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SELECTION OF EQUATIONS OF STATE MODELS FOR PROCESSSIMULATOR

Chorng H. Twu* , John E. Coon, Melinda G. Kusch, and Allan H. Harvey

Simulation Sciences, Inc., 601 South Valencia Avenue, Brea, CA 92621 (USA)

(Workbook meeting 7/26/94; Outline from MGK 7/28/94, Revised form 8/3/94)

INTRODUCTION

There are two traditional classes of thermodynamic models for phaseequilibrium calculations: one is liquid activity coefficient and the other isequation-of-state models. Activity coefficient models can be used to describemixtures of any complexity, but only as a liquid well below its criticaltemperature. What is an equation of state ? Any mathematical relation betweenvolume, pressure, temperature, and composition is called the equation of stateand most forms of the equation of state are of the pressure-explicit type. Manyequations of state have been proposed, but most all of them are essentiallyempirical in nature. The virial equation of state has a sound theoreticalfoundation and is free of arbitrary assumption. However, the virial equation isappropriate only for the description of properties of gases at low to moderatedensities. The virial equaions of state are polynomials in density. The simplestuseful polynomial equation of state is cubic, for such an expression is capableof yielding the ideal gas equation as volume goes to infinite and of representingboth liquid-like and vapor-like molar volumes at low temperatures. This latterfeature is necessary for the application of an equation of state to the calculationof vapor-liquid equilibria.

A cubic equation of state (CEOS) usually contains 2 or 3 parameters. Theseparameters in the CEOS are constrained to satisfy the critical point conditions.As a result, the cubic equations of state provide an exact duplication of thecritical temperature and critical pressure which is the end point of the vaporpressure curve. These constraints also lay out a foundation for the alpha (α)

* Corresponding author

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function (Wilson, 1964, 1966; Soave, 1972). One of the important features inapplying a cubic equation of state is that the α function in the cubic equation ofstate can be adjusted to provide an accurate description of the vapor pressure ofany nonpolar and polar components from the triple point to the critical point.This feature is important because the accurate prediction of pure componentvapor pressures is prerequisite for accurate vapor-liquid calculations.

The success of correlating vapor-liquid equilibrium data using a cubic equationof state also depends on the mixing rules upon which the accuracy of predictingmixture properties relies. Cubic equations of state, with the usual van der Waalsone-fluid mixing rule, can be used for the description of phase behavior ofnonpolar and slightly polar systems (i.e., hydrocarbons and inorganic gases).On the other hand, using asymmetric mixing rules allows cubic equations ofstate to be used for a broad range of nonideal mixtures which previously couldonly be described by activity coefficient models. Therefore, if a CEOS isequipped with a flexible α function and an advanced mixing rule, then the CEOSis applicable to important systems encountered in industry practice.

EQUATION-OF-STATE ADVANTAGES

The equation-of-state has an inherent advantage over the traditional liquidactivity coefficient methods in that it is able to directly handle supercriticalcomponents which do not form liquid (hence, liquid activity coefficients cannnotbe determined and Henry's constants are required), to handle both vapor andliquid phases in large ranges of temperature and pressure, to adequately handlehigh pressure systems, to predict a critical point of mixtures, to properlycalculate K-values near or at the critical point, and to generate all thermodynamicproperties, such as enthalpy, in a consistent way.

SOAVE-REDLICH-KWONG EQUATION OF STATE

The first CEOS that represented both vapor and liquid phases was proposedby van der Waals (1873) over a century ago. Redlich and Kwong (1949)proposed the first vdW modification that was used extensively for engineeringcalculations for vapor phase properties of mixtures containing nonpolarcomponents. The equation of state starts gaining popularity in the computationof equilibrium K-values since Soave modified the Redlich-Kwong cubic

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equation of state (SRK CEOS) in 1972. Wilson (1964) however, was the first tointroduce a general form of the temperature dependence of the "a" parameter inthe Redlich-Kwong equation of state:

