MHV2 Mixing Rule Research Articles

Critical properties and vapor-liquid equilibrium of two near-azeotropic mixtures containing HFOs

This work studies two binary mixtures of R1243zf + R1234yf and R1243zf + R245cb which can be possibly used as a long-term alternative refrigerant for heat pumps. We present critical property (critical temperature, pressure, density) and vapor liquid equilibrium (VLE) of R1243zf + R1234yf and R1243zf + R245cb two binaries. The maximum extended uncertainties (k=2) are estimated as U(T) = 0.21 K, U(p) = 0.048 MPa, and U(ρ) = 6.4 kg/m3 for critical property measurement, and U(T) = 0.06 K and U(p) = 0.015 MPa for bubble point measurement. The uncertainty of liquid-phase mole fraction is estimated less than 1.8 × 10−4. The critical property is investigated by a novel method that determines the critical point via modeling vapor-liquid coexistence points to the combined equations of the scaling law and rectilinear diameters law. The VLE of R1243zf + R1234yf and R1243zf + R245cb binary mixtures in the range of 293.45 to 353.55 K are studied by the static-synthetic method which determines the bubble point via the variable volume cell technique. The experimental bubble points are correlated by the Peng-Robinson (PR) equation of state (EoS) with vdW and MHV2 mixing rules. The modeling results are in good agreement with the measured data. The high temperature VLE of the two binary systems is predicted up to the critical point line by PR-MC-MHV2 model with the optimal binary parameters.

Vapor-liquid equilibria of α-tocopherol in transportation fuels surrogates: An experimental and modeling study

The environmental performance of advanced engines in terms of combustion and emissions relies strongly on fuel phase change properties, which can be improved by specific additives. Among sustainable additives, tocopherols are particularly promising since they exhibit high dispersion, low toxicity and antioxidant properties, which may allow their introduction as multifunctional additives in engine fuel and lubricants. The present work aims at studying the α-tocopherol synergy with surrogate automotive fuels and the volatility of the resulting ternary blends. This study deals with the experimental measurements and modeling of the phase behavior of n-pentane + ethanol + α-tocopherol mixtures: the n-pentane + ethanol mixture is considered as a base surrogate fuel, and α-tocopherol is the additive. The Peng-Robinson (PR) equation of state combined with the MHV1 mixing rules and the predictive UNIFAC and COSMO-SAC dsp activity coefficient models, is used to determine the vapor–liquid equilibria (VLE) of the n-pentane + ethanol + α-tocopherol mixture. Reid vapor pressures and distillation curves based on the ASTM D86 protocol are predicted for α-tocopherol + fuel systems. It is observed that the addition of α-tocopherol induces a change in the distillation curve (shift to higher temperatures) for large fractions of distillate volumes. The validated model allows to tailor multifunctional additives to improve fuel distillation curves.

Measurement and modeling of solubility of gliclazide (hypoglycemic drug) and captopril (antihypertension drug) in supercritical carbon dioxide

The solubility of drugs in supercritical carbon dioxide (ScCO2) is crucial information for crystal engineering designs and pharmaceutical applications. A semi-flow apparatus was used to measure the solubility of gliclazide and captopril in ScCO2 at 308.2 K, 318.2 K, and 328.2 K within the pressure range of 10.0–18.6 MPa. The newly measured solubility data were correlated and confirmed to be self-consistency with four semi-empirical correlation models: Chrastil, Méndez-Santiago & Teja (MST), Bartle, and Kumar & Johnston (K-J). The newly measured data were then used to evaluate the accuracy of three approaches based on the Peng-Robinson equation of state (PR EOS). PR EOS combining with the Wilson model through the Wong-Sandler mixing rule with two adjustable parameters shown excellent fit with experimental data, while PR EOS combining with the COSMO-SAC model through the MHV1 mixing rule provided reasonable solubility prediction without adjustable parameters.

Predictions of thermodynamic properties and phase equilibria of refrigerant systems with COSMO approaches

