I. V. Derevich

Liquid-vapor thermodynamic equilibrium in Fischer-Tropsch synthesis products

A modified Peng-Robinson equation of state is used to develop the methods for calculating the liquid-vapor thermodynamic equilibrium in Fischer-Tropsch synthesis products. The critical thermodynamic parameters of paraffin and olefin hydrocarbons with a number of carbon atoms higher than 20 are determined using the correlations proposed in the present paper. The calculated results are compared with literature data and the data obtained in the Integrated Research and Development Center.

Calculation of the reforming of oil gas by minimizing the gibbs free energy

The Gibbs free energy minimization method is used to calculate the equilibrium of a system with chemical transformations. The advantages of this method over a conventional method for calculating the equilibrium using a set of hypothetical chemical reactions are discussed. The results of calculating the equilibrium compositions in steam, oxygen, and carbon dioxide reforming of oil gas are presented.

Calculating the Parameters of Heat Transfer between Countercurrent Flows with Variable Thermophysical Properties

A method is developed for calculating the parameters of heat transfer between heat-transfer media with highly variable properties in a countercurrent heat exchanger. It is based on a stable converging algorithm that minimizes a given functional and is similar to the shooting method for solving ordinary differential equations. Heat-transfer parameters are calculated for sub- and supercritical pressures. The calculated results are compared with observed data.

Extraction of organic oil from sea buckthorn seeds with supercritical carbon dioxide

The extraction of fatty acids and their derivatives from sea buckthorn seeds with supercritical carbon dioxide is experimentally studied. A theoretical model of supercritical extraction of organic oil is constructed. The thermodynamics of dissolution of high-molecular-weight substances under supercritical conditions is described in terms of the Redlich–Kwong equation of state. The diffusion of macromolecules of substances contained in organic oil in seed pores is described using a model of a contracting core. The calculated results are compared to experimental data. The pseudocritical parameters of organic oil and its saturation vapor pressure are estimated.

Calculating the dynamic viscosity of individual substances using the Peng-Robinson equation

A method for calculating the dynamic viscosity of individual compounds in the liquid and gaseous states has been developed using Eyring and Frankl’s “excited zone” formation hypothesis. In this method, the activation energy is estimated in terms of the deviation of the enthalpy of the substance from the ideal-gas approximation. This deviation is calculated using the Peng-Robinson equation f state. The expressions obtained for viscosity contain a constant, whose value is the same for a wide variety of compounds. The results of these calculations are compared with experimental data for the viscosity of liquids and vapors along the saturation line and isobars, including supercritical pressures.

Thermodynamic model for the formation of solid paraffinic compounds in petroleum

A new model for the formation of solid compounds in petroleum is proposed. The model is based on the assumption that the solid precipitates are composed of pure immiscible heavy hydrocarbons. The weight of solid waxes is calculated using the direct numerical minimization of the Gibbs free energy of a two-phase multicomponent liquid solution-solid precipitate system. The hydrocarbon is precipitated from the solution only when the thermodynamic condition accounting for the formation of the solid phase for this component is met. The simulated results are compared with the experimental data obtained for artificial solutions and natural oils. The approach proposed in the present paper generalizes the models existing in this area.

Composition and temperature of the multicomponent liquid-vapor system under isoenthalpic pressure variations

A method based on Gibbs energy minimization is suggested for calculating the equilibrium composition of multicomponent liquid-vapor two-phase systems under isoenthalpic pressure variations. The numerical computational procedure invokes ideas of statistical physics and nonequilibrium thermodynamics. The thermodynamic parameters of the solution and vapor are determined using a cubic equation of state. The computational method is illustrated by particular calculations and by comparisons between calculated and experimental data.

Modeling of the Solubility of Solid High-Molecular-Weight Organic Substances in Supercritical Fluids

A method is proposed to calculate the solubility of solid high-molecular-weight substances in organic supercritical fluids on the basis of the Soave and Peng–Robinson equations of state. The mixing rules are modified taking into account the Gibbs energy of mixing calculated for a particular equation of state. The accuracy of calculation of the concentration of the substance dissolved in supercritical fluids is analyzed for different mixing rules. The modeling results are compared with observed data.

Calculation of solution-vapor thermodynamic equilibria by the method of minimizing the Gibbs energy

An algorithm of direct numerical minimization of the Gibbs energy for calculating the liquid-vapor thermodynamic equilibrium in multicomponent systems is proposed. The method makes it possible to simultaneously determine the distributions of concentrations in the vapor and solution and the vapor mole fractionwhen the temperature, pressure, and initial mixture composition are given. The developed algorithm is distinguished from the existing equilibrium calculation methods by a higher stability and the capability of obtaining solutions in the range of parameters in which the conventional algorithms are not able to produce a physically meaningful result. The Peng-Robinson equation of state is used to simulate the Gibbs energy. The accuracy of the proposed algorithm is illustrated by comparison with experimental data.

Semiempirical model of carbon dioxide boiling in tubes

A mathematical model of the evaporator of a heat pump with carbon dioxide as a working medium and water as a heat-transfer medium is constructed and used to calculate the hydrodynamic and heat-and mass-transfer processes in boiling liquid convection, liquid film evaporation, film breakup, drop settling, and disperse flow. The coupled heat transfer between the working medium and the heat-transfer medium in a countercurrent evaporator is considered. The calculation results are compared with the experimental data.