P RTv b

av v b

= ( )−

−+

(1)

with

a T T a Tc( ) = ( ) ( )α (2)

The constants a(Tc) and b for SRK CEOS are obtained from the criticalconstraints. Wilson later (1966) expressed α(T) as a function of the reducedtemperature, Tr = T/Tc, and the acentric factor ω for the Redlich-Kwong CEOS,but was not successful. The α(T) function that gained widespread popularitywas proposed by Soave (1972) as an equation of the form:

α =[ + ( ) ] 21 1 0 5m T r− . (3)

The m parameter was obtained by forcing the equation to reproduce the vaporpressure for nonpolar hydrocarbon compounds at Tr = 0.7 and was correlatedas a function of ω for the SRK CEOS:

m = − . + . .0 480 1 574 0 175 2ω ω (4)

Soave's development of eqns.(3) and (4) represented a significant progress inthe application of a CEOS.

PENG-ROBINSON EQUATION OF STATE

Peng and Robinson (1976) proposed the the following CEOS, which isslightly different from eqn.(1) in the volume function:

P RTv b

av v b b v b

= ( ) ( )−

−+ + −

(5)

The PR CEOS improves the calculation of liquid density for mid-rangehydrocarbons relative to the RK CEOS. For example the liquid densitycalculation is better for n-hexane, but worse for methane.

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Although the Soave's α function is found to be incorrect at high reducedtemperatures as it does not always decrease monotonically with increasingtemperature, the Soave approach was subsequently used in the work by Pengand Robinson (1976). This helped the Peng-Robinson cubic equation of state(PR CEOS) to also become one of the most widely used equations of state inindustry for correlating the vapor-liquid equilibria of systems containingnonpolar and slightly polar components

SRK OR PR CEOS WITH FREE WATER DECANTMETHODOLOGY

Refinery systems often contain both water and hydrocarbons. Mixtures withwater and hydrocarbons will form two liquid phases, one is water-rich phase andthe other is hydrocarbon-rich phase. The free water option is a simplication ofthe thermodynamics treatment for water-hydroacrbon systems. For the freewater or decant option, water is considered as forming an immiscible phase withthe hydrocarbon-rich liquid phase The free water option is a convenient,efficient method to simulate the three phase behavior exhibited by hydrocarbon-water systems when the solubility of hydrocarbons in the water liquid phase canbe neglected. It is adequate for most hydrocarbon calculations such as refinerycolumns with steam stripping and natural gasoline plants. The followingexample shows how to use the decant option for refinery columns in the water-hydrocarbon calculations:

TITLE PROBLEM=DECANT, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1, H2O / 2, H2 / 3, N2 / 4, CO2 / 5,H2S/6, C1 / 7, ETHENE / *

8, C2 / 9, PROPENE / 10, 1BUTENE / 11, BTC2 / 12, IBTE / *13, 13BD / 14, NC4 / 15, IC4 / 16, NC5

THERMO DATAMETHOD SYSTEM = SRK, SET = SET01, DEFAULTWATER DECANT = ON

The free water technology is a semi-rigorous three phase (VLLE) calculations.The vapor is first saturated with water at its vapor pressure. Water is then

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dissolved in the hydrocarbon liquid up to its solubility limit, and any remainingwater is decanted as a free water phase. The K-value of water in thehydrocarbon-rich liquid phase can then be computed from water partialpressure, pw, the solubility of water in the hydrocarbon-rich liquid phase, xw, andsystem pressure, P, using the following equation:

Kp

x Pww

w= (6)

The water partial pressure is calculated from either Antoine vapor pressureequation with coefficients properly stored for different temperature ranges orFigure 15-14 in the GPSA Data Book (1976).

The GPSA Figure 15-14, which relates the partial pressure of water vapor innatural gas to temperature and pressure, is recommended for natural gasmixtures above 2000 psia and Antoine saturated water vapor pressure is properfor most problems.