The knowledge of the phase equilibrium of refrigerant mixtures is crucial for the optimization of the production processes of refrigerant molecules, and the design of energetic systems (heat pumps, Organic Rankine Cycles, …). In this work, different predictive thermodynamic models (COSMO-RS and COSMO-SAC-dsp) have been used to determine the phase behavior of mixtures of refrigerants involving alkanes, fluorinated and chlorinated compounds. The COSMO-RS model leads to rather satisfactory predictions of the vapor-liquid equilibria of mixtures and is able to capture the azeotropic behavior for most systems. However, the original COSMO-SAC model as well as the COSMO-SAC 2010 version lead to unsatisfactory predictions of VLE for these systems, as they are unable to predict the azeotropic behavior in alkane + refrigerants. By combining COSMO-SAC with a dispersion term (COSMO-SAC dsp model) and readjusting the universal parameter for the F atom, it is possible to get very satisfactory predictions of similar accuracy as COSMO-RS. In order to predict the phase behavior at high pressure, the COSMO-SAC-dsp model can be combined with the Peng-Robinson equation of state and the MHV1 mixing rule. Excellent predictions of relative volatilities can be obtained with this approach over wide temperature and pressure ranges. COSMO calculation can also be used to predict saturated liquid densities, vaporization enthalpy and boiling points of pure refrigerants.

Estimation of gas solubility in petroleum fractions using PR-UMR and group contributions methods

Solubility of N2, CO2 and CH4 in petroleum fluids is estimated using the Peng-Robison cubic equation of state and three different mixing rules: the classical mixing rule of van der Waals (vdW), the modified Huron-Vidal of order one (MHV1) mixing rule and the universal mixing rule (UMR). The petroleum fluids were split out in pseudocomponents using a mass distribution procedure. Then, to determine equation-of-state parameters, pseudocomponents were characterized by a group contribution method, where the Gibbs free energy is minimized. In the proposed methodology, mixing-rule parameters for predicting gas solubility from binary mixtures of identifiable components were used in unidentifiable petroleum fluids. Twenty-two systems, which include bitumens, heavy oils, refinery cuts and coal liquids, were considered in order to assess the methodology. Good agreement between experimental data and predicted values were obtained for the UMR and vdW mixing rules, but significant deviations are obtained with the MHV1 mixing rule. The total absolute average deviations are 13%, 15% and 30% for the UMR, vdW and MHV1 mixing rules, respectively.

Estimation and Correlation of Phase Equilibrium of CO2–Hydrocarbon Systems with PRMHV2-UNIFAC and PRMHV2-NRTL Models

In this work, the Peng–Robinson (PR) equation of state (EoS) and MHV2 mixing rule that were combined with UNIFAC and NRTL GE models were used to predict vapor–liquid phase equilibrium (VLE) data for CO2–hydrocarbon systems. These systems included 12 binary systems and three ternary systems. The PRMHV2-UNIFAC model was used to calculate the bubble pressure, and the average absolute relative deviations (AARD %) were 17.49–32.20% for 12 binary systems. For the PRMHV2-NRTL model, the binary interaction parameters of the NRTL model dependent on temperature were regressed based on the binary VLE data. These new interaction parameters were used to estimate CO2–hydrocarbon VLE data for binary and ternary systems. The bubble pressure was predicted by the PRMHV2-NRTL model, and the AARD % values were 1.52–9.44% for binary systems, which were lower than the value of the PRMHV2-UNIFAC model. The PRMHV2-UNIFAC and PRMHV2-NRTL models were also used to calculate the liquid phase mole fraction of CO2–hydrocarbon ternary ...

Prediction of Gas and Liquid Solubility in Organic Polymers Based on the PR+COSMOSAC Equation of State

The predictive capability of gas and liquid solubility in organic polymers is examined based on the combination of the PR+COSMOSAC equation of state (EOS) and the COSMO-SAC liquid model through three different excess Gibbs free energy based mixing rules, modified Huron-Vidal (MHV1), Wong-Sandler (WS), and self-consistent mixing rule (SCMR). Using 81 binary systems consisting of 23 gas molecules and 22 polymers (81 data points) with temperatures ranging from 298 to 461 K, it is found that WS and SCMR can provide reasonable prediction accuracy (RMSE(log10 kH) = 0.746 and 1.725, respectively) for the Henry’s law parameter in polymers, while the MHV1 mixing rule results in a much larger error (RMSE (log10 kH) = 3.118) compared to experiment. The WS and SCMR, but not MHV1, provide a converged value of Henry’s law parameter of gas in polymers as the molecular weight of the polymer increases. We further propose a modification to the SCMR (mSCMR) that results in significant improvement in the solubility prediction in polymers (RMSE (log10 kH) = 0.305) and the binary vapor–liquid equilibrium for common molecules. In this new approach, referred to as PRCS/mSCMR/COSMOSAC, all species-dependent parameters are determined from quantum mechanical (QM) calculations, and no adjustable parameters are required for the gas–polymer binary pairs. We believe that this new method may provide useful assistance to the development of polymer membrane-based gas separation processes especially when experimental information is not yet available.

