G. A. Mansoori

Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres

An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine‐calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine‐calculated data.

Variational Approach to the Equilibrium Thermodynamic Properties of Simple Liquids. I

A variational technique which is based on two different inequalities for the Helmholtz free energies is used to calculate the equilibrium thermodynamic properties of simple fluids. A system with hard‐sphere potential function is used as the reference system. Helmholtz free energy of the original system is calculated by variation around the Helmholtz free energy of the reference system, and the other thermodynamic properties are calculated from free energy. By choosing a hard‐sphere reference system, it is possible to calculate the equilibrium thermodynamic properties of fluids from very low densities to densities close to solid, and from high temperatures in the gas phase to low temperatures in the liquid phase, in the ranges where experimental and machine‐calculated data are available. It is shown that the present variational technique is a better approach to the prediction of the equilibrium thermodynamic properties of liquids and vapor–liquid phase transition than any other approach so far developed. W...

Identification and measurement of petroleum precipitates

Abstract A number of procedures to identify and measure the precipitates that result from petroleum fluids are presented. The fractions considered in this study include those in the categories of asphaltenes, resins, saturates (paraffin/wax), aromatics, inorganic minerals and diamondoids. A combination of deposition techniques, separation by centrifuge, filtration, gas chromatography, gel-permeation chromatography, and SARA (LC-HPLC) separations, and a number of other techniques are utilized to identify each fraction and quantify their concentrations. These procedures provide an understanding of the overall behavior of the species that precipitate as well as of the interactions among them. The results of such analysis are the cornerstone of any predictive and preventive measures for heavy organics deposition from petroleum fluids.

A cubic hard-core equation of state

In this work, a new method to determine a suitable repulsive term for cubic equations of state is introduced. Based on this method and by using a simplified molecular theory of hard-core fluids, a new two constant parameter cubic equation of state is presented. The proposed equation of state is applied for PVT and VLE calculations of different pure fluids and fluid mixtures. The results are compared with those obtained by two commonly used cubic equations of state. The comparisons indicate that the new equation of state yields better results.

Note on the Perturbation Equation of State of Barker and Henderson

Perturbation theory of equation of state due to Barker and Henderson is reformulated. This new formulation makes it possible to calculate the Helmholtz free energy of a fluid system analytically by perturbation relations of Barker and Henderson, without use of any approximation or need of any numerical table for the hard‐sphere reference system other than the original Percus–Yevick approximations. The results are compared with the calculation of Barker and Henderson, and it is shown that the two agree with each other at all the temperatures which are compared, while the present method produces compressibilities slightly closer to the experimental and machine‐calculated data. The results of the present method, based on average Percus–Yevick hard‐sphere compressibilities, are also compared with the result of other theories of equation of state of simple fluids, molecular dynamics, and Monte Carlo calculations.

Statistical mechanical description of supercritical fluid extraction and retrograde condensation

The phenomena of supercritical fluid extraction (SFE) and its reverse effect, which is known as retrograde condensation (RC), have found new and important applications in industrial separation of chemical compounds and recovery and processing of natural products and fossil fuels. Full-scale industrial utilization of SFE/RC processes requires knowledge about thermodynamic and transport characteristics of the asymmetric mixtures involved and the development of predictive modeling and correlation techniques for performance of the SFE/RC system under consideration. In this report, through the application of statistical mechanical techniques, the reasons for the lack of accuracy of existing predictive approaches are described and they are improved. It is demonstrated that these techniques also allow us to study the effect of mixed supercritical solvents on the solubility of heavy solutes (solids) at different compositions of the solvents, pressures, and temperatures. Fluid phase equilibrium algorithms based on the conformal solution van der Waals mixing rules and different equations of state are presented for the prediction of solubilities of heavy liquid in supercritical gases. It is shown that the Peng-Robinson equation of state based on conformal solution theory can predict solubilites of heavy liquid in supercritical gases more accurately than the van der Waals and Redlich-Kwong equations of state.

Variational Approach to Melting. II

A variational approach to the equilibrium thermodynamic properties of an original system based upon an inequality for the Helmholtz free energy of that system is introduced. A system with molecules obeying the cell model of Lennard‐Jones and Devonshire, and having a harmonic‐oscillator‐type potential function inside their cells, is used for a reference system to produce the inequality for the Helmholtz free energy of the original system. Optimization upon this inequality indicates that a variational calculation based on a reference system with highly ordered structure, as the cell model, predicts the properties of the solid phase better than the liquid phase. Also, it shows that by an ordered‐structure reference model, it is possible to predict the liquid–solid phase transition. Equilibrium thermodynamic properties of the solid phase and liquid–solid phase equilibria are calculated and are compared with the machine‐calculated and the experimental data.

Phase equilibrium calculations of highly polar systems

Benmekki, E.H. and Mansoori, G.A., 1987. Phase equilibrium calculations of highly polar systems. Fluid Phase Equilibria, 32: 139-149. It is well known that highly polar and hydrogen bonding mixtures pose a serious challenge to equations of state. In the present report it is shown that excellent correlations and predictions of complex systems can be achieved when the van der Waals mixing rules are properly associated with an equation of state. In this report the proper form of the van der Waals mixing rules is used with the Peng-Robinson equation of state to predict the vapor-liquid equilibrium properties of water-ketone, water-alcohol, alcohol-ketone, and other complex mixtures, which exhibit either positive or negative azeotropy, with au accuracy which was not achievable by the original form of Peng-Robinson equation of state of mixtures.

Optimized parameters and exponents of Mie (n,m) intermolecular potential energy function based on the shape of molecules

Through the use of the second virial coefficient data, optimized parameters and exponents of the Mie (n,m) potential energy function are derived for a number of symmetric groups of molecules. In the optimizations performed, parameters of the potential function are varied for each molecule, but the exponents of the potential function are taken as functions of the shape of the groups of molecules considered. It is concluded that the attractive exponent, m = 7, is shared by all the symmetric groups considered. The repulsive exponent, n, is varied according to the shape of the molecules. Also, in this report, newly calculated parameters of the Lennard-Jones (12,6) and Mie (14,7) potential energy functions for 33 different symmetric and nonsymmetric molecules are reported. Results indicate that, generally, the Mie (14,7) pair-potential energy function is a better fit for the second virial coefficient data than the Lennard-Jones (12,6) function.

Dense fluid theory of mixtures

Previous studies have indicated that most of the existing theories of mixtures tend to fail for solutions containing species with large molecular size and intermolecular energy differences. In this work a dense fluid mixture theory, which is similar to the mixture theory of imperfect gases, is introduced. This theory is applicable for mixtures of molecules with large size and energy differences. The new theory is shown to be successful in predicting properties of Lennard‐Jones fluid mixtures at, both, finite concentrations and infinite dilution.