SELECTION OF EQUATIONS OF STATE MODELS FOR PROCESS SIMULATOR
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 phase equilibrium calculations: one is liquid activity coefficient and the other is equation-of-state models. Activity coefficient models can be used to describe mixtures of any complexity, but only as a liquid well below its critical temperature. What is an equation of state ? Any mathematical relation between volume, pressure, temperature, and composition is called the equation of state and most forms of the equation of state are of the pressure-explicit type. Many equations of state have been proposed, but most all of them are essentially empirical in nature. The virial equation of state has a sound theoretical foundation and is free of arbitrary assumption. However, the virial equation is appropriate only for the description of properties of gases at low to moderate densities. The virial equaions of state are polynomials in density. The simplest useful polynomial equation of state is cubic, for such an expression is capable of yielding the ideal gas equation as volume goes to infinite and of representing both liquid-like and vapor-like molar volumes at low temperatures. This latter feature is necessary for the application of an equation of state to the calculation of vapor-liquid equilibria. A cubic equation of state (CEOS) usually contains 2 or 3 parameters. These parameters in the CEOS are constrained to satisfy the critical point conditions. As a result, the cubic equations of state provide an exact duplication of the critical temperature and critical pressure which is the end point of the vapor pressure 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 in applying a cubic equation of state is that the α function in the cubic equation of state can be adjusted to provide an accurate description of the vapor pressure of any nonpolar and polar components from the triple point to the critical point. This feature is important because the accurate prediction of pure component vapor pressures is prerequisite for accurate vapor-liquid calculations. The success of correlating vapor-liquid equilibrium data using a cubic equation of state also depends on the mixing rules upon which the accuracy of predicting mixture properties relies. Cubic equations of state, with the usual van der Waals one-fluid mixing rule, can be used for the description of phase behavior of nonpolar and slightly polar systems (i.e., hydrocarbons and inorganic gases). On the other hand, using asymmetric mixing rules allows cubic equations of state to be used for a broad range of nonideal mixtures which previously could only be described by activity coefficient models. Therefore, if a CEOS is equipped with a flexible α function and an advanced mixing rule, then the CEOS is applicable to important systems encountered in industry practice. EQUATION-OF-STATE ADVANTAGES The equation-of-state has an inherent advantage over the traditional liquid activity coefficient methods in that it is able to directly handle supercritical components which do not form liquid (hence, liquid activity coefficients cannnot be determined and Henry's constants are required), to handle both vapor and liquid phases in large ranges of temperature and pressure, to adequately handle high pressure systems, to predict a critical point of mixtures, to properly calculate K-values near or at the critical point, and to generate all thermodynamic properties, such as enthalpy, in a consistent way. SOAVE-REDLICH-KWONG EQUATION OF STATE The first CEOS that represented both vapor and liquid phases was proposed by van der Waals (1873) over a century ago. Redlich and Kwong (1949) proposed the first vdW modification that was used extensively for engineering calculations for vapor phase properties of mixtures containing nonpolar components. The equation of state starts gaining popularity in the computation of 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 to introduce a general form of the temperature dependence of the "a" parameter in the Redlich-Kwong equation of state: P=
RT a − v −b v ( v + b)
(1)
with a ( T ) = α ( T ) a ( Tc )
(2)
The constants a(T c) and b for SRK CEOS are obtained from the critical constraints. Wilson later (1966) expressed α(T) as a function of the reduced temperature, Tr = T/Tc, and the acentric factor ω for the Redlich-Kwong CEOS, but was not successful. The α(T) function that gained widespread popularity was proposed by Soave (1972) as an equation of the form: α =[ 1 + m ( 1 − T r 0.5 ) ] 2
(3)
The m parameter was obtained by forcing the equation to reproduce the vapor pressure for nonpolar hydrocarbon compounds at Tr = 0.7 and was correlated as a function of ω for the SRK CEOS: m = 0.480 + 1.574 ω − 0.175ω 2
(4)