Experimental Study and Modeling of Phase Equilibrium of the Methanol–Tripalmitin System: Application to Palm Oil Transesterification with Supercritical Methanol

The phase behavior of the methanol–palm oil system was first experimentally assessed in the temperature range of 363–393 K and pressure range of 1–4 MPa. Second, comparative modeling of the phase equilibrium of the methanol–tripalmitin system was performed using the Peng–Robinson equation of state (PR EoS) with second-order modified Huron–Vidal (MHV2) mixing rules, in combination with the universal functional activity coefficient model (UNIFAC) and the universal quasi-chemical (UNIQUAC) excess Gibbs free-energy model. The agreement between experimental and modeling results was found to be satisfactory when MHV2 mixing rules are used in combination with the UNIQUAC model. Finally, the thermodynamic model was applied to predict fluid phase equilibria of palm oil transesterification with supercritical methanol. From the isochoric method in the temperature range of 373–693 K and the pressure range of 1–16 MPa, the model was found to predict global mixture behavior.

English

The production of natural gas (NG) is increasing considerably, contributing to the energetic matrix of the world. New reserves of NG have been discovered and explored regularly. Despite the various applications of natural gas, which allow its use as a raw material for the production of synthesis gas (syngas), for instance, there are remote wells that demand treatment before use. In this work, a simplified approach to remove the heavy species of natural gas (C5+) is presented. The specification of the treated gas is based on the methane index to use the remote NG for fuel in the drive of engines of compressors and boilers. Thus, the present approach proposes the application of two simple operations, i.e., absorption followed by a flash, to regenerate the solvent. This approach may be applied in remote production fields. Based on process simulations and physicochemical properties, 1-octanol was selected as absorbent for this separation. New measurements of absorption in laboratory scale are reported using a synthetic NG and an on-line chromatography analysis. Soave-Redlich-Kwong equation of state (EoS) with Mathias-Copeman alpha function and MHV2 mixing rule with UNIFAC was applied to describe the required equilibrium data. In order to validate this model for the absorption calculations, predictions of vapor-liquid equilibrium of alkane and alcohol binary mixtures obtained from literature data were tested and evaluated. Based on the absorption measurements and SRK-MHV2 flash calculations, curves of operation and equilibrium were provided. Using n-heptane as key-component it was demonstrated that one or up to two theoretical stages are enough to proceed the separation. This work also presents a gas absorption pilot set-up up to 70 bars that is able to evaluate scale up and pressure effect. It is demonstrated, experimentally and computationally, that the proposed approach of C5+ species absorption from NG is simple and feasible to specify the methane index of the gas for remote combustion applications.

Modeling of physical and chemical equilibrium for the direct synthesis of dimethyl carbonate at high pressure conditions

The physical and chemical equilibrium for direct synthesis of dimethyl carbonate is studied using the Soave–Redlich–Kwong equation of state coupled with five different mixing rules: one fluid van der Walls (1PVDW), modified first order Huron–Vidal (mHV1), modified second order Huron–Vidal (mHV2), linear combination of Vidal and Michelsen (LCVM), and Wong–Sandler (WS). The models parameters were adjusted from experimental vapour–liquid equilibrium data, from the literature, for the relevant binary systems. The mHV2 mixing rule showed to be the best model to predict phase equilibrium for this system. Then, the DMC equilibrium yield was modeled based on the SRK/mHV2 model. The Gibbs free energy of formation, for DMC, was adjusted from our experimental reaction equilibrium data in order to predict the equilibrium constant.

Effect of mixing rule boundary conditions on high pressure (liquid + liquid) equilibrium prediction

We examine the prediction of high pressure (liquid + liquid) equilibrium (LLE) from the Peng–Robinson equation with three excess Gibbs free energy ( G ex)-based mixing rules (MR): the first order modified Huron–Vidal (MHV1), the Wong–Sandler (WS), and a hybrid of these two (referred to as G ex B 2). These mixing rules differ by the boundary conditions used for determination of the temperature and composition dependence of parameters a and b in the PR EOS. The condition of matching the excess Gibbs free energy from the EOS at zero pressure to that from the G ex model, used in MHV1 and G ex B 2 MR, leads to a similar miscibility gap from PR EOS and the G ex model used. On the other hand, the condition of matching excess Helmholtz energy from the EOS at infinite pressure to that from the G ex model, used in the WS MR, shows remarkable deviations. The condition of quadratic composition dependence in the second virial coefficient ( B 2), used in WS and G ex B 2 MR, allows for both positive and negative values in the molar excess volume. Depending on the mixture, either the increase or decrease of the miscibility gap with pressure can be observed when the WS or the G ex B 2 MR is used. The condition of linear combination of molecular sizes of each component used in the MHV1 MR, however, often leads to small, positive molar excess volumes. As a consequence, the predicted LLE from using the MHV1 MR are insensitive to pressure. Therefore, we find that the G ex B 2 mixing rule provides the best predictive power for the LLE over a wide range of temperature and pressure.

