the prediction of vapour liquid equilibrium behaviour of propane-butane mixtures

8/20/2019 The Prediction of Vapour Liquid Equilibrium Behaviour of Propane-Butane Mixtures

1/13

The

PredictionofVapour Liquid

Equilibrium

Behaviour

of

PropaneButane

Mixture

Zakari4 Z and

Tee,

S.Y.

GasEngineeringDepartmentFaculty

of Chemical

& Natmal Resources

ngineeflng

UniversitiTeknologiMalaysia 1310

UTM Skudai

ohorDarulTakzim

Tel: 607-5535497ax:

607-5581463mail:

zainalz@fld(ksa.uhn.mv

ABSTRACT

This

paper

s a contribution o the

development fmathematical

model for

the

prediction

ofvapour

liquid

equilibrium behaviourofpropane

butale mixtue at

non-idealstate.The

proposed

model is based on the

generalized

irial

equation of

state atd GalDma,?hi

formulation.Mathematicalmodeling Mathcad s

used o numerically

solve for

fugacity,

fugacity coefficient, activity coefficient and

vapour-phase

composition

of

propane

butane

mixtue

by

taking into

consideration he effects

of temperatureand pressure.

A

tempemtur€

ange

f263.15K o 313.l5K chosenn

this modelings ofpracticabili ty

or

propane

butane mixtue in cylindrical storage.

The

prediction

of vapour liquid

equilibrium behaviour for prcpane butane mixtule is illustrated in P*y diagram at

different system temperatures. t is

clearly shown that

solution fugacity

coefficient

decreasesteadily s systememperaturel1d ressure

ncrease.

t is alsoshown

hat he

solution ugacity increaseswith s)tstememperatue and prcssure.

Activity

coefficient of

butane in mixtue becomes larger as system tempemtule

and pressure

tncrease.

Meanwhile, there is insignificant decrease n

activity coeJTicient

of

propane

with

temperatue and

prcssure.

As system empemtwe

ard

pressrre go

higher, vapour-phase

composition f propane ecreaseshile for butane,ts concentrationn vapourphase

becomesicher.


2/13

LIST

OF NOMENCLATURE

f

Activity

coefficient

A

Fugacity

co€fficient ofpue species

d

p gacity

coefficientofspecies

n solution

f

fugacity ofpue species

.f

Fugacity

ofsp€cies

n

solution

x Liquid

phase

mole fraction

P Prcssure

T Tempelatwe

./ Vapor

phase

mol€ fractio[

Subscripts

i

Component

Superscripts

L Liquid

sat

Satunted

condition

v Vapor

l


3/13

INTRODUCTION

The acculate

prcdiction

ofphase equilibrium

offluid mixtures

s extremely

mpofiant n

many

industdal applications, such as rcservoir

modeling, process

design,

and

gas

processing

nd

separation. ne

practicable

xample

fphaseequilibdum

s the

pdmary

process

n

an oil

refinery

which involves the sepa.ration

f the

crude oil into the more

valuableiactioN i.e.,

gasoline,

erosene,iesel uel,

etc.by distillation.

quilibriums

a static condition in which no changes ccur in the properfies

of a

systemwith time. A

state of equilibrium is a state of rest

(Lewis

and Rardall,

1961). Phase-equilibrium

thermodlaDmics seeks to establish the relations

among the

various

properties,

in

particular,temperature, rcssrreand composition, hat ultimately prevail when two or

morephases eacha stateof equilibrium wherein

all tendenciesor

cha.ngesaveceased.

Most of the

initial work in vapor liquid equilibrium (VLE)

behaviour of hydrocarbon

mixtue was with the systemat

low

presswe

and

low temperature

where an ideal state

was

usually assumed.Basedon the

previous

csearches,

here are no

studiescarriedout

olr the

hydrocarbon

system,

especially the light

hydrccarbon

system, at non-ideal

condition. deal model like Raoult's law model s applied to the hydrocaxbon ystemat

ideal state. Situations chaagewhen the said system s not

at ideal state since ideal

systems

haxdly exist in real life. The deviations from

mixtwe ideality should

be

accounted

n the

prediction

ofVLE for

propane

utane

mixtule.

