J. Vidal

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures☆

Huron, M.-J. and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilibria, 3: 255-271. Good correlations of vapour-liquid equilibria can be achieved by applying the same two-parameter cubic equation of state to both phases. The results primarily depend on the method used for calculating parameters and, for mixtures, on the mixing rule. True parameters are the covolume b and the energy parameter a/b. For this latter one, deviations from a linear weighting rule are closely connected to the excess free energy at infinite pressure. Thus any mixing rule gives a model for the excess free energy, or any accepted models for this property can be used as mixing rules. From the above, an empirical polynomial mixing rule is used for data smoothing and evaluation, while for practical work a local composition model is used. The mixing rule thus obtained can be reduced to the classical quadratic rule for some easily predicted values of the interaction energies. For highly polar systems, it includes three adjustable parameters. Using literature data, the new mixing rule is applied, in the low and high pressure range, to binary mixtures with one or two polar compounds, giving good data correlation and sometimes avoiding false liquid-liquid immiscibility.

Mixing rules and excess properties in cubic equations of state

Abstract The limitations implied by using conventional quadratic mixing rules for Redlich—Kwongs modified equations of state are studied. A close relation is

A versatile algorithm for calculating vapour—liquid equilibria☆

Abstract A versatile algorithm is proposed for solving vapour—liquid equilibrium problems. It has been prepared so that the search procedure is generally applicable with any analytical equation of state and any kind of data. Special attention is paid to the applicability of the method in critical and high-pressure regions. Derivatives of the quantities describing the state of the system can be obtained for any equilibrium state as soon as equilibrium is determined. Results are reported for computing based on the use of a modified Redlich—Kwong equation of state.

Prediction of phase behaviour of gas-containing systems with cubic equations of state

Abstract The Soave Redlich-Kwong (S.R.K.) equation of state is used to correlate the phase behaviour of light compounds-containing systems and gas-hydrocarbon systems. Gases considered include H 2 , CH 4 , N 2 , CO 2 , CO and SH 2 . An extensive literature search was conducted to obtain the binary experimental vapour-liquid equilibrium data which were used to build a predictive procedure of phase behaviour. Average error in bubble pressure predictions for 812 isothermal data sets (4399 experimental points) is 4%. Calculations with systems containing highly polar substances, water and methanol, are included. Good results are obtained when the proposed method is used to predict phase behaviour of some ternary systems typically encountered in petroleum and related industries.

Vapour-liquid equilibrium and critical locus curve calculations with the soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide

Abstract Huron, M.-J., Dufour, G.-N. and Vidal, J., 1978. Vapour-liquid equilibrium and critical locus curve calculations with the Soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide. Fluid Phase Equilibria, 1: 247–265 The aim of this work is to test the value of the Soave-Redlich-Kwong equation of state for predicting phase behaviour of mixtures. Special attention is paid to systems containing hydrogen sulphide or carbon dioxide with hydrocarbons. The properties analysed are critical loci and liquid vapour equilibria, with calculations of standard deviations for pressures and compositions. Optimum values of binary interaction parameters are proposed for these mixtures. Calculation methods to avoid trivial solutions in phase equilibria calculations and for finding critical loci with temperature extrema are described.

Calculation of thermodynamic properties and vapor-liquid equilibria of refrigerants

Abstract Saturated state thermodynamic properties of refrigerants are predicted from critical coordinates and normal boiling points by using Soaves equation of state. Binary vapor-liquid equilibria are correlated by determining interaction parameters for the following six systems: CCl2F2/CH3CHF2, CCl2F2/CHClF2, CHF3/CClF3, CClF3/CCl3F, CCl2F2/CClF3, CF4/CHF3. On the whole the method gives reliable results over broad temperature and pressure ranges for practical engineering uses.

A segmental interaction model for liquid-liquid equilibrium calculations for polymer solutions

Abstract This paper gives a detailed account of a newly developed segment-based thermodynamic model containing the combinatorial, free-volume, and energetic contributions to the excess Gibbs energy for correlation/prediction of liquid–liquid equilibrium (LLE) of polymer solutions. The model is derived from the entropic free-volume (entropic-FV) model, following the idea to associate the nonideality of polymer–solvent mixture with polymer segment–solvent interaction parameters. The energetic contribution is based on interactions between individual segments (repeating units) of polymer or copolymer and solvent molecule, as in the application of the mean field theory. Segment activity coefficients are calculated through the UNIQUAC model. In the present state of development, 29 binary segmental interaction parameters have been estimated. The capability of the model is demonstrated with successful representation of LLE correlation/prediction for more than 60 polymer–solvent systems. The model is capable to correlate and to predict the most common types of phase diagrams of LLE of polymer solutions (i.e. phase diagrams of the UCST, LCST, combined UCST and LCST, and “hourglass” types) with satisfactory accuracy and provides a thermodynamic framework to describe the LLE phase behavior of polymer solutions, using weakly temperature dependent FV-UNIQUAC parameters.

A group contribution equation of state for polar and non-polar compounds

Abstract Lermite, C. and Vidal, J., 1992. A group contribution equation of state for polar and non-polar compounds. Fluid Phase Equilibria, 72: 111-130. The UNIFAC model is applied to the excess Helmholtz energy at constant packing fraction associated with the equations of state of Soave—Redlich—Kwong and of Peng—Robinson. The mixing rule thus defined is applied to vapor-liquid equilibria of mixtures containing methane, ethane, carbon dioxide, paraffinic and aromatic hydrocarbons, alcohols and ketones. Satisfactory accuracy is obtained in calculating the bubble-point pressures and the compositions of the phases in equilibrium.

High pressure polar compounds phase equilibria calculation : Mixing rules and excess properties

Abstract Phase equilibria are usually calculated by methods that depend on the pressure range : excess functions at low pressure and equations of state at high pressure. These methods are actually closely linked. The measurement or the prediction of excess functions may replace mixing rules, as shown by an examination of the research being done in this direction. The field of application of equations of state is thus considerably widened, and vapour-liquid equilibria of polar mixtures can be calculated all the way to the critical zone. The same method can be used to solve difficulties related to > ldmultiparameter” equations of state.

An improved group method for hydrocarbon-hydrocarbon systems arising from a comparative study of asog and unifac

Abstract A comparison of the formalism of ASOG, in the version of Kojima and Tochigi, and of UNIFAC shows the total formal equivalence of both empirical group methods for calculating activity coefficients in mixtures. The most advantageous features of each method are taken into account in the formulation of an improved method for hydrocarbon-hydrocarbon systems. Parameters for CH 2 /ArCH, CH 2 /CyCH, CH 2 CH, ArCH/CyCH, ArCH/CH and CyCH/CH are evaluated from total pressure- liquid composition and heats of mixing data using the SIGMA procedure. The results obtained with the three empirical group methods are compared with experimental data. The ability to predict activity coefficients at infinite dilution is discussed.