vdW Mixing Rules Research Articles

Solubility measurement of Ceftriaxone sodium in SC-CO2 and thermodynamic modeling using PR-KM EoS and vdW mixing rules with semi-empirical models

The complete investigation of the solubility of Ceftriaxone sodium drug has not yet been conducted. This communication investigates the solubility of Ceftriaxone sodium drug in supercritical CO2 (SC-CO2) for the first time. The drug solubility measurements were performed using utilizing UV–vis analysis under different operation conditions (at P (bar) = 120–270 and T (K) = 308–338). The results demonstrated that the solubility of Ceftriaxone sodium ranged from 0.90 × 10−6 to 8.01 × 10−6. The mole fraction solubility of Ceftriaxone sodium increases proportionally with an increase in the pressure, while maintaining a constant temperature. However, a crossover was noted. The solubility behavior of Ceftriaxone sodium drug in SC-CO2 was modeled by Peng-Robinson equation of state (PR EoS) with Kwak-Mansoori and van der Waals mixing rules and seven semi-empirical correlations (Bian et al., Kumar-Johnston, Chrastil, Garlapati-Madras, Bartle et al., Sung-Shim and Sodeifian et al.,). The vaporization, total and solvation enthalpies of the Ceftriaxone sodium/SC-carbon dioxide system were obtained by KJ, Chrastil, and Bartle et al. correlations. The evaluation of two methods was performed by absolute average relative deviation (AARD%). Both models exhibited a satisfactory level of agreement with the experimental data. Finally, PR/KM EoS and the Chrastil models, with AARD% values of 8.70 % and 8.10 % respectively, showed superior precision in accurately fitting the solubility data.

A temperature-independent prediction model predicts the vapor-liquid equilibrium of CO2-based binary mixtures

CO2-based binary mixtures are considered good alternative working fluids in the refrigeration and power cycle due to their excellent performance and environmental friendliness. The vapor-liquid phase equilibrium of CO2-based binary mixtures is the basis for calculating mixing enthalpy and heat capacity, which is essential for thermodynamic analysis. In this work, based on the vdW mixing rules, we proposed a kij model (kij=θjki-θikj). In the proposed model, ki and kj are defined as pure interaction factors of the pure components, θj is the influence factor of component j to component i, and θi is the influence factor of component i to component j. After continuous fitting and trial calculation, we developed a semi-empirical formula, which is called a temperature-independent prediction model. The model does not have any adjustable parameters, which are only related to the physical properties (critical pressure (kPa), critical temperature (K), and acentric factor) and molecular structure (carbon-carbon double bonds, carbon-fluorine, chlorine, iodine, and oxygen atoms) of the components. The temperature-independent prediction model can predict the bubble-point pressures, vapor phase molar fractions, and relative volatilities very well, which is better than the prediction model based on the vdW mixing rules by others and the group contribution model based on the excess free energy (GE) mixing rules (PR+MHV1+UNIFAC). The total average absolute relative deviation of pressures, the total average absolute deviation of vapor phase molar fractions, and the total average absolute relative deviation of relative volatilities by the temperature-independent prediction model are 2.23%, 0.0095, and 5.21%, respectively.

Study on environmentally friendly refrigerant R13I1/R152a as an alternative for R134a in automotive air conditioning system

Abstract Aiming at solving the problem of high global warming potential of R134a, a new mixed refrigerant R13I1/R152a (molar fraction ratio of 35:65) with no ozone depletion potential and low global warming potential was proposed as a substitute for R134a in automotive air conditioning. The computational models for the thermodynamic properties of R13I1/R152a were established by using the PR equation of state combined with the vdW mixing rule. Based on these models, the cycle performance of this working fluid was calculated, which was also compared with that of R134a and R1234yf under the different operating conditions. The results show that R13I1/R152a is a near azeotropic refrigerant whose temperature glide is approximately 0, and the saturated vapor pressure curve of which is equivalent to that of R134a. Moreover, compared to R134a, R13I1/R152a has an average 5.7% improvement in coefficient of performance as well as similar volumetric cooling capacity. The average coefficient of performance and volumetric cooling capacity of R13I1/R152a are significantly higher than those of R1234yf by 13.8% and 12.0%, respectively. However, the average discharge temperature of R13I1/R152a is approximately 13.3 K higher than that of R134a, but it is also within reasonable limits. Hence, the application of the proposed refrigerant R13I1/R152a in automotive air conditioning system is technically feasible.

