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User Guide for

Models and Physical Properties

Infochem Computer Services Ltd

Version 4.1

26 January 2012

Infochem Computer Services Ltd

4 The Flag Store

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London SE! 2L"

Tel# $44 %&'2& (3)( &*&&

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This User Guide and the information contained within is the copyright of Infochem Computer Services Ltd.

Infochem Computer Services Ltd4 The Flag Store

! "ueen #li$a%eth StreetLondon S#& L'( U)

Tel*+44 ,-- /!0/ -1--Fa2*+44 ,-- /4-/ !3/

email*info5infochemu6.com

Disclaimer

7hile every effort has %een made to ensure that the information contained in this document iscorrect and that the software and data to which it relates are free from errors( no guarantee isgiven or implied as to their correctness or accuracy. 8either Infochem Computer Services Ltd norany of its employees( contractors or agents shall %e lia%le for direct( indirect or conse9uentiallosses( damages( costs( e2penses( claims or fee of any 6ind resulting from any deficiency( defector error in this document( the software or the data.

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Contents

Overview......................................................................................................................

Introduction.................................................................................................................07hat types of model are availa%le:........................................................................0

!hermodynamic properties from an "#uation of State.....................$

Introduction.................................................................................................................1

#nthalpy........................................................................................................................1#ntropy..........................................................................................................................3Fugacity coefficients................................................................................................&-Gi%%s #nergy and Internal #nergy........................................................................&&;eat Capacity( constant pressure.........................................................................&&;eat Capacity( constant volume...........................................................................&&Isothermal compressi%ility....................................................................................&Iso%aric e2pansivity or thermal e2pansion........................................................&

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Models for solid phases....................................................................................($

Introduction..............................................................................................................!1Solid free$eout model............................................................................................!1Eodelling hydrate formation and inhi%ition.....................................................!3

Salinity Eodel............................................................................................................4!Eodelling wa2 precipitation..................................................................................44Eodelling asphaltene flocculation.......................................................................44ther thermodynamic models..............................................................................40

!ransport property models............................................................................&*

Introduction..............................................................................................................4/iscosity.....................................................................................................................4/Thermal conductivity..............................................................................................0-Surface Tension........................................................................................................0Hiffusion coefficients..............................................................................................0!

+inary interaction parameters......................................................................Introduction..............................................................................................................008um%er of DI's related to any model..................................................................00Units for DI's.............................................................................................................0@DI's availa%le in Eultiflash....................................................................................0/

Model data re#uirements.................................................................................,

Components............................................................................................................-(

Introduction..............................................................................................................@!8ormal components................................................................................................@!

'etroleum fractions................................................................................................./&

Inde............................................................................................................................*&

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Overview

IntroductionEultiflash is an advanced software pac6age for performingcomple2 e9uili%rium calculations 9uic6ly and relia%ly. The mainutility is a multiple phase e9uili%rium algorithm that is interfacedto Infochems pac6age of thermodynamic models and a num%er ofphysical property data %an6s.

The purpose of this guide is to provide more detailed descriptionsof the models availa%le in Eultiflash than you will find in our mainUser Guide. The correlation e9uations for storing pure componentproperties in our physical property data%an6s will also %edescri%ed.

This section defines what a model is in terms of the Eultiflash

nomenclature( what models are availa%le and when you might wishto use them.

/hat types of model are availa0le17ithin the conte2t of Eultiflash( a model is a mathematicaldescription of how one or more thermodynamic or transportproperties of a fluid or solid will depend on pressure( temperatureor composition.

The 6ey thermodynamic property calculation carried out withinEultiflash is the determination of phase e9uili%rium. This is %ased

on the fundamental relationship that at e9uili%rium the fugacity ofa component is e9ual in all phases. For a simple vapourli9uidsystem

f fiv

i

l=

where fiv is the fugacity of component i in the vapour phase and

fil is the fugacity of component i in the li9uid phase.

The models used in Eultiflash to represent the fugacities from thephase e9uili%rium relationship in terms of measura%le statevaria%les >temperature( pressure( enthalpy( entropy( volume andinternal energy? fall into two groups( e9uation of state methods

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and activity coefficient methods. The %asis of each of thesemethods is descri%ed %elow.

7ith an e9uation of state method( all thermal properties for anyfluid phase can %e derived from the e9uation of state. 7ith anactivity coefficient method the vapour phase properties are derivedfrom an e9uation of state( whereas the li9uid properties aredetermined from the summation of the pure component propertiesto which a mi2ing term or an e2cess term has %een added.

Eultiflash may also %e used to calculate the phase e9uili%rium ofsystems containing solid phases( either mi2ed or pure. These mayoccur either when a normal fluid free$es or may %e a particularsolid phase such as a hydrate( wa2 or asphaltene. Eodels used torepresent these solids are discussed %elow.

The transport properties of a phase >viscosity( thermalconductivity and surface tension? are derived from semiempiricalmodels( which will %e discussed later.

"#uation of state methods

'T? %ehaviour of pure components and mi2tures.Eost e9uations of state have different terms to represent theattractive and repulsive forces %etween molecules.

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The ideal solution assumes that all molecules in the li9uid solutionare identical in si$e and are randomly distri%uted. This assumptionis valid for mi2tures made up of molecules of similar si$e andtype( %ut for mi2tures of unli6e molecules you must e2pect varying

degrees of nonideality. The activity coefficient( i ( represents the

deviation of the mi2ture from ideality( as defined %y the idealsolution.

The fugacity coefficients for the activity coefficient e9uations arecalculated from the standard relationship*

ln ln ln ln ln i i isat

i

sat

ip p= + + +

where i is the activity coefficient of component i which isderived from the e2cess Gi%%s energy as follows*

ln

i

E

i

G

n=

.

pisat is the saturated vapour pressure of component i ( i

sat is the

fugacity coefficient of the pure saturated vapour of component i>calculated from the gas phase model associated with the activitycoefficient e9uation? and p is the total pressure.

The 'oynting correction( i ( corrects the fugacity coefficient fromthe standard state pressure >i.e.the saturation pressure? to thesystem pressure. It is evaluated on the assumption of ideality( i.e.assuming that there is $ero e2cess volume of mi2ing( and that theli9uid is incompressi%le*

i isat

i

sat

p p vRT=

( )

where visat is the saturated li9uid volume of component i .

*

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!hermodynamic propertiesfrom an "#uation of State

Introduction

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%e chosen at will. Eultiflash has two possi%le reference states thatare user selecta%le*

&. KCompound datum >default?* The enthalpy of each purecomponent in the perfect gas state at 31.&0 ) and & atm is set to$ero. This is done %y setting*

Href=Hpg298 (

where Hpg298

is the value of Hpg at T 31.&0 ).

. K#lements datum* The enthalpy of each element is set to $ero inthe perfect gas state at 31.&0) and & atm.( which is done %ysetting*

Href=HfoHpg

298(

where Hfo

is the standard enthalpy of formation of the

compounds in the perfect gas state at 31.&0 ) and & atm.

This datum produces enthalpy values that are much largernumerically than the Kcompound datum %ut enthalpy differences%etween two states are the same. 7hen calculating chemicalreaction e9uili%rium the Kelements datum must %e used %ecause itis the elemental entities that are conserved rather than themolecular entities.

The overall enthalpy is o%tained %y multiplying the mole num%ersof each phase with the enthalpy of each phase( and summing overall phases*

H=j

NP

njHj .

"ntropyThe entropy is in Eultiflash calculated as*

S=Sref+Spg+Sres (

where*

Srefis the >ar%itrary? entropy value in a reference state to %edefined.

