Composition-dependent Mixing Rules Research Articles

PVTx properties of H 2O–H 2S fluid mixtures at elevated temperature and pressure based on new experimental data

The volumetric properties of H 2O–H 2S fluid mixtures have been determined experimentally at temperatures of 150 to 400 °C and pressures up to 240 bar. Using these data and existing equations of state, we have developed a thermodynamic model for H 2O–H 2S fluid mixtures. This model is based on an asymmetric description of phases, which includes an activity model and a P–T-dependent Henry’s law constant for the liquid, and equations of state with mixing rules for the vapour. The fugacity of the vapour was calculated using the cubic equations of state of Peng and Robinson (1976) and Patel and Teja (1982) with density-dependent and composition-dependent mixing rules. Sets of binary interaction parameters for these equations were fitted to the experimental data obtained in this study supplemented by high-temperature PVTx data for H 2O–H 2S fluid mixtures reported in the literature. The Peng–Robinson equation used in conjunction with density-dependent mixing rules was found to be the most accurate of the available equations in representing the properties of the vapour phase. The errors in the pressure of the homogeneous vapour mixtures estimated using the above equations of state (relative deviation from the experimentally determined pressure) were comparatively low, ∼5% to 8%. However, the errors were significantly higher for the estimated pressure of vapour saturated with liquid, i.e., along the vapour–liquid phase boundary (11–15%), due to the polar nature of H 2O and H 2S and the resulting highly non-ideal behaviour of the fluid mixtures. The results of this study make it possible to reliably estimate the volumetric properties of aqueous fluids containing H 2S at temperatures and pressures up to 400 °C and 240 bar, i.e., for conditions commonly encountered in natural hydrothermal systems.

A new formulation of the predictive NRTL-PR model in terms of kij mixing rules. Extension of the group contributions for the modeling of hydrocarbons in the presence of associating compounds

A generalized NRTL model was previously proposed for the modeling of non ideal systems and was extended to the prediction of phase equilibria under pressure according to the cubic NRTL-PR EoS. In this work, the model is reformulated with a predictive kij temperature and composition dependent mixing rule and new interaction parameters are proposed between permanent gases, ethane and nitrogen with hydrocarbons, ethane with water and ethylene glycol. Results obtained for excess enthalpies, liquid–vapor and liquid–liquid equilibria are compared with those provided by the literature models, such as VTPR, PPR78, CPA and SRKm. A wide variety of mixtures formed by very asymmetric compounds, such as hydrocarbons, water and ethylene glycols are considered and special attention is paid to the evolution of kij with respect to mole fractions and temperature.

Application of the crossover lattice equation of state for fluid mixtures

In previous work, we developed the crossover lattice equation of state (xLF EOS) for pure fluids and the xLF EOS yielded the saturated vapour pressure and the density values with a much better accuracy than the classical LF EOS over a wide range. In this work, we extended xLF EOS to fluid mixtures. Classical composition-dependent mixing rules with only adjustable two binary interaction parameters same as the LF EOS are used. A comparison is made upon experimental data for fluids mixtures in the one- and two-phase regions. The xLF EOS shows more improved representations than the LF EOS, especially in the critical region.

Prediction of VLE data for alternative refrigerant mixtures

The inevitability of a disaster associated with the depletion of the ozone layer led to the decision to phase out conventional chlorine containing refrigerants and their mixtures. This necessitates the use of non-chlorine substances as refrigerants. In the present work, three different types of mixing rules, namely (i) the classical van der Waals one fluid mixing rule, (ii) the composition dependent mixing rules of the Margules type, and (iii) the conformal solution van der Waals mixing rules are used with the Peng-Robinson (PR) equation of state, to predict the VLE data of 27 alternative refrigerant mixtures, and the results are compared with the experimental data. It is found that the compositiondependent mixing rule coupled with the PR equation of state is quite suitable for predicting the VLE data.