Modeling and simulation of biphasic catalytic hydrogenation of a hydroformylated fuel

A model was developed based upon PR78 CEOS, Twu's alpha function and vdW mixing rules for simulating a pioneering chemical process of fuel upgrading. The chemical process of aqueous biphasic hydrogenation of a real hydroformylated fuel was experimentally conducted and simulated. The hydrogenation of the fuel occurred in aqueous media with in situ produced Ru-catalyst converting containing aldehydes to the corresponding alcohols. The above heterogenization of the homogeneous catalyst offered to the process an efficient and convenient way of catalyst recovery. The reaction temperature effect and the influence of hydrogen pressure in aqueous biphasic catalytic hydrogenation were examined. RuCl3/TPPTS catalytic system proved to be an effective catalyst for fuel upgrading process, with the highest conversion of the aldehydes present in a hydroformylated fuel to reach 98.9% at 120 °C, 75 bar and at a short reaction time (2 h). A complete phase behavior of the fuel as well as a validation test of the simulation model were accomplished.

Solubility of methane in octamethylcyclotetrasiloxane: Experimental measurement and thermodynamic modeling

Liquid storage is a potential method for low-pressure storage of natural gas. In this work, octamethylcyclotetrasiloxane (OMCTS) was selected as a solvent for methane storage. Experimental measurements were carried out in a Cailletet apparatus, according to the synthetic method, from low to high pressures. One hundred experimentally-measured phase equilibrium data points are presented for methane + OMCTS in the form of bubble-points. The pressure, temperature, and methane mole fraction ranges are (0.61–8.07) MPa, (287.73–368.25) K, and (0.0534–0.4038), respectively. Furthermore, phase equilibrium calculations based on the ϕ−ϕ approach were carried out to model the methane + OMCTS binary system. In this regard, the Peng-Robinson EoS (PR EoS), coupled with the classical van der Waals (vdW) mixing rule, was applied. The vdW mixing rule was used in three modes: a) with no binary interaction parameters (kij=0,lij=0), b) with one constant binary interaction parameter (kij=constant), and c) with one temperature-dependent binary interaction parameter (kij=a+bT). It was concluded that both modes (b) and (c) give accurate results for methane solubility in OMCTS, with AAD(MPa) values of 0.11 and 0.10, respectively.

Experimental measurements and thermodynamic modeling of high-pressure propane solubility in triethylene glycol

The solubility of propane in TEG was measured via bubble point experiments using the Cailletet equipment. The results indicated that within some ranges of the P-T -x space, this system shows an inverse temperature effect, i.e., an increase of propane solubility with increasing temperatures, contrary to most gas solubilty measurements. Thermodynamic modeling of the phase behavior of propane + TEG system was undertaken using the Peng-Robinson EoS and various mixing rules. The UNIQUAC GE model was used together with the WS and HV mixing rules. The results indicated that the GE mixing rules provides satisfactory results for this system, with the WS mixing rule demonstrating the best results (AARD% of 5.06% in bubble point pressure calculations). The modeling results also indicated that the temperature-dependency of the binary interaction coefficient, kij, in the vdW mixing rules is very important for accurate results.

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.

