Transcript Non_ideal_VLE

PETE 310
Lecture # 26
Chapter 12
Gas-Liquid Equilibrium
Non-ideal VLE
Gas-Liquid Equilibrium
Non Ideal Behavior
Applications to low & high pressures
 Use models for the equilibrium ratios (ki-values)
Simpler models ki = f (P,T)
More complex models
ki = f(P,T,compositions)
use equations of state EOS, convergence
pressure
VLE general (same)
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
Statement of Equilibrium
y i  x iK i
P1
Most general case is
that Ki is a function of
P, T, and compositions
1

2
P
T
3
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
Bubble Point Evaluation
(Non-Ideal Behavior Model)
The bubble point pressure at a
given T is
y
1
i

 z K P
i
i
 z K P
i
i
bp
bp
, T )
,T
Bubble Point

P1
T
zi=xi

P2
x1,y1
Dew Point Calculation
At the dew point the overall fluid
composition coincides with the gas
composition. That is.
zi  yi
Dew Point Calculation
(Non-Ideal Behavior Model)
Find DP pressure and equilibrium
liquid compositions
yi  x iK i
z i  x i K i ( Pdp , T )
Dew Point

P1
T

P2
zi=yi
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
(Non-Ideal Behavior
Calculations)
Start with the equilibrium equation
y i  x iK i
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 Ki values
(exercise derive the expression)
Flash Calculations
Objective function (flash function)
is


zi Ki
F(f v )   
 1  0
 1  f v   K i f v 
Flash Calculations
There are several equivalent expressions
for the flash function
(a)

yi  1  0
(b)

xi  1  0
(c)

yi 

xi  0
One of the Models for
Equilibrium Ratios
1. Require critical properties &
acentric factors

Tci  

Ki 
 exp  5 . 37  1   i    1 
 
P
T 


Pci
Example calculations in excel file VLE_310