MHV2 Mixing Rule Research Articles

A Modification of α in SRK Equation of State and Vapor-Liquid Equilibria Prediction

Based on results of saturated vapor pressures of pure substances calculated by SRK equation of state, the factor α in attractive pressure term was modified. Vapor-liquid equilibria of mixtures were calculated by original and modified SRK equation of state combined with MHV1 mixing rule and UNIFAC model, respectively. For 1447 saturated pressure points of 37 substance including alkanes; organics containing chlorine, fluorine, and oxygen; inorganic gases and water, the original SRK equation of state predicted pressure with an average deviation of 2.521% and modified one 1.673%. Binary vapor-liquid equilibria of alcohols containing mixtures and water containing mixtures also indicated that the SRK equation of state with the modified α had a better precision than that with the original one.

Prediction of phase equilibria for mixtures containing water, hydrocarbons and alcohols at high temperatures and pressures by cubic equation of state with GE type mixing rule based on COSMO-RS

The phase equilibria for the mixtures containing water, hydrocarbons and alcohols at high temperatures and pressures were predicted by a cubic equation of state with an excess Gibbs free energy ( G E) type mixing rule using information from the conductor—like screening model for real solvents (COSMO-RS) method. The systems predicted were water + hydrocarbon, water + alcohol, hydrocarbon + alcohol binary systems and water + hydrocarbon + hydrocarbon and water + hydrocarbon + alcohol ternary systems. COSMO-RS method was used to calculate activity coefficients of the mixtures. UNIQUAC equation was adopted as an activity coefficient model in G E type mixing rule. The interaction parameters in UNIQUAC equation were determined with the activity coefficients calculated by COSMO-RS method. The modified Huron–Vidal mixing rule (MHV1) and a modified Soave–Redlich–Kwong (MSRK) equation of state were chosen as the G E type mixing rule and the cubic equation of state, respectively. Further, the MHV1 mixing rule was modified to apply in high temperature regions. It was found that the prediction method proposed here can represent the phase behavior of the mixtures containing water, hydrocarbons and alcohols at high temperatures and pressures. The predicted results are compared with those calculated by a predictive Soave–Redlich–Kwong (PSRK) equation of state. The predicted results in this work are more accurate than those calculated by PSRK equation of state.

Calculation of critical lines of hydrocarbon/water systems by extrapolating mixing rules fitted to subcritical equilibrium data

The phase behavior of water/hydrocarbon mixtures in a wide range of pressures is important for various applications ranging from reservoir engineering to environmental engineering. In this work, mutual solubility and critical loci of hydrocarbon/water systems are calculated using the Peng–Robinson–Stryjek–Vera cubic equation of state with four mixing rules: (1) van der Waals mixing rules with one binary interaction parameter (vdW-1), (2) van der Waals mixing rules with asymmetric composition dependent binary interaction parameter (vdW-A), (3) Wong–Sandler mixing rules (WS) and (4) second-order modified Huron–Vidal mixing rules (MHV2). It was found that the parameters obtained from correlating liquid–liquid equilibria using different mixing rules would lead to prediction of completely different forms of critical behavior. Unusual branches of critical loci were found with WS and MHV2 mixing rules. Therefore, equation of states models must be used with extreme caution when applied for predicting phase behavior over wide ranges of temperatures and pressures.

Vapour–liquid equilibrium measurements and correlation of the difluoromethane (R32) + propane (R290) + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) ternary mixture at temperatures from 269.85 to 328.35 K

Vapour–liquid equilibrium (VLE) data of the ternary mixture composed of difluoromethane (R32), propane (R290) and 1,1,1,2,3,3,3-heptafluoropropane (R227ea) have been measured for three compositions at temperatures between 269.85 and 328.35 K. The experimental method is a synthetic one with a variable volume cell. Our results about each of the three corresponding binary systems are compared to literature data using a Soave–Redlich–Kwong (SRK) equation of state with MHV1 mixing rules involving the NRTL model.