Continuous Production of Biodiesel with Supercritical Methanol: a Simple Compressible Flow Model for Tubular Reactors

From an industrial point of view, the continuous process for biodiesel production with supercritical methanol (SCM) is more appropriate than the batch process. However, lab-scale studies on the continuous process have shown that the maximum conversion always remains slightly lower than that obtained in the batch process. This work proposes a simple compressible flow model to predict the conversion of methanol and oils into methyl esters (ME) along the length of a tubular reactor and further demonstrates the effect of the development of the compressibility factor of the reaction mixture upon the conversion efficiency to ME. The governing equation was derived from a general molar balance in the tubular reactor using transesterification kinetics of refined-bleached-deodorized (RBD) palm oil in SCM coupled with a suitable thermodynamic model with adjusted binary interaction parameters. Vapor-liquid equilibrium data for triolein + methanol, methyl oleate + methanol and glycerol + methanol mixtures were obtained from the literature and then refitted with the thermodynamic model consisting of the Peng-Robinson equation of state and MHV2 mixing rules to find the set of adequate interaction parameters. In order to check the validity of the proposed model, the predicted ME contents were compared with observed values in a lab-scale continuous reactor at various operating temperatures, pressures and methanol to oil molar ratios. The proposed model proved to be adequate for predicting the final conversion to ME for operating temperatures below 320°C, when the thermal degradation reactions of unsaturated fatty acids did not interfere. Our results also illustrate the importance of taking into account the development of the compressibility factor with time and reactor length, since this was shown to be the cause of the lower transesterification reaction rate in the tubular SCM process. The findings in this work could be employed as a knowledgebase to further develop a better model for continuous production of biodiesel with SCM in a tubular reactor.

A priori predictions of critical loci from the combined use of PRSV equation of state and the COSMO-SAC model through the MHV1 mixing rule

In this study we examine the prediction of critical points in fluid mixtures from the Stryjek–Vera version of the Peng–Robinson equation of state (PRSV EOS) combined with the COSMO-SAC liquid activity coefficient model (LM) through the modified first order Huron–Vidal (MHV1) mixing rule. This approach requires input of only pure component properties, such as the critical properties and acentric factor. No binary interaction parameter or experimental data on vapor–liquid or liquid–liquid equilibrium is needed. Six different types of binary mixtures are studied, including alkane/alkane, ketone/alkane, alkanol/alkane, alkanol/aromatic, alkanol/alkanol, and water/alkane mixtures. In general, the predicted critical loci are in semi-quantitative to quantitative agreement with experiments. The mean absolute relative errors are found to be 2.99% for critical temperature and 11.22% for critical pressure. Therefore, this approach (PRSV + MHV1 + COSMOSAC) could provide reasonable a priori predictions of critical loci without the use of any experimental data of the mixture.

Modeling Phase Equilibria Relevant to Biodiesel Production: A Comparison of gE Models, Cubic EoS, EoS−gE and Association EoS

Liquid−liquid equilibrium (LLE) and vapor−liquid equilibrium (VLE) data of binary and ternary systems formed at the biodiesel production and purification industrial units were used to evaluate the performance of commonly used excess Gibbs energy (gE) models, cubic equations of state (EoS), equations of state with EoS−gE mixing rules, and association equation of state models. The models used in this study are the UNIFAC, Soave−Redlich−Kwong (SRK) EoS, the SRK-MHV2, the Peng−Robinson (PR) EoS using the MHV2 mixing rule, the predictive Soave−Redlich−Kwong (PSRK) EoS, and the Cubic-Plus-Association (CPA) EoS. All models were used with previously established parameters, and the applicability of each model to the various systems investigated and the quality of the description of the phase equilibria are discussed. The results obtained show that the CPA EoS is the most adequate model to be used for the description of the phase equilibria of importance for the design and optimization of biodiesel production plants.

Vapor–liquid equilibrium measurement and modeling for the difluoromethane + pentafluoroethane + propane ternary mixture

Vapor–liquid equilibrium data for the difluoromethane (R32) + pentafluoroethane (R125) + propane (R290) ternary mixture were measured at 5 isotherms between 263.15 K and 323.15 K. The measurement was carried out using a circulation-type apparatus recently developed, which was validated with binary mixtures. With binary interaction parameters obtained for the three corresponding binary mixtures, VLE modeling and prediction were performed for the ternary mixture using the Peng–Robinson equation of state with the classical mixing rules and MHV1 mixing rules. Hou's group contribution model for VLE of new refrigerant mixtures was further tested with the experimental data for the ternary system. The predicted pressure and vapor phase composition were compared with experimental ones.

