be calculated with simplifiedrelationships outlined above.

n SDB I 9.4-5 through 9.4-9

n Avoids using an activity coefficient method

n Of course, an activity coefficient method can be

used.

n This is the most general approach

n Highly non-ideal systems other than water-hydrocarbon

Two Liquid Phases


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q

n Rigorous VLLE n Water decant option

L1

L2

V

L

W

V

Rigorous VLLE Calculations


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Vapor

Liquid 2Liquid 1

VLE K-valuesVLE K-values

LLE K-values

Must enable two-liquid phase calculations.

Water Decant Option


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Vapor

PureWater

Liquid

Water VaporPressure

VLE K-values

Water Solubility

WATER DECANT = ON



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Decant feature in PRO/II

n Special water calculations for water/hydrocarbon mixtures.

n Possible only for a hydrocarbon K-value type, e.g., SRK,

CS, BK10, etc.

WATER DECANT = OFF

Water K-value calculated by chosen K-value method.



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WATER DECANT = ON, SOLUBILITY = SIMSCI

n DECANT=ON is a modification of the chosen K-value

methodn K-value method must be a hydrocarbon method

n A hybrid method - separate methodology for water and

hydrocarbons



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WATER DECANT = ON, SOLUBILITY = SIMSCI

n Water K-Value in hydrocarbon phase calculated from

solubilities.n Solubilities from choice of methods.

n Water K-Value in water phase calculated from vapor

pressure.

n Hydrocarbon K-values from chosen K-value method

n Logic in flash and column to detect second liquid phase.

n Also is an option to calculate water properties from steamtables.

Azeotropes


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n A solvent that forms a heterogeneous azeotropewith one of the components of a homogeneous

azeotrope can be added specifically to break the

azeotrope.n Example: Add benzene to recover pure ethanol from

an aqueous mixture.


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Azeotropic system for the production of absolute


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ethanol using benzene

thermophysical properties useful equations

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