VLE general (same)
The equilibrium criteria between 2 phases a and b is,
cii Ni
TT
PP
,....2,1,ˆˆ
ba
ba
ba
Vapor-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 Computations from Different k-value models
Observe & Discuss
Pressure effect on computation of bubble point T and dew point T
Statement of Equilibrium
iii Kxy
P
T
1
2 3
The Most general case isthat Ki is a function ofP, T, and compositions
with
In general
Mathematical Relationships
vl fyfxz 111 vv fyfxz 111 1 )(
lv
vv
nnnn
nnf
2121
21
)(
11
1 1
xy
xzfv
ii
iiv
xy
xzf
Bubble Point Evaluation (Non-Ideal Behavior Model)
The bubble point pressure at a given T is
)T,PKzy bpiii
T,PKz1 bpii
Dew Point Calculation
At the dew point the overall fluid composition coincides with the gas composition. That is.
ii yz
Dew Point Calculation
At the dew point the overall fluid composition coincides with the gas composition. That is.
ii yz
Dew Point Calculation (Non-Ideal Behavior Model)
Find DP pressure and equilibrium liquid compositions
)T,P(Kxz
Kxy
dpiii
iii
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 andT.
Flash Calculations (Non-Ideal Behavior Calculations)
Start with the equilibrium equation
Material balance
iii Kxy
vivivilii fyfxfyfxz 1
Flash Calculations
Now replace either liquid or gas compositions using Ki values (exercise derive the expression)
Flash CalculationsThere are several equivalent expressions for the flash function
(a)
(b)
(c)
01 iy
01 ix
0 ii xy
One of the Models for Equilibrium Ratios
Wilson’s model
Requires critical properties & acentric factors
T
T1137.5exp
P
PK ci
ici
i