LITERATURE REVIEW

Fugacityand

Fugacity

Coeflicient

The fugacity is a

quantity

that conesponds

o the pressule

or a non-ideal gas.

Fugacity

is a

pseudo

or effective

pressrre.

t is the

pressule

at which the

chemical

potential

ofan

ideal

gas

s the sameas hat ofthe r€al

gas

at the

true

prcssue.

Fugacity

ofa component

in

a

gas

mixtue is a

pseudo

or eff€ctive

partial pressue

for that component.


4/13

Fugacity

fi

is a

property

of a

pwe

materialand t

depends pon

emperature

nd

pressue,

which must be uniform

tfuoughoutboth

phases

t equilibrium.

The criterion

of

r,apour

iquid

quilibriumor multicomponenrystem

sas oilowsl

r,'(r.p,*)=1(r,p,*)

( l )

Fugacitycoefficient s anothernew

propelty,

which

is dimensionless.

he fugacity

coefficient fpure speciesi,

,

is defined s:

f.

o,=+

(2)

' '

P

Whendealingwith ideal

gas,

At

=l

ardlt

=

P.

On

the

otherhand, he

definition f

the ugacity fa species

n

solutions

parallel

o thedefinition

ofthe

pure-species

fugacity.

ugacity oefficient fspecies in solution

s exprcssed

sl

a/

0,='/,,,

(3)

Activity Coefficient

In contrast o fugacity, activity coefficient s inherently

a multicomponent

o[cept that s

useful only for mixtures. It is introduced nto Raoult's

law to account or

liquid-phase

non-idealities. n llon-ideal mixtures, activity coefficients depend

stongly on liquid-

phase

composition. deal solution serves

as a

standaxdo which

real-solutionbehaviour

canbe compared.Activity coeflicient s defined n the following

expression:

^. , i ,

i

-

----;

(:4)


5/13

Gamma,/Phi ormulationof VLE

Modified Raoult's law includes he

activity coefficient to

account or liquid-phase

non-

idealities, but it is limited by the assumption

of vapour-phase

deality. This can

be

overcomeby

introducing

the vapour-phaseugacity coefficient.

For speciesi

n vapour

mixture and n liquid solution, ugacity of species

in vapour phase

and n liquid phase

caobe rcpresented y:

The criterion for

phase

equilibrium is that thesebe

equal:

i:

=

y,6,

p

ard

]i

=

x,y,f,

6)

(6)

PredictionofVLE

In order to calculatewith confide[ce the

fugacities

n a

gas

mixture, it

is advantageous

to use a.nequationof stat€where the

parameters

ave

physical

significance, .e. where

the

parameterc

ar be relatedo

intermolecularorces.

Oneequation fstate

hathas his

desirableability is the virial equationof state.The fundamertal

advantage f the virial

equation

is that it directly rclates fugacities in mixtures

to intermolecular forces

(Prausnitz

et

^L,

1999).

Vapour

phase

non-idealities

in the calculation

of

thermodynamics

roperti€s

near atmosphedc

ressure

nd often up to

about 1.5MPacan

be represented y the virial equation of state with the inclusion

of the secondvirial

coe{ficient only

(Virendra

et al., 1995).The

gereralized

virial

equationhas beenwidely

used because

t

only

requires he substance-dependent

ritical

paxameten

anctacentnc

factor.

Generalized

virial equation s of

greater

applicability

to

all

gases.

The most

important dvartage fthe vidal equatio[

ofstate

or applicationo

phase

quilibriums

its directextensiono mixtues

(Prausnitz t al.,

1999).Mixing rulesshould

e

ncluded

when

dealing with mixtue. For two-term truncated form,

mixture second virial

coefficient s a function oftemperatue only.


6/13

MATHEMATICAL

MODELING

This research

project

involves mathernaticalmodeling.

Mathcad

s used o numerically

solve fugacity, fugacity coefficient and activity coefficient

for propane

butanemixtule.

All the required nputs ike

properties

ofpropa.neand

n-butare should

be defined n the

early stage.Then suitable equationsare listed in

coffect sequencesn

order to

get

the

final results. There are four

paxameteN

o be solved

n this study. They

are fugacity,

fugacity coefficients, activity coefficie[ts

and

vapour

phase

compositions for each

species n

propale

butane mixhfe.