Soave's development of eqns.(3) and (4) represented a significant progress in the application of a CEOS. PENG-ROBINSON EQUATION OF STATE Peng and Robinson (1976) proposed the the following CEOS, which is slightly different from eqn.(1) in the volume function: P=
RT a − v −b v ( v + b) + b( v − b)
(5)
The PR CEOS improves the calculation of liquid density for mid-range hydrocarbons relative to the RK CEOS. For example the liquid density calculation 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 reduced temperatures as it does not always decrease monotonically with increasing temperature, the Soave approach was subsequently used in the work by Peng and 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 in industry for correlating the vapor-liquid equilibria of systems containing nonpolar and slightly polar components SRK OR PR METHODOLOGY
CEOS
WITH
FREE
WATER
DECANT
Refinery systems often contain both water and hydrocarbons. Mixtures with water and hydrocarbons will form two liquid phases, one is water-rich phase and the other is hydrocarbon-rich phase. The free water option is a simplication of the thermodynamics treatment for water-hydroacrbon systems. For the free water or decant option, water is considered as forming an immiscible phase with the hydrocarbon-rich liquid phase The free water option is a convenient, efficient method to simulate the three phase behavior exhibited by hydrocarbonwater systems when the solubility of hydrocarbons in the water liquid phase can be neglected. It is adequate for most hydrocarbon calculations such as refinery columns with steam stripping and natural gasoline plants. The following example shows how to use the decant option for refinery columns in the waterhydrocarbon calculations: TITLE PROBLEM=DECANT, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 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 DATA METHOD SYSTEM = SRK, SET = SET01, DEFAULT WATER 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 remaining water is decanted as a free water phase. The K-value of water in the hydrocarbon-rich liquid phase can then be computed from water partial pressure, pw, the solubility of water in the hydrocarbon-rich liquid phase, xw, and system pressure, P, using the following equation: Kw = x
pw wP
(6)
The water partial pressure is calculated from either Antoine vapor pressure equation with coefficients properly stored for different temperature ranges or Figure 15-14 in the GPSA Data Book (1976). The GPSA Figure 15-14, which relates the partial pressure of water vapor in natural gas to temperature and pressure, is recommended for natural gas mixtures above 2000 psia and Antoine saturated water vapor pressure is proper for most problems. The water solubility in the hydrocarbon-rich liquid phase can be computed by either the method developed by SimSci, Figure 9A1.2 in the API Technical Data Book (1982), which relates the solubility of water in kerosene to temperature, or the cubic equation of state. The K-value of water in the hydrocarbon-rich liquid phase is computed in the way just mentioned above. On the other hand, the properties of pure water phase including vapor pressure, enthalpy, entropy and density are predicted either from saturated condition, which is the default and adequate for most problems, or from steam table (i.e. the Keenan and Keyes equation of state, 1969). The Keenan and Keyes equation of state is recommended for superheated water vapor. The following example indicates that the K-value of water in the hydrocarbonrich liquid phase is calculated from GPSA and SimSci methods and the properties of pure water liquid phase are calculated from the Keenan and Keyes equation of state : TITLE PROBLEM=DECANT, USER=SIMSCI PRINT INPUT=FULL 5
COMP DATA LIBID 1, H2O/2, H2S/3, N2/4, CO2/5, C1/6, C2/7, C3/8, IC4/* 9, NC4/10,IC5/11, NC5/12, NC6 PETRO 13, CUT1,100,715.0,94.44/14, CUT2,164,820.3,204.44/* 15, CUT3,310,921.8,376.66 ASSAY CHAR=SIMSCI THERMODYNAMIC DATA METHOD SYSTEM=SRK,SET=SET01,DEFAULT WATER DECANT=ON,GPSA,SOLUBILITY=SIMSCI,* PROPERTY=STEAM Note that all of the SRK and PR equations of state in PRO/II are capable of predicting three phase behavior, however, not all these equations have the necessary binary interaction parameters to do the proper split. When the standard SRK or PR CEOS are selected for three phase calculations, the free water (decant) option must be deactivated. The example given below shows how to use SRK CEOS for three-phase (VLLE) calculations: TITLE PROBLEM=VLLE, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 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 DATA METHOD SYSTEM(VLLE) = SRK, SET = SET01, DEFAULT WATER DECANT = OFF SRK CEOS WITH KABADI-DANNER MIXING RULE Although for most refining and natural gas calculations, the free water option is adequate to represent water-hydrocarbon phase behavior, however, the free water phase contains no dissolved hydrocarbons or light gases. When hydrocarbon or light gas solubility in the water phase is an important consideration for the problem being analyzed, e.g., an enviromental question, the free water option is not adequate and a rigorous three phase calculation must be performed for hydrocarbon-water systems. 6
