PETE 310Lecture # 26

Chapter 12

Non Ideal Gas-Liquid Equilibrium

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

Equilibrium Ration Charts

Phase Equilibria Computations

More in Appendix A from your textbook page 495…

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

Bubble Point

P2s

P1sT

x1,y1

zi=xi

Bubble Point from Raoult's law

P 2 s

P 1 s T

x 1 ,y 1

zi=xi

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

Dew Point

P2s

P1sT

x1,y1

zi=yi

Dew Point from Raoult's law

P 2 s

P 1 s T

x 1 ,y 1

zi=yi

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 Calculations

Objective function (flash function) is

01

fKf1

Kz)f(F

viv

iiv

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

Link to Example calculations in excel file VLE_310