The water solubility in the hydrocarbon-rich liquid phase can be computed byeither the method developed by SimSci, Figure 9A1.2 in the API Technical DataBook (1982), which relates the solubility of water in kerosene to temperature, orthe cubic equation of state.

The K-value of water in the hydrocarbon-rich liquid phase is computed in theway just mentioned above. On the other hand, the properties of pure waterphase including vapor pressure, enthalpy, entropy and density are predictedeither from saturated condition, which is the default and adequate for mostproblems, or from steam table (i.e. the Keenan and Keyes equation of state,1969). The Keenan and Keyes equation of state is recommended forsuperheated water vapor.

The following example indicates that the K-value of water in the hydrocarbon-rich liquid phase is calculated from GPSA and SimSci methods and theproperties of pure water liquid phase are calculated from the Keenan and Keyesequation of state :

TITLE PROBLEM=DECANT, USER=SIMSCIPRINT INPUT=FULL

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COMP DATALIBID 1, H2O/2, H2S/3, N2/4, CO2/5, C1/6, C2/7, C3/8, IC4/*

9, NC4/10,IC5/11, NC5/12, NC6PETRO 13, CUT1,100,715.0,94.44/14, CUT2,164,820.3,204.44/*

15, CUT3,310,921.8,376.66ASSAY CHAR=SIMSCI

THERMODYNAMIC DATAMETHOD SYSTEM=SRK,SET=SET01,DEFAULTWATER DECANT=ON,GPSA,SOLUBILITY=SIMSCI,*

PROPERTY=STEAM

Note that all of the SRK and PR equations of state in PRO/II are capable ofpredicting three phase behavior, however, not all these equations have thenecessary binary interaction parameters to do the proper split. When thestandard SRK or PR CEOS are selected for three phase calculations, the freewater (decant) option must be deactivated. The example given below showshow to use SRK CEOS for three-phase (VLLE) calculations:

TITLE PROBLEM=VLLE, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1, H2 / 2, N2 / 3, CO / 4, CO2 / 5, C1 / 6, ETHENE / 7, C2 / *

8, PROPENE / 9, 1BUTENE / 10, BTC2 / 11, IBTE / 12, 13BD / *13, NC5 / 14, H2O / 15, IC4 / 16, 3BT1 / 17, O2

THERMO DATAMETHOD SYSTEM(VLLE) = SRK, SET = SET01, DEFAULTWATER DECANT = OFF

SRK CEOS WITH KABADI-DANNER MIXING RULE

Although for most refining and natural gas calculations, the free water option isadequate to represent water-hydrocarbon phase behavior, however, the freewater phase contains no dissolved hydrocarbons or light gases. Whenhydrocarbon or light gas solubility in the water phase is an importantconsideration for the problem being analyzed, e.g., an enviromental question, thefree water option is not adequate and a rigorous three phase calculation must beperformed for hydrocarbon-water systems.

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Kabadi and Danner (1985) proposed a two-parameter mixing rule for the SRKequation of state. The rigorous three phase calculation can be performed forhydrocarbon-water systems by using the Soave-Redlich-Kwong-Kabadi-Danner(SRKKD) equation. The example given below shows how to use SRKKD forthree-phase (VLLE) calculations:

TITLE PROBLEM=SRKKD, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1, H2 / 2, N2 / 3, CO / 4, CO2 / 5, C1 / 6, ETHENE / 7, C2 / *

8, PROPENE / 9, 1BUTENE / 10, BTC2 / 11, IBTE / 12, 13BD / *13, NC5 / 14, H2O / 15, IC4 / 16, 3BT1 / 17, O2

THERMO DATAMETHOD SYSTEM(VLLE) = SRKKD, SET = SET01, DEFAULT

Note that the SRKKD mixing rule leads to inconsistencies when a component issplit into two or more identical fractions. This method was also found to givelarge errors for the aqueous phase.

