Georgios M. Kontogeorgis

Multicomponent phase equilibrium calculations for water–methanol–alkane mixtures

Abstract Prediction of phase equilibrium for multicomponent systems containing associating compounds (e.g., water and alcohols) is essential in a number of engineering applications (e.g., environmental technology, gas hydrate inhibition) and at the same time represents one of the most stringent tests for a thermodynamic model. Conventional models (e.g., cubic equations of state and excess Gibbs free energy models) provide rapid and often reliable estimates of phase equilibrium in many cases but extension to multicomponent systems, especially those containing water is often troublesome. On the other hand, novel association equations of state perform considerably better but are slower compared to conventional models. Furthermore, the extension of several of them to cross-associating systems (e.g., water–alcohols) exhibits problems. In this work, the performance of two well-known conventional models (SRK and NRTL) is compared for multicomponent systems to a recently proposed association equation of state both in terms of accuracy of predictions and timing. The proposed model incorporates the Wertheim chemical association theory (employed previously in models such as SAFT) and the SRK equation. The model is applied in this work to multicomponent systems in such a way that the inclusion of the Wertheim theory does not give execution times much higher than conventional models. The model yields very satisfactory predictions of multicomponent equilibria for aqueous (both vapor–liquid and liquid–liquid equilibria) systems containing methanol, gases and hydrocarbons, which are moreover, as will be demonstrated in this work, considerably better compared to SRK and NRTL.

A Flory–Huggins model based on the Hansen solubility parameters

Abstract The Hansen solubility parameters are typically used, especially in the paint and coatings industry, for selecting suitable solvents for polymer binders. In such applications, the radius of solubility needs to be determined by experiments. Moreover, other calculations, e.g. related to drying of paints, require thermodynamic description over extended concentration ranges. On the other hand, the well-known Flory–Huggins model captures satisfactorily several of the characteristics of polymer solutions, but the interaction parameter of the model usually also has to be determined by experiments. In this work, we present a methodology, based on which the Hansen solubility parameters can be incorporated in the Flory–Huggins model. The resulting model is predictive and yields good predictions of solvent activity coefficients at infinite dilution in several acrylate and acetate polymers. The results are as accurate as other predictive polymer models based on the group-contribution (GC) principle, but in contrast to these models, knowledge of molecular structures is not required in the Hansen/Flory–Huggins model. The new model makes thus use of the extensive literature of Hansen solubility parameters, which are tabulated for very many solvents, pigments and polymers.

Vapor-liquid equilibria for alcoholhydrocarbon systems using the CPA Equation of state

Abstract The recently developed Cubic-Plus-Association Equation of State (CPA EoS) is extended in this study to binary systems containing one associating compound (alcohol) and an inert one (hydrocarbon). CPA combines the Soave-Redlich-Kwong (SRK) equation of state for the physical part with an association term based on perturbation theory. The classical van der Waals one-fluid mixing rules are used for the attractive and co-volume parameters, α and b, while the extension of the association term to mixtures is rigorous and does not require any mixing rules. Excellent correlation of Vapor-Liquid Equilibria (VLE) is obtained using a small value for the interaction parameter (kij) in the attractive term of the physical part of the equation of state even when it is temperature-independent. CPA yileds much better results than SRK and its performance is similar to that of other association models, like the Anderko EoS, and the more complex SAFT and Simplified SAFT EoS.

Binary interaction parameters for nonpolar systems with cubic equations of state: a theoretical approach 1. CO2/hydrocarbons using SRK equation of state

Abstract This work shows that, when suitable theoretically based combining rules are used for the cross energy and cross co-volume parameters, cubic equations of state (EoS) with the van der Waals one-fluid mixing rules can adequately represent phase equilibria for the asymmetric CO 2 /hydrocarbon mixtures. These combining rules lead to semi-theoretical yet simple, meaningful and successful correlations for the interactions parameters K ij (of the cross-energy term) and l ij (of the cross volumef term). Unlike previous correlations, the proposed equations relate the interaction parameters only to the pure component co-volume ( b i ) parameters, meaning that no additional critical volume), besides those required by the EoS itself (the critical temperature T c , the critical pressure P c and the acentric factor) are used. Furthermore, the form of the correlations enables us to tune easily the cubic EoS when this is required for the prediction of phase behavior of petroleum fluids. A brief theoretical analysis on the temperature dependency of the K ij interaction parameter is also presented.

Application of the CPA equation of state to glycol/hydrocarbons liquid–liquid equilibria

Abstract The Cubic Plus Association (CPA) equation of state is a thermodynamic model, which combines the well-known cubic SRK (Soave–Redlich–Kwong) equation of state and the association term proposed by Wertheim, typically employed in models like SAFT (statistical associating fluid theory). CPA has been shown in the past to be a successful model for phase equilibria calculations for systems containing water, hydrocarbons and alcohols. In this work, CPA is applied for the first time to liquid–liquid equilibria (LLE) for systems containing glycols and hydrocarbons. It is shown that excellent correlation is achieved with solely a single interaction parameter per binary system. The correlation procedure as well as the nature of the experimental data play a crucial role in the parameter estimation and they are thus extensively discussed.

