Soave Equation Of State Research Articles

Entropy production minimization in a multicomponent diabatic distillation column

This work presents a procedure for direct numerical minimization of entropy production in a diabatic tray column with heat exchanged on the trays as control variables, as opposed to previously used procedures with temperature on the trays as control variables. The procedure, which had previously been demonstrated on a binary mixture, was in this work applied to a multicomponent mixture, with minor modifications. The procedure comprised the complex optimization method and the Ishii-Otto method for solving the equations of a column model based on the iterative Newton-Raphson technique with partial linearization of the equations. The desired separation of the components was realized by the addition of a penalty function to the goal function, i.e. entropy production in the column. The required thermodynamic characteristics were calculated by the Soave equation of state. As an illustration, an industrial debutanizer with five components was used whose data, obtained by simulation, were compared with the optimization results of a diabatic column with the same desired separation and number of trays. After the diabatic column optimization procedure, the value of 91.91 J/Ks was obtained as the best result for entropy production. According to the best solution, entropy production in the diabatic column was 23.2% lower than in the adiabatic column. The heat to be removed from the column increased by 24.7%, while the heat to be added to the column increased by 28.8%.

Multiphase Equilibrium Calculations from Soave Equation of State with Chang-Twu/UNIFAC Mixing Rules for Mixtures Containing Water, Alcohols, and Esters

Various versions of the Soave–Redlich–Kwong (SRK) equation of state incorporating different mixing rules were applied to calculate vapor–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), and vapor–liquid–liquid equilibrium (VLLE) properties for the systems containing water, alcohols, and esters. The calculated results showed that the SRK equation with the T-type α function and the Chung–Twu (CT) mixing rules embedded in the UNIFAC–Lyngby model (SRK-T/CT–UNIFAC– Lyngby) not only predicts accurately the VLE properties of the constituent binaries but also represents the ternary LLE and VLLE phase behavior reasonably well. Using this model, the vapor pressure data of the pure constituent components are the only required property for the phase equilibrium calculations.

Development of a Kinetic Model for Supercritical Fluids Fischer−Tropsch Synthesis

Kinetic models for Fischer−Tropsch synthesis (FTS) were derived to express the reaction behavior in either conventional reaction media (gas-phase) or nonconventional media (near-critical and supercritical solvent media). These models we developed from experimental data generated from a commercial alumina supported cobalt catalyst (15% Co/Al2O3) in a fixed bed reactor. Two models were developed: the first one assumes ideal gas phase behavior for the gas phase reaction and uses partial pressures to express reactant and product concentrations in rate expressions while the second model accounts for the nonideal behavior of the reaction mixture under elevated pressures via the utilization of fugacity parameters and fugacity coefficients. The fugacity coefficients were estimated from a modified Redlich−Kwong−Soave equation of state. A comparison was conducted between the estimated kinetic parameters from the fugacity-based kinetic model and the partial pressure based kinetic model. The heat of adsorption of car...

A new approach to entropy production minimization in diabatic distillation column with trays

Previous approach to direct numerical minimization of entropy production in diabatic distillation column in order to determine heat quantity to be exchanged at trays was based on temperatures on trays as control variables and it was applied only to simple binary columns. Also, previously developed theoretical models for determining optimal exchanged heat profile were determined only at such columns and while they were approximated they produced worse results than numerical minimum of entropy production. In this paper, as control variables for minimization, exchanged heat on the trays is used. It enables application to complex multicomponent diabatic columns. Ishii-Otto global method, based on model linearization and iterative solution by Newton-Raphson technique, is applied for solving column mathematical model. Needed thermodynamical properties for ideal systems are calculated using Lewis-Randall ideal solution model, and for non-ideal slightly polar systems they are calculated using Soave equation of state. Five direct methods are used for numerical optimization. Applied approach is successfully demonstrated at frequently used example of distillation of benzene and toluol mixture by using for these purposes specially written program. Simplex method appeared to be the most convenient optimization method for the considered problem.