ALPHA (α) FORMULATION

The accurate prediction of pure component vapor pressures is required foraccurate vapor-liquid calculations and the ability of predicting vapor pressurefrom any CEOS is controlled by the selection of an appropriate temperaturedependent α function. In fact, vapor pressures of both nonpolar and polarcomponents can be very accurately represented by any cubic equation of state ifthe temperature dependent α function is sufficiently flexible.

Numerous α functions have been proposed for this purposed. They containusually 1 to 3 empirical parameters to be derived from vapor pressures ofindividual compounds. Among them, a two-parameter α function proposed byTwu (1988) and a three-parameter α function proposed by Twu et al.(1991) arerecognized as the most flexible ones with correct extrapolation to high reducedtemperatures. These two α functions, which become SimSci α functions, are:

α = − −T M L Tr

rM

e2 1 1 2( ) ( ) (7)

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α = − −T N M L Tr

rN M

e( ) ( )1 1 (8)

where the integer 2 in eqn.(6) has been replaced by a parameter N to improvevapor pressure prediction for highly polar substances with high normal boilingpoint temperatures, such as glycols. PRO/II allows the user to utilize a choiceof 12 different alpha formulations for SRK, PR, ans vdW cubic equations ofstate. To use component-dependent α function in the calculations,ALPHA=SIMSCI must be specified for SRK or PR CEOS in the input file asshown below:

TITLE PROBLEM=ALPHA, USER=SIMSCIPRINT INPUT=FULL

COMPONENT DATALIBID 1,NITROGEN/2,CO2/3,METHANE/4,ETHANE/ *

5,PROPANE/6,IBUTANE/7,BUTANE/8,IPENTANE/ *9,PENTANE/10,HEXANE/11,HEPTANE, BANK=PROCESS

THERMODYNAMIC DATAMETHOD SYSTEM=SRK,SET=SET01,DEFAULTKVALUE ALPHA=SIMSCI, BANK=PROCESS

CLASSICAL QUADRATIC MIXING RULES

The success of correlating vapor-liquid equilibrium data using a cubic equationof state primarily depends on two things: one is the α function, which isdescribed in the previous section; the other is the mixing rules upon which theaccuracy of predicting mixture properties relies. The mixing rules originallyproposed for a CEOS are derived from van der Waals one-fluid approximation:

a x x aiji j= ∑∑ (9)

where

aij aiaj kij= −( ) ( )( / )1 2 1 (10)

The Kay’s mixing rule was applied to the constant b:

b x bi i= ∑ (11)

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The quadratic mixing rule is the most widely used for equations of state. Thestandard method for introducing a binary interaction parameter, kij, into thisclassical mixing rule is to correct the assumed geometric mean rule for the "aij"parameter in the eqn.(10). The cubic equations of state with classical quadraticmixing rules are capable of accurately representing vapor-liquid equilibria fornon-polar hydrocarbon systems with only one adjustable binary parameter.

The quadratic mixing rule is used for standard SRK and PR cubic equationsof state. The SYSTEM=SRK in previous examples are standard SRK equationof state.

ADVANCED MIXING RULES

Equations of state with the classical mixing rules are applicable only to thecomputation of phase equilibria in mixtures of nonpolar and weakly polarsystems. While this is a good approximation for hydrocarbon mixtures, itcannot be applied to systems containing strongly polar or associatingcomponents.

Therefore, in the 1970's and 1980's, equations of state were used virtually onlyfor nonpolar hydrocarbons and slightly polar components. Since the equation-of-state method does not effectively model strongly polar/polar and/orpolar/nonpolar systems, liquid activity coefficient methods are typically ultilizedfor such kind of chemical systems.