Liquid

phase

composition and

system empenture

are set beforc solving the above

parameters.n

order to establish

a mathematicalmodel,

appropriateassumptionsare made. The generalized irial equationof state method s

suitable

or

propane

butanemixtwe. That is, the operating

condition of

propane

butane

mixture

at 10 baxs is assumedas moderate

presswe

while

appllng this method.

Limitation

ofthis method s its applicabilityo low andmoderate ressure.

n thisstudy,

10 bars

is consideredhigh

pressure

or

propane

butane system

but in the other way

round it is consideredas

moderate

prcssue

when applying this method.

Next, the

rcquired

iquid compositionofpropane butanemixture is referred

o the composrhonat

equilibrium statewhich is obtained hrough hecompositionanalyzer.Besides, utane n

the

mixture is actually consisting of n-butanea.nd sobutane. n

this

project,

butane s

refefied to

a mixture of 50% ofn-butane ard 50% of isobutane.

n addition,

propane

and

butane

are chemically similar speciesand both speciesale non-reactive

n a mixture.

Therefore, n assumption

f fugacity oefficientn

gas

phase

f')

equalso the ugacity

coefficientn

liquid

phase fr

)

is made. This assumption

s based n the act hat he

pure

species

ugacitycoefficientn

gasphase / )

equals

o the

pwe

speciesugacity

coetllclentn LLqurc

nase

@_).


7/13

RESULTSAND DISCUSSIONS

This researchstudy focuseson the effect of temperature

alld

pressure

on the vapour

liquid equilibrium behaviour of

propane

butare mixture.

Mathematical modeling has

been developed n order to

predict

the

VLE

behaviow. The

model cuaently

proposed

cal be used

or theprediction fVLE ofpropane

utanemixture n the

ull composition

range.

EffectofComposition

A t

?ical

Prl diagam

for

six

different tempemtures

an be seen n Figure 1. It clearly

shows that when there is an increase n temperatue,there is an i[crcase in system

prcssure.For each emperatue, the upper curv€ rcprcsents

bubble

point

line while the

lower curye

epresentsew

point

line. A temperatwemnge

of

263.15

K to 313.15K

chosen n this

modeling is of

practicability

for

propane

butare mixtue in cylindrical

storage.

Effect ofTemperature

Figure

2 displays he effect of temperature

ha[ges

on the fugacity coefficient. Here, t

is assumed hat mole llactions

in liquid

phase

or both

the

propane

alld butaneare 0.6

and 0.4,

rcspectively. The sameassumption

also

goes

o Figures 3, 4 and

6.

It

can be

seenclearly that fugacity coafficients

of solution as

well as of individual specresn

mixtwe decrcases teadilyas the

system emperaturencreases.

hat is, the deviationof

fugacity coefficient from unity becomes

arger as

the system tempemtue becomes

higher.

Figure

3

shows he effect oftemperature

changes

n fugacity aswell as system

pressue.

As shown

n Figure 3, solution fugacity

ncreases

s he system emperaturencreases.t

is showed hat the solution

fugacity appears ery closely

to

the fugacity

of

propane n

mlxture.


8/13

Figure 1: P4r diagram or several

temp€ratules

Figwe 3 Fugacityand vaporr

pressrre

at differcnt temperatwes

€i*l

Figue 2: Fugacity

oefficients

t

different

temperatues

Figwe 4: Activity

coefficients

at

differenttemperatures

This is becauseugacity s known as a

parameter

epresentingh€

effective

pressure

n

vapourphase

Prausnitz

et a1.,1999).Since here s

more

propane

n vapourphass,

thereforeboth the solution fugaciryard fugacityof propane

n mixture

show he similar

trend.That is, there s negligible

gap

between hese

wo

pammeters.

On the otherhand,

t *


9/13

Figure 3

showsclearly that the systempressure

lways greater

han he

solution fugacity.