Vapor−Liquid Equilibrium Data for the Azeotropic Difluoromethane + Propane System at Temperatures from 294.83 to 343.26 K and Pressures up to 5.4 MPa

Isothermal vapor-liquid equilibrium data for the Difluoromethane (R32) + Propane binary system are presented at 278.10, 294.83, 303.23, 313.26 and 343.26 K and pressures up to 5.4 MPa. The experimental method is the static-analytic type. It takes advantage of mobile pneumatic capillary samplers (Rolsi™, Armines' patent) developed in our laboratory. At a fixed temperature the azeotrope vapor pressure is larger then those of the pure component. The particularity of R32-Propane azeotropic binary system is to present in two critical point over the critical temperature if the azeotrope. This particular behavior has been proved and even shown visually by means of two supplementary experiments with equipment based on the static-synthetic method involving a variable volume cell. Data along the five isotherms have been represented with the Soave-Redlich-Kwong (SRK) equation of state and MHV1 mixing rules involving the NRTL model. We have calculated the location of the azeotrope using the equality of Equation of State attractive parameter between the two phases.

Fluid phase equilibria of the reacting mixture in the dimethyl carbonate synthesis from supercritical CO 2

In order to investigate the dimethyl carbonate synthesis from methanol and supercritical CO 2, the thermodynamic behaviour of the reacting mixture, i.e. the quaternary methanol–CO 2–DMC–water mixture, has to be known. The SRK equation of state with MHV2 mixing rules has been chosen to predict fluid phase equilibria in the reactor. The first part of this work is dedicated to the determination of binary interaction parameters, needed in the use of this model. These parameters are deduced from the fitting of experimental data concerning binary or ternary sub-systems existing in the quaternary mixture. Literature data was used for most of the binary sub-systems, but for the DMC–CO 2 and DMC–water mixtures, specific experiments were carried out. The agreement between experimental and predicted fluid phase equilibria was found to be satisfactory. With a view to studying of the operating conditions for the reaction, the thermodynamic model was used to predict fluid phase equilibria in the reactor, by considering several hypothetical feed ratios and conversions. This work shows that CO 2 has to be used in large excess in order to be sure of running the reaction in a homogeneous fluid medium.

Phase equilibria of (methane-long chain ester cuts) systems in drilling conditions

During the drilling operation, the drilling fluid interacts with the formation at the well bore leading to the dissolution of hydrocarbons in the mud. Berthezene et al. [J. Petroleum Sci. Eng. 23 (1999) 71] studied the methane solubility in different fluids representing the drilling mud. They concluded that the ester remains immiscible with methane up to very high pressures. Additional experimental work at pressures up to 100 MPa has been performed on different esters. The effect of chain length and the presence of the ester group onto the chain on the phase equilibrium with methane is investigated. The conclusions of this work are identical to that of Berthezene et al. for critical points: the high molecular weight esters yield very high critical pressures, but the lower the molar mass, the lower the critical pressure. The position of the ester group in the chain has been found to have a negligible influence on the phase envelope. Several cubic equations of state have been used to model the bubble pressure data. The Peng–Robinson (PR) and the Elliott–Suresh–Donohue (ESD) equations of state have been combined with the classical mixing rule using binary interaction parameters equal to zero ( k ij =0) and the Soave–Redlich–Kwong (SRK) equation-of-state has been used with the MHV2 and UNIFAC mixing rule. In all cases, group contribution methods have been used for predicting the critical properties of the pure components since we are looking for a completely predictive method. We have found that the SRK/MHV2/UNIFAC gives very poor results. The PR/ k ij =0 model gives the best results for the low pressures but the predictions are poor for high pressures. The ESD/ k ij =0 model appears to provide much better predictions, especially for high pressures, which is interesting for us.

Dynamic modelling of a fractionation process for a liquid mixture using supercritical carbon dioxide

This work presents a simple dynamic modelling of a process of separation of a quaternary mixture using supercritical CO 2. Thermodynamic description is accomplished using efficient available models (SRK equation of state with MHV2 mixing rules). An approximate approach was compared to the rigorous resolution of the system of algebro-differential equations, and was shown to enable a correct description of the dynamic behaviour. The modelling was compared to experiments performed on a small pilot composed of one 200-ml contactor and a cascade of three cyclonic separators. Good results were obtained for the contactor, although they were not very satisfactory for the description of the fractionation in the cyclonic separators. Even if discrepancies between experimental and calculated results may probably originate from the experimental procedure, the hydrodynamic description of the separators here is likely to be oversimplified. The cyclonic separator cannot be regarded as a simple theoretical stage (TSM), and we have proposed an alternate description (EPSM), that, although more suitable, still needs to be improved.

