PETE 310PETE 310

Lecture # 26Lecture # 26

Chapter 12 Chapter 12

Gas-Liquid Gas-Liquid EquilibriumEquilibrium

Non-ideal VLENon-ideal VLE

Gas-Liquid Equilibrium Gas-Liquid Equilibrium Non Ideal BehaviorNon Ideal Behavior

Applications to low & high pressuresApplications to low & high pressures

Use models for the equilibrium ratios (ki-Use models for the equilibrium ratios (ki-values)values)Simpler models ki = f (P,T)Simpler models ki = f (P,T)More complex models More complex models

ki = f(P,T,compositions) ki = f(P,T,compositions)

use equations of state EOS, use equations of state EOS, convergence pressureconvergence pressure

VLE general (same) VLE general (same)

The equilibrium criteria The equilibrium criteria between 2 phases between 2 phases and and is, is,

cii Ni

TT

PP

,....2,1,ˆˆ

Statement of EquilibriumStatement of Equilibrium

iii Kxy

P

T

1

2 3

1P

Most general case isMost general case isthat Ki is a function ofthat Ki is a function ofP, T, and compositionsP, T, and compositions

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

Bubble Point Evaluation Bubble Point Evaluation (Non-Ideal Behavior (Non-Ideal Behavior

Model)Model) The bubble point pressure at a The bubble point pressure at a

given given TT is is

)T,PKzy bpiii

T,PKz1 bpii

Bubble PointBubble Point

P 2

P 1 T

x 1 ,y 1

zzii=x=xii

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 (Non-Ideal Behavior (Non-Ideal Behavior

Model)Model)Find DP pressure and Find DP pressure and

equilibrium liquid equilibrium liquid compositionscompositions

)T,P(Kxz

Kxy

dpiii

iii

Dew PointDew Point

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 (Non-Ideal Behavior (Non-Ideal Behavior

Calculations)Calculations)Start with the equilibrium Start with the equilibrium

equationequation

Material balanceMaterial balance

iii Kxy

vivivilii fyfxfyfxz 1

Flash CalculationsFlash Calculations

Now replace either liquid or Now replace either liquid or gas compositions using Ki gas compositions using Ki values values (exercise derive the (exercise derive the expression) expression)

Flash CalculationsFlash Calculations

Objective function (flash Objective function (flash function) is function) is

01fKf1

Kz)f(F

viv

iiv

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

One of the Models for One of the Models for Equilibrium RatiosEquilibrium Ratios

1. Require critical properties & 1. Require critical properties & acentric factorsacentric factors

T

T1137.5exp

P

PK ci

ici

i

Example calculations in excel file VLE_310Example calculations in excel file VLE_310