Correlation of liquid-liquid equilibria for alcoholhydrocarbon mixtures using the CPA equation of state

Abstract A recently developed equation of state, which combines the physical term of the classical SRK EoS with the association term based on the perturbation theory of Wertheim, called the Cubic Plus Association Equation of State (CPA EoS) (Kontogeorgis et al. [1]), is applied to liquid-liquid equilibrium (LLE) calculations in alcohol hydrocarbon mixtures. The CPA EoS performs very well in all cases using the conventional van der Waals one-fluid mixing rules in the parameters of the physical term and a temperature-independent interaction parameter. The performance of the CPA EoS is compared to that of the conventional SRK EoS and UNIFAC models, and with another association model, the ESD EoS of Suresh and Elliott [2]. The CPA EoS gives much better results than the two conventional models and results comparable to those obtained with the ESD model.

Application of the van der Waals equation of state to polymers. I: Correlation

Kontogeorgis G.M., Harismiadis V.I., Fredenslund A., and Tassios D.P., 1994. Application of the van der Waals equation of state to polymers. I. Correlation. Fluid Phase Equilibria, 96: 65-92. A reliable methodology for evaluating the energy and co-volume parameters of cubic equations of state for polymers is proposed. Only two low-pressure volumetric data points are used. The procedure is applied to the van der Waals equation of state and bubble-point pressure calculations are performed for a number of polymer solutions. The usual combining and mixing rules are used. It is shown that the van der Waals equation can correlate the equilibrium pressures of polymer solutions using one binary interaction parameter. The accuracy of the correlation is very good; it is comparable to or better than that achieved using the Flory-Huggins model. It is also shown that the necessary binary interaction parameters for the van der Waals equation of state can be estimated using a simple scheme based on the Berthelot combining rule. It is, thus, demonstrated that the van der Waals equation of state can be a simple and successful tool for the description of the vapor-liquid equilibria in polymer solutions.

Prediction of solid–gas equilibria with the Peng–Robinson equation of state

Abstract 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.

Modeling the phase behavior in mixtures of pharmaceuticals with liquid or supercritical solvents.

The concept of solubility parameter, which is widely used for the screening of solvents in pharmaceutical applications, is combined with a thermodynamic theory that is able to model systems with large deviations from ideal behavior. The nonrandom hydrogen-bonding (NRHB) theory is applied to model the phase behavior of mixtures of six pharmaceuticals (i.e., ibuprofen, ketoprofen, naproxen, benzoic acid, methyl paraben, and ethyl paraben). The pure fluid parameters of the studied pharmaceuticals were estimated using limited available experimental (or predicted) data on sublimation pressures, liquid densities, and Hansens solubility parameters. The complex hydrogen-bonding behavior was explicitly accounted for, while the corresponding parameters were adopted from simpler molecules of similar chemical structure or/and fitted to the aforementioned pure fluid properties. In this way, the solubility of the studied pharmaceuticals in liquid solvents was calculated. The average root-mean-square deviation between experimental and calculated solubilities is 0.190 and 0.037 in log(10) units for prediction (calculations without a binary interaction parameter adjustment) and for correlation (calculations using one binary interaction parameter fitted to experimental data), respectively. In addition, using one temperature-independent binary interaction parameter the phase behavior of pharmaceuticals in supercritical CO(2) and ethane was satisfactorily correlated. Finally, preliminary encouraging results are shown concerning two ternary mixtures where the model is able to predict accurately the solubility of pharmaceuticals in mixed solvents based on interaction parameters fitted to corresponding single solvent data.

Modeling of Dielectric Properties of Aqueous Salt Solutions with an Equation of State

The static permittivity is the most important physical property for thermodynamic models that account for the electrostatic interactions between ions. The measured static permittivity in mixtures containing electrolytes is reduced due to kinetic depolarization and reorientation of the dipoles in the electrical field surrounding ions. Kinetic depolarization may explain 25-75% of the observed decrease in the permittivity of solutions containing salts, but since this is a dynamic property, this effect should not be included in the thermodynamic modeling of electrolytes. Kinetic depolarization has, however, been ignored in relation to thermodynamic modeling, and authors have either neglected the effect of salts on permittivity or used empirical correlations fitted to the measured static permittivity, leading to an overestimation of the reduction in the thermodynamic static permittivity. We present a new methodology for obtaining the static permittivity over wide ranges of temperatures, pressures, and compositions for use within an equation of state for mixed solvents containing salts. The static permittivity is calculated from a new extension of the framework developed by Onsager, Kirkwood, and Fröhlich to associating mixtures. Wertheims association model as formulated in the statistical associating fluid theory is used to account for hydrogen-bonding molecules and ion-solvent association. Finally, we compare the Debye-Hückel Helmholtz energy obtained using an empirical model with the new physical model and show that the empirical models may introduce unphysical behavior in the equation of state.