Spgis the perfect gas contri%ution to the entropy( given %y*

Spg=Tref

T CP , pg

T dT(

where CP , pgis the perfect gas heat capacityJ

Sres is the residual entropy at specified T and '( which iscalculated from the thermodynamic model specified for thermalproperties( using the standard thermodynamic relation*

Sres=0

P

[(PT

)V

R

V

]dV+R lnZ(

,

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where A is the compressi%ility factor*

Z= P V

n RT.

default?* The entropy of each purecomponent in the perfect gas state at 31.&0 ) and & atm is set to$ero. This is done %y setting*

Sref=Spg298

(

where Spg298

is the value of Spg at 31.&0 ).

. K#lements datum* The entropy of each element is set to $ero in

the perfect gas state at 31.&0) and & atm( %y setting*Sref= Sf

oSpg298

(

where Sfo

is the entropy of formation at 31.&0 ) and & atm.

This datum produces values that are much larger numerically thanthe Kcompound datum %ut entropy differences %etween two statesare the same. 7hen calculating chemical reaction e9uili%rium theKelements datum must %e used.

!. KStandard datum >sometimes called the Kthirdlaw or Ka%soluteentropy?* The reference entropy is chosen so that the entropy ofeach component in the perfect gas state at 31.&0) and & atm is

e9ual to the standard entropy of that component. This is done %ysetting*

Sref=SoSpg

298

The standard entropy( So is relative to a $ero value at a%solute

$ero. The Kstandard datum may also %e used in chemical reactionanalysis since the results are e9uivalent to the Kelements datum.

The overall entropy is o%tained %y multiplying the mole num%ersof each phase with the entropy of each phase( and summing overall phases.

2u3acity coefficientsThe fugacity coefficient( i is the ratio %etween the fugacity andthe partial pressure of a given component*

i=fi

P xi

It is calculated as*

ln i=1RT

V

[(P ni

)T ,V ,n

j

RT

V

]dVlnZ

%4

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Isothermal compressi0ilityThe 9uantity isothermal compressi%ility( ( is the response of amaterial in terms of volume change when pressure is applied atconstant temperature.

It is determined using the following e2pression*

=1V

Vp T=const

7here Vis the volume( pis the pressure and Tis the temperature.

The inverse of the compressi%ility is called the %ul6 modulus.

Iso0aric epansivity or thermal epansionThe 9uantity iso%aric e2pansivity( ( is the response of a materialin terms of volume change when temperature changes at constantpressure.

It is determined using the following e2pression*

=1

V

VTp=const

7here Vis the volume( pis the pressure and Tis the temperature.

'ctivity CoefficientThe activity coefficient of a component is defined as the activity ofthat component divided %y the mole fraction*

iai(T , P , n)

xi(

and it is in Eultiflash calculated as the fugacity of the componentin the mi2ture divided %y the pure component fugacity at the sametemperature and pressure*

i=i(T ,P ,n)i(T , P)

.

Speed of SoundThe Speed of Sound of each phase is calculated as*

c= CPV

2

CV!VP

(

%)

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where ! is the molecular weight of the phase

For multiple phases the overall speed of sound is estimated usingthe e9uation of 7allis. =eference* G. D. 7allis* Mne dimensionaltwophase flowM( EcGraw;ill( &3@3.

c=j

NP

njCP , j

CV , jVjP

%(

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"#uations of state provided inMultiflash

/hen to use e#uation of state models#9uations of state can %e used over wide ranges of temperatureand pressure( including the su%critical and supercritical regions.They are fre9uently used for ideal or slightly nonideal systemssuch as those related to the oil and gas industry where modellingof hydrocar%on systems( perhaps containing light gases such as;S( Cand 8(is the norm. #9uation of state methods do notnecessarily represent highly nonideal chemical systems( such asalcoholwater( well. For this type of system( at low pressure( anactivity coefficient approach is prefera%le %ut at higher pressure

you may need to use an e9uation of state with e2cess Gi%%s energymi2ing rules( see NEi2ing =ulesO on page &1.

DI's? have %een derived fromthe regression of e2perimental phase e9uili%rium data. DI's areadPusta%le factors( which are used to alter the predictions from amodel until these reproduce as closely as possi%le thee2perimental data.

=)S? and 'eng=o%inson >'=? cu%ice9uations of state where the e9uation of state parameters can %efitted to reproduce %oth the saturated vapour pressure using adata%an6 correlation and the saturated li9uid density at 31) orTr-./ >'enelou2 method?. These are referred to in Eultiflash as theadvanced version of the particular e9uation of state.

Further guidance on the use of specialised e9uations of state isgiven in the following sections.

%&

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Ideal 3as e#uation of stateThe ideal gas e9uation of state is defined as

p=

N RT

V .

This model is normally used in conPunction with an activitycoefficient method when the latter is used to model the li9uidphase. It could also %e used to descri%e the %ehaviour of gases atlow pressure.

Pen378o0inson e#uation of stateThe 'eng=o%inson >'=? e9uation is a cu%ic e9uation of state. It isdescri%ed %y

p NRTV "

aV "V "

=

++ 2 22

where a and " are derived from functions of pure componentcritical temperatures and pressures and acentric factor.

( )( )a a T T i ci i ci= + 1 12

a R T

pci

ci

ci

= 04!242 2

"

and

i i i= + 0 #!4$4 1422$ 0 2$9922

" " "

e2cept for water when T Tci Q -.10 where the following

alternative relation is used*

( )( )a a T T i ci ci= + 1008$!! 08214 12

" "

The standard >an der 7aals &fluid? mi2ing rules are*

N nii

=

a a a # n ni jij

ij i j= ( )1

" " ni ii

=

"RT

pici

ci

= 00!!80"

#ij is usually referred to as a %inary interaction parameter( the use

of such parameters is discussed in a later section.

%

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Pen378o0inson %,*$ 9P8*$: e#uation of stateThe &3/1 revised version of the 'eng=o%inson e9uation has adifferent treatment for the parameter . If the acentric factor

49"0

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e2cept for hydrogen( which in the

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!he Penelou density correction

This correlation is used to match the density calculated from thee9uation of state to that stored in the chosen physical propertydata system. For light gases( the density is matched at a reduced

temperature of -./ and the volume correction is assumed constant.For li9uid components the volume shift is a function oftemperature.

TcTccc iiii &210 ++=

iixcVV = '

The three coefficients may %e stored as part of the purecomponent data record.

Eultiflash usually treats the volume shift as a linear function oftemperatureJ the density is matched at 3-./) and !&0./) so as toreproduce the density and thermal e2pansivity of li9uids over a

range of temperatures centred on am%ient. ;owever( users mayalso use the third term and enter the coefficient values directly.

2ittin3 the vapour pressure curve

The function for ia is generalised to the following form*

( )a a t t t t t ci i i i i i i i i i i= + + + + +1 1 22

#

#

4

4

2

where

t T Ti ci= 1 .

For each component the constants( i1 to i are fitted %y linearregression to the vapour pressure over a range of reducedtemperatures corresponding to the stored data. Fewer than 0coefficients will %e fitted if there is insufficient data or if thee2trapolation to low temperatures is unrealistic. If the vapour

pressure is undefined( the correlation for ai reverts to the

standard e9uation for that component.

Miin3 8ules

For highly nonideal systems it is often useful to %e a%le to use anyGi%%s energy e2cess model >e.g. U8I"U

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" " nii

i=

a RT"

s

$ s N

$

=

1

2

2

( )

( )

$ G

RTn $

"

N"

E

i

i

i i

i

( ) ( ) ln = + +

$s s s

i i

i i( )

( )

=

+1 1

2

24

2

For the =)S e9uation s1 2= ln and s2 1! 2= "

For the '= e9uation

s1

1

2 2

2 2

2 20$2#22

=

+

=ln "

ands2 20129= " .