Measurement and calculation of solubility of quinine in supercritical carbon dioxide

Solubility of quinine in supercritical carbon dioxide (SCCO2) was experimentally measured in the pressure range of 8 to 24MPa, at three constant temperatures: 308.15K, 318.15K and 328.15K. Measurement was carried out in a semi-dynamic system. Experimental data were correlated by iso-fugacity model (based on cubic equations of state, CEOS), Modified Mendez–Santiago–Teja (MST) and Modified Bartle semi-empirical models. Two cubic equations of state: Peng–Robinson (PR) and Dashtizadeh–Pazuki–Ghotbi–Taghikhani (DPTG) were adopted for calculation of equilibrium parameters in CEOS modeling. Interaction coefficients (kij& lij) of van der Waals (vdW) mixing rules were considered as the correlation parameters in CEOS-based modeling and their contribution to the accuracy of model was investigated. Average Absolute Relative Deviation (AARD) between correlated and experimental data was calculated and compared as the index of validity and accuracy for different modeling systems. In this basis it was realized that the semi-empirical equations especially Modified MST can accurately support the theoretical studies on phase equilibrium behavior of quinine–SCCO2 media. Among the cubic equations of state DPGT within two-parametric vdW mixing rules provided the best data fitting and PR within one-parametric vdW mixing rules demonstrated the highest deviation respecting to the experimental data. Overall, in each individual modeling system the best fitting was observed on the data points attained at 318K, which could be perhaps due to the moderate thermodynamic state of supercritical phase.

Vapor–liquid equilibria measurements of 1,1,1,2-tetrafluoroethane (HFC-134a) + 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + isobutane (HC-600a) ternary system

Vapor–liquid equilibrium data for the ternary mixture of 1,1,1,2-tetrafluoroethane (HFC-134a) + 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + isobutane (HC-600a) were measured at temperatures from 283.15 K to 323.15 K using a recirculation apparatus. The uncertainties of the experimental data are estimated within 5 mK, 0.5 kPa, and 0.003 for the temperature, pressure, and the equilibrium liquid and vapor mole fractions, respectively. The experimental data were compared with the predicted data by the Peng Robinson equation of state with the vdW mixing rule and the Wong Sandler mixing rule, respectively. The binary interaction parameters of each binary mixture were determined from the experimental data in literature. The results show that the predicted data agree well with the experimental data. It indicates that the PR equation can be used to predict VLE data of ternary mixture of HFC-134a + HFO-1234yf + HC-600a. The proposed ternary mixture has potential to be refrigerant with low GWP and excellent thermodynamic performance.

Solubility of Ethene in n-Hexane and n-Heptane as Common Slurry-Phase Polymerization Solvents: Experimental Measurement and Modeling

To evaluate solvent performance, mass transfer calculation of gas–liquid phases and good prediction of catalyst activity and polymer product yield, precise experimental solubility data are required in slurry-phase ethene polymerization. The solubility of ethene in n-hexane and n-heptane as commercial solvent of ethene slurry-phase polymerization was measured at pressures from 0.18 to 1.6 MPa and temperatures ranging from 303 to 348 K. A static apparatus is used to measure the experimental data. The experimental data are modeled using Peng–Robinson cubic equation of state (PR CEOS) with vdW mixing rule with two adjustable parameters. The modeling results show the PR CEOS is capable to represent the experimental data well.

Isothermal VLE measurements for the binary mixture of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + 1,1-difluoroethane (HFC-152a)

Isothermal vapor–liquid equilibrium (VLE) data for the binary mixture of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf)+1,1-difluoroethane (HFC-152a) were measured at temperatures from 283.15K to 323.15K using a recirculation apparatus. The experimental data were correlated by using PR EoS with vdW mixing rule, the comparison between the correlation results and experimental data showed a good agreement. HFO-1234yf (1)+HFC-152a (2) system shows not only azeotropic behavior but also near azeotropic behavior with a very small temperature glide of less than 0.4K within the complete range of composition and of temperature.