A system s consider€d

s an deal systemwhe[

these wo

parametem

how

negligible

difference.As shown n Figure

3, differencebetween

systempressure

nd solution

fugacitybecomesarger when system emperatue

becomes

igher. That

s, deviation

liom ideality for propane

butanemixture s more

apparent

t higher temperatrre.

I

€

i

rft)

Figue 5

Vapour

phase

ompositionsat

different empgratues

As can be seen iom Figure 4, it is known that activity coefTicientof butare tncreases

appreciably

as

temperatwe

glows

higher. Mearwhile,

there are only insignificant

decreasesn activity coefficient of

propane

with temperature.

As can be

seen,activity

coefficient of

propane

sta)€ closely to unity while the

activity coefficient

of butane

deviates iom unity. Activity coe{ficient s a

pam.rreter

sed o account or liquid-phase

non-idealities.n

general,

here s morcbutanen liquid phase.

herefore,he effect

of

temperatureon activity coefficient of

propane

n liquid solution

is

quite

imignificant

1 while the effect of tempemtulebdngs relatively significantchangeson butane.Figue 5

shows he effect

of temperatrrg

on

yaporr

phase

composition.As

temperatue becomes

higher, more butare vaporizes therefore the vapour

phase

composition

of butare

increaseswhile the vapour

phase

compositionof

propane

decrcases.How€ver,

here s

always more

propane

n vapour

phase

due to its higher vapour pressule.

These

vapour


10/13

phase

compositions

are then used n the study

of discharging

Focess

of propane

buta.ne

mixtue ftom cylindrical

stomge.

Effect ofPressure

Figwe 6 displays he effect

of

pressrue

on activity

coefficient at

different temperatures.

At constant emperature,as pressuregoes

higher deviations

of activity

coefficient for

butanebecomemore noticeable.Even though

therc is a deviation

from unity,

the said

deviation can actually be neglected

because,as can be seen

rom Figure

6, the highest

value of activity coefEcient s less than 1.02 for

these six

temperutwes.This

value is

actually

not far fiom

unity. Sometimes,his value can

even be approximated

o unity.

Unless near the critical region, activity coeJficient s little affected by pressureand is

strongly affected by the natue of

pure

chemicals

comprising the

liquid solution

(Alvarado,

1993).This statement learlyexplains

hat it is reasonable

o neglect he

deviation of activity coefficient when

pressure

haages.Meanwhile,

activity coefficient

ofpropane approaches nity at certain

pressure.

Apart from

that

paxticularpressure,

t

is

clearly shown hat activi ty coefficient

goes

arger han

unity at lower pressure

nd

smaller than unity at higher

pressure. Besides,

larger

range of value of activity

coefllcients accounteds empemtwencreases.

Figue 7 depicts the effect of system

pressure

on solution

fugacity at differcnt

temperatu€s. It is cleaxly shown that as the

pressure

ncreases,solution

fugacity

inqeases at coNtant temperature.At

higher

tempemture,

solution fugacity becomes

larger and it obviously accounts or larger range of values.

Figwe 7 clearly tells that

solution fugacity is always smaller thar system

pressure

due to the non-idealities n

t propanebutare mixtwe. However, the difference betweenthese tlvo parametersor

propane

butanemixtue is always small. Judging rom

the modeling, the ratio

between

solution ugacityand system

ressue ?P)

always anges

Aom 0.73 o 0.87.Figure

8

depicts

the effect of system

pressrue

on solution

fugacity coefficient at

different

temperatures.

t is

clearly shown

that as the

prcssurc

increases,

solution fugacity


11/13

coeffrcient deoeasesat coDstant

emperature.At higher

temperature, olution fugacity

coefficient accounts or larger angeofvalues and

he deviations

rom unity are arger.

i

9.,

Figure 6: Effect ofpresswe on activity

coefficient

at differcnt

remperanres

Figure 7 : Effect

ofpressureon

solution tugacity

at

different temperatures

t Figwe 8 : Effect ofpressureon solution

fugacity coefficient at

diff€rent temperatures


12/13

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(1993).

Studies

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ron

Equation f

,S/are.

exasA

&

M

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(2003).

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Neau, E. and Rogalski, M.

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't

the prediction of vapour liquid equilibrium behaviour of propane-butane mixtures

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