Equation of State Models

Ross and Olivier [55], in their extensive development of the van der Waals equation of state model have, however, provided a needed balance to the Langmuir picture. 

Equation-of-state measurements add to the scientific database, and contribute toward an understanding of the dynamic phenomena which control the outcome of shock events. Computer calculations simulating shock events are extremely important because many events of interest cannot be subjected to test in the laboratory. Computer solutions are based largely on equation-of-state models obtained from shock-wave experiments which can be done in the laboratory. Thus, one of the main practical purposes of prompt instrumentation is to provide experimental information for the construction of accurate equation-of-state models for computer calculations. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

For the evaluation of the solubility it is necessary to know the pure component properties and to use an equation-of-state model for the evaluation of the fugacity coefficients. In general, two problems arise ... 

The phase behaviour of binary polymer - supercritical fluid systems can be modelled with an equation of state model. In general, non-cubic equations of state are used, mainly from the PHCT and SAFT families. Lattice-fluid equations of state are also commonly used for the... 

Table l.l. Physical Properties Used in Equation-of-State Modeling... 

Hua, J. Z. Brennecke, J. F. Stadtherr, M. A. Reliable Computation of Phase Stability Using Interval Analysis Cubic Equation of State Models. Comput. Chem. Eng. 1998a, 22, 1207-1214. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

It is believed that ASPEN provides a state-of-the-art capability for thermodynamic properties of conventional components. A number of equation-of-state (EOS) models are supplied to handle virtually any mixture over a wide range of temperatures and pressures. The equation-of-state models are programmed to give any subset of the properties of molar density, residual enthalpy, residual free energy, and the fugacity coefficient vector (and temperature derivatives) for a liquid or vapor mixture. The EOS models (named in tribute to the authors of such work) made available in ASPEN are the following ... 

Traditional approaches for the calculation of the phase equilibria and sorption of penetrant molecules in polymers are based on equation-of-state models [27,28,29], which take into account the PVT properties of both gas and polymer, and the activity coefficient models [30], which take into account the specific interactions between... 

The experimental data are correlated with equation of state models. The calculation of binary phase equilibrium data for FAEE is commonly based on the Peng-Robinson-equation-of-state, Yu et al. (1994). Up to now only the solubility of the oil components in the solvent has been subject of various studies. No attention was paid to a correlation of ternary data. The computation of ternary or multicomponent phase equilibrium is the basis to analyse and optimise the separation experiments. 

A study of the representation of liquid-fluid equilibria with the "Excess Function-Equation of State" model and the choice of a group-contribution method. Promising results were obtained here (references [3] and [4]). 

The "Excess Function-Equation of State" model is based on the relation between the excess Helmholtz energy of the mixture and the equations of state of its components. The excess Helmholtz energy is calculated in Guggenheim s quasi-reticular theory. We chose van der Waals - like equations of state for the constituents of the mixture ... 

The interaction parameter Eg was first adjusted to the experimental data of the liquid-fluid and solid-fluid equilibria. The representation of both types of equilibria was very satisfactory, which proves that the "Excess Function-Equation of State" model with an adjusted parameter is well adapted to both cases ([4-6], [13]). 

The transformation of the "Excess Function-Equation of State" model into a group-contribution method is possible through the interaction energy parameter. The interaction parameter Eg between the molecules i and j is expressed by ... 

Daridon, J. L. Lagourette, B. Saint-Guirons, H. Xans, P. A cubic equation of state model for phase equilibrium calculation of alkane -H carbon dioxide -H water using a group contribution kij. Fluid Phase Equilib. 1993, 91, 31-54. 

Values of the critical temperature and pressure are needed for prediction methods that correlate physical properties with the reduced conditions. It is also important to know the critical conditions when applying equation of state methods, as some of the equation of state models are unreliable close to the critical point. Experimental values for many substances can be found in various handbooks and in Appendix C. Critical reviews of the literature on critical constants and summaries of selected values have been published by Kudchadker et al. (1968), for organic compounds, and by Mathews (1972), for inorganic compounds. An earlier review was published by Kobe and Lynn (1953). 

A broad range of cubic equation of state models (EOS) are successfully used today. The EOS range from the standard Soave-Redlich-Kwong and Peng-Robinson, which is widely used in the hydrocarbon processing and related industries (oil gas and petrochemicals), to a new class of models that extend the range of applications to chemicals. " New models are continually being developed and are too numerous to cite. 

The Electrolyte NRTL model " and the Extended UNIQUAC model" are examples of activity coefficient models derived by combining a Debye-Hiickel term with a local composition model. Equation of state models with electrostatic terms for... 

Solute/solute interactions are also important in SCF solutions, as observed by Kurnik and Reid and Kwiatkowski and coworkers (27,28), in the synergistic effects on the solubilities of mixed solutes. When a physical mixture of naphthalene and benzoic acid is extracted with SCF COj the solubilities of both components is greater than the solubility of either pure component. This phenomenon occurs at concentrations as low as 10 to 10" mol fraction. Frequently, equation of state models assume infinite dilution of the solutes due to the low solubilities. Clearly, recognition and a better understanding of these solute/solute interactions are important for the prediction of SC phase equilibria. 

Equation of State Models for Vapor-Liquid Phase Equilibrium Calculations... 

The Combination of Equation of State Models with Excess Free-Energy (EOS-G ) Models An Overview... 

Anderko, A., 1990. Equation of state models for modeling of phase equilibria. Fluid Phase 9., 61 145-225. 

Dahl, S., Fredenslund, A., and Rasmussen, R, 1991. The MHV2 model A UNlFAC-based equation of state model for prediction of gas solubility and vapor-liquid equilibria at low and high pressures. Ind. Eng. Chem. Res., 30 1936-1945. 

Orbey, H., and Sandler, S, I., 1996a. An analysis of excess free energy based equation of state models. AIChEJ., 42 2327-2334. 

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