Chemical systems consisting of components with varying chemical nature canexhibit highly non-ideal phase behavior and thus are difficult to predict.Interactions are strong between different chemical types, and the standard SRKor PR CEOS do not work well for prediction of such highly non-ideal phasebehavior. For predicting such highly non-ideal systems, the advanced mixingrules in addition to the advanced α function are required for the equations ofstate. Over the past decade, the equations of state have significantly progress inthe development of the most appropriate α functions and advanced asymmetricmixing rules for systems containing strongly polar components. An appropriatetemperature dependent α function is required to represent accurately the vaporpressure of pure components and a proper mixing rule is essential to correctly

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predict vapor-liquid and/or vapor-liquid-liquid phase behavior of highly non-ideal chemical systems.

The inability of classical quadratic mixing rules to represent the phase behaviorof strongly nonideal mixtures can be explained in terms of infinite dilutionactivity coefficients (Twu et al., 1992). The derivation of the infinite dilutionactivity coefficients from the equation of state indicates that k12 or k21 is directlyrelated to the infinite dilution activity coefficients γ

1

∞ or γ2

∞ , respectively. While

it is a good approximation for hydrocarbon mixtures to assume that k12 = k21,this assumption cannot be applied to highly asymmetric systems containingstrongly polar or associating components.

The failure of classical quadratic mixing rules for strongly nonideal mixturescan therefore be overcome by using two binary parameters and accurate resultscan be obtained for such mixtures when different values of binary parameters areused for, for example, the water-rich and hydrocarbon-rich phases. The mixingrule proposed by Kabadi and Danner (1985) is an example of using two binaryparameters, although it is not quite successful in the aqueous phase.

Another particular example of using two binary interaction parameters wasproposed by Panagiotopoulos and Reid (1986). They have proposed modifiedclassical quadratic mixing rules that use composition-dependent binaryinteraction parameters.

aij aiaj kij kij kji x i= − + −( ) [( ) ( ) ]( / )1 2 1 (12)

If kij = kji, the classical quadratic mixing rule is recovered.

The Panagiotopoulos-Reid mixing rule provides an excellent representation ofthe phase equilibria of highly non-ideal binary mixtures. Unfortunately, however,it should not be extended to multicomponent mixtures because it is not invariantwhen a component is split into two or more identical fractions (Michesen andKistenmacher, 1990).

Because the Panagiotopoulos-Reid mixing rule is very powerful and yet verysimple, and can make use of available binary interaction parameters for SRKCEOS, SimSci has modified the Panagiotopoulos-Reid mixing rule to reduce thedilution effect to a minimum for better prediction of phase behavior of

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multicomponent mixtures. This modified Panagiotopoulos-Reid mixing rule isnamed as SRKM mixing rule. The SRKM mixing rule is given below:

aij aiaj kij kij kji x x x ci i i

ij= − + − +( ) [( ) ( )( / ( )) ]( / )1 2 1 (13)

As mentioned previously, typical natural gas processing plants are bestrepresented with the SRK and PR equations of state. These methods also havebeen found to be quite accurate for cryogenic processes such as nitrogenrejection plants and air separation plants. When accurate calculations are neededfor natural gas mixtures with e.g. methanol and water, the SRKM method isrecommended. The follwoing example shows that the SRKM mixing rule isapplied to natural gas mixtures with methanol and water:

TITLE PROBLEM=SRKM, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1, H2O/2, MEOH/3, N2/4, CO2/5, C1/6, C2/7, C3/ *

8, NC4/9, NC5/10, NC6THERMODYNAMIC DATA

METHOD SYSTEM(VLLE)=SRKM, SET=01, DEFAULT,*L1KEY=10, L2KEY=1

KVALUE BANK=SIMSCI

Although the SRKM mixing rule reduces the dilution effect, the varianceproblem still exists. Twu et al. (1991) have proposed a mixing rule not only toovercome the flaw for multicomponent mixtures as exhibited by thePanagiotopoulos-Reid mixing rule, but also to reproduce the activity coefficientsin the infinite dilution region as well as to model phase behavior throughout thefinite range of concentration. The mixing rule proposed by Twu et al. (1991)was called SRKS mixing rule.

