PETE 310 Lectures # 25 -26 Chapter 12 Gas-Liquid Equilibrium.
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Transcript of PETE 310 Lectures # 25 -26 Chapter 12 Gas-Liquid Equilibrium.
PETE 310PETE 310Lectures # 25 -26Lectures # 25 -26
Chapter 12 Chapter 12
Gas-Liquid Gas-Liquid EquilibriumEquilibrium
Gas-Liquid Equilibrium Gas-Liquid Equilibrium Ideal BehaviorIdeal Behavior
Applications to low pressuresApplications to low pressuresSimplifications Simplifications
the gas phase behaves as anthe gas phase behaves as an Ideal Gas Ideal Gas
the liquid phase exhibitsthe liquid phase exhibits Ideal Ideal Solution BehaviorSolution Behavior
Ideal BehaviorIdeal Behavior
The equilibrium criteria The equilibrium criteria between 2 phases between 2 phases and and is, is,
cii Ni
TT
PP
,....2,1,ˆˆ
Equilibrium ConditionsEquilibrium Conditions
The last criteria implies The last criteria implies “tendency of a component to “tendency of a component to be in phase be in phase or or is balanced” is balanced” – “net mass transfer across – “net mass transfer across phases is zero”phases is zero”
cii N,....2,1i,ˆˆ
Ideal Behavior Model Ideal Behavior Model
Gas phase behaves as an ideal gas Gas phase behaves as an ideal gas (IG), and liquid phase behaves as an (IG), and liquid phase behaves as an ideal solution (IS). ideal solution (IS).
These assumptions imply thatThese assumptions imply thatIG:IG: molecular interactions are zero, molecular interactions are zero,
molecules have no volume.molecules have no volume.IS:IS: forces of attraction/repulsion forces of attraction/repulsion
between molecules are the same between molecules are the same regardless of molecular species. regardless of molecular species. Volumes are additive Volumes are additive (Amagat’s Law).(Amagat’s Law).
Forces between molecular Forces between molecular speciesspecies
A A B B A B
ABBBAA FFF
Statement of EquilibriumStatement of Equilibrium
iii PxPy
P
T
1
23
1P
IG/IS Raoult’s lawIG/IS Raoult’s law
Types of VLE CalculationsTypes of VLE Calculations
Temperature x1, y1
Pre
ssu
re
P2v
TaCP1
Bubble Curv
e
Dew
Cur
ve
Flash
Liquid
Vapor
P1v P1
v
CP2
P2v
Ta0 1
Recall Molar CompositionsRecall Molar Compositions
By convention liquid compositions By convention liquid compositions (mole fractions) are indicated with an (mole fractions) are indicated with an xx and gas compositions with a and gas compositions with a yy..
liquidnn
nx
21
11
gasnn
ny
21
11
withwith
In generalIn general
Mathematical Mathematical RelationshipsRelationships
vl fyfxz 111 vv fyfxz 111 1 )(
lv
vv nnnn
nnf
2121
21
)(
11
1 1
xy
xzfv
ii
iiv xy
xzf
Depletion PathDepletion PathIsothermal Reservoir Depletion Process for aIsothermal Reservoir Depletion Process for a
Reservoir Oil with 2 ComponentsReservoir Oil with 2 Components
Temperature
Pre
ssu
re
PD
PB
T = Ta
Ta
CPM
z1 = fixed
z1 y1x1 10
AB
C
z1=overall mole fraction of [1], y1=vapor mole fraction of [1], x1=liquid mole fraction of [1]
Quantitative Phase Quantitative Phase Equilibrium ExerciseEquilibrium Exercise
P-xy Diagram
0
400
800
1200
1600
2000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Composition (%C1)
Pre
ssu
re (
psi
a)
T=160F
Bubble Point Evaluation Bubble Point Evaluation (Ideal Behavior Model)(Ideal Behavior Model)
The bubble point pressure at a The bubble point pressure at a given given TT is is
iibpi PzPy
iibp PzP
Bubble Point from Raoult's Bubble Point from Raoult's lawlaw
P 2
P 1 T
x 1 ,y 1
zzii=x=xii
Bubble Point EvaluationBubble Point Evaluation
Under Raoult’s law, the bubble Under Raoult’s law, the bubble point has a point has a linear dependencelinear dependence with with the vapor pressures of the pure the vapor pressures of the pure components.components.