Kabadi and Danner (1985) proposed a two-parameter mixing rule for the SRK equation of state. The rigorous three phase calculation can be performed for hydrocarbon-water systems by using the Soave-Redlich-Kwong-Kabadi-Danner (SRKKD) equation. The example given below shows how to use SRKKD for three-phase (VLLE) calculations: TITLE PROBLEM=SRKKD, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 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 DATA METHOD SYSTEM(VLLE) = SRKKD, SET = SET01, DEFAULT Note that the SRKKD mixing rule leads to inconsistencies when a component is split into two or more identical fractions. This method was also found to give large errors for the aqueous phase. ALPHA (α) FORMULATION The accurate prediction of pure component vapor pressures is required for accurate vapor-liquid calculations and the ability of predicting vapor pressure from any CEOS is controlled by the selection of an appropriate temperature dependent α function. In fact, vapor pressures of both nonpolar and polar components can be very accurately represented by any cubic equation of state if the temperature dependent α function is sufficiently flexible. Numerous α functions have been proposed for this purposed. They contain usually 1 to 3 empirical parameters to be derived from vapor pressures of individual compounds. Among them, a two-parameter α function proposed by Twu (1988) and a three-parameter α function proposed by Twu et al.(1991) are recognized as the most flexible ones with correct extrapolation to high reduced temperatures. These two α functions, which become SimSci α functions, are: α = Tr 2 ( M −1) e L ( 1− Tr
2M
)
(7)
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α = Tr N ( M −1) e L ( 1− Tr
N M
)
(8)
where the integer 2 in eqn.(6) has been replaced by a parameter N to improve vapor pressure prediction for highly polar substances with high normal boiling point temperatures, such as glycols. PRO/II allows the user to utilize a choice of 12 different alpha formulations for SRK, PR, ans vdW cubic equations of state. To use component-dependent α function in the calculations, ALPHA=SIMSCI must be specified for SRK or PR CEOS in the input file as shown below: TITLE PROBLEM=ALPHA, USER=SIMSCI PRINT INPUT=FULL COMPONENT DATA LIBID 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 DATA METHOD SYSTEM=SRK,SET=SET01,DEFAULT KVALUE ALPHA=SIMSCI, BANK=PROCESS CLASSICAL QUADRATIC MIXING RULES The success of correlating vapor-liquid equilibrium data using a cubic equation of state primarily depends on two things: one is the α function, which is described in the previous section; the other is the mixing rules upon which the accuracy of predicting mixture properties relies. The mixing rules originally proposed for a CEOS are derived from van der Waals one-fluid approximation: a=
∑ ∑ x x aij
(9)
i j
where aij = ( aiaj ) (1 / 2 ) (1 − kij )
(10)
The Kay’s mixing rule was applied to the constant b: b=
∑xb
(11)
i i
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The quadratic mixing rule is the most widely used for equations of state. The standard method for introducing a binary interaction parameter, kij, into this classical 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 quadratic mixing rules are capable of accurately representing vapor-liquid equilibria for non-polar hydrocarbon systems with only one adjustable binary parameter. The quadratic mixing rule is used for standard SRK and PR cubic equations of state. The SYSTEM=SRK in previous examples are standard SRK equation of state. ADVANCED MIXING RULES Equations of state with the classical mixing rules are applicable only to the computation of phase equilibria in mixtures of nonpolar and weakly polar systems. While this is a good approximation for hydrocarbon mixtures, it cannot be applied to systems containing strongly polar or associating components. Therefore, in the 1970's and 1980's, equations of state were used virtually only for nonpolar hydrocarbons and slightly polar components. Since the equationof-state method does not effectively model strongly polar/polar and/or polar/nonpolar systems, liquid activity coefficient methods are typically ultilized for such kind of chemical systems. Chemical systems consisting of components with varying chemical nature can exhibit highly non-ideal phase behavior and thus are difficult to predict. Interactions are strong between different chemical types, and the standard SRK or PR CEOS do not work well for prediction of such highly non-ideal phase behavior. For predicting such highly non-ideal systems, the advanced mixing rules in addition to the advanced α function are required for the equations