HRX-SAFT Equation of State for Fluid Mixtures: Application to Binary Mixtures of Carbon Dioxide, Water, and Methanol

In this work, we extend the pure fluid crossover statistical associating fluid theory (HRX-SAFT) equation of state (EOS) (Kiselev et al., Fluid Phase Equilib. 2001, 183−184, 53) to fluid mixtures of polar and associating components. HRX-SAFT incorporates non-analytic scaling laws in the critical region and is transformed into the analytical, classical HR-SAFT EOS far away from the critical point. Pure CO2, H2O, and CH3OH are modeled as associating chain molecules with two association sites (i.e., model 2B). For all three pure substances, the HRX-SAFT EOS reproduces the vapor pressure data from the triple point to the critical temperature with an average absolute deviation (AAD) of about 1%, the saturated liquid and vapor densities with an AAD of about 1−3%, and the single-phase pressures in the one-phase region with an AAD of about 2−3%. Using classical composition-dependent mixing rules, we have also applied the HRX-SAFT EOS to binary mixtures. For the non-association terms in the classical HR-SAFT, we used the vdW1 mixing rules with one constant binary interaction parameter (kij). For the mixture association term, we assumed that there is cross association between the carbon dioxide oxygens and the hydrogens in methanol and water. The HRX-SAFT mixture model was tested against extensive experimental data for VLE, PVTx, and excess properties in carbon dioxide + water, carbon dioxide + methanol, and water + methanol mixtures.

PVTx Measurements for the R116 + CO2 and R41 + CO2 Systems. New Isochoric Apparatus

A new isochoric apparatus was built for PVTx measurements in an extended temperature range from (210 to 360) K and at pressures up to 6.0 MPa. The setup was used to measure PVTx properties for the R116 + CO2 and R41 + CO2 systems, both in the two-phase and superheated vapor regions. The binary interaction parameters were derived from experimental data in the two-phase region by applying the flash method and the Carnahan−Starling−DeSantis equation of state (CSD EOS). The dew-point parameters were found by interpolating the P−T isochoric sequences, again applying the CSD EOS. A composition-dependent mixing rule implemented in the CSD EOS improved the VLE data representation of both binary systems. The resulting binary interaction parameters were used for VLE parameter derivation. The superheated vapor region data were compared with those obtained by the Burnett method and using REFPROP 7.

High-Pressure Phase Equilibrium of CO2 + 2-Phenylethanol and CO2 + 3-Methyl-1-butanol

Phase equilibrium for CO2 + 2-phenylethanol and CO2 + 3-methyl-1-butanol was measured. The two alcohols are both major constituents of wine aroma. The experimental apparatus includes a transparent high-pressure cell made of a sapphire cylinder, which allows full visual observation of the inside. Measurements were performed at temperatures of (313.1 and 323.1) K and at pressures from (8 to 24) MPa for the system CO2 + 2- phenylethanol and pressures from (5 to 10) MPa for the system CO2 + 3-methyl-1-butanol. The experimental results were fitted with the Stryjek−Vera modification of the Peng−Robinson cubic equation of state, using the composition-dependent mixing rules of Panagiotopoulos and Reid.

Generalization of composition-dependent mixing rules for multicomponent systems: prediction of vapor–liquid and liquid–liquid equilibria

A consistent generalization to mixing rules depending on the composition proposed by Adachi and Sugie, Panagiotopoulos and Reid, and Stryjek and Vera for the two-parameter mixing rule and by Schwartzentruber and Renon for the three-parameter mixing rule is presented. The invariance problem and dilution effect shortcomings pointed out by Michelsen and Kistenmacher when the original mixing rules are applied to multicomponent mixtures, are avoided by the generalized mixing rules. The proposed mixing rules involving their respective excess function models associated with a cubic equation of state (PRSV or PRCRP), were used on the representation of binary vapor–liquid (hydrocarbon–hydrocarbon, acetone–alcohol, acetone–water, alcohol–water, and alcohol–hydrocarbon) and liquid–liquid (hydrocarbon–water) equilibrium data. The binary interaction parameters of the model were used to test the performance of the generalization on the prediction of ternary vapor–liquid (acetone–methanol–water, acetone–ethanol–water and hexane–ethanol–benzene) and liquid–liquid (water–methanol–benzene, water–ethanol–hexane and water–1-propanol–benzene) equilibria. In addition, it is shown that a more satisfactory prediction of the ternary vapor–liquid and liquid–liquid equilibria can be obtained by using a limit form of the generalized three-parameter excess function model.

