Local Composition Mixing Rules Research Articles

Helmholtz energy, extended corresponding states and local composition model for fluid mixtures

We present a model for the calculation of mixture properties. This model is based on the mixture residual Helmholtz energy given by the sum of two terms: one is the residual Helmholtz energy calculated by an extended corresponding states (ECS) model while the other is a correction term. The ECS model is based on methane as the reference fluid and shape factors that carry out the scaling of properties between the fluid of interest and the reference fluid. These shape factors are given by correlations in terms of reduced temperature and density. The application to mixtures is carried out with the one-fluid van der Waals mixture model. The correction term is temperature- and density-dependent as is given by a local composition mixing rule. Local compositions were calculated from a coordination number model based on lattice gas theory. With respect to binary-mixture properties, densities were calculated with an average absolute deviation (AAD) of 0.12%; speeds of sound were calculated with an AAD of 0.16% and bubble pressures were calculated with an AAD of 1.77%. Also, natural gas densities were calculated with AAD of 0.03% and natural gas speeds of sound were calculated with AAD of 0.049%. All these results are very satisfactory when compared with those obtained by modern mixture models.

Cubic Equation of State and Local Composition Mixing Rules: Correlations and Predictions. Application to the Solubility of Solids in Supercritical Solvents

A family of new mixing rules for the cubic equation of state through a synthesis between the classical van der Waals mixing rule and the local composition concept is proposed. The binary interaction parameter in the van der Waals mixing rule, which is devoid of physical meaning, is thus replaced with a more physically meaningful parameter. The new mixing rules were used to correlate the dependence on pressure of the solubilities of a number of solid substances, including penicillins, in supercritical fluids. Because the new mixing rules contain physically meaningful parameters, dependent on the energies of the binary intermolecular interactions, the calculations of those energies can allow one to predict the solubilities of solids in supercritical fluids. Such predictions were made for the solubility of solid CCl4 in the supercritical CF4. The required binary intermolecular energies were computed with the help of quantum mechanical ab initio calculations, and a good agreement between the predicted and exp...

New local composition model and mixing rule for the mixtures asymmetric both in size and energy

A new DDLC (density dependent local composition) model which possesses sound theoretical background describing both size and energy asymmetries of molecules has been developed. Dividing the radial distribution function into packing and attractive effects new local composition model naturally satisfies high and low density boundary conditions and it shows desirable characteristics to represent computer simulated local composition data correctly. Based on the new local composition model, DDLC mixing rule for the cubic equation of state has been derived and utilized to calculate the solubilities of solids in supercritical fluid mixtures. It has been found that new version of DDLC mixing rule shows excellent capabilities to predict solubilities of solids in various supercritical fluid systems including solid mixtures or entrainers.

Simulation of binary refrigerant mixture vapor-liquid equilibria using a quasi-regular nonrandom fluid theory and local composition mixing rules

A new model and a novel approach are presented for correlation/prediction of refrigerant mixture phase equilibria. The excess Gibbs free energy in binary halogenated alkane mixtures is described by a recently proposed two-liquid theory with a regular solution reference for mixtures of nonpolar species. The single g E model parameter, obtained by correlating near-ambient binary vapor-liquid equilibria (VLE), is used in Wong-Sandler mixing rules in the Peng-Robinson-Stryjek-Vera equation of state to predict binary VLE at elevated temperatures. This model is applied to the tetrafluoromethane-chlorotrifluoromethane (R14-R13), tetrafluoromethane-trifluoromethane (R14-R23), and the trifluoromethane-chlorotrifluoromethane (R23-R13) binary systems. The one-parameter quasi-regular g E model provides good correlation of VLE for the binary systems at near ambient conditions. However, successful prediction of high temperature VLE depends on the accuracy of the g E model, the consistency of the EOS mixing rule model, and the method used to solve the model equations and associated material balances.

The MKS-EOS with new mixing rules: the MKS/1 model

The MKS-EOS proposed by Chu et al. (1992) has been further improved in order to apply it to near-critical, polar, and highly asymmetric gas condensate mixtures. The Kurihara density-independent local-composition mixing rule for the energy parameter a has been included (Kurihara et al., 1987), and test results for selected high quality VLE data indicate that a net improvement is obtained for polar mixtures.

High Pressure Solubility of Carbon Dioxide and Carbon Monoxide in Dimethyl Ether

An apparatus has been constructed for precisely measuring the solubility of gases in liquids. The equipment is designed for use at temperatures from 0 to 200 o C and pressures up to 18 MPa. Measurements were made on carbon dioxide (1) + dimethyl ether (2) at three isotherms in order to verify the apparatus and techniques by comparing with data from the literature. Measurements were also made on the system carbon monoxide (1)+dimethyl ether (2) which has not been previously studied. The results have been correlated using the Soave-Redlich-Kwong equation of state. Two different local composition mixing rules have been used: the MHV2 mixing rule in combination with the modified UNIFAC model and the MHV2 mixing rule in combination with the original UNIQUAC model

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.