of state. Over the past decade, the equations of state have significantly progress in the development of the most appropriate α functions and advanced asymmetric mixing rules for systems containing strongly polar components. An appropriate temperature dependent α function is required to represent accurately the vapor pressure 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 nonideal chemical systems. The inability of classical quadratic mixing rules to represent the phase behavior of strongly nonideal mixtures can be explained in terms of infinite dilution activity coefficients (Twu et al., 1992). The derivation of the infinite dilution activity coefficients from the equation of state indicates that k12 or k21 is directly related to the infinite dilution activity coefficients γ 1 ∞ or γ 2 ∞ , respectively. While it is a good approximation for hydrocarbon mixtures to assume that k12 = k21, this assumption cannot be applied to highly asymmetric systems containing strongly polar or associating components. The failure of classical quadratic mixing rules for strongly nonideal mixtures can therefore be overcome by using two binary parameters and accurate results can be obtained for such mixtures when different values of binary parameters are used for, for example, the water-rich and hydrocarbon-rich phases. The mixing rule proposed by Kabadi and Danner (1985) is an example of using two binary parameters, although it is not quite successful in the aqueous phase. Another particular example of using two binary interaction parameters was proposed by Panagiotopoulos and Reid (1986). They have proposed modified classical quadratic mixing rules that use composition-dependent binary interaction parameters. aij = ( aiaj ) ( 1 / 2) [(1 − kij ) + ( kij − kji ) x i ]
(12)
If kij = kji, the classical quadratic mixing rule is recovered. The Panagiotopoulos-Reid mixing rule provides an excellent representation of the phase equilibria of highly non-ideal binary mixtures. Unfortunately, however, it should not be extended to multicomponent mixtures because it is not invariant when a component is split into two or more identical fractions (Michesen and Kistenmacher, 1990). Because the Panagiotopoulos-Reid mixing rule is very powerful and yet very simple, and can make use of available binary interaction parameters for SRK CEOS, SimSci has modified the Panagiotopoulos-Reid mixing rule to reduce the dilution effect to a minimum for better prediction of phase behavior of 10
multicomponent mixtures. This modified Panagiotopoulos-Reid mixing rule is named as SRKM mixing rule. The SRKM mixing rule is given below: aij = ( aiaj ) (1 / 2 )[(1 − kij ) + ( k ij − kji )( xi / ( x i + xi )) cij ]
(13)
As mentioned previously, typical natural gas processing plants are best represented with the SRK and PR equations of state. These methods also have been found to be quite accurate for cryogenic processes such as nitrogen rejection plants and air separation plants. When accurate calculations are needed for natural gas mixtures with e.g. methanol and water, the SRKM method is recommended. The follwoing example shows that the SRKM mixing rule is applied to natural gas mixtures with methanol and water: TITLE PROBLEM=SRKM, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 1, H2O/2, MEOH/3, N2/4, CO2/5, C1/6, C2/7, C3/ * 8, NC4/9, NC5/10, NC6 THERMODYNAMIC 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 variance problem still exists. Twu et al. (1991) have proposed a mixing rule not only to overcome the flaw for multicomponent mixtures as exhibited by the Panagiotopoulos-Reid mixing rule, but also to reproduce the activity coefficients in the infinite dilution region as well as to model phase behavior throughout the finite 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-ideal system in following example. The binary interaction parameters between ethanol and benzene, which was not found in SIMSCI databank, should be input through SRKS keyword to improve the calculation results.
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TITLE PROBLEM=SRKS, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBI 1,ETOH/2,BNZN/3,H2O THERMO DATA METHOD SYSTEM(VLLE)=SRKS, LIKEY=2, L2KEY=3 KVALUE 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 used in the HF alkylation process and in the manufacture of refrigerants and other halogenated compounds. Hydrogen fluoride strongly associated by hydrogen bonding and strong evidence indicates that the vapor exists primarily as monomer and hexamer. A monomer-hexamer chemical equilibrium model is built into the cubic equation of state to account for association of hydrogen fluoride (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 of binary interaction parameters for hexamer equation of state for HF alkylation process and manufacture of refrigerants. Hexamer equation of state provides a new method for calculating the properties of HF mixtures. The calculated fugacity coefficient, vapor compressibility factor, heat of vaporization, and enthalpy departure of HF mixtures exhibit significant deviations from ideal behavior. Failure to take this chemical association into account can lead to serious errors in vapor-liquid and vapor-liquid-liquid equilibrium and energy balance calculations. Alkylation processes and the manufacture of refrigerants simulated by the use of hexamer equation of state are given by the following two examples: TITLE PROBLEM=ALKYLATION, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 1,HF/2,C3/3,NC4/4,IC4, BANK=PROCESS