Isothermal Vapor−Liquid Equilibrium Data of 1,1,1,2-Tetrafluoroethane (R134a) + Dimethylformamide (DMF) Working Fluids for an Absorption Heat Transformer

Vapor−liquid equilibrium data of 1,1,1,2-tetrafluoroethane (R134a) + dimethylformamide (DMF) were measured in the temperature range from (303.30 to 353.24) K by the static analytic method. The results are of interest to test the possibility of using R134a as a refrigerant in combination with an organic absorbent, that is, DMF, in an absorption heat transformer. The experimental data are correlated using the Peng−Robinson equation of state in combination with the Mathias−Copeman α function, MHV1 mixing rules, and the non-random two liquid (NRTL) activity coefficient model. We have compared our experimental results to predictions obtained using the predictive Soave−Redlich−Kwong (PSRK) group contribution equation of state.

HI x system thermodynamic model for hydrogen production by the Sulfur–Iodine cycle

The HI x ternary system (H 2O–HI–I 2) is the latent source of hydrogen for the Sulfur–Iodine thermo-chemical cycle. After analysis of the literature data and models, a homogeneous approach with the Peng–Robinson equation of state used for both the vapor and liquid phase fugacity calculations is proposed for the first time to describe the phase equilibrium of this system. The MHV2 mixing rule is used, with UNIQUAC activity coefficient model combined with of hydrogen iodide solvation by water. This approach is theoretically consistent for HI x separation processes operating above HI critical temperature. Model estimation is done on selected literature vapor–liquid, liquid–liquid, vapor–liquid–liquid and solid–liquid equilibrium data for the ternary system and the three binaries subsystems. Validation is done on the remaining literature data. Results agree well with the published data, but more experimental effort is needed to improve modeling of the HI x system.

VLE calculation of carbon dioxide+n-alkanes binary mixtures with MHV2 mixing rule

Vapor-liquid equilibria for binary and asymetric systems include carbon dioxide+C1-C8, C10 are calculated by using the Peng-Robinson-Stryjek-Vera equation of state coupled with the modified MHV2 mixing rule. The modified UNIFAC model is used for determining activity coefficient and excess Gibbs free energy. Calculated equilibrium pressures and mole fractions in vapor phase are compared with the experimental data. The average absolute deviation percent (AAD%)s indicates that the error involved in the application of the MHV2 mixing rule by optimized q1 and q2 is less than WS and PRSK mixing rules in most cases.

Thermodynamic properties of THF + CO2 hydrates in relation with refrigeration applications

AbstractClathrate hydrate slurries are promising systems in the field of cold distribution. In this work, the Lw‐H‐V equilibrium conditions, the dissociation enthalpy, and the CO2 hydration number of a clathrate hydrate formed from THF/CO2/water mixtures were studied, using a DSC method. For equilibrium condition determination, THF concentration was varied from 1.0 to 16.0 wt % and CO2 partial pressure range was 0.2 to 2.0 MPa. For enthalpy measurements, THF concentration was fixed at 19 wt % and CO2 partial pressure investigated from 0.2 to 2.0 MPa. Experimental equilibrium temperatures and enthalpy values were in good agreement with the results of a model combining the van der Waals and Platteeuw approach with the RKS equation of state associated to a MHV2 mixing rule and UNIFAC model. Equilibrium conditions and dissociation enthalpy show that THF + CO2 hydrate slurries are promising mixtures for refrigeration application. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Prediction of high-pressure viscosities for binary liquid mixtures using the EOS- GE mixing rule with low-pressure viscosity data

A viscosity model, based on Eyring's absolute rate theory combined with a cubic PRSV equation of state and G E mixing rule, has been proposed in order to correlate and predict mixture viscosities at atmospheric and high pressure, respectively. In the proposed method, the energy and size parameters in EOS have been obtained using the MHV1 mixing rule combined with the NRTL equation. The NRTL parameters for 22 binary systems have been calculated using viscosity data at atmospheric pressure. The average deviation between the experimental and calculated viscosities is 2.1%. This accuracy is better than the accuracy obtained using the Wong-Sandler mixing rule. The high-pressure viscosities for 10 binary systems have been predicted using NRTL parameters determined and atmospheric pressure viscosity data, and shown to have a deviation of 4.6%.