Equation-of-state methods for the modelling of phase equilibria

Anderko, Andrzej

doi:10.1016/0378-3812(90)90011-b

Cited by 106 publications

(48 citation statements)

References 258 publications

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“…A detailed review of several of the fit methods has been discussed by Anderko [53]. As pointed out by Anderko, the simultaneous fit of saturation volumes and vapor pressures is of current interest, and it requires the modification of the volumetric dependence of current cubic equation of state, in addition to the introduction of improved a (T r ) functionalities yielding non-traditional EoS as shown in the work of Trebble and Bishnoi [54], Salim and Trebble [55] and Solimando et al [56]. No general short-cut procedure seems to be available for non-standard EoS.…”

Section: The Peng-robinson and Soave-redlich-kwong Equations Of Statementioning

confidence: 98%

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Ghosh¹

1999

Chem. Eng. Technol.

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Knowledge of vapor-liquid equilibria is essential for chemical process design. Development of algebraically simple cubic equations of state, particularly Peng-Robinson and Soave-Redlich-Kwong equations of state has encouraged vapor-liquid equilibria calculation using the equation of state approach. To extend applicability to complex mixtures, several modifications to these equations of state were proposed. Also, many new mixing rules have been developed besides the already existing ones that incorporate excess free energy models. Some of these EoS/G E models are found to be applicable to complex systems in which the components can be highly polar, differ vastly in size or may be forming association. In spite of a large number of publications on this field, this subject is still open for further research. In this article, an overview on the work done using the most successful of the cubic equations of state, i.e., Peng-Robinson and Soave-Redlich-Kwong equations of state is presented. In the later part of this article, VLE predictions (using these two equations of state) of some interesting systems like water/hydrocarbon mixtures, polymer solutions, electrolyte solutions and refrigerant mixtures are discussed. The objective is to present the available information for ready reference that will prove to be useful from a designers point of view. It is seen from the existing literature that with a proper choice of equation of state and mixing rule based on the available knowledge on the properties of the system of interest, VLE of highly complex systems can be predicted with accuracy. Several comparative studies that are cited here (and discussed) will help the designer to pick-up the right combination for the system under investigation.

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Section: The Peng-robinson and Soave-redlich-kwong Equations Of Statementioning

confidence: 98%

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Ghosh¹

1999

Chem. Eng. Technol.

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“…Many specific articles and reviews dealing with EOS exist in the chemical and physicochemical literature, e.g., more recent reviews by Anderko (1990), Ferry and Baumgartner (1987), Prausnitz et al (1999), Sandler (1994, Sengers et al (2000), and Wei and Sadus (2000). In the geological literature, knowledge about EOS and its state-of-the-art is much less widespread and, therefore, a brief overview is given here.…”

Section: Types Of Eosmentioning

confidence: 99%

Equations of State for Complex Fluids

Gottschalk¹

2007

Reviews in Mineralogy and Geochemistry

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INTRODUCTIONCompositions of coexisting fluids at elevated pressure-temperature conditions can be calculated by applying thermodynamics as in any other chemical equilibrium. This calculation requires the evaluation of the thermodynamic properties of the phase components i at the respective pressure P, temperature T, and the individual abundances x i , i.e. composition. In comparison with solids, fluids normally have distinct PVT-behaviors. Furthermore, because of their disordered state and the relatively weak bonding between molecules, fluid species mix much more easily than solid-phase components. The evaluation of the thermodynamic properties of fluids requires, therefore, special treatment and procedures that differ significantly from those used for solids. For fluids, this treatment includes a distinct and different standard state than for solids and a special description of the volume V as a function of P, T (or P as a function of V and T) and x i , i.e. an equation of state (EOS). PRINCIPLESFor geological systems, which are usually defined by the variables P and T, the Gibbs free energy G is the function of choice to describe equilibria. At constant P and T the chemical equilibrium condition is defined by (the Table 1 lists the symbols used):The partial derivative of G with respect to P is the volume VTherefore, the pressure-dependence of G is obtained by integration of Equation (2) with boundaries from the reference pressure P r , i.e. ambient pressure of 0.1 MPa, to the required P G (P,T ) = G (P r ,T ) + VdP For solids using the standard state of a pure phase component at reference conditions P r and T r , (i.e. 0.1 MPa, 298 K) integration over P leads to,where h i o and s i o are the molar enthalpy and entropy at P r and T, v i o the molar volume as a function of P at T of the pure phase component i, and a i is its activity, which also incorporates in this case any volume effects of mixing.However, for fluids the standard state is defined differently, and Equation (5) is not used in this form. The principal thermodynamic equations are rearranged in such a way that, at the standard state, the properties of a pure fluid are taken as if this fluid would behave like an ideal gas. For fluids, the standard state is, therefore, that of a hypothetical ideal gas at P r at any required temperature T. The use of this standard state leads to the following expression,in which the asterisk denotes the hypothetical ideal gas standard state properties. Details of the derivation of Equation (6), and Equation (11) in the following, can be found for example in Beattie (1955) or in Appendix A.The integral term in Equation (6) provides the definition of the fugacity coefficientThus Equation (6) can be written asand with definition of the fugacity f i m 1 The term phase component is used as a synonym for a endmember of a solution, i.e. for fluids specific species or molecules, whereas the term component is used in the classic thermodynamical sense.2 The lower integration boundary is strictly 0 MPa and not just some low pre...

