Wong – Sandler Research Articles

Modified Redlich-Kwong and Peng-Robinson Equations of State for Solubility Calculation of Solid Compounds in Supercritical Carbon dioxide

The modified Redlich-Kwong (βRK) and modified Peng-Robinson (βPR) Equations of State (EoSs) combined with the van der Waals mixing rule (vdW0) have been proposed to evaluate the solubilities of ten solid compounds in supercritical CO 2 . These ten solid compounds are including Methimazole, Ascorbic acid, Ascorbyl palmitate, Propyl gallate, Aspirin, Fluoranthene, Triclocarban, Hinokitiol, Phenol, and Climbazole. In order to recognize the accuracy of the proposed EoSs, the results of these models have been compared with the calculation results of SRK and PR equations of state in combination with the vdW1 and the Wong-Sandler (WS) mixing rules and other models reported in the literature. The results showed that the proposed models are well for solubility calculation of these ten solid compounds in supercritical CO 2 and the RK EoS in combination with the vdW0 mixing rule led to better correlation (AARD = 5.1%) compared with other ones.

Modeling of gas–solid equilibrium of binary systems aided by Frankenstein PSO

Binary systems containing supercritical CO 2 + hydrocarbons were used for modeling gas–solid equilibrium by a combined method including a thermodynamic model and a meta-heuristic algorithm. The Peng–Robinson (PR) equation of state was used in the classical solubility equation. In addition, Wong–Sandler (WS) mixing rules were used, and the van Laar model (VL) was included in order to evaluate the excess Gibbs free energy that appears in these mixing rules. Then, a variant of particle swarm optimization (PSO), called Frankenstein PSO (FPSO) was implemented for minimizing the difference between calculated and experimental solubility values. The results showed that the FPSO algorithm is a very powerful tool for parameter estimation on the PR-WS-VL model with good performance and accuracy, and considerably low deviations. Therefore, values calculated by the combined method (PR-WS-VL + FPSO) are considered accurate enough for physical and engineering calculations, among other uses.

Application of supercritical fluid processes

The present work deals with the storage of Hydrogen where promising ways are based on the solubility of organic or inorganic compounds in supercritical fluids, inducing specific interactions to retain this non polluting energy vector.Consequently the modeling of the solubility of polar organic compounds like Ortho Hydroxy benzoic acid (o-HBA), and Para Hydroxy benzoic acid (p-HBA), Dichloro diphenyl Trichloro ethane (DDT) and 2,4-Dichloro phenoxyacetic acid (usually referred to by its abbreviation, (2,4-D) as well as their mixtures, in supercritical fluids such as carbon dioxide, is presented.For the two binary systems i.e. o-HBA-CO2, DDT-CO2 the model combining the cubic Redlich Kwong (RK) equation of state (EOS) with the van der Walls (VW) mixing rule (MR) at constant temperature of 313 K and a pressure range of 120–220bar, showed quite good results compared to the experimental values. However the model Redlich–Kwong–Soave (RKS)–Wong–Sandler (WS) provided a better correlation.Similarly the model RK-WS gave better results for the solubility of o-HBA in CO2 and for the mixture o-HBA–2,4-D in CO2.The obtained solubilities of p-HBA in supercritical carbon dioxide were found to be higher than that of o-HBA. This can be explained by the differences in the intermolecular interactions which are relatively weak for the case of o-HBA.The results obtained from the combinations Patel–Teja (PT)-VW and PT-WS showed important deviations compared to the experimental values and this for all the considered systems.