Huron-Vidal type mixing rules:

N nii

=

" " nii

i=

a " G

s n a

"

E

i i

ii= +

1

For the =)S e9uation s1 2= ln

For the '= e9uation

s11

2 2

2 2

2 20$2#22=

+

=ln "

PSRK type mixing rules:

N nii

=

ii

i n"" =

+

+=

i i

i

i

i i

i

E

"

an

"

"n

s

RT

s

G"a ln

11

$4$$#"01=s

Infochem mixing rules:

These mi2ing rules are similar to the original ;uronidal mi2ing

rules apart from the form of the interaction parameters ij# ( ji#

%,

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and ij which gives a different form of temperature dependence.

These rules reduce to the conventional van der 7aals mi2ing rules

when jiij ## = and 0=ij .

N nii

=

" " nii

i=

a " nn " G

n " Gi

i

j j j ji ji

j j j ji

=

where*

jii j ji

i j

a a #

" "=

+

2 1( )

and*

GRT

ji

ji ji ii=

e%p

( )

/hen to use cu0ic e#uations of state

The simple cu%ic e9uations of state( '= and =)S( are widely usedin engineering calculations. They re9uire limited pure componentdata and are ro%ust and efficient. Doth '= and =)S are used in gas

processing( refinery and petrochemical applications. They willusually give %roadly similar results( although if one model has%een fitted to e2perimental data and there are no interactionparameters for the other then the optimised model is alwaysprefera%le. There is some evidence that =)S gives %etter fugacitiesand '= %etter volumes >densities? %ut %oth can %e improved if the'enelou2 correction is used.

For most applications we would recommend the use of the =)Sor '=

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The form of the model is*

p=

i

ni%

i (1&i)

V0"4" +

NRT

V"+

a

V(V+")

The parameters cia and i" are set for each component to satisfy

the critical conditions 02

2

=

=

V

p

V

pat the 6nown critical point

of that component. The parameter a is a function of temperaturegiven %y*

( ) ( ) 24

4

#

#

2

211 iiiiiiiiiicii tttttaTa +++++=

where*

t T Ti ci= 1 .

For each component the constants( i0 to i are fitted %y linearregression to the vapour pressure over a range of reducedtemperatures corresponding to the stored data. Fewer than 0coefficients will %e fitted if there are insufficient data or if thee2trapolation to low temperatures is unrealistic.

The model uses the standard >an der 7aals &fluid? mi2ing ruleswhich are*

N nii

=

a a a # n ni jij

ij i j= ( )1

" " ni ii

=

"RT

pici

ci

= 008$$4"

The 7ertheim association term is comple2 and( for a completediscussion( the user should refer to the scientific literature. In

summary( the terms i& are found %y simultaneously solving the

7ertheim e9uations( which in the C'< model have the form*

"V

&%'

&

j

jjij

i 4"01

1

+=

where i% are the num%er of >donor? %onding sites on component i

and ij' is the association constant for components i and j .

The C'< model also uses the 'enelou2 density correction to matchthe li9uid density calculated from the e9uation of state to thatstored in the chosen physical property data system. The volumeshift is a linear function of temperature which is set to match thesaturated li9uid density at two different temperatures. For light

)%

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gases( a constant volume shift is used that is fitted to the gassli9uid density at a reduced temperature of -./.

/hen to use CP'

The C'< model may %e used for hydrate calculations withmethanol( ethanol( E#G( H#G( T#G and salt inhi%ition( as these arethe only cases for which parameters are currently provided.'arameters for additional su%stances may %e added in futureversions of Eultiflash.

PC7S'2! e#uation of stateThe 'CS--!?.

Polymer Components

'olymers are not welldefined chemical compounds %ut rather adistri%ution of chain molecules of varying molecular weight. In

))

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Eultiflash( polymers must %e represented %y one or more pseudocomponents( which must %e set up as userdefined components.

Using 'CS

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the DI's %etween normal components andRor segments. 8ote thatin the fluid composition( the amounts of the segments must all %eset to $ero( as the segments are not real components of themi2ture.

PS8; e#uation of stateThis model consists of the =)S< e9uation of state with vapourpressures fitted using EathiasCopeman parameters >if availa%le?(the 'enelou2 volume correction and the 'S=) type mi2ing rules.The e2cess Gi%%s energy is provided %y the 'S=) variant of theUnifac method. This is the same as the normal L# Unifac modele2cept that the group ta%le has %een e2tended to include a largenum%er of common light gases.

/hen to use PS8;

The 'S=) model is an e2tension of the Unifac method. It isintended to predict the phase %ehaviour of a wide range of polarmi2tures using the solution of groups concept as em%odied inUnifac. The main %enefit of 'S=) is that it is a%le to handlemi2tures containing gases much %etter than Unifac and unli6e anormal e9uation of state it can handle polar li9uids. This is%ecause >a? it uses an e9uation of state with an e2cess Gi%%senergy mi2ing rule there%y avoiding pro%lems of how to handlesupercritical components in an activity coefficient e9uationJ >%? theUnifac group parameter ta%le has %een e2tended in 'S=) toinclude ! common light gases.

PS8;7?8!L e#uation of stateThis model is the same as the 'S=) model e2cept that the e2cessGi%%s energy is provided %y the 8=TL e9uation. So unli6e the 'S=)e9uation( the 'S=)8=TL variant re9uires that DI's are providedfor the 8=TL e9uation in order to give accurate results. Itsadvantage is that( provided the DI's are fitted to relevant phasee9uili%rium data( the model can give more accurate predictionsthan the 'S=) e9uation.

Lee7;esler 9L;: and Lee7;esler7Pl@c=er 9L;P:e#uations of state

The L) and L)' methods are ! parameter corresponding statesmethods %ased on interpolating the reduced properties of ami2ture %etween those of two reference su%stances. The e9uationfor each property is of the form*

[ ]( ( ( ()ix = + ( ) ( )( ) ( )0

1

1 0

where )0(( and)1(

( are the compressi%ility factors of the two

reference fluids e2pressed as functions of reduced temperature(pressure and volume. To apply the method to a mi2ture( therefore()&

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it is necessary to o%tain averaged critical properties %y the use ofmi2ing rules. The only difference %etween the L) and L)' methodslies in the value of the parameter in the mi2ing rules which aredefined as follows. First the critical compressi%ility factor for eachcomponent i is defined from the acentric factor %y*

iciZ 08"0290"0 =

and hence the critical molar volumes*

cicicici pRTZv &=

The main mi2ing rules have the form*

i

i

i)ixc ZxZ =,

##&1#&1

,2

+=

ij

cjci

ji)ixc

vvxxv

ijcjci

ij

cjci

ji

c

)ixc #TTvv

xxv

T

##&1#&1

,2

1

+=

)ixc)ixc)ixc)ixc vZRTp ,,,, &=

where cT and cp denote the critical pressure and temperature(

ij# denotes the DI' the default value of which is &( and R

denotes the gas constant. Su%script i denotes component i . Forthe L) method 1= ( whereas for the L)' method 2"0= .

In Eultiflash( all the DI's for the L) method are set to the defaultvalue of &. For the L)' method( it is 9uite important to adPust theDI's in order to get reasona%le phase e9uili%rium predictions.Eultiflash uses correlations for the DI's proposed %y )napp et al.In these correlations the DI's are all set to constant values(although Eultiflash allows the user to use temperature dependentDI's if re9uired. < complete description of the method can %efound in Vapor-&iquid Equilibria for Mi(tures of &o$ Boilin! PointSubstanes%y )napp( Hring( ellrich( 'lc6er and 'rausnit$(Chemistry Hata Series olume I( Hechema &31.

/hen to use L; or L;P

The methods predict fugacity coefficients( thermal properties andvolumetric properties of a mi2ture. ;owever( they are rather slowand comple2 compared to the cu%ic e9uations of state and are notparticularly recommended for phase e9uili%rium calculations(although they can yield accurate predictions for density andenthalpy. They would normally %e applied to nonpolar or mildlypolar mi2tures such as hydrocar%ons and light gases.