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“…The attractive term of the generalized cubic EOS such as SRK equation under-predicts compressibility factors compared to molecular simulation results [2,11]. Accordingly, an additional term was proposed to eliminate one of the deficiencies of the cubic EOS attractive …”

Section: Modification Of the Attractive Termmentioning

confidence: 99%

Phase Behavior of Light Gases in Hydrocarbon and Aqueous Solvents

Gasem¹,

Robinson²

1998

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Under previous support from the Department of Energy, an experimental facility has been established and operated to measure valuable vapor-liquid equilibrium data for systems of interest in the production and processing of coal fluids. To facilitate the development and testing of models for prediction of the phase behavior for such systems, we have acquired substantial amounts of data on the equilibrium phase compositions for binary mixtures of heavy hydrocarbon solvents with a variety of supercritical solutes, including hydrogen, methane, ethane, carbon monoxide, and carbon dioxide.The present project focuses on measuring the phase behavior of light gases and water in Fischer-Tropsch (F-T) type solvents at conditions encountered in indirect liquefaction processes and evaluating and developing theoretically-based correlating frameworks to predict the phase behavior of such systems. Specific goals of the proposed work include (a) developing a state-ofthe-art experimental facility to permit highly accurate measurements of equilibrium phase compositions (solubilities) of challenging F-T systems, (b) measuring these properties for systematically-selected binary, ternary and molten F-T wax mixtures to provide critically needed input data for correlation development, (c) developing and testing models suitable for describing the phase behavior of such mixtures, and (d) presenting the modeling results in generalized, practical formats suitable for use in process engineering calculations.During the present period, the Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to enhance the flexibility of the model, and a new expression was developed for the temperature dependence of the attractive term in this segmentsegment interaction model.The predictive capability of the modified PGR EOS for vapor pressure, and saturated liquid and vapor densities was evaluated for selected normal paraffins, normal alkenes, cycloparaffins, light aromatics, argon, carbon dioxide and water. The generalized EOS constants and substance-specific characteristic parameters in the modified PGR EOS were obtained from the pure component vapor pressures, and saturated liquid and vapor molar volumes. The calculated phase properties were compared to those of the Peng-Robinson (PR), the simplified-perturbedhard-chain theory (SPHCT) and the original PGR equations. Generally, the performance of the proposed EOS was better than the PR, SPHCT and original PGR equations in predicting the pure fluid properties (%AAD of 1.3, 2.8 and 3.7 for vapor pressure, saturated liquid and vapor densities, respectively).A manuscript we have prepared for publication is attached in lieu of detailed technical information. EXECUTIVE SUMMARYThe Park-Gasem-Robinson (PGR) equation of state (EOS) has been modified to improve its volumetric and equilibrium predictions. Specifically, the attractive term of the PGR equation was modified to...

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Equation-of-state methods for the modelling of phase equilibria

Cited by 106 publications

References 258 publications

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Equations of State for Complex Fluids

Phase Behavior of Light Gases in Hydrocarbon and Aqueous Solvents

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