Application of the CORGC equation of state with a new mixing rule to polar and nonpolar fluids

Abstract This paper presents a new group contribution equation of state (EOS) applicable to both polar and nonpolar compounds. This EOS is based on the chain-of-rotator group contribution (CORGC) equation considering an NRTL type local composition mixing rule. The parameters for 37 organic and inorganic groups have been calculated. Several pure components and mixtures have been studied including polar and multicomponent systems. Comparison between the predicted and experimental thermodynamic properties are also presented.

High-pressure phase equilibria for carbon dioxide-methanol-water system: experimental data and critical evaluation of mixing rules

Equilibrium phase compositions for the carbon dioxide-methanol-water system were measured at 313.2 K and pressures of 70, 100, and 120 bar. Three-phase equilibria for this system were also measured at 305.15, 308.15, and 311.15 K, temperatures and pressures near the critical point of carbon dioxide. The two- and three-phase equilibrium data were correlated with the Soave-Redlich-Kwong and Patel-Teja equations of state incorporated with various types of the local composition and Huron-Vidal mixing rules. The Huron-Vidal mixing rules were found to be superior to the local composition models in predicting two-phase equilibria. Since the pressure range covering the three-phase region was very narrow, the Huron-Vidal mixing rules could not accurately predict the experimental three-phase equilibria. However, if there were a slight change of pressure in phase calculation, the Huron mixing models could correctly predict the experimental three-phase region and equilibrium compositions

Isothermal vapor-liquid equilibrium data for the binaries propane-2-propanol and propylene-2-propanol

Vapor-liquid equilibria for the 2-propanol-propane and 2-propanol-propylene systems were measured in the temperature range of 313-370 K, and at pressures up to 40 bar. The results show no azeotrope formation in either of the systems studied. The data were correlated using the Soave-Redlich-Kwong (SRK) equation of state with local composition mixing rules, and a group contribution equation of state (GCEOS).

The experimental determination and modelling of VLE for binary subsystems of the quaterhary system N 2 + CH 4 + C 4H 10 + C 14H 30 UP to 1000 bar and 440 K

As a part of a laboratory study on nitrogen displacement in light-oil reservoirs, in which a mixture of methane, butane and tetradecane is used as a model oil, the phase behaviour of the binary subsystems of the quaternary system nitrogen + methane + butane + tetradecane is investigated in the temperature and pressure range of interest. The phase behaviour of the binary systems nitrogen + methane and methane + butane is known from literature. VLE of the binary systems nitrogen + tetradecane and methane + tetradecane were determined experimentally at 320 – 440 K according to the synthetic method using a high pressure cell with sapphire windows. VLE of the binary system butane + tetradecane were determined experimentally in the same temperature range according to the same method but now using the so-called Cailletet equipment. The experimental data were fitted using several equations of state in combination with a number of mixing rules. It is found that local composition mixing rules of the Huron-Vidal type and density dependent mixing rules as used by Mohammed and Holder and a new density dependent mixing rule, are superior to the conventional mixing rules with one or two binary interaction parameters. With these improved mixing rules a satisfactory description of the experimental data, even at pressures as high as 1200 bar can be realized.

摂動型状態方程式による超臨界流体に対する高沸点化合物の溶解度の相関

A perturbed-hard-sphere equation of state (PHS-EOS) was applied to correlate the solubilities of high boiling compounds such as coal liquefaction products in supercritical fluids. A suitable mixing rule for the constants contained in the PHS-EOS is needed to apply the equation of state to a mixture composed of high boiling compound and supercritical fluid. In this study, mixing rules for the constants were examined and discussed. It was found that a local composition mixing rule with three characteristic parameters introduced into both molecular attraction and molecular size terms gives a good result because the solubility is quite small near infinite dilution.

A study of density-dependent local composition mixing rules for prediction of multicomponent phase equilibria

Density-dependent local composition (DDLC) mixing rules have the potential to correlate highly non-ideal systems. These rules were thoroughly tested for their ability to correlate binary systems and to predict multicomponent systems with a Carnahan-Starling-Redlich-Kwong-UNIQUAC model. It is concluded that prediction results for multicomponent systems are generally superior with the non-conformal model. Nevertheless, in many cases the conformal mixing rules predicted results comparable with the local composition model.