)

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+enedict7/e0078u0in7Starlin3 9+/8S: e#uation ofstate

The D7=S e9uation method is an && parameter noncu%ic e9uationof state. It is descri%ed %y

+++++=

2

2

2

2

22e%p1

'

VVV

C

V

*

V

C

V

+N

V

RTp

where*

++=

4

0

#

0

2

0

00

1

T

E

T

*

T

C

RT++

+=

T

da

RT

"C#

## 1

+=

T

da

RT*

##

#

#

#

'RT

cC=

Ei2ing rules are used to calculate the parameters from purecomponent properties as follows*

N nii

=

=i

ii n++ 00

( ) jiij

ijji nn# = 1000

( ) jiij

ijji nn#CCC#

000 1 =

( ) jiij

ijji nn#***4

000 1 =

( ) jiij

ijji nn#EEE

000 1 =

" " ni ii

=

=i

ii naa

=i

ii ncc

)-

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=i

ii ndd

=i

ii n

=i

ii n

where #ij is a %inary interaction parameter. For methane( ethane(

ethylene( propane( propylene( iso%utane( n%utane( isopentane( npentane( he2ane( heptane( octane( car%on dio2ide( hydrogen

sulphide and car%on dio2ide( the pure component parameters i+0 (

i0 ( iC0 ( i* 0 ( iE0 ( i" ia ( ic ( id ( i and i are set to valuesrecommended %y Starling in his %oo6 KFluid Thermodynamic'roperties for Light 'etroleum Systems( Gulf 'u%lishing Co.(;ouston( &3/!. For other su%stances the pure component

parameters are estimated using correlations developed %y Starlingand ;an which are given in the same %oo6.

/hen to use the +/8S e#uation

The D7=S e9uation gives much more accurate volumetric andthermal property predictions for light gases and hydrocar%ons.Given suita%le interaction parameters it should give reasona%levapourli9uid phase e9uili%rium predictions %ut owing to itscomple2ity( it re9uires more computing time than the cu%ice9uations of state.

Multi7reference fluid correspondin3 states 9CSM:model

The CSE model is %ased on a collection of very accurate e9uationsof state for a num%er of reference fluids. It will provide accuratevalues of properties for any of the reference fluids >see %elow for alist? and it uses a &fluid corresponding states approach toestimate mi2ture properties. It is formulated so that mi2tureproperties will reduce to the >accurate? pure component values asthe mi2ture composition approaches each of the pure componentlimits.

In Eultiflash 4.&( the G#=G--1 models for natural gas and othermi2tures are implemented. The models( %ased on the G#=GTechnical Eonograph &0--/ %y . )un$ et al( not only have theaccurate reference eos for each su%stance %ut also includes adeparture function ta6ing into account the residual mi2ture%ehaviour. There are & main and secondary natural gascomponents considered in the G#=G models. They are methane8( C( ethane( propane( n%utane( iso%utane( npentane( isopentane( nhe2ane( nheptane( noctane( nnonae( ndecane( ;(;S( ( C( water( ;elium and

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The CSE and G#=G model definition can %e considered in twodistinct parts* the definition of pseudocritical properties for ami2ture >mi2ing rules?( and the prescription for com%ining theproperties of the reference su%stances to give the total mi2tureproperties >com%ining rules?.

Miin3 rules for critical properties

The mi2ing rule for the CSE and G#=G model is different and thedetails are descri%ed as follow.

For the CSE model( the mi2ture >pseudo? critical volume is definedas

ijijc

i j

ji)ixc -VnnN

V ,1 1

2,

1 = =

=

where =

i

inN

is the total mole num%er of the mi2ture( in

isthe mole num%er of component i. ij- is a temperaturedependent

%inary interaction parameter for the critical volume( normally closeto & and

( )##&1,#&1

,,8

1jcicijc VVV +=

The mi2ture >pseudo? critical temperature is defined as

)ixcijijcijc

i j

ji)ixc V'VTnn

NT

,,,

1 12,

1 = =

=

here jcicijc TTT ,,, = nd ij' is a temperaturedependent

%inary interaction parameter >DI'?( normally close to &.-. This DI'has a significant effect on phase e9uili%rium calculations and must%e fitted to match e2perimental data.

For the G#=G models in Eultiflash( the mi2ture >pseudo? criticalvolume is defined as

( )

= = +

+=

1 1

,

2,

1

i j j

V

jii

V

ij

ijc

V

ijjiji

)ixcnn

Vnnnn

NV

cc

c

where in is the mole num%er of component i*cV

ij

is a linear

temperaturedependent %inary interaction parameter for thecritical volume( normally close to & and

( )##&1,#&1

,,8

1jcicijc VVV +=

The cV

ij andcV

ji are the asymmetric constant with and the

values are usually close to &.

The mi2ture >pseudo? critical temperature in G#=G models isdefined as

)$

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( )

= = +

+=

1 1

,

2,

1

i j j

T

jii

T

ij

ijc

T

ijjiji

)ixcnn

Tnnnn

NT

cc

c

here jcicijc TTT ,,, = nd cT

ij is a linear temperature

dependent %inary interaction parameter >DI'?.

For the G#=G--1 models( the DI's for the special selected &natural gas components are stored in the I8FDI'S data%an6. Ifthe DI's are not availa%le in the data%an6( the values are set to &%y default.

In order to improve the phase e9uili%rium prediction( the DI's thatare not availa%le in the data%an6 for %oth CSE and G#=G modelsshould %e o%tained %y fitting the e2perimental data.

The mi2ture >pseudo? critical compressi%ility factor is defined as

=

i

ici)ixc ZxZ ,,

ic

icic

jcRT

VPZ

,

,,

, =

The mi2ture >pseudo? critical pressure is then defined as

)ixc

)ixc)ixc

)ixcV

RTZP

,

,,

, =

Com0inin3 rule for miture thermodynamic

properties

The total mi2ture reduced Gi%%s energy is o%tained %y com%iningthe pure component reduced properties as follows*

( ) ( )=i

rriirr)ix PTGxPTG ,0

,

where the reduced properties are defined as

)ixcr TTT ,=

)ixcr PPP ,=

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The departure function of the multicomponent mi2tures(additional contri%ution to the total reduced Gi%%s energy is thesum of all %inary specific and generalised departure functions ofthe involved %inary su%systems and is e2pressed %y

( ) ( ) = = = 1 1 ,,21,, i j rrr

ijrrr &PT&PT

with

( ) ( )rrrijijjirrrij PT%xx&PT ,,, =

The parameter ij% , the ei*htin* fctor of the component, indj

in the mi%ture, is o+tined from fittin* the specific +inr mi%tures"

-he vlues of ij% for the nturl *ses in the ./.2004 model

re stored in the I8FDI'S data%an6. If there is no departure

function for a %inary components( the value of ij% is set to ero

+ defult" The +inr deprture function, ( )rrr

ij PT , is similr to

the structure of pure su+stnce e3ution of stte +ut ith different

e3ution coefficients for tpicl pir of +inr mi%ture"

8eference fluids

The current model implementation includes reference e9uations ofstate for the following su%stances* ammonia( argon( iso%utane( n%utane( C( C ( ethane( ethylene( fluorine( helium( heptane(he2ane( hydrogen( ;S( methane( neon( nitrogen( octane( o2ygen(npentane( propane( propylene( water >I

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/ater

< highaccuracy model for water is availa%le as a separate modeloption and is also included as part of the CSE mi2ture model. Thereference e9uation of state is the I&331?. The thermal conductivity formulationis* +A %eferene Multipara"eter Ther"al Conduti5ity Equation forCarbon 4io(ide $ith an 1pti"i9ed Funtional For"3( G. Scala%rin('. Earchi( F. Fine$$o and =. Span( B. 'hys. Chem. =ef. Hata.( ol.!0( &043 >--@?.

(%

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'ctivity coefficient e#uationsin Multiflash

< num%er of activity coefficient e9uations are availa%le inEultiflash and are descri%ed %elow. The nomenclature is to denote

%inary interaction parameters %etween components i and j%y ij .