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THERMO DATA METHOD SYSTEM(VLLE)=HEXAMER TITLE PROBLEM=REFRIGERANT, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 1,HF/2,TFETH,,R134A, BANK=SIMSCI THERMO DATA METHOD SYSTEM(VLLE)=HEXAMER BENEDICT-WEBB-RUBIN-STARLING EQUATION OF STATE Although the cubic equations of state proved to be especially useful in their simplicity, efficient computation time and reliability in the K-value calculations, the accuracy of predicting liquid density and liquid enthalpy are not quite high even for nonpolar hydrocarbons. On the other hand, the non-cubic equation of state such as the Benedict-Webb-Rubin-Starling (BWRS) equation of state (Starling, 1973) is capable of representing for both liquid and vapor phases the density, enthalpy, and entropy, in addition to vapor pressure for hydrocarbons in the cryogenic liquid region in addition to higher temperature regions. However, unlike the constants (a and b) of cubic equation of state, which are constrained to satisfy the critical point conditions, the constants (total is 11) of Benedict-Webb-Rubin-Starling equation are not satisfied with the critical contraints. Therefore, the K-value calculations from BWRS for hydrocarbons near 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 the cryogenic liquid region in addition to higher temperature regions. One of the typical examples is given below: TITLE PROBLEM=BWRS, USER=SIMSCI PRINT INPUT=FULL COMP DATA LIBID 1,H2/2,ETLN/3,IC4/4,HXE1,BANK=SIMSCI THERMO DATA 13
METHOD SYSTEM=BWRS KVALUE BANK=SIMSCI In general, the BWRS equation of state is better for representing pure fluid properties and less attractive for mixtures because it does not offer any advantages over cubic equations of state in K-value calculations. It may also require considerably more computing times. The following example applies BWRS equation of state to pure hydrocarbon for the prediction of properties at any temperature and pressure: TITLE PROBLEM=BWRS, USER=SIMSCI DIME ENGLISH, PRES=PSIG COMP DATA LIBID 1,ETLN,BANK=SIMSCI THERMO DATA METHOD SYSTEM=BWRS DATABANK: ALPHA PRO/II allows the user to utilize a choice of 12 different alpha formulations for SRK, PR, ans vdW cubic equations of state. SimSci has compiled a data bank of α parameters for all the components in the SimSci component library using the α functions given by eqn.(7) and (8) for SRK, PR, and vdW CEOS. The following is an example showing how to retrieve component-dependent α parameters from SimSci databank and to input you own α parameters for SRK CEOS: TITLE PROJECT=TRAINING, PROBLEM=ALPHA, USER=SIMSCI PRINT INPUT=FULL COMPONENT DATA LIBID 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 DATA METHOD SYSTEM=SRK,SET=SET01,DEFAULT KVALUE 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 modelling flowsheet. For hydrocarbon systems, which behave in an orderly fashion, the Soave-Redlich-Kwong and Peng-Robinson equations of state are the proven methods for most hydrocarbon applications involving mixtures of non-polar hydrocarbons and non-hydrocarbon gases (e.g. CO2, H2S, N2, etc.). However, for these cubic equations of state, the accuracy of the K-value calculations can often be improved by supplying binary interaction parameters, (kij, in eqn.10), to tune the classical quadratic mixing rule for the equation of state. The binary interaction parameter, kij, are usually obtained from the regression of PTXY data. PRO/II already contains a large data bank of binary interaction parameters for SRK, PR, SRKM, and SRKS, equations which fit a wide range of hydrocarbon applications and in most of cases does not require additional input binary interaction parameters from the user. The accuracy of the K-value calculation from BWRS can, as usually, be improved by supplying binary interaction parameters to the BWRS mixing rules (Starling, 1973). PRO/II has a data bank of binary interaction parameters supplied in DECHEMA (1982) for the Benedict-Webb-Rubin-Starling equation. It is good practice to inspect the reprint of binary interaction parameters and verify that parameters are present for key binary components which accurate calculations are needed. The following example shows all the binary interaction parameters and their sources can be retrieved from SIMSCI databank by using the INPUT=FULL in the input file: TITLE PROBLEM=KIJ, USER=SIMSCI PRINT INPUT=FULL COMPONENT DATA LIBI 1, H2/2, H2S/3, NC6/4, BNZN