Essential oils from seeds: solubility of limonene in supercritical CO 2 and how it is affected by fatty oil

Fatty oil influence on the solubility of limonene in CO 2 was investigated under pressures 8–12 MPa at 313.2 K, a temperature typically applied in supercritical fluid extraction of essential oils. Solubility in CO 2 was measured using the dynamic method both for limonene and for the mixture of limonene and blackcurrant seed oil. In the whole range of pressures applied, the concentration of fatty oil in the vapour phase is negligible in comparison with the concentration of limonene. Limonene is distributed between the liquid phase rich in fatty oil and the vapour phase rich in CO 2, and its equilibrium concentration in the latter decreases with the diminishing limonene-to-oil ratio in the saturator. There is a steep increase of the limonene partition coefficient with pressure between 8 and 10 MPa, near the critical pressure of the binary mixture of limonene and CO 2. The observed behaviour of the three-component system was confirmed and explained by thermodynamic modelling. The thermodynamic model applied was the Soave–Redlich–Kwong cubic equation of state with either the one fluid linear van der Waals mixing rule or with the MHV2 mixing rule. Appropriate conditions for an efficient supercritical fluid extraction of essential oils from seeds follow from the results obtained. Extraction pressure should be approx. 20% larger than the critical pressure of the essential oil+CO 2 binary mixture and rather tight packing of the ground seed in the bed should be applied.

High-Pressure Vapor−Liquid Equilibria in the Systems Nitrogen + Dimethyl Ether, Methanol + Dimethyl Ether, Carbon Dioxide + Dimethyl Ether + Methanol, and Nitrogen + Dimethyl Ether + Methanol

Isothermal (P, T, x, y) data have been measured for the binary and ternary systems nitrogen + dimethyl ether at 15, 35, and 45 °C, dimethyl ether + methanol at 80 °C, carbon dioxide + dimethyl ether + methanol at 40 and 60 °C, and nitrogen + dimethyl ether + methanol at 40 and 15 °C. The pressure range under investigation was up to 9.5 MPa. The experimental data for the binary systems were correlated with the SRK equation of state using the MHV2 mixing rule combined with the UNIFAC or UNIQUAC model for the expression of the excess Gibbs energy. The experimental data for the ternary systems have been compared with those predicted by means of the same models, and the results are discussed by comparison. The binary system of nitrogen + dimethyl ether as well as the two ternary systems have not previously been studied.

Vapor−Liquid Equilibria of Systems Containing Dichloromethane and Gaseous Components

Isothermal pressure−composition data were measured for three binary systems: carbon monoxide + dichloromethane; propene + dichloromethane; 1-butene + dichloromethane. Each system was measured at three temperatures (30.0, 60.0, and 90.0 °C) and pressures up to 70 bar. The experimental data were correlated with the SRK equation of state using the MHV2 mixing rule and the UNIQUAC method for the expression of the excess Gibbs energy.

Evaluation of vapor–liquid equilibrium of ethane binary systems using UNIQUAC-based mixing rules and its extension to multicomponent systems

In order to investigate the ability and accuracy of the UNIQUAC-based SRK EOS for prediction of high-pressure vapor–liquid equilibrium (VLE) the UNIQUAC parameter for 19 ethane binary systems have been determined. The missing binary interaction parameters are reported for PSRK, MHV1, MHV2, and LCVM mixing rules. These parameters were determined using the VLE experimental data reported in literature. The percentage average relative pressure error for 19 C 2H 6 binary systems is 1.93, 1.99, 2.21, and 2.03 using PSRK, MHV1, MHV2, and LCVM mixing rules, respectively. The regressed binary interaction parameters then, without any further modification, were applied to six multicomponent systems over a wide range of temperature covering more than 300 data points. The calculated percentage average relative pressure error for six multicomponent systems is 3.47, 3.75, 5.57, and 4.51 for PSRK, MHV1, MHV2, and LCVM mixing rules, respectively. Based on the results obtained in this study, it is concluded that the PSRK/UNIQUAC model has reasonable accuracy for VLE calculations and gives the most accurate results among the four mixing rules tested.

Prediction of excess enthalpies at low and high pressures using a modified MHV1 mixing rule

A modified MHV1 mixing rule was proposed which relaxed the limitation of the MHV1 mixing rule for reproduction of H E from the G E model incorporated. The SRK EOS with the proposed mixing rule coupled with the modified unifac model gives good low-pressure H E prediction for 23 systems tested. The accuracy is much better than that with the original MHV1 mixing rule, and is comparable to that of the modified unifac model incorporated. The proposed mixing rule was further applied to predict high pressure H E using the existing modified unifac parameters. The results show that it works well for high-pressure systems without losing predictive accuracy compared to that of low-pressure ones.

