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A group-contribution model for the prediction of vapor pressures of organic solids is presented, based on the concept of the hypothetical liquid. The group-contribution parameters are applied in the prediction of vapor pressures for a variety of organic solids involving aliphatic and aromatic hydrocarbons, halogenated hydrocarbons, oxygenated hydrocarbons (alkanols, phenols, acids and ketones), and some multifunctional ones. Satisfactory results are obtained with errors below one order of magnitude down to very low pressures well below the Pa level. The required entropy of fusion is also predicted with a simple group-contribution method developed. The obtained predictions are—as expected from a simple method—not very accurate, but sufficient for the purpose of this study. Extrapolation, finally, of the method in the liquid range up to 1 atm gives satisfactory predictions provided that the temperature range of the vapor pressure data is not far beyond that involved in the parameter estimation.

In many applications related to Supercritical-Fluid (SCF) technology, solids are dissolved in SC fluids. Experimental data are now available for many systems but cannot cover all cases of potential practical interest. The prediction of solid solubilities in SC fluids, often in the presence of co-solvents, is useful for rational design of SCF extraction and related processes. Recently, thermodynamics has made considerable steps towards describing complex systems (gases with polar compounds) at high pressures using the so-called Equation of State/Excess Gibbs Free Energy (EoS/G E ) models. The success of these models is so far restricted to Vapor–Liquid Equilibria (VLE) for which they have been primarily developed and tested. In this work we evaluate such a predictive model, the LCVM EoS, for solid–gas equilibria (SGE) including systems with co-solvents. LCVM is chosen due to its success for VLE of asymmetric systems such as CO 2 with heavy alkanes and alcohols. Successful predictions are obtained for several solids as well as for some systems with co-solvents, but the results are less satisfactory for complex, multifunctional solids. A discussion of several factors, which affect modeling of SGE with cubic EoS, is included.

A novel method for investigating the performance of the repulsive and attractive terms of a cubic equation of state (EoS) along with different combining rules for the cross covolume (b12) and cross-energy (a12) parameters used with the van der Waals one-fluid theory is presented. The method utilizes the EoS-derived liquid-phase activity coefficient which is separated into a combinatorial-free volume part (γc-fv), obtained from the repulsive term of the EoS, and a residual one (γres) obtained from the attractive term. Athermal systems (alkane solutions) are used where we can reasonably expect that the residual part will be close to one and, consequently, the combinatorial-free volume part will be close to the experimental value. For these solutions the main effect of nonideality comes from size/shape differences rather than energetic ones. Thus, it is reasonable to assume that γres is approximately unity. It is demonstrated that the empirically used combining rules, the arithmetic mean (AM) for b12 and the geometric mean (GM) for a12, while not giving completely satisfactory results, are the best choices by far. Moreover, the qualitative agreement between the γc-fv values with the experimental ones suggest that the van der Waals (vdW) repulsive term is applicable not only to mixtures with spherical molecules, as originally suggested by van der Waals, but also to very asymmetric ones. On the other hand, the attractive term leads to γres values that can be substantially different from unity for asymmetric athermal systems. Furthermore, we show that the lij interaction parameter (correction to the covolume term) is, for athermal systems, more important that the commonly employed kij parameter (correction to the cross-energy term). What is particularly interesting is that a single (per system) lij value yields, simultaneously, physically meaningful activity coefficient values and excellent vapor-liquid equilibria correlation. Thus, the whole ethane/n-alkane series (up to n-C44) can be described with a unique lij value.

Using an extensive database of experimental critical properties for heavy compounds, which have been compiled mostly from recent literature sources, it is shown that the ratio Tc: Pc (critical temperature over critical pressure) can be expressed in terms of the van der Waals surface area (Qw), which is readily available for any compound from the group contributions of Bondi (given also in UNIFAC tables). The proposed correlation is based on the hole theory of Kurata and Isida for n-paraffin liquids, which is mathematically equivalent to Flory's theory of polymer solutions. The method is suitable for medium to high molecular weight compounds with unknown critical constants. For example, if only one of the two critical constants is available, then the proposed generalized equation offers a useful rapid procedure for the estimation of the other critical property for use in corresponding states, and other relevant applications where knowledge of the critical properties is required. Furthermore, the Tc: Pc method can be used in many cases for identifying the most suitable among the existing group contribution methods for estimating the critical properties of heavy and complex compounds for which experimental values are, very often, not available.