Solubility of Carbon Dioxide and Hydrogen Sulfide in Aqueous N-Methyldiethanolamine Solutions

In this work, 72 new experimental solubility data points for H2S and CO2 mixtures in aqueous N-methyldiethanol amine (MDEA) solutions at different methane partial pressures (up to 69 bara) are presented. They are correlated using an electrolyte equation of state (E-EOS) thermodynamic model. This model has already been used to estimate the CO2 solubility in aqueous MDEA (Huttenhuis et al. Fluid Phase Equilib. 2008, 264, 99−112) and the H2S solubility in aqueous MDEA (Huttenhuis et al. Int. J. Oil, Gas Coal Technol. 2008, 1, 399−424). Here, the model is further extended to predict the behavior of CO2 and H2S when they are present simultaneously in aqueous MDEA. The application of an equation of state is a new development for this type of system, i.e., of acid-gas−amine systems. The molecular interactions are described by Schwarzentruber et al.’s modification of the Redlich−Kwong−Soave equation of state, with terms added to account for ionic interactions in the liquid phase. The model is used to describe aci...

Vapor−Liquid Equilibria for the 1,1-Difluoroethane (HFC-152a) + Propane (R-290) System

Isothermal vapor−liquid equilibrium data of the binary system 1,1-difluoroethane (HFC-152a) + propane (R-290) were measured in the temperature range from 273.15 K to 313.15 K at 10 K intervals and in the composition range from 0.2 to 0.8 mole fraction of propane. The temperature, pressure, and compositions of the liquid and vapor phases were measured with a circulation-type apparatus. The experimental data were correlated with the Carnahan−Starling−De Santis, Peng−Robinson, and Redlich−Kwong−Soave equations of state. Azeotropic behavior was revealed near 0.73 mole fraction of propane. The vapor pressure of the azeotropic system was compared with those of chlorodifluoroethane (HCFC-22) and the zeotropic mixture of difluoroethane (HFC-32) + pentafluoroethane (HFC-125) (50−50) (alternative refrigerant blend R-410A), the zeotropic mixture of HFC-32 + HFC-125 + 1,1,1,2-tetrafluoroethane (HFC-134a) (23−25−52) (alternative refrigerant blend R-407C), dichlorodifluoromethane (HCFC-12), and HFC-134a. It was found t...

Calculating the Liquid–Gas Equilibrium in the Fischer–Tropsch Synthesis

The problem of determining the equilibrium composition of the gas phase from the known composition of the liquid phase is analyzed in terms of the Redlich–Kwong–Soave equation of state modified by Wang. An effective algorithm is suggested for solving this problem for systems with an arbitrary number of components. The molecular-weight distribution of the Fischer–Tropsch synthesis products can be estimated by calculating the composition of the gas phase from composition data for the liquid phase resulting from the reaction.

Vapor−Liquid Equilibria for the Pentafluoroethane (HFC-125) + Propane (R-290) System

Isothermal vapor−liquid equilibrium data of the binary system pentafluoroethane (HFC-125) + propane (R-290) were measured in the temperature range from 273.15 K to 313.15 K at 10 K intervals and in the composition range from 0.1 to 0.8 mole fraction HFC-125. Temperature, pressure, and compositions of the liquid and vapor phases were measured with a circulation-type apparatus. The experimental data were correlated with the Carnahan−Starling−De Santis, Peng−Robinson, and Redlich−Kwong−Soave equations of state. Azeotropic behavior was revealed near 0.77 mole fraction HFC-125. The vapor pressure of the azeotropic system is between those of chlorodifluoromethane (HCFC-22) and the zeotropic mixture of difluoroethane (HFC-32) + HFC-125 (50−50). This azeotropic system hasu good potential to replace the use of HCFC-22 as a refrigerant.

Vapor−Liquid Equilibria for the Difluoromethane (HFC-32) + Pentafluoroethane (HFC-125) System

Isothermal vapor−liquid equilibrium data of the binary system difluoromethane (HFC-32) + pentafluoroethane (HFC-125) were measured in the temperature range from 268.15 K to 308.15 K at 10 K intervals and in the composition range from 0.1 to 0.8 mole fraction. Temperature, pressure, and compositions of the liquid and vapor phases were measured with a circulation type apparatus. The experimental data were correlated with the Carnahan−Starling−De Santis, Peng−Robinson, and Redlich−Kwong−Soave equations of state.

Concentrating Glycerol Mixed with Fatty Acids and Water by Supercritical Fluid Extraction

The binary solubilities of palmitic acid, stearic acid, oleic acid, and water in carbon dioxide under supercritical conditions were calculated by the Soave equation of state with empirical intermolecular interaction parameters. It was demonstrated that supercritical fluid extraction can be used for concentrating glycerol in raffinate and for separating fatty acids. Both batch and circulation extraction techniques were tested in concentrating glycerol.