Vapor–liquid equilibria for binary system of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) + isobutane (HC-600a)

Isothermal vapor–liquid equilibrium data for the binary mixture of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf)+isobutane (HC-600a) were measured at temperatures from 283.15 to 323.15K using a recirculation apparatus. The experimental data were correlated using the Peng–Robinson equation of state with vdW mixing rule and Wong–Sandler mixing rule, respectively. The comparison between the correlation results and experimental data showed a good agreement, and Wong–Sandler mixing rule gave more accurate calculations for this binary system. Azeotropic behavior was found at high mole fraction of HFO-1234yf.

Vapor–liquid equilibria for the 1,1,1,2-tetrafluoroethane (HFC-134a) + 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) and 1,1,1-trifluoroethane (HFC-143a) + 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) systems

Isothermal vapor–liquid equilibria (VLE) data for the binary 1,1,1,2-tetrafluoroethane (HFC-134a)+1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) and 1,1,1-trifluoroethane (HFC-143a)+2,3,3,3-tetrafluoropro-1-pene (HFO-1234yf) systems were measured at temperatures from 283.15K to 323.15K at 10K intervals. The VLE experimental data for the HFC-134a+HFC-227ea system agree well with the literature data. The experimental data were correlated using PR EoS with vdW mixing rule, and binary interaction parameters in mixing rules were optimized to fit the experimental data of each binary mixture. The comparison between the experimental data and the correlated results shows a good agreement.

Measurement of the (pressure, density, temperature) relation of a (methane + nitrogen) gaseous mixture using an accurate single-sinker densimeter

A single-sinker magnetic suspension densimeter based on Archimedes’ buoyancy principle is described. Density measurements on high-purity nitrogen demonstrate the performance of the densimeter. Comprehensive (p,ρ,T) measurements at low densities on a gaseous mixture with mole fraction of (0.8977CH4+0.1023N2) were carried out on this densimeter at six temperatures from (170.586 to 270.054)K and at pressures ranging from (0.1333 to 1.5945)MPa. The overall uncertainty in density is estimated to be 0.1%. The uncertainty in temperature is estimated to be 5mK and that in pressure is 250Pa for (0 to 1.5)MPa and 390Pa for (1.5 to 3)MPa, respectively. The experimental results of the (methane+nitrogen) mixture were compared with REFPROP 9.0, which used GERG-2008 and AGA8 equations of state to predict thermophysical properties of natural gas. The absolute relative deviations of density measurements are all within 0.1%. Meanwhile the experimental results were correlated using the virial equation of state (Virial EOS) with three different mixing rules. The calculated results using the virial EOS combined with VDW mixing rule show good agreement with the experimental data.

A modified differential-model for interaction parameters in PR EoS with vdW mixing rules for mixtures containing HFCs and HCs

In a previous work, a predictive model for the interaction parameter kij was proposed as kij=ki−kj. The assumed mixing factor ki for the pure components can be obtained by fitting to the correlated kij of mixtures which have available experimental data. In this work, up to 62 binary mixtures containing HFCs and HCs were involved and their reported experimental VLE data were correlated using the PR equation of state with the vdW mixing rules. According to the correlation results, a modified differential-model was proposed for the prediction of the interaction parameter kij with the introduction of the acentric factors and the critical properties of the components. The values of mixing factors ki in the modified model were obtained by the least square fitting of the correlated 62 kij data for 15 HFCs and HCs, namely HFC23, HFC32, HFC125, HFC143a, HFC134a, HFC134, HFC152a, HFC161, HFC227ea, HFC236fa, HFC236ea, HFC245fa, propane, isobutane, and n-butane. 105 predicted kij for mixtures containing these HFCs and HCs were given. The predicted results by using the modified model show a good agreement compared to the correlation results. The overall average absolute deviations of pressures and vapor phase compositions of the predicted results are 1.77% and 0.0086, respectively.

