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The Prediction of Vapour Liquid Equilibrium Behaviour of Propane-Butane Mixtures
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8/20/2019 The Prediction of Vapour Liquid Equilibrium Behaviour of Propane-Butane Mixtures
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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.
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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
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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.
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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)
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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.
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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
@_).
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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.
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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 *
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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
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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
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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
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REFERENCES
Alvarado, . F. J.
(1993).
Studies
n PhaseEquilihrium
Calculations
ron
Equation f
,S/are.
exasA
&
M
University.
h.D. Thesis.
Ganguly,S.
(2003).
Predictionof VLE
Data
Using Radial BasisFunctionNetwork.
Jo
rnal of Computels nd Chemical
ngineering.27
1445-1454.
Ghosh,P.
(1999).Predictionof Vapor-LiqoidEquilibriaUsing Peng-Robinsonnd
Soave-Redlich
Kwong Equations
of State.
Jow'nal of Che ical Engineeri
g
&
Technology
22
(5).
379-399
Hall, K. R.
and glesias-Silv4G.
A.
(1993).
Quadratic
Mixing
Rules or Equations f
State:Origins
andRelationshipso
theVirial
ExpaNion.F/&ldPhase quilibtia.
9r (1):67-16
Hemandez-Garduza,
., Garcia-Sanchez,
.,
Neau, E. and Rogalski, M.
(2000).
Equation f State
Associated ith
Activity
CoefficientModels o PredictLow
and
High PressureVaporJiquid
Eqtrillbia. ChemicalEngineering
Journal.
79:
87-101
Kleiber,
M. ard Axmann, J.
K.
(1998).
EvolutionaryAlgorithms for the Optimization
of Modified UNIFAC
Paramete$. nmputers nd ChemicalEilgl eeling.
23:
63-82
Lewis,G. N.,
andRandall,M.
(1961).Thermodynamics.
ew
York: Mccraw-Hill Book
Company.
Modell,M.
andReid,R. C.
(1983).Themodynamicsnd lts Applications. ndedltion.
New Jersey:
rcntica-Hall.
Oreski,S.,
Zupan,J. and Glavie,
P.
(2001).
Newal Network Classification f Phase
Equilibdum
Methods. ournal
of Chemical iochemical ngineering. 5
l):3
t12
Prausnitz, J.
M., Lichtenthaler,
R. N. and Azevedo, E. G.
(1999).
Molecular
Thermodlmamics
f Ftuid-Phase
quilibfia.3'd edition.New Je$ey: Prentice
Hall.
-
8/20/2019 The Prediction of Vapour Liquid Equilibrium Behaviour of Propane-Butane Mixtures
13/13
Tischmeyer,M.
and tult, W.
(2004).
Detemination
of Binary Vapor
liquid F4uilibria
(\'LE)
of
Three
Fast Reacting Esterification
Syslf,'rns.
ournol of Chemical
Engineering
ard
Processing.
43l.357 367.
Virendr4 U., Rajiah, A. and Prasad,D. H. L.
(1995).
Dependence
f the
Second
Virial
Coellicient on Temperatue.The Chernical
Engiheering
Journal. 56.. 3-76.
't