Experimental vapour–liquid equilibrium data of the quaternary system Methanol (1) + Isopropyl alcohol (2) + Water (3) + Glycerol (4) along with Isopropyl alcohol (2) + Glycerol (4) and Isopropyl alcohol (2) + Water (3) binary data at atmospheric and sub-atmospheric pressures

The vapour–liquid equilibrium (VLE) behaviour of the quaternary system, Methanol (1) + Isopropyl alcohol (IPA) (2) + Water (3) + Glycerol (4) at 53.33, 66.66, 79.99 and 95.2 kPa, has been studied experimentally using a Sweitoslawsky-type ebulliometer. The VLE data of this quaternary system at sub-atmospheric and ambient conditions will be useful in the process intensification design of bio-diesel production. Experimental VLE data were compared with predictions from Wilson and NRTL models using only the constituent binary interaction parameters. The predictions of equilibrium temperatures thus obtained using Wilson model compared well with the experimental values with an average root mean square deviation (rmsd T) of 0.3153 K. The binary system IPA (2) + Glycerol (4) was studied experimentally at 53.33, 66.66, 79.99 and 94.93 kPa and the data correlated with Wilson, NRTL, UNIQUAC and Peng–Robinson (PR) and Soave–Redlich-Kwong (SRK) equations of state (EoS) combined with Wong–Sandler (WS) mixing rules. Experimental data of this binary system was also compared with predictions from UNIFAC model. The VLE data of the binary system IPA (2) + Water (3) at 94.66 kPa is reported here and correlated with Wilson and NRTL activity-coefficient models. Wilson model represented the binary systems better than other models with a mean rmsd T of 0.2853 K for IPA (2) + Glycerol (4) and an rmsd T of 0.1390 for the IPA (2) + Water (3) system. MATLAB programming has been used for all the calculations.

Isobaric ternary vapour–liquid equilibrium of methanol(1) + diisopropyl ether(2) + isopropyl alcohol(3) along with methanol + isopropyl alcohol binary data at atmospheric and sub-atmospheric pressures

Experimental vapour–liquid equilibrium (VLE) data of the ternary system methanol(1)+diisopropyl ether(2)+isopropyl alcohol(3) at 53.33, 66.66, 79.99 and 95.33kPa, studied using a Sweitoslawski-type ebulliometer over the entire composition range is reported here. VLE data of one of the constituent binaries of this ternary system, methanol(1)+isopropyl alcohol(3) was also measured at 53.33, 66.66, 79.99 and 94.79kPa. Wilson, NRTL, UNIQUAC, Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state (EoS) combined with Wong–Sandler (WS) mixing rules were used to correlate the experimental binary data. The experimental binary data has also been compared with predictions from UNIFAC model. NRTL model was found to represent the methanol(1)+isopropyl alcohol(3) system best. Experimental ternary VLE data was found to be in good agreement with predictions from NRTL model with an average root mean square deviation of 0.1164 between experimental and predicted temperatures.

Vapor–liquid equilibria of fluoroethane (HFC-161) + 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf)

In this study, isothermal vapor–liquid equilibrium (VLE) data were measured for the binary system of fluoroethane (HFC-161)+2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) over the whole composition range in the temperature range from 283.15 to 323.15K at 10K intervals. The experimental VLE data were correlated with the Peng–Robinson equation of state. The van der Waals (vdW) one-fluid mixing rule and the Wong–Sandler (WS) mixing rule with the non-random two-liquid (NRTL) activity coefficient model were both used. The correlation results show good agreement with the experimental data.

A New Simple Equation of State for Calculating Solubility of Solids in Supercritical Carbon Dioxide

In this work, a modified Redlich–Kwong (βRK) equation of state has been proposed to calculate the solubilities of twenty solids including Ascorbic acid, Fluoranthene, Propyl gallate, Acenaphthene, Asprin, Climbazole, Cinnamic acid, Triclocarban, 4-methoxyphenylacetic acid, Phenoxyacetic acid, Cholesterol,Cholesteryl butyrate, Cholestrol acetat,Triphenylene, Ibuprofen, Acetanilide, Propanamide, Butanamide, Chrysene and Dodecyl gallate in supercritical carbon dioxide (440 data points). The proposed equation of state has been coupled with the van der Waals zero (vdW0) mixing rule. To distinguish the accuracy of the proposed model, the results of the model have been compared with the results of Peng–Robinson (PR) equation of state in combination with the van der Waals one (vdW1) and the Wong-Sandler (WS) mixing rules. The calculation results showed that the proposed model performed well for reproducing the solubility of these twenty solids in supercritical carbon dioxide with absolute average relative deviation (AARD) = 5.7 %.