Study on elution ability of salicylic acid on ion exchange resins in supercritical carbon dioxide

The elution ability of salicylic acid on ion exchange resins in supercritical carbon dioxide has been studied. Some factors influencing elution recovery, including entrainer, temperature, pressure and the flow rate of supercritical fluid CO2 are discussed in this work. The addition of a small amount of entrainer, such as ethanol, triethanolamine and their mixture to supercritical CO2 can cause dramatic effects on the elution ability. The results show that the salicylic acid can be only slightly eluted from the resin with supercritical CO2 alone with temperatures ranging from 307.15 to 323.15 K and pressures ranging from 10 to 30 MPa. Meanwhile, with the same T, P conditions, 40.58% and 73.08% salicylic acid can be eluted from the ion exchange resin with ethanol and ethanol + triethanolamine as the entrainer, respectively. An improved PR equation of state with VDW1 mixing rules is used to calculate the elution recovery of salicylic acid in supercritical CO2 and the results agree well with the experimental data.

Study on the Interaction Coefficients in PR Equation with vdW Mixing Rules for HFC and HC Binary Mixtures

The Peng-Robinson equation of state with the van der Waals mixing rules was used to correlate vapor–liquid equilibrium (VLE) data for HFC/HC, HFC/HFC, and HC/HC binary mixtures. The interaction parameter k ij was obtained for every binary mixture. It was assumed that k ij has contributions from the two components, and each component has its own constant contribution factor k i for the mixture, and the values of k ij indicate the degree in difference of properties between the two components. Therefore, the interaction parameters k ij is proposed as: k ij = k i − k j . The values of the mixing factor k i for Hydrofluorocarbons (HFCs) and Hydrocarbons (HCs), including propane, isobutane, n-butane, R23, R32, R125, R143a, R134a, R152a, R227ea R236fa, R236ea, and R245fa, were obtained by least-square fitting. In total, 39 refrigerant binary mixtures were analyzed on the basis of this method, and the results showed good agreement with experimental data. The overall average absolute deviations of pressure and vapor mole fraction are 1.3 % and 0.0089, respectively.

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.

Binary solid–liquid–gas equilibrium of the tripalmitin/CO 2 and ubiquinone/CO 2 systems

A conventional method was used to measure the melting points of the natural lipid tripalmitin and of the coenzyme ubiquinone (coQ10) under high pressure carbon dioxide. The pressure–temperature behavior of the binary three-phase solid–liquid–gas (SLG) equilibrium for these and other systems, namely naphthalene and biphenyl with carbon dioxide, ethylene and ethane, were investigated using the Peng–Robinson equation of state (PR-EoS) with the van der Waals one fluid (vdw-1) mixing rules and with the NRTL equation to calculate the solute activity in the liquid phase. When the interaction parameter in the vdw-1 mixing rules could be determined by the PR-EoS through the correlation of the solid–fluid phase equilibrium data, the two NRTL parameters were used as adjustable parameters. The results showed that fairly good correlations could be achieved for the experimental pressure–temperature data of all the asymmetric systems studied here, indicating that the NRTL parameters are crucial for describing the pressure–temperature behavior but have little effect on the phase compositions at the SLG equilibrium.

Comparison of different mixing rules for prediction of density and residual internal energy of binary and ternary Lennard–Jones mixtures

Mixing rules are necessary when equations of state for pure fluids are used to calculate various thermodynamic properties of fluid mixtures. The well-known van der Waals one-fluid (vdW1) mixing rules are proved to be good ones and widely used in different equations of state. But vdW1 mixing rules are valid only when molecular size differences of components in a mixture are not very large. The vdW1 type density-dependent mixing rule proposed by Chen et al. [1] is superior for the prediction of pressure and vapor–liquid equilibria when components in the mixture have very different sizes. The extension of the mixing rule to chain-like molecules and heterosegment molecules was also made with good results. In this paper, the comparison of different mixing rules are carried out further for the prediction of the density and the residual internal energy for binary and ternary Lennard–Jones (LJ) mixtures with different molecular sizes and different molecular interaction energy parameters. The results show that the significant improvement for the prediction of densities is achieved with the new mixing rule [1], and that the modification of the mixing rule for the interaction energy parameter is also necessary for better prediction of the residual internal energy.