A new mixing rule for the Patel-Teja equation of state. study of vapor-liquid equilibria

The Patel-Teja equation of state (PT EOS), coupled with the new mixing rule for the energy parameter ( a) developed by Kurihara et al. (1987), has been successfully applied to vapor-liquid equilibrium (VLE) calculations for strongly non-ideal mixtures. Three excess Gibbs energy ( g E) models—Wilson, NRTL and UNIQUAC—were used to represent the residual part of excess Gibbs energy at infinite pressure ( g E∞) in the new mixing rule. The UNIQUAC model is recommended. Fourteen sets of low pressure and eight sets of high pressure binary/ternary VLE data were examined. For low pressure VLE calculations, comparable results were obtained using the activity coefficient approach, the EOS density dependent local composition mixing rule approach, and the proposed new model. The chief advantages of the new model lie in its applicability to high pressure VLE calculations, its improved liquid density predictions, its capacity to describe liquid-liquid equilibria, and its retention of the simple cubic EOS form.

Density-dependent local-composition mixing rules for cubic equations of state

A computer simulation technique (Monte Carlo method) using 256 particles was carried out to determine the local compositions of the “LB 2” model mixture, and the local composition ratio τ ij (r) was found to be density dependent. A mole fraction dependence was introduced in this work instead of the density dependence and used to develop the Wilson type and Renon-Prausnitz type mixing rules for the parameters “a” and “b” of the van der Waals equation. However, the calculated vapor-liquid equilibrium values indicate that strong density dependence of local composition mixing rules is not generally necessary in VLE calculations using cubic equations of state.

Excess enthalpies of {x(CH3)2CO+(1–x)C6H14} in the supercritical region

Excess molar enthalpies HmE of acetone–n-hexane mixtures have been measured at the critical temperature 493.2 K of the x= 0.5 mixture, and at the supercritical temperatures 510.2, 523.2 and 548.2 K. The HmE measurements for {x(CH3)2CO+(1–x)C6H14} were made at fixed mole fractions x at pressures up to 7.94 MPa. At 510.2 K measurements were made at x= 0.25, x= 0.50 and x= 0.75, but at all other temperatures the measurements were made at x= 0.50 only. The HmE values measured at 493.2 K have been combined with the enthalpies of acetone and n-hexane to obtain the enthalpy vs. pressure isotherm at the critical temperature Tc(x= 0.5) of the mixture. The HmE values in the supercritical region exhibit double maxima similar to those observed for carbon dioxide–ethane mixtures at supercritical temperatures. The double maxima fade as the temperature increases. The shape of the HmE against p graphs is well reproduced by the Patel–Teja equation of state using k12= 0.14 in the combining rule a12=(1 –k12)(a11a22)1/2. Density-dependent local composition mixing rules were found not to improve the fit to the measurements. The Patel–Teja equation has been used to explore the shape of the HmE(x,p,T) surfaces in the supercritical region. The surfaces are similar to those for carbon dioxide–ethane mixtures.

A new density-dependent mixing rule for the SRK equation of state

A new procedure for obtaining density-dependent mixing rules is applied to the Soave-Redlich-Kwong equation of state. The result is a one-parameter local-composition mixing rule which adequately represents the nonidealities possible in dense fluid mixtures but approaches the classical mixing rule at low densities. A three-parameter version of the mixing rule is also presented which allows for the local-composition effect in the low density limit. The expressions are tested with the Soave-Redlich-Kwong equation of state. Results for vapor-liquid and gas-liquid systems are discussed.

Representation of the vapor-liquid equilibrium of the ternary system carbon dioxide - propane - methanol and its binaries with a cubic equation of state : a new mixing rule

Erroneous liquid phase splitting is often predicted when correlating the vapor-liquid equilibrium of alcohol-alkane systems with a cubic equation of state. It is shown that even the local-composition mixing rules are not sufficiently flexible for an accurate representation of the propane-methanol system, and a new empirical three-parameter mixing rule is introduced. The ternary system carbon-dioxide - propane - methanol is well-predicted from the binary data.

Cubic chain-of-rotators equation of state with density-dependent local composition mixing rules

A local comparison form fo the Cubic Chain-of-Rotators (CCOR) equation of state is developed for the description of molecular fluid mixtures. The density dependent local composition expression obtained from a recent computer simulation of square-well molecules is used in the development. Calculations from the CCOR equation of state in both the local composition form and the classical one-fluid mixing form are compared with vapor-liquid equilibrium data on a number of polar fluid mixtures.

High-pressure vapor-liquid equilibria with cubic equations of state

This paper considers the prediction of high-pressure VLE with cubic equations of state, extending work presented at the 1984 Otto Redlich symposium (Tsonopoulos and Heidman, 1985). Three cubic equations of state are examined: Redlich-Kwong-Soave, Peng-Robinson, and the cubic chain-of-rotators. The capabilities of these equations are tested against vapor pressure data for selected components and VLE data for mixtures containing H 2, CO 2, or water. Both conventional and the more recent local composition mixing rules are used in the calculations, and correlations are presented for the binary interaction parameter used in the conventional mixing rules.