The 8=TL e9uation has an additional parameter ij .

/hen to use activity coefficient models

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The ideal solution model may %e used when the mi2ture is ideal(i.e. when there are no mi2ing effects. It an also %e used for singlecomponents to calculate some pure component properties fromthe physical property data%an6.

/ilson e#uation

/ilson " e#uation

This is defined %y*

G

RTn

G n

n

E

i

j ij j

j ji

=

ln

where*

GV

V

RTij

j

i

ij=

*

*e%p

Vi* is the saturated li9uid molar volume of component i

>e2trapolated in the case of supercritical gases? evaluated at a fi2edreference temperature of 31.&0).

This model may %e used for vapourli9uid e9uili%rium calculations%ut it is not capa%le of predicting li9uidli9uid immisci%ility. Dinaryinteraction parameters are provided in our I8FDI'S %an6 forsome component pairs. If no DI's are included for your particularmi2ture then to o%tain accurate predictions you must supply%inary interaction parameter values in the correct units.

/ilson ' e#uation

G

RTn

n

n

E

i

j ij j

j ji

=

ln

This model which is a simplified form of the 7ilson # model( may%e used for vapourli9uid e9uili%rium calculations %ut it is notcapa%le of predicting li9uidli9uid immisci%ility. To o%tain accuratepredictions you must supply %inary interaction parameters >DI'?

values( which are dimensionless.

?8!L e#uation

G

RTn

G n

n G

E

i

j ij ji j

j j jii

=

ln

where*

Ga

RTij

ij ij=

e%p

((

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The 8=TL model may %e used for vapourli9uid( li9uidli9uid andvapourli9uidli9uid calculations >the L# option should %e usedfor LL#?.

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pure component i according to the principle of solution ofgroups. The U8IFor pure

component?. #N is the total num%er of moles of group # ( #$

is the surface area parameter for group # and l# is the

interaction parameter*

=RT

l#l# e%p

In original U8IF

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method. Li6e original U8IF&31/?J A Modified )#,FAC Model. . PresentPara"eter Matri( and %esults for 4ifferent Ther"odyna"iProperties( i%id.( !( &/1( >&33!?J A Modified )#,FAC ;4ort"und&331?J A Modified)#,FAC ;4ort"und< Model. >. %e5ision and E(tension( i%id.( 4&(&@/1( >--?.

8e3ular solution theory

=

iii

ij

ijjijiE

VnRT

,VVnn

RT

G

where*

( )ijji

ji

ij #

=2

2

i and iV are the solu%ility parameters and molar volumes at

0C of component i .

=egular solution theory can %e used for vapourli9uid calculationsfor mi2tures of nonpolar or slightly polar components. The theoryis applica%le to systems which e2hi%it negligi%le entropies and

volumes of mi2ing. ;owever( it has %een largely superseded %ye9uations of state.

2lory75u33ins theoryThe Eultiflash implementation of Flory;uggins theory includes acorrection term. It is defined %y*

+

=

i

ii

ij

ijjiji

i

j

jj

j

ji

i

E

VnRT

VVnn

Vn

nV

nRT

G

2ln

The Eultiflash e2pression reduces to the standard Flory;uggins

theory if all interaction parameters ij, are set to $ero. ;owever(

to o%tain reasona%le results it is usually necessary to adPust thevalues of the interaction parameters to fit the data.

Flory;uggins theory is a%le to descri%e systems which includesome long chain molecules. It has conse9uently applied to modelpolymer systems %ut it has %een to some e2tent superseded %yother models such as 'CS

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Gas phase models for activity coefficient methods

The 9uantity ln isat can %e calculated from any of the gas phase

models in Eultiflash. The normal choices would %e the perfect gas

e9uation( the =) e9uation of state or a virial e9uation of state.The first two are descri%ed in the section on e9uations of state andthe ;C second virial model is descri%ed %elow.

!he 5ayden7OBConnell 95OC: model

The Eultiflash implementation of the ;C model treats eachcomponent in the gas phase as forming a monomerdimere9uili%rium. For most components that deviate only slightly fromideal %ehaviour( the model reduces to the volumee2plicit viriale9uation*

+p

RTV +=

The second virial coefficient B is estimated for each componentfrom a generalised correlation >B.G. ;ayden and B.'. Connell( Ind.#ng. Chem. 'roc. Hes. Hev( &4( -3 >&3/0??. This correlationaccounts for nonpolar( polar and chemical association effects. Thepure component properties re9uired %y the model are* criticaltemperature( critical pressure( radius of gyration( dipole momentand an empirical association parameter. alues for these 9uantitiesare stored in the Infodata data%an6.

< second virial coefficient model such as ;C can account for gasphase nonidealities up to pressures of a%out 0 to &- %ar. Theimplementation of the ;C model in Eultiflash allows the vapourphase association of su%stances such as acetic acid to %erepresented.

(*

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Models for solid phases

IntroductionEultiflash may also %e used to calculate the phase e9uili%rium ofsystems containing solid phases( either mi2ed or pure. These mayoccur either when a normal fluid free$es or may %e a particulartype of solid phase such as a hydrate.

Solid freee7out modelThis model is used to calculate the thermodynamic properties ofsolid phases formed %y free$ing one or more of the components inthe fluid mi2ture. It may %e applied to any component where thismay %e a consideration. The free$eout model in general is defined

%y*

ln 2i=3 ln 2ili/

4HTref 4CpR ( 1T 1Tref)+

Scorr

R +

4Cp

Rln( TTref)

(ppat))4V

RT

For the free$eout of pure solids( the parameters are as follows*

i is the fugacity coefficient of pure solid component i ( ili/ is

the fugacity coefficient of the same component as a pure li9uid atthe same pressure p and temperature T >calculated from theli9uid phase model associated with the free$eout model?( 1= (H ( Cp and V are the changes in molar enthalpy( molar

heat capacity and molar volume respectively on fusion at themelting point( refT is a reference temperature which corresponds

to the normal melting point when 0=corrS which is assumed inthis case. pat) is atmospheric pressure. H ( Cp and Vare constants( which are normally o%tained from the chosen datasource.

Solid free$eout can %e used to model the solidification ofcompounds such as water( car%on dio2ide or methane( for e2amplein natural gases. It can also %e used to model eutectics.

($

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Scalin3 and 3eneral freee7out model

In its general form( the free$eout model can %e applied to anysolid phase of fi2ed composition( which must %e defined. Themodel can for e2ample %e applied to hydrated salts such as

monoethylene glycol >E#G? monohydrate or to crystalline mineralsalts( i.e. scales. If 1= ( the solid fugacity coefficient is definedrelative to the li9uid phase of the same composition whereas( if

0= ( the solid fugacity coefficient is an a%solute value. corrS isa molar enthalpy correction factor that allows the reference

temperature refT to %e different from the normal melting point.

For solid phases that are not pure su%stances( the parameters

H ( Cp V ( corrS and refT must %e defined specificallyfor the phase in 9uestion.

Modellin3 hydrate formation and inhi0ition8atural gas hydrates are solid iceli6e compounds of water and thelight components of natural gas. They form at temperatures a%ovethe ice point and are therefore a serious concern in oil and gasprocessing operations. The phase %ehaviour of systems involvinghydrates can %e very comple2 %ecause up to seven phases mustnormally %e considered. The %ehaviour is particularly comple2 ifthere is significant mutual solu%ility %etween phases( e.!. wheninhi%itors or Care present. Eultiflash offers a powerful set of

thermodynamic models and calculation techni9ues for modellinggas hydrates.

5ydrate model

The original Infochem model uses a modification of the =)Se9uation of state for the fluid phases plus the van der 7aals and'latteeuw model for the hydrate phases.

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included. These compounds are* SF@( ethylene(

propylene( cyclopropane( o2ygen( argon( 6rypton and2enon.

