Hasan Orbey

Accurate Equation of State Predictions at High Temperatures and Pressures Using the Existing UNIFAC Model

Abstract Orbey, H., Sandler, S.I. and Wong D.S.H., 1993. Accurate equation of state predictions at high temperatures and pressures using the existing UNIFAC model. Fluid Phase Equilibria , 85:41-54. A recently developed mixing rule for cubic equations of state is combined with the UNIPAC group contribution method to yield a completely predictive thermodynamic model for the vapor-liquid and liquid-liquid phase behavior of slightly and highly non-ideal mixtures over large ranges of temperature and pressure. We find that the quality of predictions is very good for systems for which UNIFAC provides an accurate low pressure description. The mixing rule + UNIFAC model developed is an accurate and very simple extension of the UNIFAC group contribution method to high temperatures and high pressures. Further, since existing UNIFAC parameters are used, no refitting of experimental data is needed.

On the combination of equation of state and excess free energy models

Abstract In this communication we review the bases for a collection of equation of state mixing rules which have been developed that combine activity coefficient (or excess free energy of mixing) models with equations of state. We show that combining equations of state and activity coefficient models at infinite pressure produces mixing rules that are free of ad hoc assumptions, and are easy to understand and implement. In contrast, when the link is made at zero or low pressure, problems arise because the liquid volume appears in the mixing rule. In principle, this requires solving the equation of state for the liquid volumes of each of the pure components and for the mixture. To avoid such calculations, and to deal with the problem that a liquid phase solution to the equation of state may not exist for one or more of the pure components at the temperature of interest, several ad hoc procedures have been proposed. It is these procedures that differentiate between the various zero (low) pressure mixing rules. Each of the mixing rules reviewed here is successful for at least some range of temperatures, though some of their shortcomings are discussed. Finally, two new variants of this class of mixing rules are proposed, of which one is tested and found to be simple, and at least as satisfactory as presently used zero-pressure mixing rules.

Vapor-liquid equilibrium from infinite dilution activity coefficients: measurement and prediction of oxygenated fuel additives with alkanes

Abstract Pividal, K.A., Sterner, C., Sandier, S.I. and Orbey, H., 1992. Vapor-liquid equilibrium from infinite dilution activity coefficients: measurement and prediction of oxygenated fuel additives with alkanes. 72: 227-249. Comparative ebulliometry was used to measure activity coefficients at infinite dilution for binary systems of the oxygenated fuel additives methyl tertiary butyl ether, diisopropyl ether and ethanol with alkanes. The possibility of obtaining parameters for equations of state mixing rules from infinite dilution activity coefficients data was studied. The predictive abilities of some recent equation of state mixing rules which incorporate excess Gibbs free energy models were critically evaluated, and a simple empirical technique for the evaluation of binary interaction parameters in cubic equations of state using infinite dilution activity coefficient data is proposed.

Vapor-liquid equilibria of some hydrogen + hydrocarbon systems with the Wong-Sandler mixing rule

Abstract Huang, H., Sandler, S.I. and Orbey, H., 1994. Vapor-liquid equilbria of some hydrogen + hydrocarbon systems with the Wong-Sandler mixing rule. Fluid Phase Equilibria , 96: 143-153. Owing to the highly supercritical nature of hydrogen in hydrogen-hydrocarbon systems, it is difficult to accurately predict, or even correlate, the phase behavior of such mixtures with cubic equations of state and conventional mixing rules, especially as the critical point of the mixture is approached. Here we show that an extended Peng-Robinson equation of state and the recently introduced Wong-Sandler mixing rule can correlate these systems successfully, and more importantly that the mixing rule parameters can be generalized in terms of temperature and acentric factor of the hydrocarbon so that quite acceptable extrapolations and predictions are possible.

A comparison of various cubic equation of state mixing rules for the simultaneous description of excess enthalpies and vapor-liquid equilibria

Abstract Recent new mixing and combining rules for cubic equations of state (EOS) have extended the range of such equations to the accurate description of the vapor-liquid equilibria (VLE) of highly nonideal mixtures. However, the simultaneous correlation and/or prediction of vapor-liquid equilibrium (VLE) and liquid mixture excess enthalpies ( H ex ) by either activity coefficient models or equations of state has been a difficult problem in applied thermodynamics. In this communication, we re-examine this problem using a modified version of the Peng-Robinson equation of state and the two-parameter van der Waals one-fluid, Wong-Sandler and modified Huron-Vidal mixing rules. For comparison, the direct use of activity coefficient models is also considered. In each case a temperature dependence of the model parameters is introduced in an attempt to represent simultaneously VLE and H ex behavior. Four highly nonideal binary mixtures (2-propanol + water, methanol + benzene, benzene + cyclohexane, and acetone + water) are considered. The results indicate that while all the models can accurately correlate VLE and H ex data separately, attempting to predict the values of one property with parameters obtained from the other does not give satisfactory results with any model. Also, we find that the simultaneous correlation of both VLE and H ex with the EOS models at one temperature is possible, but extrapolations to other temperatures with parameters obtained in this way did not result in accurate predictions of either VLE or H ex . The main problem appears to be that the excess free energy (activity coefficient) models used are not capable of representing both VLE and H ex over a range of temperatures, and so equations of state that incorporate these free energy models have the same shortcoming.

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Abstract Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.

A segment contribution method for the vapor pressure of tall-oil chemicals

A segment-contribution method for the estimation of vapor pressure of large, oligomeric molecules encountered in oleochemical industry is described. The method makes use of segment composition, number of segments, and four parameters per segment to estimate vapor pressure as a function of temperature. For major components that occur in crude tall-oil (CTO) distillation, the optimum parameters are reported and the method is shown to be accurate. The open architecture of this segment contribution approach permits the use of new segments, or the treatment of whole molecules as segments if necessary.

The thermodynamics of long-lived organic pollutants

Abstract A thermodynamic model is presented for determining the distribution of pollutants in the various compartments of the global environment. The data needed to use this model are the vapor pressure, infinite dilution activity coefficient, Henrys law coefficient and/or solubility in water, and the octanol-water partition coefficient. It is only this latter quantity, which involves liquid-liquid equilibrium, that traditionally has not been measured by thermodynamicists. We also report infinite dilution and Henrys law coefficient measurements for some U.S. Environmental Protection Agency Priority Water Pollutants.

Mixing Rules for the Estimation of Vapor-Liquid Equilibrium of Highly Non-Ideal Mixtures Using Cubic Equations of State

The capabilities and limitations of some recent mixing rules for cubic equations of state are discussed in the context of vapor-liquid equilibrium with supercritical components. New mixing rules can be useful tools in correlating and even predicting behavior of highly nonideal mixtures at broad ranges of temperature and pressure. Some possible routes for further research in the area are indicated.

A FOUR PARAMETER PITZER-CURL TYPE CORRELATION OF SECOND VIRIAL COEFFICIENTS

The Pitzer-Curl ( 1957) correlation of second virial coefficients is slightly modified to accommodate high temperature data ( TT4 4.0) of He and H2 and extended successfully to “ nonstandard” fluids as defined by Tarakad and Danner (1977), by introducing a fourth parameter per compound. The new version improves results at the high temperature limit while it gives comparable results with the previous versions presented by Pitzer and Curl ( 1957) and Tsonopoulos ( 1974) at lower temperatures. The present approach enhances the applicability of the method for polar and associating compounds by introducing a correcting term for 129 such fluids. The extension of the correlation to mixtures requires an additional parameter per binary. Successful results were obtained for thirty nine binary systems investigated in this work