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THER DATA METHODS SYSTEM=SRK KVALUE BANK=SIMSCI The follwoing reprint from the simulation run indicates that all the binary interaction parameters but one were found in SIMSCI databank. The proprietary MW correlation was then used to estimate the binary parameter for this 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 --- --1 2 1 3 1 4 2 3 2 4 3 4
A(I,J) B(I,J) ---------- ---------0.0830 0.00 -0.0800 0.00 0.5000 0.00 0.0680 0.00 0.0600 0.00 0.0141 0.00
C(I,J) ---------0.00 0.00 0.00 0.00 0.00 0.00
UNITS --------DEG K DEG K DEG K DEG K DEG K DEG K
FROM ------------------SIMSCI BANK SIMSCI BANK SIMSCI BANK SIMSCI BANK MW CORRELATION SIMSCI BANK
APPLICATION GUIDELINES We have discussed that the success of correlating vapor-liquid equilibrium data 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 advanced mixing rule allow cubic equation of state to be used for a broad range of nonideal mixtures which previously could only be described by activity coefficient models. Having these two elements, the key application guideline of a CEOS primarily depends upon the availability of binary interaction parameters for the system. Soave-Redlich-Kwong and Peng-Robinson equations of state are recommended for most hydrocarbon applications involving mixtures of nonpolar 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 pure hydrocarbons and gases at any temperature and pressure and is suitable for the application to non-polar hydrocarbon and industrial gas mixtures. The SRK-Kabadi-Danner mixing rule is composition dependent. It was developed specifically for water and well-defined light hydrocarbon systems. Although SRKKD is recommended in API Technical Data Book (1982) for water and light hydrocarbons mixtures, the calculated results may not be reliable due to the inconsistency problem in its mixing rule. SRKM is recommended for polar/polar and/or polar/nonpolar systems which the standard SRK or PR equation of state cannot handle. SRKM is reduced to the standard SRK CEOS for nonpolar mixtures (e.g. hydrocarbons and inorganic gases). SRKS is recommended for HF alkylation process and the manufacture of refrigerants and other halogenated compounds. SRKS is also suitable for polar/polar and/or polar/nonpolar systems. The success of applying either SRKM or SRKS equation of state to nonideal systems is to verify that parameters are present for key binary components. REFERENCES API Technical Data Book-Petroleum Refining, American Petroleum Inst., New York, 1982. GPSA Engineering Data Book, Gas Processors Suppliers Association, Tulsa, Oklahoma, 1976. Kabadi, V.N. and Danner, R.P., 1985, "A Modified Soave-Redlich-Kwong Equation 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”, John Wiley & 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”, published by DECHEMA, Chemistry Data Series, Vol. VI., Germany. Michelsen, M.L. and Kistenmacher, H., 1990. "On Composition-dependent Interaction Coefficients," Fluid Phase Equilibria, 59:229-230.
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Panagiotopoulos, A.Z. and Reid, R.C., 1986. "A New Mixing Rule for Cubic Equations 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 of State", 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. 44:233244. Soave, G., 1972. "Equilibrium Constants from a Modified Redlich-Kwong Equation of State", Chem. Eng. Sci., 27:1197-1203. Starling K.E., 1973. “Fluid Thermodynamic Properties for Light Petroleum Systems”, Gulf Publ. Co., Houston, TX. Twu, C.H., 1988. "A Modified Redlich-Kwong Equation of State for Highly Polar, supercritical Systems," International Symposium on Thermodynamics in Chemical Engineering and Industry, May 30-June 2, 1988. Twu, C.H., Bluck, D., Cunningham, J.R., and Coon, J.E., 1991. "A Cubic Equation of State with a New Alpha Function and a New Mixing Rule", Fluid Phase Equilibria, 69:33-50. Twu, C.H., Bluck, D., Cunningham, J.R., and Coon, J.E., 1992. "A Cubic Equation of State: Relation Between Binary Interaction Parameters and Infinite Dilution Activity Coefficients,", Fluid Phase Equilibria, 72:25-39. Twu, C.H., Coon, J.E., and Cunningham, J.R., 1993. "An Equation of State: for Hydrogen Fluoride,", Fluid Phase Equilibria, 86:47-62. van der Waals, J.D., 1873. “Over de Constinuiteit van den gas-en Vloeistoftoestand”, Doctoral Dissertation, Leiden, Holland. Wilson, G.M., 1964. "Vapor-liqumid Equilibria Correlated by Means of a Modified Redlich-Kwong Equation of State", Adv. Cryog. Eng., 9:168-176. Wilson, G.M., 1966. "Calculation of Enthalpy Data from a Modified RedlichKwong Equation of State", Adv. Cryog. Eng., 11:392-400.
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