'arameters are provided for the following compounds

that form hydrate structure II in the presence of smallKhelpgases such as methane or nitrogen* cyclopentane(%en$ene and neopentane. These compounds and thestructure ; formers listed %elow may %e present incondensate and oil systems.

Structure ; hydrates form in the presence of smallKhelpgases such as methane or nitrogen %ut theformation temperatures are significantly higher >a%out&- )? than pure methane or nitrogen hydrate. Inpractice it seems that structure II hydrates form %eforestructure ; %ut( if there is enough water( structure ;may %e formed too. The structure ; model includesparameters for*

isopentaneneohe2ane(!dimethyl%utane((!trimethyl%utane(dimethylpentane!(!dimethylpentanemethylcyclopentanemethylcyclohe2anecis&(dimethylcyclohe2ane(!dimethyl&%utene!(!dimethyl&%utene

cyclohepteneciscycloocteneadamantaneethylcyclopentane&(&dimethylcyclohe2aneethylcyclohe2anecyclohe2anecycloheptanecyclooctane

The thermal properties >enthalpies and entropies? of thehydrates and ice are included permitting isenthalpicand isentropic flashes involving these phases.

Calculations can %e made for any possi%le com%inationof phases including cases without free water. 8omodification of the phase models is re9uired to do this.

The properties of the hydrates have %een fi2ed %yinvestigating data for natural gas components in %othsimple and mi2ed hydrates to o%tain relia%lepredictions of structure I( structure II and structure ;hydrates.

The properties of the empty hydrate lattices have %eeninvestigated and the most relia%le values have %eenadopted.

&4

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'roper allowance has %een made for the solu%ilities ofthe gases in water so that the model parameters are notdistorted %y this effect. This is particularly importantfor car%on dio2ide and hydrogen sulphide which arerelatively solu%le in water.

Correct thermodynamic calculations of the most sta%lehydrate structure have %een made.

The model is used to calculate the hydrate e9uili%rium formationtemperature at a given pressure or pressure at a given temperaturewhere the first very small 9uantity of hydrate appears after asufficiently long time. This point corresponds to thethermodynamic formation point( also 6nown as the hydratedissociation point. Defore the thermodynamic formation point isreached hydrate annotform this point is also called the sta%ilitylimit. Deyond the sta%ility limit hydrate anform %ut may not doso for a long time.

The model has %een tested on a wide selection of open literatureand proprietary e2perimental data. In most cases the hydratedissociation temperature is predicted to within V&).

5ydrates in water su07saturated systems

;ydrates can form even in systems where there is no free waterpresent. ur hydrate model( with %oth =)S

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The model was generalised to cover in principlenucleation from any li9uid or gas phase.

< correction for heterogeneous nucleation was includedthat was matched to availa%le hydrate nucleation data.

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hydrate dissociation temperatures( depression offree$ing point data and vapourli9uid e9uili%rium data.

Two salt inhi%ition models are availa%le. The oldermodel is %ased on a salt component. The new model isa >restricted? electrolyte model. < salinity calculator toolis provided( see User Guide for Eultiflash for 7indows(which allows the salt composition to %e entered in avariety of ways. The salt component model e2pressesthe salt composition in terms of an e9uivalent NsaltcomponentO present in I8FHTotal HissolvedSolid?. If an Ion

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model cannot %e used with the C'< model or any other e9uationof state.

The electrolyte salt model is designed to %e added on to anye9uation of state. The models selection form allows it to %eselected for use with the

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hydrocar%ons( the concentration of resins goes down and a pointmay %e reached where the asphaltene is no longer sta%ilised and itflocculates to form a solid deposit. Decause the sta%ilising actionof the resins wor6s through the mechanism of polar interactions(their effect %ecomes wea6er as the temperature rises( i.e.

flocculation may occur as the temperature increases. ;owever( asthe temperature increases further the asphaltene %ecomes moresolu%le in the oil. Thus( depending on the temperature and thecomposition of the oil( it is possi%le to find cases whereflocculation %oth increases and decreases with increasingtemperature.

The asphaltene model is %ased on the =)S cu%ic e9uation of statewith additional terms to descri%e the association of asphaltenemolecules and their solvation %y resin molecules. The interactions%etween asphaltenes and asphaltenesresins are characterised %y

two temperaturedependent association constants* ' and R' .

The remaining components are descri%ed %y the van der 7aals &

fluid mi2ing rule with the usual %inary interaction parameters ij# so the asphaltene model is completely compati%le with e2istingengineering approaches that are ade9uate for descri%ing vapourli9uid e9uili%ria. The model is a computationally efficient way ofincorporating comple2 chemical effects into a cu%ic e9uation ofstate.

Other thermodynamic modelsEultiflash also incorporates a corresponding states method forestimating the density of li9uid mi2tures( the CST

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The CST

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!ransport property models

IntroductionFor each of the transport properties( viscosity( thermalconductivity and surface tension( Eultiflash offers two approachesto o%taining values for mi2tures. ne route is to calculate theproperty for a mi2ture %y com%ining the property values for thepure components of which it is composedJ the mi2ing ruleapproach. The other is to use a predictive method suita%le for theproperty in 9uestion.

iscosity

Super!8'PP viscosity model

The SuperT=-(T-?. In order toimprove the viscosity prediction for cycloal6anes and highly%ranched al6anes( the concept of mass shape factor in introducedin this method. In order to apply the method( the following arere9uired*

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!hermal conductivity

Chun37Lee7Starlin3 thermal conductivity

methodThis is a predictive method for %oth gas and li9uid mi2ture

thermal conductivities. It re9uires the critical properties( Tci ( Vci

and ci for nonpolar components. For polar and associating fluidsthe dipole moment and an association parameter are also re9uired.&31/?.

Super!8'PP thermal conductivity method

The SuperT=ST=

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in units of "?"?7. R is the molar gas constant in units of

')ol8 && and x is the molecular weight for the mi2ture in

unit of gRmol and the e2pression of )(To

x for a mi2ture is given

as follows.

=

==n

i

ix

n

i

i

o

ii

o

x

x

Tx

T

1

2&1

1

2&1)(

)(

and =

=n

i

iix x1

7hereo

i is the dilute gas viscosity given %y Lucas correlation in

unit of P .

The e2pression of the residual contri%ution term is evaulated usingthe e2tended corresponding state method and is related to thethermal conductivity of a reference fluid of propane at a

corresponding state( ),( oo T .

%TT oores

o

res

x ),(),( =

where the % calculation re9uires mi2ing and com%ining rules for

the mi2tures.

=eferences*

Bames F. #ly and ;.B.E. ;anley ( N'rediction of transport properties. .Thermal conductivity of pure fluids and fluid mi2tures. Ind. #ng.Chem. Fund.( ( 3-3/ > &31!?.

E.L. ;u%er and ;.B.E. ;anley( N The CorrespondingStates 'rinciple*

Hense FluidsO( p1!( edited %y B rgen Eillet( Bohn ;. Hymond and C.

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where i and i are the molecular weight and pure saturatedli9uid thermal conductivity of component i .

apour thermal conductivity miin3 rule

The thermal conductivity of a gas mi2ture at low density iscalculated from the correlations for $ero density gas thermalconductivity of the pure components at the same temperature.

=

i i i i

i i i

n

n

Surface !ension

Linear Gradient !heory method

This method predicts the interfacial tension %etween two phases.The possi%le pairs of phases are* Li9uid R Gas and Li9uid R Li9uid.The predition of interfacial tension %etween Li9uid R Solid andGas R Solid phases is not yet possi%le.

The model uses the difference in densities %etween the two phasesand the energy gradient that arrives from the fact that the phasesare immisci%le to predict the interfacial tension.

( )( ) ( )( ) ref99ref:

ref9

e/e/

ii

i

i d:P:P;:;:<

2c

The varia%le is characteristic of the mi2ture and varies withtemperature. The mi2ing rule used for this parameter is of thefollowing type*

( )ijjjiiij lccDI'?.

