lecture 11 - south dakota school of mines and...
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Chapter 5Lecture 11
- 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
Phase Equilibrium 2
4. Ideal liquid phase 1i satPxPy Raoult’s Law. dea qu d p ase i iii PxPy Raoult s Law
• T-xy diagram• P-xy diagramP xy diagram• y vs x diagram• Bubble point• Dew point
AspenPlus Examples(benzene – toluene)
Phase Equilibrium (uses)3
4. Ideal liquid phase 1i satPxPy Raoult’s Law. dea qu d p ase i iii PxPy Raoult s Law
• T-xy diagram• P-xy diagramP xy diagram• y vs x diagram• Bubble point• Dew point• Flash separation
Phase Equilibrium (uses)4
4. Ideal liquid phase 1i satPxPy Raoult’s Law. dea qu d p ase i iii PxPy Raoult s Law
• Flash separation
Phase Equilibrium (Flash Separation: Raoult’s Law)5
LVF Overall mole balance Vya
VOve a o e ba a ce
FZa &
V
LxVyFZ aaa mole balance on a
sataaa PxPy
a
LxaLxVyFZ bbb mole balance on b
equilibrium eqn for a aaayequilibrium eqn for a
Px sat
flbLxVPPxFZ a
aaa mole balance on a axforsolveFby &
Z Z
FL
FV
PP
Zx sata
aa
FL
FV
PP
Zx satb
bb
FFP FFP
Phase Equilibrium (Flash Separation: Raoult’s Law)6
1 ixFlash separation: Vya
1 ixas sepa a o : V
LVPZ
LVPZ
satb
sata1 FZa &
FL
FV
PP
FL
FV
PP ba
a
Lxa
Specify: vaporizedfracZT a .&, Find: aa yxP ,,
a = n-pentane
5.0Za
pb = n-hexane
barP
barPsat
b
sata
16.0
57.0
???P
31
20
FV
CT
3F
Phase Equilibrium (Flash Separation: Raoult’s Law)7
Flash separation: Generalizing to multi-components
1 ix
as sepa a o : Ge e a g o u co po e s
11
m
isat
i
i
LVPZ
1
i i
FL
FV
PP
AspenPlus example:AspenPlus example:
Phase Equilibrium (Flash Separation: Raoult’s Law)8
Motivation/uses: Processing engineering
Phase Equilibrium (uses)9
ˆV3. Ideal vapor phase 1Vi sat
iiii PxPy
4 Id l li id h 14. Ideal liquid phase 1i satiii PxPy Raoult’s Law
Raoult’s Law used to explore for VLE (binary):aou t s aw used to e p o e o V (b a y):• T-xy diagram• P-xy diagram• y vs x diagram• Bubble point• Dew point• Flash separation
Phase Equilibrium (uses)10
3. Ideal vapor phase Modified R lt’ l1ˆ V
isat
iiii PxPy 3. dea vapo p ase Raoult’s lawi iiiiy
sat
Choose T = 95 oC• Generate a P-xy diagramSet xa
satbbbb
sataaaa
PxPy
PxPy
Px
PxPxPsat
aaa
satbba
sataaa
1a
satbbb
sataaaba PxPxPyPy
satbba
sataaaba PxPxPyy 1
Py aaa
a
baba xxTfNOTE
,,&:
Phase Equilibrium (modified Raoult’s Law)11
Phase Equilibrium (Deviations from Raoult’s Law)12
satbba
sataaa PxPxP 1
Phase Equilibrium (modified Raoult’s Law)13
Phase Equilibrium (modified Raoult’s Law)14
Phase Equilibrium (modified Raoult’s Law)15
Phase Equilibrium (modified Raoult’s Law)16
Phase Equilibrium (Azeotropes)17
AspenPlus: T-xy for systems: MeOH-Water & EtOH-Waterp y y
Phase Equilibrium (Azeotropes)18
P-xy; T-xy; and YX diagrams for binary systemy; y; g y y
Phase Equilibrium (Azeotropes)19
at Azeotrope: xy satPxPy a eo ope: aa xy iiii PxPy
sataaaa PxPy
sataa
az PP sata
az
a PP
Example:Example:
Phase Equilibrium (Azeotropes)20
at Azeotrope: xy satPxPy a eo ope: aa xy iiii PxPy
sataaaa PxPy
sataa
az PP sata
az
a PP
Example:Example:
2
ln
ba BxAx
BxART
2
ln
ab
ba
BAAxBRT
BxAx
ba
b BxAx
Phase Equilibrium (uses)21
non-ideal vapor & liquid phases
satiii
Vii PxPy ˆ
Raoult’s Law used to explore for VLE (binary):• T-xy diagram• P-xy diagram Vˆy d ag a• y vs x diagram• Bubble point• Dew point
satbbb
Vbb
sataaa
Vaa
PxPy
PxPy
ˆ
ˆ
• Flash separationbbbbb
1
Chapter 5Lecture 11
- 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 / Equilibrium (SUMMARY)2
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)
Henry’s Law (uses)3
OsatPxPy Raoult’s LawO2
H2O
iii PxPy Raoult s Law
satOHOHOH PxPy
222
satOOO PxPy
22225 oC; 1.013 bar
TCBAPsat
O
2ln
TC
Henry’s Law (uses)4
OsatPxPy Raoult’s LawO2
H2O
iii PxPy Raoult s Law
satOHOHOH PxPy
222 Henry’s Law
COHOOO HxPy
2222 25 oC; 1.013 bar Constant
O Pyx 2
OHOO H
x22
2
Henry’s Law (examples)5
Henry’s Law (example)6
O Py 610*8074 xAir:O2
H2O OHO
OO H
Pyx
22
2
2
10807.4
2OxAir:
Pure O2: 610*891.22
2
Ox
25 oC; 1.013 bar
Walas; 1985
Henry’s Law (example)7
O St t blsatPPO2
H2O
Steam tables:
barPsatOH 031691.0
2
satOHOHOH PxPy
222
25 oC; 1.013 bar