Once the bubble point pressure is Once the bubble point pressure is found, the equilibrium vapor found, the equilibrium vapor compositions are found from compositions are found from Raoult’s law.Raoult’s law.
Dew Point CalculationDew Point Calculation
At the dew point the overall At the dew point the overall fluid composition coincides fluid composition coincides with the gas composition. That with the gas composition. That is.is.
ii yz
Dew Point Calculation Dew Point Calculation (Ideal Behavior Model)(Ideal Behavior Model)
Find DP pressure and Find DP pressure and equilibrium liquid equilibrium liquid compositionscompositions
iii
iii
PxPz
PxPy P
x
P
z i
i
i
1
1
cN
i i
idp
P
zP
Dew Point from Raoult's lawDew Point from Raoult's law
P 2
P 1 T
x 1 ,y 1
zzii=y=yii
Flash CalculationsFlash Calculations
In this type of calculations the In this type of calculations the objective is to:objective is to:
findfind fraction of vapor vaporized fraction of vapor vaporized (fv)(fv) and equilibrium gas and and equilibrium gas and liquid compositionsliquid compositions
givengiven the overall mixture the overall mixture composition, composition, P P andand T T..
Flash Calculations Flash Calculations (Ideal Behavior (Ideal Behavior Calculations)Calculations)
Start with the equilibrium Start with the equilibrium equationequation
Material balanceMaterial balance
iii PxPy
vivivilii fyfxfyfxz 1
Flash CalculationsFlash Calculations
Now replace either liquid or Now replace either liquid or gas compositions using gas compositions using equilibrium equation equilibrium equation
vivi
ii fyfP
Pyz 1
i
i
i xP
Py
Here replaced Here replaced xxii
Flash CalculationsFlash Calculations
Rearrange and sum over all yiRearrange and sum over all yi
vvi
ii
ffPP
zy
1
vvi
ii
ffPP
zy
1
Separation processSeparation process
zi(T1,P1)
xi(T1,P2)
yi(T1,P2)
PP11 > > PP22
T1,P2
Flash CalculationsFlash Calculations
Objective function (flash Objective function (flash function) is function) is
01
1)(
vvi
iv
ffPP
zfF
This is 1/ki – ideal equilibrium ratioThis is 1/ki – ideal equilibrium ratio
Flash CalculationsFlash CalculationsThere are several equivalent There are several equivalent
expressions for the flash function expressions for the flash function
(a) (a)
(b) (b)
(c) (c)
01 iy
01 ix
0 ii xy
Flash CalculationsFlash Calculations
Once Once ffvv is found the is found the equilibrium gas and liquid equilibrium gas and liquid compositions are evaluated compositions are evaluated fromfrom
vvi
ii
ffPP
zy
1
i
i
i xP
Pyandand
Vapor Pressure Models Vapor Pressure Models (Antoine Equation)(Antoine Equation)
1. Constants depend upon the 1. Constants depend upon the component – Different Unitscomponent – Different Units
ii
iii cT
baP
ln
1111
cN
i iv
i
kf
z
1111
cN
i iv
ii
kf
kz
cN
i iv
ii
kf
kz
1 11
)1(
Example in our web site excel file VLE_310Example in our web site excel file VLE_310
Flash Functions and Rachford Rice Function
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
0.00 0.20 0.40 0.60 0.80 1.00
Molar Fraction of vapor (fv)
F(f
v)
Sum Xi
Sum Yi
Rachford Rice