1

Chapter 5Lecture 8

- Thermodynamic Web- Departure Functions- Review Equations of state (chapter 4, briefly)

Chapter 6Chapter 6- Equilibrium (chemical potential)

* Pure Component* Mixtures

Ch t 7Chapter 7- Fugacity (chemical potential fugacity equilibrium calculations)

* Vapor (overview), liquid, solids- Activity Coefficients [Fugacity Coefficients (overview)]y [ g y ( )]

Chapter 8- Phase Equilibrium

* Diagrams* Vapor Liquid (VLE)* Vapor – Liquid (VLE)* Liquid – Liquid (LLE)* Solid – Liquid (SLE)

Chapter 9- Reaction Equilibria

Fugacity Coefficient (methods to calculate)2

i1. Data2. Equations of State3. Generalized correlations

a. Pure Fluid

b. Multicomponent system: i

i

3. Generalized correlations i

P

idPZ 1ln

a. Pure Fluid1. Data

at 38oC, 13.79 bar2CO

i PZ

0

1ln

P dPP

1. DataP [bar] Z

1 0.99645 0.9805

i P

dPRTP

0

1ln 10 0.960720 0.9195

P

i dPPRT0

1ln 95.02data

CO

Fugacity Coefficient (methods to calculate)3

ia. Pure Fluidi

2. Equations of State

See handout on website from Kyle for Peng Robinson EOS

0)()23()1( 23223 ABBBZBBAZBZ

for Peng-Robinson EOS

BZABZZ 21ln)ln(1ln

BZB

BZZ21

ln22

)ln(1ln

at 38oC, 13.79 bar2CO

935.02

PREOSCO

Fugacity Coefficient (methods to calculate)4

1. Data a. Pure Fluid ii 2. Equations of State3. Generalized correlations b. Multicomponent system: i

vdw EOS

RT

aayayb

bRT

bPPy

f babaa

mix

amixva

a

va

2lnˆln

ˆln

c

Peng Robinson EOS (see Kyle handout on web)

Z

BB

BZBZ

A

A

BB

BA ij

ijji

i

1

2121ln

2

22ˆln 1

BZ

BBZABB

ln

2122

Fugacity Coefficient (Continued)5

Fugacity Coefficient (Continued)6

Fugacity Coefficient (PREOS)7

c BZZ

BB

BZBZ

A

A

BB

BA ij

ijji

i

ln1

2121ln

2

22ˆln 1

22

1

2 1145724.0

i T

PA i

ri ir

i

PB 07780.02

ir

iT i

ri

iri T

c

BB c c

AA

i

iiBB1

i j

ijji AA1 1

AAkAA 1 jiijjiij AAkAA 1

0)()23()1( 23223 ABBBZBBAZBZ 0)()23()1( ABBBZBBAZBZ

Fugacity Coefficient (AspenPlus Examples)8

1. for ethylene at 25oC and 40 bari

2. for CO2 in 50:50 (mole) mixture with toluene at 45oC and 40 bar

2CO

Fugacity Coefficient (multicomponent approximation)9

Lewis fugacity approximation (rule)

ii ˆLewis fugacity approximation (rule)

ii

Valid near ideal solution conditions, i.e. yi in excess ( >0.9)yi ( )

Fugacity / Equilibrium (SUMMARY)10

LV ff ˆˆ ii ff

1) Vapor phase: good; liquid phase: good for HC or moderate – high pressures

Lii

Vii PxPy ˆˆ

(compressible liquid phase)

2) ..ˆ CPPxPy sati

satiii

Vii Typically used for liquid phase

fugacity calculations

3) iiVii HxPy Used for special cases (like gases

dissolving into liquid phase)dissolving into liquid phase)