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Macleod7Su3den method

This method predicts the surface tension of a li9uid mi2ture %asedon the pure component parachors stored in a data%an6.

1 4&

( )= P x yi l i v i

where*

Pi is the parachor for component i

lis the li9uid molar density

v is the vapour molar density

xi is the li9uid mole fraction

yi is the vapour mole fraction.

It is mainly applica%le to the types of component found in oil andgas processing.

=eference* 'edersen( Fredenslund and Thomassen( Properties of1ils and #atural 2ases( Gulf 'u%lishing Co.( >&313?.

Surface tension miin3 rule

The surface tension for a li9uid mi2ture may %e calculated fromthe correlations for the surface tension of the pure saturatedli9uids at the same temperature and pressure using a power lawmodel.

11

=

i i

i

i i

n

n

where i is the surface tension of the pure saturated li9uid forcomponent i .

=eference* 'edersen( Fredenslund and Thomassen( Properties of1ils and #atural 2ases( Gulf 'u%lishing Co.( >&313?.

Diffusion coefficients

2uller method

The Fuller method calculates gas diffusion coefficients. It is anempirical modification of Chapman#ns6og theory. The Fullere2pression for the diffusion coefficient for components i and j in SI units is*

( )

2&1

2#&1#&1

!"12211100112"1

+

+

=

jiji

ij

ijp

#T*

(

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T is the temperature( p is the pressure( i is the relative

molecular weight of component i >in g mol&? and i is acharacteristic volume that is found for each component using

Fullers ta%les. ij# is an empirical adPustment factor for the user

to match the Fuller method to e2perimental data if availa%leJ too%tain the standard result from Fullers method( ij# should %e set

to unity.

=eference* Chapter && of The Properties of 2ases and &iquids( 0th.#d. %y 'oling( 'rausnit$ and Connell( EcGraw;ill( 8ew Yor6(--&.

5aydu=7Minhas method

The ;aydu6Einhas method calculates li9uid diffusioncoefficients. It consists of a num%er of empirical correlations for

different classes of mi2ture. For e2ample for normal paraffins thediffusion coefficient of a trace amount of component i incomponent j in SI units is*

( )

!91"01002"1

100010#09"!

!1"0

4!"11$

0

=

=

i

i

j

ij

V

V

T*

T is the temperature( iV is the molar volume of component i

and j is the li9uid viscosity of component j . The viscosity is

calculated from the li9uid viscosity model specified %y the user.Hetails of the other correlations that form the ;aydu6Einhasmethod are descri%ed in the =eference. Eultiflash actually returnseffective diffusion coefficients for a li9uid of defined composition.The e2pression used is*

( ) ( )

j

j

j

i

ii

ij

x

ji

x

ijij

xx

xx

#*** ij

+=

+=

=

ln1

ln1

00

where ix and i are the mole fractions and activity coefficients

of component i in the %inary mi2ture. For the sa6e of efficiency(the activity coefficients are calculated from the Eargulese2pression which in turn is fitted to the activity coefficients for ane9uimolar %inary mi2ture calculated with the thermodynamic

model for the li9uid phase specified %y the user. ij# is an

empirical adPustment factor for the user to match the calculatedresult to e2perimental data if availa%leJ to o%tain the standard

result( ij# should %e set to unity.

=eference* Chapter && of The Properties of 2ases and &iquids( 0th.#d. %y 'oling( 'rausnit$ and Connell( EcGraw;ill( 8ew Yor6(--&.

&

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+inary interaction parameters

IntroductionDinary interaction parameters >DI's? are adPusta%le factors whichare used to alter the predictions from a model until thesereproduce as closely as possi%le the e2perimental data. DI's areusually generated %y fitting e2perimental L# or LL# data to themodel in 9uestion( with the e2ception of U8IF=)( =)S( '=? re9uire only a single DI'. The closer the %inarysystem is to ideality the smaller the si$e of the DI'( which will %e$ero for ideal systems. It is unli6ely that the value of the DI' will%e greater than &( although it is possi%le for it to %e negative. Forthe L) and L)' models the default value of the interactionparameter is &.

7hen nonstandard mi2ing rules are used( e.g.when using=)SInfochem?( then the num%er of DI's increases. For the e2cessGi%%s energy type mi2ing rules >E;type and ;uronidaltype?

the num%er of DI's will %e determined %y the activity coefficientmodel used to descri%e the li9uid phase. For the Infochem mi2ingrule ! DI's are needed.

'CS

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more that one set may ade9uately represent the samee2perimental data. The DI's for the activity models are asymmetricand it is important to define the %inary pair of components i andj in the correct order to agree with the fitted or reported DI's.

The 8=TL parameter defaults to -.! for L# calculations and-. for LL# calculations. alues derived from fitting toe2perimental data will vary %ut are unli6ely to %e much greaterthan -.@.

The =egular Solution and Flory ;uggins models %oth use a DI'sthat are symmetrical( dimensionless and with a default value of$ero.

Units for +IPsThe DI's for e9uation of state methods are dimensionless( with the

e2ception of two of the C'< association parameters. For some ofthe activity coefficient models they are dimensioned with thee2ception of 7ilson

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where

dij="

ij/R

eij=a

ij/R

fij

=cij

/R

The 8=TL parameter is dimensionless so it is given %y

3ij=a ij+"ij T+c ij T2

for all units e2cept the

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missing they will %e set to default values. The L# variants of theactivity methods only access I8FDI'S( %ut the LL# variants accessI8FLLDI'S( followed %y I8FDI'S.

Detween releases of Eultiflash we may amend( or add to( the DI'sstored. For the IL

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Model data re#uirements

#ach model re9uires a certain amount of pure component data.These are listed in the following ta%le.

1odel 1inimum input

Thermodnamic

7S criticl temperture (-CI-), criticl pressure

(CI-), centric fctor (C/:-IC;C-

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(L=/:S), idel *s Cp (CI=/L) )"

L7 criticl temperture (-CI-), criticl pressure

(CI-), centric fctor (C/:-IC;C-:IE>C vpour pressure (S-), sturted li3uid densit

(L=/:S), surfce nd volume prmeters(>:IEE, >:IE)

>:I;C vpour pressure (S-), sturted li3uid densit

(L=/:S), >:I;C su+*roup structures

(>:I;C)

=ortmund Bodified

>:I;C

vpour pressure (S-), sturted li3uid densit

(L=/:S), >:I;C su+*roup structures

(>:I;C)

e*ulr Solution vpour pressure (S-), sturted li3uid densit

(L=/:S), solu+ilit prmeter (S) nd

molr volume t 2FC (A2)"

;lorGu**ins vpour pressure (S-), sturted li3uid densit

(L=/:S), solu+ilit prmeter (S) nd

molr volume t 2FC (A2)"

-4

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Idel *s idel *s Cp (CI=/L)

7 criticl temperture (-CI-), criticl pressure

(CI-), idel *s Cp (CI=/L)

Gden

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Surfce tension mi%in*

rule

surfce tension (S-/:SI

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Components

IntroductionEultiflash recognises three types of component. 8ormalcomponents are pure compounds such as hydrocar%ons(petrochemicals and chemicals( which may e2ist as gas( li9uid orsolid depending on conditions of temperature and pressure. at & atm?Li9uid Eolar olume at 31.&0)Standard Ideal Gas #nthalpy ofFormation at 31.&0)

Standard Ideal Gas Gi%%s #nergy ofFormation at 31.&0)Standard Ideal Gas #ntropy at 31.&0)#nthalpy of Fusion at Eelting 'oint#ntropy of Fusion at Eelting 'oint;eat capacity change on fusionolume change on fusionStandard 8et #nthalpy of Com%ustion at 31.&0)U8I"U

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virial coefficient and relative permittivity( %oth used for modelcalculations.