Experimental isobaric vapor–liquid equilibrium at atmospheric and sub-atmospheric pressures, excess molar volumes and deviations in molar refractivity from 293.15 K to 318.15 K of diisopropyl ether with methanol and isopropyl alcohol

Experimental isobaric vapor–liquid equilibrium data for the binary systems, diisopropyl ether+isopropyl alcohol and methanol+diisopropyl ether at the local atmospheric pressure of 94.79kPa and at sub-atmospheric pressures of (53.3, 66.7, 79.9) kPa were obtained over the entire composition range using a Sweitoslawsky-type ebulliometer. The experimental temperatures were compared with predictions made using Wilson, NRTL, UNIQUAC, UNIFAC, Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state (EoS) with Wong–Sandler (WS) mixing rules. Model parameters along with the deviations in temperature have been presented. Experimental temperatures were found to be in good agreement with the predicted values. NRTL model was found to represent the VLE behavior of these systems better than the other models used. Density and refractive indices of mixtures are reported from 293.15K to 318.5K.

Prediction of Vapor-Liquid Equilibrium of Polypropylene Oxide Solution Systems by Cubic Equations of State

In this research, vapor-liquid equilibrium behavior of Polypropylene oxide (PPO)/solvent and Polypropylene glycol (PPG)/solvent were calculated using cubic equation of states. Eight models containing PRSV and SRK CEOS with four mixing rules namely vdW1, vdW2, Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results of absolute average deviations (%AAD) between predicted and experimental bubble point pressure were calculated and presented. The PRSV+vdW2 model was the best predictive model with the highest accuracy (AAD=1.021%) between other models.

Application of cubic equation of state models in prediction of vapor–liquid equilibria for binary polyvinyl acetate/solvent solutions

ABSTRACTThe cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non‐ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibria calculations of polyvinyl acetate (PVAc)/solvent solutions were performed. In this approach, eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely vdW1, vdW2, Wong–Sandler (WS), and Zhong–Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. Absolute average deviations (%AAD) between predicted results and experimental bubble point pressure data were calculated and presented. The capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, but the performance of the PRSV + vdW2 was more reliable than the other models with 2.65% in AAD for total of solution systems. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40651.

Modeling of vapor-liquid equilibrium for binary polypropylene glycol/solvent solutions using cubic equation of state models: optimization and comparison of CEoS models

Abstract The cubic equation of state (CEoS) is a powerful method for calculation of the vapor-liquid equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, VLE calculations of polypropylene glycol (polypropylene oxide) [PPG(PPO)]/solvent solutions were carried out. In this approach, eight models containing Peng-Robinson-Stryjek-Vera (PRSV) and Soave-Redlich-Kwong (SRK) CEoS separately combined with four mixing rules, namely van der Waals one-fluid mixing rule with one adjustable parameter (vdW1), van der Waals one-fluid mixing rule with two adjustable parameters (vdW2), Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For a better correlation, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations (%AAD) between computed results and experimental bubble point pressure data were calculated and presented. Although the capability of two CEoS had a good agreement with experimental data and illustrated the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

Phase equilibria modeling of binary systems containing ethanol using optimal feedforward neural network