Ability of the MHV2 mixing rule to describe the effect of salt on gas solubility in brines at high temperature and high pressure

An empirical model for gas solubility in brines under high temperatures and high pressures has been developed by modification of the modified Huron-Vidal second order (MHV2) model and evaluated by least squares fitting to available p - T-X (pressure - temperature -composition) data. The model is based on the MHV2 mixing rule. It combines the Soave -Redlich - Kwong (SRK) equation of state with a model for the excess Gibbs energy to calculate the mixture parameter, a. The ability of the MHV2 mixing rule to describe the effect of salt on gas solubility (CH4, CO2) in water-sodium chloride systems over a wide range of temperature and pressure has been investigated. A modified Wilson activity coefficient model was chosen, which is more flexible than the modified UNIFAC activity coefficient model which yields an unsatisfying evolution with temperature of the calculated gas solubility when a gas, such as methane, exhibits very low solubility in water - salt mixtures.

Connection between zero-pressure mixing rules and infinite-pressure mixing rules

Infinite-pressure mixing rules and zero-pressure mixing rules are related by a very simple equation. The zero-pressure models and the infinite-pressure models are interchangeable through this connection. This paper will show how to convert the Huron–Vidal infinite-pressure mixing rule to a zero-pressure mixing rule, or vice versa. The MHV1 zero-pressure mixing rule will be reformulated to satisfy second virial coefficient constraint. The Twu–Coon and Wong–Sandler infinite-pressure mixing rules will be modified to improve their accuracy for reproducing the incorporated G E model. A simplification of the Twu–Coon–Bluck [TCB( r)] zero-pressure mixing rule will be presented. The MHV1 mixing rule will be shown to be a special case of TCB( r).

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO 2-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.

Correlation of solubilities for CO2 and NH3 in H2 O using Soave-Redlich-Kwong equation of state with MHV2 mixing rule

Correlation of solubilities for CO2 and NH3 in H2 O using Soave-Redlich-Kwong equation of state with MHV2 mixing rule

Matching equation of state mixing rules to activity coefficient model expressions

Procedures for deriving equation of state mixing rules based on matching the zero pressure excess Gibbs energy to that of a previously parameterized activity coefficient model are discussed. I have investigated the conditions required for accurate reproduction of the original model and provide a simple graphical tool for evaluating the error of the equation of state mixing rule. An extension of the MHV-2 mixing rule to incorporate mixtures containing components with very low volatility is suggested.

Prediction of supercritical fluid-liquid equilibria for carbon dioxide and fish oil related compounds through the equation of state — excess function (EOS-g E) approach

This paper compares the correlative and predictive abilities of three forms of models based on the approach which combines an equation of state (EOS) with a g E-model in an EOS framework. In particular, the MHV1 mixing rule with a quadratic mixing rule for the mixture b parameter, the LCVM method and a variation of the LCVM method have been investigated. Estimation of supercritical fluid-liquid (SCFL) phase behavior of mixtures involving carbon dioxide and ethane as the “light” compound and fatty acid esters (carbon number > 10) and hydrocarbons (n-Alkanes) as the “heavy” compounds have been considered. Finally, a generalized expression for the mixture α-parameter, from which several other mixing rules (including the ones investigated in this paper) can be derived, is presented. The derivation of the MHV1 mixing rule and the LCVM method from the generalized expression is given together with the estimated phase equilibria.

Some Properties of Equation of State Mixing Rules Derived from Excess Gibbs Energy Expressions

Several recent proposals for using excess free energy models in constructing mixing rules for cubic equations of state have been analyzed. The reproduction of the base model behavior at the correlating temperature and the nature of the extrapolation to higher temperatures have been examined. The Wong−Sandler, LCVM, and MHV-1 mixing rules in an equation of state result in excess Gibbs free energies with contributions in addition to those from the base activity coefficient model. As a result, considerable degradation of calculated equilibrium behavior can occur. The excess enthalpies produced by these mixing rules are generally more positive than would be found from the temperature derivative of the G excess models, with only the MHV-2 mixing rule giving a reasonably quantitative reproduction. The success of the Wong−Sandler mixing rule in extrapolating to higher temperatures appears to derive in part from this positive addition to the excess enthalpy.