Fugacity (Liquid Phase)11

Lif 1. Compressible liquidsif 2. Ideal and real solutions

3. Dissolved gases

1. Compressible liquids (mod – high P, and hydrocarbons)L

iiL

i Pxf ˆ LLLi orZ &ˆ

1. Compressible liquids (mod high P, and hydrocarbons)

Use EOS for:

oii

idealii

ideali

Li fxfxff ˆˆ

2. Ideal liquid solution

oif Pure species fugacity

real solutionoidealL fxff ˆˆ Lewis/Randall basisiiiiii fxff Lewis/Randall basis

i Activity coefficiento

Li

id l

Li

i fff ˆ

ˆˆ

i oii

ideali

i fxf

Fugacity (Liquid Phase)12

real solution oiii

Li fxf ˆ Lewis/Randall basisea so u o iiii fxf ew s/ a da bas s

oif

P L

isati

sati dPP exp at system T and Pif

Pii

sati

RT p at system T and P

P L

isati

satiii

Li dP

RTPxf expˆ

Psati

RT

Fugacity (Typical Liquid Phase Models)13

real solution Lewis/Randall basisˆ CPPxf satsatL ea so u o ew s/ a da bas s..CPPxf iiiii

?i

real solution – behaves ideally in the liquid phase then: satii

Li Pxf ˆ

real solution – behaves non-ideally in the liquid phase then: satiii

Li Pxf ˆ

Activity Coefficient (ways to calculate)14

idealE GGG id l iflL

ifbˆ

idealii

Ei GGG ideal

ii uu ideal

i

i

ffRT ˆln

ideali

ii f

fbut ˆ:

E E i

Ei RTG ln

jnPTi

ETE

i ngnG

,,

jnPTi

ET

i ngnRT

,,

ln

Now, need models for calculating and then can find Eg i1 2-suffix Margules (simple symmetric) [binary] xAxg E 1. 2 suffix Margules (simple, symmetric) [binary]

21xAxg

2

221

l

ln

ART

AxRT 1ln

2

11 1exp xA212ln AxRT

iln 2ln

11 pRT

explim A

0 11x0

110explim

1

RTx

Activity Coefficient (2 suffix Margules model)15

1. 2-suffix Margules (simple, symmetric) [binary] xAxg E . su a gu es (s p e, sy e c) [b a y]21xAxg

Find A: take data…sat

iiii PxPy

Example: binary mix of cyclohexane (a) and dodecane (b) at 39.33oC88.06

Ccyclo

86.012

6

C

Ccyclo

explim A

110explim

1

RTx

Activity Coefficient (Models)16

1. 2-suffix Margules (simple, symmetric) [binary] xAxg E . su a gu es (s p e, sy e c) [b a y]21xAxg

Asymmetric models:

2. Three-suffix Margules: (additional parameter)3. Van Laar: (older model but still good and easy to work with)4. Wilson: (not good for liquid-liquid-equilibria)5 NRTL (N R d T Li id d fi h i ll )5. NRTL: (Non-Random-Two-Liquid; good first choice, usually)6. UNIQUAC: (UNIversal QUAsi-Chemical; also good)7. UNIFAC: (only predictive model)

Activity Coefficient (Binary Models)17

Koretsky, 2004

Activity Coefficient (Binary Models)18

Activity Coefficient (Binary Models)19

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)20

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)21

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)22

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)23

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)24

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)25

r and q depend on molecular size

(volume) and external surface areas of pure

components.

Prausnitz, et.al., 1999

Activity Coefficient (Binary Models)26

Prausnitz, et.al., 1999

Activity Coefficient (Example)27

Temperature-composition diagram at 1.013 bar (1 atm) pressure for system:formic acid (1) and acetic acid (2)formic acid (1) and acetic acid (2)

Prausnitz, et.al., 1999

28

Chapter 5Lecture 8

- Thermodynamic Web- Departure Functions- Review Equations of state (chapter 4, briefly)

Chapter 6Chapter 6- Equilibrium (chemical potential)

* Pure Component* Mixtures

Ch t 7Chapter 7- Fugacity (chemical potential fugacity equilibrium calculations)

* Vapor (overview), liquid, solids- Activity Coefficients [Fugacity Coefficients (overview)]y [ g y ( )]

Chapter 8- Phase Equilibrium

* Diagrams* Vapor Liquid (VLE)* Vapor – Liquid (VLE)* Liquid – Liquid (LLE)* Solid – Liquid (SLE)

Chapter 9- Reaction Equilibria