Analysis of a Two-Phase Perfectly Mixed Reactor under the Condition of a Phase Equilibrium

A mathematical model is formulated for a gas–liquid perfectly mixed flow reactor under the condition that the two-phase flow at the reactor outlet is at thermodynamic equilibrium. The phase equilibrium is calculated using the Redlich–Kwong–Soave equation of state. The set of nonlinear algebraic equations of the model is numerically solved by the efficient algorithm of the homotopy method. The steady-state modes of reactor operation are analyzed for liquid-phase benzene hydrogenation. It is shown that, under isothermal isobaric conditions, there can be a multiplicity of steady-state solutions, which is, on the one hand, due to the nonlinearity of the kinetic law and, on the other, due to the deviation of the properties of the reaction mixture from the properties of an ideal system. The stability of the steady-state solutions is analyzed, and the causes of the multiplicity and instability are explained.

Phase Equilibria of R22 (CHClF2) Hydrate Systems in the Presence of NaCl, KCl, and MgCl2

The three-phase (hydrate−aqueous liquid−vapor) equilibria of the R22 (CHClF2 = chlorodifluoromethane) hydrate forming systems in aqueous solutions containing NaCl, KCl, and MgCl2 were measured at pressures ranging from 0.140 to 0.790 MPa, temperatures between 273.9 and 287.8 K, and several compositions of each electrolyte. The upper quadruple points (hydrate−liquid R22−aqueous liquid−vapor) were also measured at each electrolyte concentration. The addition of electrolytes to the aqueous solutions caused inhibition of the hydrate formation. A thermodynamic model that predicts the three-phase hydrate equilibria was developed. The inhibiting effect of electrolytes was accounted for using a Pitzer model. A van der Waals and Platteeuw model and Redlich−Kwong−Soave equation of state with a modified Huron−Vidal mixing rule were used. The calculated results were found to be in good agreement with the experimental data.

Phase Equilibria of Carbon Dioxide Hydrate System in the Presence of Sucrose, Glucose, and Fructose

The three-phase (H−Lw−V) equilibria of the carbon dioxide hydrate formation system in aqueous solutions containing sucrose, glucose, and fructose were experimentally determined at pressures ranging from 1.580 to 4.355 MPa and at temperatures between 273.6 and 281.7 K. The upper quadruple points (H−Lw−LCO2−V) were also measured at concentrations of 10, 20, and 30 mass % sucrose, glucose, and fructose. The addition of carbohydrates exhibited a similar inhibition effect as that observed for electrolytes and alcohols. A thermodynamic model predicting the three- and four-phase hydrate equilibria while accounting for the inhibition effect of carbohydrates was developed on the basis of the van der Waals−Platteeuw model and the Redlich−Kwong−Soave equation of state with a modified version of the Huron−Vidal mixing rule. The calculated results were found to be in good agreement with the experimental data.

Pressure–volume–temperature behavior of binary mixtures of hydrogen fluoride with HCFC-22, HFC-32 and HFC-134a

Vapor phase pressure–volume–temperature ( P– V– T) measurements have been performed for binary mixtures of hydrogen fluoride (HF) with three different alternative refrigerants. A total of 62 mixtures were tested at temperatures ranging from 283.15 to 343.15 K. Pressures ranged from 100 to 1400 kPa, and HF concentrations varied from about 0.2 to 0.9 mole fraction HF. Several data were also obtained for the system HF/Nitrogen at 323.15 K. Data have been compared to a model based on a monomer–hexamer chemical association model and the Soave equation of state. Deviations in compressibility factors between the model and the experimental data averaged 1.5%.

Group-Contribution Equation of State for the Prediction of Vapor−Liquid Equilibria of Mixtures Containing Hydrofluorocarbons and Alkanes

This work is aimed to present and validate a thermodynamic model that enables the prediction of vapor−liquid equilibria of refrigerant mixtures of alkanes and hydrofluorocarbons, in the temperature and pressure ranges of interest for refrigeration cycles and heat pump applications. A modified Redlich−Kwong−Soave equation of state is used with Huron−Vidal mixing rules and a modified UNIFAC group-contribution approach for calculating the component infinite-pressure activity coefficients. A new classification of functional groups is suggested, and the values of interaction parameters between groups are provided. These parameters are regressed from selected binary vapor−liquid equilibrium data. A good regression is obtained for all group pairs, with a maximum root-mean-square deviation on relative pressure residuals of 1.86%. The proposed method is totally predictive since only the structure, critical constants, and vapor pressure of pure components are needed in order to calculate thermodynamic properties of...