A comprehensive understanding of vapor liquid equilibrium (VLE) data is one of the most important information for designing and modeling of process equipment. Because, it is not always possible to completely carry out experiments at all of the possible operational temperatures and pressures range, generalized thermodynamic models, e.g. equations of state are constructed for computing of required VLE data. In this work, artificial neural network (ANN) was used to derive predictive models of bubble point pressure and vapor phase composition of binary ethanol (C2H5OH) mixtures. In the neural network model, it is assumed that the considered VLE data depend on critical properties, acentric factor, normal boiling point, liquid phase composition of the solutes, and temperature. The proposed ANN model has been constructed and trained with VLE experimental data of nine different binary systems containing C2H5OH collected from various literatures. Optimal configuration of the ANN model has been determined using minimizing the average absolute relative deviation percent (%AARD), mean square errors (MSE) and the maximizing the correlation coefficient (R2) between observed and predicted VLE data with the ANN model. By using this procedure a two-layer ANN model with twenty-three hidden neuron has been found as an optimal topology. The accuracy of our optimal two layers ANN model has been compared with the Peng–Robinson cubic equation combined with Wong–Sandler (WS) mixing rules including a Van Laar (VL) model for the excess Gibbs free energy. Comparison with available literatures data and Peng–Robinson equation of state confirm that the present ANN model is more accurate and superior than the other published works. The sensitivity errors analysis clarify that our ANN model could predict vapor phase composition and bubble point pressure of all of the nine binary ethanol systems with %AARD of 1.52% and 2.59% respectively. The study demonstrates that the neural network model is a good alternative method for the estimation of VLE properties of the binary system containing C2H5OH.

The Equilibrium Data and Thermodynamic Modeling of Hydrate Formation for CO2 and Mixtures of CO2 and CH4 in the Presence of Methanol

Equilibrium data for the novel formation of hydrates of carbon dioxide and mixtures of carbon dioxide and methane in 20 wt% aqueous methanol solution were measured by the constant-volume method. For CO2, these data were taken at the temperature and pressure ranges of 264.7–270.7 K and 1,470–3,160 kPa, respectively. For mixtures of carbon dioxide and methane, these data were taken at the temperature and pressure ranges of 262.9–273.7 K and 1,370–5,100 kPa, respectively. The data obtained for CO2 in 20 wt% aqueous methanol solution were in disagreement with previously published data, but there was good agreement between our data and the predictions of thermodynamic models. The Peng-Robinson equation of state (PR EOS) coupled with the Wong-Sandler (WS) mixing rule was used to obtain the fugacities of the components in the gas and aqueous liquid phases. The PR EOS was then coupled with van der Waals-Platteeuw (vdW-P) hydrate model and applied to predict hydrate-formation conditions in the system containing methanol. The model predictions demonstrated good agreement with the experimental data.

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO2 + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO2 + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013

Correlation of Viscosity of Aqueous Solutions of Alkanolamine Mixtures Based on the Eyring's Theory and Wong-Sandler Mixing Rule

A viscosity model, based on Eyring's absolute rate theory combined with a cubic PR equation of state and Wong-Sandler mixing rule, has been proposed in order to correlate viscosities of aqueous solutions of alkanolamine mixtures at atmospheric pressure and different temperatures. In the proposed method, the energy and size parameters in studied Equation of State (EoS) have been obtained using the Wong - Sandler (WS) mixing rule combined with the NRTL and Wilson Gibbs equations. The NRTL and Wilson parameters for aqueous solutions of alkanolamine mixtures have been correlated using measured viscosity data at atmospheric pressure and different temperatures. The overall average deviation between the experimental and calculated viscosities of studied aqueous solutions of alkanolamine mixtures using Wilson model is 0.92%.

Assessment, measurement and correlation of (vapour + liquid) equilibrium of (carbon dioxide + butyl, isobutyl, and amyl formate) systems

