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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