Influence of the mixing rule on the liquid-liquid equilibrium calculation

Liquid-liquid equilibrium data were correlated with three mixing rules that incorporate excess Gibbs energy model into a equation of state: Wong-Sandler, Heidemann-Kokal and MHV2 methods. The Soave equation of state is employed to several binary mixtures, coupled with NRTL, UNIQUAC and UNIFAC models for excess Gibbs free energy. The best results for binary mixtures were obtained with NRTL and Wong-Sandler, then this combination was used to predict the ternary liquid-liquid equilibria.

Asphalt flocculation and deposition: I. The onset of precipitation

AbstractFormation of asphalt aggregates and their deposition on the pore surfaces of a porous medium, which alter the structure of the medium and its effective properties, is a critical problem to catalytic and oil recovery and refinery processes. Extensive new experimental data for the amount of precipitated asphalt formed with crude oil and various solvents are presented. Results indicate that, contrary to the previous assumptions, asphalt formation is at best partially reversible. A thermodynamic model based on the Flory–Huggins theory of polymer solutions is used, together with the Soave equation of state, to predict the data. Critical evaluation of the model shows that its predictions do not agree well with our data. As an alternative, we propose a new model that employs a scaling equation, somewhat similar to those encountered in aggregation and gelation phenomena. The scaling function takes on a very simple form, and its predictions are in very good agreement with the data. It also predicts that the onset of precipitation may obey a simple universal equation.

A simulator for the study of phase behaviour based on the SOAVE equation of state and material balance calculations.

This paper shows the predictive features, speed and accuracy of a phase behavior simulator which calculates and analyzes the vapor-liquid equilibrium of volatile oils and gas condensates. The simulator calculates the PVT properties (gas volumetric factor (Bg), oil volumetric factor (Bo), gas/ oil ratios (Rso, Rsg) required by reservoir simulators and used in two-phase flow equations and reservoir material balances.The model uses the Soave-Redlich-Kwong equation of state (SRK-EOS) to predict phase behavior without any parameter adjustment. lt only utilizes the concept of volume translation and a simple C7+ characterization. A rigorous material balance checks the consistency of the measured PVT data and· calculates properties such as: liquid composition at different pressures, K values, molecular weight, liquid densities and PVT properties, among others. The C7+ characterization method used by the simulator was compared to that presented by Pedersen et al. (1984). The CPU time in the constant volume depletion test (CVD) was significantly reduced (up to 80%) by using the simple C1+ characterization method.

Liquid-liquid equilibria with an equation of state based on the significant structure model

Liquid-liquid equilibrium data for class II + class V, class I + class II, and class I + class V mixtures were correlated with a recently proposed equation of state (EOS) and local composition mixing rules. It was found the Suzuki EOS with the local composition mixing rules was successful in correlating liquid-liquid equilibrium data for mixtures of an alcohol and shorter chain hydrocarbons (class II + class V) with two interaction parameters, k ij and l ij, which correct the interaction energy and the local composition terms. However, for alcohol and long chain hydrocarbon mixtures, we found that only qualitative agreement was possible for the more polar phase. This can be explained in terms of the dielectric constants of the pure components. For class I + class II mixtures and class I + class V mixtures, the local composition mixing rules gave fair agreement with the data. Correlation of the data with random mixing rules is also shown for comparison along with the Soave EOS equation. It was found that both the Soave EOS and Suzuki EOS produced similar results with random mixing rules and that the liquid density had little effect on the calculations.

Comparison between a noncubic equation of state particularly suitable for polar fluids and the Soave equation of state

Recently, Brandani et al. (1992) have presented a new equation of state based on theoretical results of a system of hard spheres with dipoles and on the computer simulation data for n-butane. This new equation of state was applied to the correlation of thermodynamic properties for 10 pure polar and nonpolar fluids. In the communication, the new equation of state has been tested using a data base constituted by the vapor pressures of 59 pure polar and nonpolar fluids. The aim was to find a correlation for the two adjustable parameters of the equation as a function of the acentric factor. The results were compared with those obtained using the equation of state of Soave (1972), which is widely used by chemical engineers for VLE calculations, even for polar substances (Bazua, 1983; Joffe et al., 1983)