I8FH

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( ) ( )( )C R a a a y y % yp & ( )= + + # 4 #21 1

where % y a a y a y a y( )= + + +$ ! 82

9

# ( y T

T a=

+

HI''= e9uation &-/( / coefficientsa!( a4( a0( a@( a/( Tmin( Tma2

( ) ( )C a a

a T

a Ta

a T

a Tp= +

+

# 4

2

$!

!

2

&

sinh &

&

cosh &

0 HI''= e9uation &--( / coefficientsa!( a4( a0( a@( a/( Tmin( Tma2

C a a T a T a T a T p= + + + +# 4 2

$

#

!

4

Cpliquid li9uid Cp correlation >BRmol )?

- data un6nown( - coefficients

& HI''= e9uation &&4( 3 coefficients

a&( a( a!( a4( a0( a@( a/( Tmin( Tma2

C a a a a a a ap= + + + + + +1 2 # 42

#

$

4

!

&

where = 1 T Tc&0 HI''= e9uation &--( / coefficients

a&( a( a!( a4( a0( Tmin( Tma2

C a a T a T a T a T p= + + + +1 2 #2

4

#

4

Cpsolid solid Cp correlation >BRmol )?


0 HI''= e9uation &--( / coefficientsa&( a( a!( a4( a0( Tmin( Tma2

C a a T a T a T a T p= + + + +1 2 # 2 4 # 4

psat saturated vapour pressure >'a?


& 7agner >form &? 0 coefficientsa&( a( a!( Tmin( Tma2

ln lnp p a a a

Tc

r

= + + +1 2

2

#

#

where T T Tr c= & ( = 1 Tr form ?( @ coefficientsa&( a( a!( a4( Tmin( Tma2

ln lnp p a a a a

Tc

r

= + + + +1 2

#

2#

#

4

$

where T T Tr c= & ( = 1 Tr

4 7agner >form !?( @ coefficientsa&( a( a!( a4( Tmin( Tma2

--

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ln lnp p a a a a

Tc

r

= + + + +1 2

#

2#

24

where T T Tr c= & ( = 1 Tr0 HI''= e9uation &--( / coefficients

a&( a( a!( a4( a0( Tmin( Tma2

p a a T a T a T a T= + + + +1 2 #

2

4

#

4

/ I

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( )1 1 2 #& = +a a a 6

where6= +1

2

! ( = 1 T Tc&

4 HI''= e9uation &-0( @ coefficients

a&( a( a!( a4( Tmin( Tma21 2 1& & = a a

6

where ( )6 T a a= + 1 1 #

4&


= + + + +a a T a T a T a T 1 2 #2

4

#

4

/ I

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=+ + +

T

a a T a T a T

r

r r r1 2 #

2

4

#

where T T Tr c= &

! Eonatomic ideal gas( coefficients( Tmin( Tma2 = #!0 0R &


= + + + +a a T a T a T a T 1 2 #2

4

#

4

lvisc li9uid viscosity correlation>'a s?


& =eid( 'rausnit$ and 'oling e9uation &(4 coefficients a&( a( Tmin( Tma2

= a Ta1

2

HI''= e9uation &-&( / coefficientsa&( a( a!( a4( a0( Tmin( Tma2

ln & ln = + + +a a T a T a T a1 2 # 4

! =educed correlation( / coefficientsa&( a( a!( a4( a0( Tmin( Tma2

( )ln & a a & a & 11

#2

4

#= +

where & a a

T a=

# 44

1

4 =eid( 'rausnit$ and 'oling e9uation R!( @coefficients a&( a( a!( a4( Tmin( Tma2

ln & = + + +a a T a T a T 1 2 # 4 2


= + + + +a a T a T a T a T 1 2 #2

4

#

4

vvisc vapour viscosity correlation>'a s?


& HI''= e9uation &-( @ coefficientsa&( a( a!( a4( Tmin( Tma2

=+ +

a T

a T a T

a

1

# 4

2

2

1 & &

=eichen%erg e9uation( 0 coefficientsa&( a( a!( Tmin( Tma2

( )( ) =

+

a T

a T T

r

r

a

r

1

2

1

$1 1#

where T T Tr c= &! Chapman#ns6og e9uation( 0 coefficients

a&( a( a!( Tmin( Tma2

( )

( )

= 2$ $9 10 !

1

2

1

2 2 2

#

"

,, *

T

a T a

-,

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where

( ) ( ) 2 2 #202

, * * * *e%p e%p " &= + + +T C *T E %T a T+

T T a* &= 2 ( = 11$14" ( += 0148!4" ( C= 0248!" (

*= 0!!#20"(

E= 21$1!8"(

%= 24#!8!"0 HI''= e9uation &--( / coefficientsa&( a( a!( a4( a0( Tmin( Tma2

= + + + +a a T a T a T a T 1 2 #2

4

#

4

stension surface tension correlation >8Rm?


& HI''= e9uation &-@( / coefficientsa&( a( a!( a4( a0 Tmin( Tma2

( ) = a Tr6

1 1

where 6 a a T a T a T r r r= + + +2 # 42

# ( T T Tr c= &

#2tended Sprow and 'rausnit$ e9uation( 0coefficients a&( a( a!( Tmin( Tma2

( ) = +a aa1 #2 1where = 1 T Tc&


= + + + +a a T a T a T a T 1 2 #

2

4

#

4

virialcoeff second virial coefficient correlation >m!Rmol?


& HI''= e9uation &-4( / coefficientsa&( a( a!( a4( a0 Tmin( Tma2

+ a a a a a= + + + +1 2 # # 4 8 9 where = T Tc &


+ a a T a T a T a T= + + + +1 2 #2

4

#

4

dielectric relative permittivityRdielectric constant correlation


& EaryottSmith e9uation &( @ coefficientsa&( a( a!( a4( Tmin( Tma2

>=a1+a2T+a#T2+a4 T

#

EaryottSmith e9uation ( 4 coefficientsa&( a( Tmin( Tma2

>=e%p (a1+a2T)! Infochem e9uation( @ coefficients

a&( a( a!( a4( Tmin( Tma2

>=1+a1e%p (a2Ta#T2a4T#)

*4

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Petroleum fractionsTo define a single petroleum fraction the program re9uires certaincharacteristic properties and Eultiflash will then estimate theother properties needed to support the range of calculationsavaila%le in the program.

The list of possi%le properties to support characterisation of thefraction are*

Car%on num%er

Eolecular weight >gRmol?

Specific gravity at @-oF relative to water at @-oF

8ormal %oiling point

Critical temperature

Critical pressure

'it$ers acentric factor

;owever( not all of these are necessary. The minimum input setsare molecular weight( molecular weight and specific gravityJmolecular weight and %oiling pointJ %oiling point and specificgravityJ critical temperature( critical pressure and acentric factor.

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Property Calculation

The order in which properties are calculated depends on theamount of input data provided. In general the following referencesare used as a %asis for the calculations*

Eolecular weight =ia$i( E.=. and &301?Drule( E.=. and 7hitson( C.;.( S'#Eonograph - >---?=ia$i( E.=. and &330?

c

( '

c

( )esler( E.G. and Lee( D.I.( 'ydroarbonProessin!00>!? &0! >&3/@?

Drule( E.=. and 7hitson( C.;.( S'#Eonograph - >---?=ia$i( E.=. and &330?

#nthalpy of Formation and Standard #ntropy

=eid( =.C.( 'rausnit$( B.E. and 'oling( D.#.JThe Properties of 2ases and &iquids*Gulf(;ouston >&31/?

Ideal C

p

)esler( E.G. and Lee( D.I.( 'ydroarbonProessin!00>!? &0! >&3/@? and;armens(

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Li9uid Giscosity r%ey( ;. and Sandler( S.I.( Canadian . Che.En!.( /44!/ >&33!?

*(

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Inde

Models Man 41

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