SRKS mixing rule and SimSci α function are applied to a highly non-idealsystem in following example. The binary interaction parameters between ethanoland benzene, which was not found in SIMSCI databank, should be inputthrough SRKS keyword to improve the calculation results.

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TITLE PROBLEM=SRKS, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBI 1,ETOH/2,BNZN/3,H2O

THERMO DATAMETHOD SYSTEM(VLLE)=SRKS, LIKEY=2, L2KEY=3KVALUE ALPHA=SIMSCI

SRKS 1, 2, 0.275771, 1.00971, -42.9063, -322.428, *0, 0, -3.68601, -0.998951

HEXAMER EQUATION OF STATE

Hydrogen fluoride is an important chemical in the chemical industry. It is usedin the HF alkylation process and in the manufacture of refrigerants and otherhalogenated compounds. Hydrogen fluoride strongly associated by hydrogenbonding and strong evidence indicates that the vapor exists primarily asmonomer and hexamer. A monomer-hexamer chemical equilibrium model isbuilt into the cubic equation of state to account for association of hydrogenfluoride (Twu et al., 1993). The SRKS mixing rule proposed by Twu et al.(1991) was used in the hexamer equation of state. PRO/II has a large bank ofbinary interaction parameters for hexamer equation of state for HF alkylationprocess and manufacture of refrigerants.

Hexamer equation of state provides a new method for calculating theproperties of HF mixtures. The calculated fugacity coefficient, vaporcompressibility factor, heat of vaporization, and enthalpy departure of HFmixtures exhibit significant deviations from ideal behavior. Failure to take thischemical association into account can lead to serious errors in vapor-liquid andvapor-liquid-liquid equilibrium and energy balance calculations.

Alkylation processes and the manufacture of refrigerants simulated by the useof hexamer equation of state are given by the following two examples:

TITLE PROBLEM=ALKYLATION, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1,HF/2,C3/3,NC4/4,IC4, BANK=PROCESS

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THERMO DATAMETHOD SYSTEM(VLLE)=HEXAMER

TITLE PROBLEM=REFRIGERANT, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1,HF/2,TFETH,,R134A, BANK=SIMSCI

THERMO DATAMETHOD SYSTEM(VLLE)=HEXAMER

BENEDICT-WEBB-RUBIN-STARLING EQUATION OF STATE

Although the cubic equations of state proved to be especially useful in theirsimplicity, efficient computation time and reliability in the K-value calculations,the accuracy of predicting liquid density and liquid enthalpy are not quite higheven for nonpolar hydrocarbons. On the other hand, the non-cubic equation ofstate such as the Benedict-Webb-Rubin-Starling (BWRS) equation of state(Starling, 1973) is capable of representing for both liquid and vapor phases thedensity, enthalpy, and entropy, in addition to vapor pressure for hydrocarbonsin the cryogenic liquid region in addition to higher temperature regions.

However, unlike the constants (a and b) of cubic equation of state, which areconstrained to satisfy the critical point conditions, the constants (total is 11) ofBenedict-Webb-Rubin-Starling equation are not satisfied with the criticalcontraints. Therefore, the K-value calculations from BWRS for hydrocarbonsnear the critical point may not be as reliable as that from CEOS.

The BWRS is quite often employed to calculate K-value, enthalpy, entropy,and density for hydrocarbon and industrial important gas systems in thecryogenic liquid region in addition to higher temperature regions. One of thetypical examples is given below:

TITLE PROBLEM=BWRS, USER=SIMSCIPRINT INPUT=FULL

COMP DATALIBID 1,H2/2,ETLN/3,IC4/4,HXE1,BANK=SIMSCI

THERMO DATA

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METHOD SYSTEM=BWRSKVALUE BANK=SIMSCI

In general, the BWRS equation of state is better for representing pure fluidproperties and less attractive for mixtures because it does not offer anyadvantages over cubic equations of state in K-value calculations. It may alsorequire considerably more computing times. The following example appliesBWRS equation of state to pure hydrocarbon for the prediction of properties atany temperature and pressure:

TITLE PROBLEM=BWRS, USER=SIMSCIDIME ENGLISH, PRES=PSIG

COMP DATALIBID 1,ETLN,BANK=SIMSCI

THERMO DATAMETHOD SYSTEM=BWRS

DATABANK: ALPHA

PRO/II allows the user to utilize a choice of 12 different alpha formulations forSRK, PR, ans vdW cubic equations of state. SimSci has compiled a data bankof α parameters for all the components in the SimSci component library usingthe α functions given by eqn.(7) and (8) for SRK, PR, and vdW CEOS. Thefollowing is an example showing how to retrieve component-dependent αparameters from SimSci databank and to input you own α parameters for SRKCEOS:

TITLE PROJECT=TRAINING, PROBLEM=ALPHA, USER=SIMSCIPRINT INPUT=FULL

COMPONENT DATALIBID 1,NITROGEN/2,CO2/3,METHANE/4,ETHANE/ *

5,PROPANE/6,IBUTANE/7,BUTANE/8,IPENTANE/ *9,PENTANE/10,HEXANE/11,HEPTANE, BANK=PROCESS

THERMODYNAMIC DATAMETHOD SYSTEM=SRK,SET=SET01,DEFAULTKVALUE ALPHA=SIMSCI, BANK=PROCESS

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SA06 11,0.340339,0.844963,2.38332

DATABANKS: BINARY INTERACTION PARAMETERS

The data bank of binary interaction parameters is essential in modellingflowsheet. For hydrocarbon systems, which behave in an orderly fashion, theSoave-Redlich-Kwong and Peng-Robinson equations of state are the provenmethods for most hydrocarbon applications involving mixtures of non-polarhydrocarbons and non-hydrocarbon gases (e.g. CO2, H2S, N2, etc.).However, for these cubic equations of state, the accuracy of the K-valuecalculations can often be improved by supplying binary interaction parameters,(kij, in eqn.10), to tune the classical quadratic mixing rule for the equation ofstate.

The binary interaction parameter, kij, are usually obtained from the regressionof PTXY data. PRO/II already contains a large data bank of binary interactionparameters for SRK, PR, SRKM, and SRKS, equations which fit a wide rangeof hydrocarbon applications and in most of cases does not require additionalinput binary interaction parameters from the user.

The accuracy of the K-value calculation from BWRS can, as usually, beimproved by supplying binary interaction parameters to the BWRS mixing rules(Starling, 1973). PRO/II has a data bank of binary interaction parameterssupplied in DECHEMA (1982) for the Benedict-Webb-Rubin-Starling equation.

It is good practice to inspect the reprint of binary interaction parameters andverify that parameters are present for key binary components which accuratecalculations are needed. The following example shows all the binary interactionparameters and their sources can be retrieved from SIMSCI databank by usingthe INPUT=FULL in the input file:

TITLE PROBLEM=KIJ, USER=SIMSCIPRINT INPUT=FULL

COMPONENT DATALIBI 1, H2/2, H2S/3, NC6/4, BNZN

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THER DATAMETHODS SYSTEM=SRKKVALUE BANK=SIMSCI

The follwoing reprint from the simulation run indicates that all the binaryinteraction parameters but one were found in SIMSCI databank. Theproprietary MW correlation was then used to estimate the binary parameter forthis binary which parameters were not found in the databank.

