Transcript VLE
PETE 310
Lectures # 25 -26
Chapter 12
Gas-Liquid Equilibrium
Gas-Liquid Equilibrium
Ideal Behavior
Applications to low pressures
Simplifications
the gas phase behaves as an Ideal
Gas
the liquid phase exhibits Ideal
Solution Behavior
Ideal Behavior
The equilibrium criteria between 2
phases a and b is,
a
P
T
a
ˆ i
a
P
b
T
b
b
ˆ i , i 1 , 2 ,.... N c
Equilibrium Conditions
The last criteria implies “tendency
of a component to be in phase a or
b is balanced” – “net mass transfer
across phases is zero”
ˆ i
a
b
ˆ i , i 1, 2 ,.... N c
Ideal Behavior Model
Gas phase behaves as an ideal gas (IG),
and liquid phase behaves as an ideal
solution (IS).
These assumptions imply that
IG: molecular interactions are zero,
molecules have no volume.
IS: forces of attraction/repulsion
between molecules are the same
regardless of molecular species. Volumes
are additive (Amagat’s Law).
Forces between molecular
species
A
A
B
B
A
FAA FBB FAB
B
Statement of Equilibrium
y i P x i Pi
IG/IS Raoult’s law
1
P1
2
P
T
3
Types of VLE Calculations
CP1
Ta
Liquid
P1v
Pressure
P1v
P2
Flash
CP2
P2v
v
Ta
Temperature
0
Vapor
x1, y1
1
Recall Molar Compositions
By convention liquid compositions (mole
fractions) are indicated with an x and gas
compositions with a y.
n1
x 1
n1 n 2
liquid
n1
y 1
n1 n2
gas
Mathematical Relationships
z 1 x 1f l y 1fv
with
fv
z1 x
1
y1 x1
In general
z 1 x 1 (1 fv ) y 1fv
fv
( n 1 n 2 )v
n 1 n 2 v
fv
n 1 n 2 l
zi x i
yi xi
Depletion Path
Isothermal Reservoir Depletion Process for a
Reservoir Oil with 2 Components
z1 = fixed
T = Ta
CP M
Pressure
PB
A
B
C
PD
Ta
Temperature
z1=overall mole fraction of [1],
0
x1
y1=vapor mole fraction of [1],
z1
y1 1
x1=liquid mole fraction of [1]
Quantitative Phase Equilibrium
Exercise
P -xy D ia g ra m
2000
P r essu r e (p sia)
1600
T=160F
1200
800
400
0
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
C o m p o sitio n (% C 1)
0 .6
0 .7
0 .8
Bubble Point Evaluation
(Ideal Behavior Model)
The bubble point pressure at a
given T is
yi P
Pbp
bp
z
i
Pi
z i Pi
Bubble Point from Raoult's law
T
P1
zi=xi
P2
x1,y1
Bubble Point Evaluation
Under Raoult’s law, the bubble point has
a linear dependence with the vapor
pressures of the pure components.
Once the bubble point pressure is found,
the equilibrium vapor compositions are
found from Raoult’s law.
Dew Point Calculation
At the dew point the overall fluid
composition coincides with the gas
composition. That is.
zi yi
Dew Point Calculation
(Ideal Behavior Model)
Find DP pressure and equilibrium
liquid compositions
y i P x i Pi
z i P x i Pi
Pdp
zi
Pi
Nc zi
i 1 Pi
1
xi
P
Dew Point from Raoult's law
T
P1
zi=yi
P2
x1,y1
Flash Calculations
In this type of calculations the
objective is to:
find fraction of vapor vaporized (fv)
and equilibrium gas and liquid
compositions
given the overall mixture composition,
P and T.
Flash Calculations
(Ideal Behavior Calculations)
Start with the equilibrium equation
y i P x i Pi
Material balance
z i x i f l y i f v x i 1 f v y i f v
Flash Calculations
Now replace either liquid or gas
compositions using equilibrium
equation
zi yi
P
Pi
yi P
x
i
P
i
1
fv yi fv
Here replaced xi
Flash Calculations
Rearrange and sum over all yi
yi
zi
P
Pi
yi
1
fv fv
zi
P 1 f f
v
v
Pi
Separation process
yi(T1,P2)
zi(T1,P1)
T1,P2
P1 > P 2
xi(T1,P2)
Flash Calculations
Objective function (flash function)
is
zi
1 0
F ( fv )
P 1 f f
v
v
Pi
This is 1/ki – ideal equilibrium ratio
Flash Calculations
There are several equivalent expressions
for the flash function
(a)
yi 1 0
(b)
xi 1 0
(c)
yi
xi 0
Flash Calculations
Once fv is found the equilibrium gas
and liquid compositions are
evaluated from
yi
zi
P
Pi
1
fv fv
and
yi P
x
i
P
i
Vapor Pressure Models
(Antoine Equation)
1. Constants depend upon the
component – Different Units
bi
ln Pi a i
Ti c i
Example in our web site excel file VLE_310
F la s h F u n c tio n s a n d R a c h fo rd R ic e
F u n c tio n
zi
1
i 1 f v k i 1 1
Nc
S um X i
6 .0 0
S um Yi
R a chfo rd R ice
4 .0 0
zi ki
1
i 1 f v k i 1 1
Nc
F (fv )
2 .0 0
0 .0 0
-2 .0 0
Nc
-4 .0 0
i 1
-6 .0 0
0.00
0.20
0.40
0.60
0.80
M o la r F ra c tio n o f v a p o r (fv )
1.00
z i ( k i 1)
f v k i 1 1