In this work, three formates (butyl, isobutyl, and amyl formate) were considered as relative perfect CO2 absorption performance based on the excess Gibbs function as the thermodynamics criterion. An online static-analytical method was used to measure the (vapour + liquid) equilibrium (VLE) data for the CO2+butyl, isobutyl, and amyl formates under the pressure of (0.2 to 6)MPa and the temperatures at a range from (283.15 to 343.15)K. Then the VLE data were correlated by Peng–Robinson (PR) equation of state (EOS) with classic mixing rule, PR EOS with Wong–Sandler (WS) mixing rule and Soave–Redlich–Kwong (SRK) EOS with classic mixing rule. It is shown that SRK EOS is comparatively appropriate for CO2+butyl formate binary system. Both PR EOS with classic mixing rule and SRK EOS can be used to correlate the binary systems of CO2+isobutyl, amyl formate. It is found that the solubility order of three formates for CO2 from high to low is arranged as CO2+amyl formate>CO2+butyl formate>CO2+isobutyl formate, showing the system of CO2+amyl formate has the best absorption performance. By comparison, it indicates that formates have a greater solubility for CO2 than acetates on the condition of the same temperature and pressure. In addition, the thermophysical properties, mole absorption and mass absorptive amount of several industrial absorbents were assessed and the absorption performance of amyl formate for CO2 is better than other physical absorbents. Thus, the study concluded that amyl formate has potential research value as physical absorbent for CO2 capture.

Thermodynamic modeling of PVTx properties for several water/hydrocarbon systems in near-critical and supercritical conditions

E ) model and the cubic plus association (CPA) equa- tion of state (EoS) are compared in this study with respect to their accuracy in the correlation of PVTx for systems such as water/methanol, water/ethanol, water/benzene, water/toluene, water/methane, water/n-butane, water/n-pentane, water/ n-hexane, water/heptane, and water/octane, in supercritical conditions within temperature and pressure ranges of (573- 698 K) and (7.0-276.0 MPa), respectively. In the proposed EoS/G E model, Peng-Robinson (PR) equation of state, linear combination Vidal-Michelsen (LCVM) and Wong-Sandler (WS) mixing rules in conjunction with UNIQUAC activity coefficient model were used. Correlation of both CPA and EoS/G E models was evaluated by comparing the results with the experimental data. Average absolute relative deviation (AARD) for WS, LCVM, and CPA was found to be 2.99, 11.11 and 5.14%, respectively, indicating better correlation of WS model with the experimental data.

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.

Measurement and correlation of the isothermal vapor-liquid equilibrium data for carbon dioxide and dimethyl ether system

Vapor-liquid equilibrium (VLE) data for the binary system of carbon dioxide (CO2)+dimethyl ether (DME) were measured at six equally spaced (10 K) temperatures between 283.15 and 333.15 K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continuously recirculated. The equilibrium compositions of vapor and liquid phases and pressure were reported at each temperature. The experimental VLE data were correlated with PR-EoS using the Wong-Sandler (W-S) mixing rule and the universal mixing rule (UMR). The overall average values of AAD-P (%) and AAD-y through the temperature range from 283.15 to 333.15 K were 1.0% and 0.012 for the W-S mixing rule and 0.88% and 0.014 for the UMR, respectively. All values are small and acceptable. Calculated results with these equations have given satisfactory results compared with the experimental data.

Applications of cubic equations of state for determination of the solubilities of industrial solid compounds in supercritical carbon dioxide: A comparative study

Representation/predictions of the solubilities of industrial solid compounds in supercritical carbon dioxide have been a challenge since the last two decades. In this communication, the Soave–Redlich–Kwong (SRK), the Peng–Robinson (PR), the Patel–Teja–Valderrama (PTV), the Esmaeilzadeh–Roshanfekr (ER) and the modified Esmaeilzadeh–Roshanfekr (m-ER) equations of state (EoS) accompanied with several mixing rules including the Wong–Sandler (WS), the covolume-dependent (CVD) and the van der Waals one (vdW1) and two (vdW2) fluid mixing rules are applied to calculate/estimate the solubilities of 23 mostly used solid compounds in supercritical carbon dioxide. In addition, the Van-Laar excess Gibbs energy (Gex) activity model is also used in phase equilibrium calculations. The probable global optimal values of the proposed thermodynamic model parameters are evaluated by the differential evolution (DE) optimization strategy. The results indicate that the combination of the m-ER EoS with the WS mixing rule leads to more accurate predictions (AARD=7%) in comparison with other ones. Finally, application of Chrastil semi-empirical correlation for estimation of the solubilities of several compounds in supercritical carbon dioxide is investigated at wide ranges of temperatures.