SRK INTERACTION PARAMETERS

KIJ = A(I,J) + B(I,J)/T + C(I,J)/T**2

I J A(I,J) B(I,J) C(I,J) UNITS FROM--- --- ---------- ---------- ---------- --------- -------------------1 2 0.0830 0.00 0.00 DEG K SIMSCI BANK1 3 -0.0800 0.00 0.00 DEG K SIMSCI BANK1 4 0.5000 0.00 0.00 DEG K SIMSCI BANK2 3 0.0680 0.00 0.00 DEG K SIMSCI BANK2 4 0.0600 0.00 0.00 DEG K MW CORRELATION3 4 0.0141 0.00 0.00 DEG K SIMSCI BANK

APPLICATION GUIDELINES

We have discussed that the success of correlating vapor-liquid equilibriumdata using a cubic equation of state primarily depends on two things: one is the α function; the other is the mixing rule. A flexible α function and an advancedmixing rule allow cubic equation of state to be used for a broad range ofnonideal mixtures which previously could only be described by activitycoefficient models. Having these two elements, the key application guideline ofa CEOS primarily depends upon the availability of binary interaction parametersfor the system.

Soave-Redlich-Kwong and Peng-Robinson equations of state arerecommended for most hydrocarbon applications involving mixtures of non-polar hydrocarbons and inorganic gases such as H2S, CO2, H2, etc.

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BWRS is an excellent equation of state for predicting properties of purehydrocarbons and gases at any temperature and pressure and is suitable for theapplication to non-polar hydrocarbon and industrial gas mixtures.

The SRK-Kabadi-Danner mixing rule is composition dependent. It wasdeveloped specifically for water and well-defined light hydrocarbon systems.Although SRKKD is recommended in API Technical Data Book (1982) forwater and light hydrocarbons mixtures, the calculated results may not be reliabledue to the inconsistency problem in its mixing rule.

SRKM is recommended for polar/polar and/or polar/nonpolar systems whichthe standard SRK or PR equation of state cannot handle. SRKM is reduced tothe standard SRK CEOS for nonpolar mixtures (e.g. hydrocarbons andinorganic gases).

SRKS is recommended for HF alkylation process and the manufacture ofrefrigerants and other halogenated compounds. SRKS is also suitable forpolar/polar and/or polar/nonpolar systems. The success of applying eitherSRKM or SRKS equation of state to nonideal systems is to verify thatparameters are present for key binary components.

REFERENCES

API Technical Data Book-Petroleum Refining, American Petroleum Inst., NewYork, 1982.

GPSA Engineering Data Book, Gas Processors Suppliers Association, Tulsa,Oklahoma, 1976.

Kabadi, V.N. and Danner, R.P., 1985, "A Modified Soave-Redlich-KwongEquation of State for Water-Hydrocarbon Phase Equilibria", Ind. Eng. Chem.Proc. Des. dev., 24(3), 537-541.

Keenan, J.H., Keyes, F.G., Hill, P.G., and Moore, J.G., “Steam Tables”, JohnWiley & Sons Inc., NY, 1969.

Knapp, H., Doring, R., Oelirich, L., Plocker, U., and Prausnitz, J.M., 1982.“Vapor-liquid Equilibria for Mixtures of Low Boiling Substances”, publishedby DECHEMA, Chemistry Data Series, Vol. VI., Germany.

Michelsen, M.L. and Kistenmacher, H., 1990. "On Composition-dependentInteraction Coefficients," Fluid Phase Equilibria, 59:229-230.

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Panagiotopoulos, A.Z. and Reid, R.C., 1986. "A New Mixing Rule for CubicEquations of State for Highly Polar Asymmetric Systems." ACS Symp. Ser.300, American Chemical Society, Washington, DC, pp. 571-582.

Peng, D.Y. and Robinson, D.B., 1976. "A New Two-constant Equation ofState", Ind. Eng. Chem. Fundam., 15:58-64.

Redlich, O. and Kwong, N.S., 1949. "On the Thermodynamics of Solutions. V:An Equation of State. Fugacities of Gaseous Solutions", Chem. Rev. 44:233-244.

Soave, G., 1972. "Equilibrium Constants from a Modified Redlich-KwongEquation of State", Chem. Eng. Sci., 27:1197-1203.

Starling K.E., 1973. “Fluid Thermodynamic Properties for Light PetroleumSystems”, Gulf Publ. Co., Houston, TX.

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