Equilibrium solubilities of p-quinone (1,4-benzoquinone) and 9,10-anthraquinone at 35 °C and 45 °C in supercritical carbon dioxide over a pressure range of about (85−300) bar have been measured using a supercritical fluid extractor coupled with a high-pressure liquid chromatography apparatus. The solubility results, along with those reported in the literature for 1,4-naphthoquinone, are correlated with a modified Peng−Robinson equation of state.

A recently developed equation of state-excess Gibbs free energy (EOS/GE) model with the LCVM (linear combination of Vidal and Michelsen) mixing rule, capable of successful VLE prediction in asymmetric systems is applied to the prediction of solubilities of alkenes, ethers, acids, alcohols, and esters in supercritical carbon dioxide. Considering the experimental uncertainties, excellent correlation of binary data and satisfactory prediction of ternary and multicomponent equilibria are obtained in most cases over a wide range of temperature, pressure, and system asymmetry. These promising results render the LCVM model a useful tool for the preliminary design of processes involving mixtures with organic compounds and supercritical carbon dioxide.

Equilibrium solubilities of pure anthracene at 50 °C, 1-naphthol at 35, 45, and 55 °C, and hydroquinone at 35 and 45 °C in supercritical carbon dioxide over a pressure range of about 85-300 bar have been measured using a supercritical fluid extractor coupled with an external high-pressure liquid chromatographer. The solubility results, along with those for other phenols reported in the literature, are correlated with the translated-modified Peng Robinson equation of state.

An analysis of the mixing rules proposed by Wong and Sandler (1992) for the attractive and covolume parameter of a cubic equation of state is presented. This set of mixing rules (WS MR) reproduces the correct quadratic composition dependence of the second virial coefficient and, in addition, retains the ability to predict directly high pressure-high temperature phase equilibria from existing low-pressure GE models. It is demonstrated that the proposed mixing rules are valid for symmetric systems, but not for asymmetric ones, where the basic assumptions behind them do not hold anymore.

An analysis of EoS/GE models, which are based on matching the EoS-derived expression for the excess Gibbs free energy GE with that from a GE model at zero pressure, is presented, with the focus on the most successful and widely used of these models, MHV2 and PSRK. It shows why zero-reference-pressure models do not reproduce exactly the GE models at zero pressure and the ensuing implications on the prediction of asymmetric systems. The development of EoS/GE models that reproduce exactly the GE model is discussed. However, such reproducibility at zero pressure is impossible for systems containing components with reduced temperatures higher than about 0.9. Therefore, extrapolation schemes that allow treatment of such systems are examined.

Thirty years of research and the use of EoS/GE mixing rules in cubic equations of state are reviewed. The most popular approaches are presented both from the derivation and application points of view and they are compared to each other. It is shown that all methods have significant capabilities but also limitations which are discussed. A useful approach is presented for analyzing the models by looking at the activity coefficient expression derived from the equations of state using various mixing rules. The size-asymmetric systems are investigated in detail, and an explanation is provided on how EoS/GE mixing rules should be developed so that such asymmetric mixtures are adequately represented. © 2012 American Chemical Society.

Boukouvalas, C., Spiliotis, N., Coutsikos, P., Tzouvaras, N. and Tassios, D., 1994. Prediction of vapor-liquid equilibrium with the LCVM model: a linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-mPR equation of state. Fluid Phase Equilibria, 92: 75-106. A new mixing rule, a linear combination of the Vidal and Michelsen rules, for the attractive term parameter in cubic equations of state (EoS) has been developed. This mixing rule, coupled with a translated and modified Peng-Robinson EoS and the original UNIFAC, leads to the LCVM model which provides successful prediction of vapor-liquid equilibria (VLE) of nonpolar and polar systems at low and high pressures. This also applies to systems of dissimilar component size, such as those containing gases (C2H6, CO2 and CH4) with large n-alkanes, where other EoS/GE predictive models, such as MHV2 and PSRK, perform poorly.