A comparison between Anderko's model with composition-dependent physical interaction parameters and SRK-based hexamer model for HFC and HF systems

A new composition-dependent mixing rule in physical contribution term of AEOS by Anderko [A. Anderko, Phase equilibria in aqueous systems from an equation of state based on the chemical approach. Fluid Phase Equilibria, 1991, 65, 89.] was introduced to predict the phase behavior for HFC-134a+HF and HFC-32+HF binary systems. The approach developed in this work gives better results for systems containing strongly associating compounds in the vapor phase such as hydrogen fluoride than the SRK-based hexamer model developed by Twu et al. [C.H. Twu, J.E. Coon, J.R. Cunningham, A new cubic equation of state for hydrogen fluoride, Fluid Phase Equilibria 1993, 86, 47.] with fewer binary adjustable parameters. The equation of Peng and Robinson [D.Y. Peng, D.B. Robinson, A new two-constant equation of state. Ind. Eng. Chem. Fundam., 1976, 15, 59.] is used to describe the physical interactions. The van der Waals mixing rule was replaced by composition-dependent mixing rules to improve the predictability of this model. This study shows more accurate results for VLE phase behavior for HFC and HF systems than the SRK-based hexamer model or any other activity coefficient-based hexamer models developed so far.

Use of carbon dioxide to shift benzene/acetonitrile and benzene/cyclohexane azeotropes

Bendale, P.G. and Enick, R.M., 1994. Use of carbon dioxide to shift benzene/acetonitrile and benzene/cyclohexane azeotropes. Fluid Phase Equilibria, 94: 227-253. A semi-continuous flow apparatus with an on-line gas Chromatograph was designed and constructed for conducting experiments to obtain high pressure supercritical fluid-liquid phase equilibrium data for binary and ternary systems. Isothermal P-x-y data were obtained for CO2/benzene, CO2/cyclohexane, CO2/acetonitrile, CO2/benzene/cyclohexane and CO2/benzene/acetonitrile systems up to the mixture critical pressure. Ternary data were obtained with three initial concentrations of liquid mixture to investigate the potential of using supercritical CO2 in breaking or shifting the benzene/acetonitrile and benzene/cyclohexane azeotropes. The analyses of the experimental data indicated that for the CO2/benzene/cyclohexane system at 42.3°C and a pressure of 1.926 MPa, the benzene/cyclohexane azeotrope was shifted from 50.0 mol% cyclohexane to greater than 71.2mol% cyclohexane (on a CO2-free basis). Similarly, in the case of the CO2/benzene/acetonitrile system at 45.3°C and 2.326 MPa, the benzene/acetonitrile azeotrope shifted from 54.3 mol% benzene to greater than 70.3 mol% benzene. These systems are among the few documented shifts in azeotropic composition attained using supercritical fluids. For the Peng-Robinson equation of state with the one-parameter mixing rule, relative errors of the order of 15% in the prediction of bubble point pressures were encountered at higher pressures, i.e. in the near-critical region. At lower pressures, however, the fit results were in agreement with the experimental bubble point pressures. Excellent representation of binary supercritical fluid-liquid phase behavior for these systems was obtained up to the mixture critical point when pressure- and composition-dependent mixing rules were incorporated. Although the two-parameter mixing rules provided very good descriptions of the two-phase envelope for the ternary mixtures, it was unable to predict any shift in the azeotropic composition (on a CO2-free basis) in the presence of supercritical CO2.

Phase equilibria of CO 2 + dl-α-tocopherol at temperatures from 292 K to 333 K and pressures up to 26 MPa

Phase equilibria for the system carbon dioxide + dl-α-tocopherol were studied, at temperatures from 292 K to 333 K and pressures up to 26 MPa. Pressure-composition isotherms were measured for the liquid and vapour phases in equilibrium, using the analytical method, from 9 MPa to 26 MPa, and at five temperatures between 298 K and 333 K. The projection of the liquid-liquid-vapour three phase equilibrium surface on the pressure-temperature plane has been followed from 292 K up to the critical end point, close to the critical temperature of CO 2. The results were modelled using the Peng-Robinson equation of state and the composition-dependent mixing rules of Panagiotopoulos and Reid. Good agreement with experimental results was obtained.

Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state

Stryjek, R. and Vera, J.H., 1986. Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state. Fluid Phase Equilibria, 25: 279–290. The PRSV cubic equation of state and a new Margules-type composition-dependent mixing rule previously proposed have been used to correlate vapor—liquid equilibrium data for hydrochloric acid solutions. In total, four adjustable parameters are used for pure hydrogen chloride, pure water and their mixtures. The two binary parameters are determined from azeotropic point data. Results obtained for this highly nonideal system, presenting negative deviations from ideality, are better than those obtained with the modified cubic equation of Gibbons and Laughton.