Predictive Soave – Redlich – Kwong Research Articles

Mathematical Analysis of Discontinuous Rectification Columns at Pilot Scale Based on the Continuous Stable States Concept and MESH Equations

Mathematical analysis and simulation of a discontinuous rectification column was performed using an operational strategy during the start-up before reaching a pseudo-stable state in discontinuous operation. The mathematical model was formulated focusing on the equilibrium state (ES) and implementing MESH equations (M: Mass balance, E: Equilibrium thermodynamics, S: Stoichiometry relations, H: Enthalpy or heat balance) to provide solutions using the Thomas method and the Wang-Henke algorithms internally coupled to the Fourth Order Runge-Kutta method. The results were validated with experimental data from a distillation column at a pilot scale using an ethanol-water system with an equilibrium behavior described by the UNIQUAC Functional-group Activity Coefficients (UNIFAC) and Predictive Soave-Redlich-Kwong (PSRK) thermodynamic models with a global error of 1.84%. The molar ethanol concentrations presented deviations from the mathematical model predictions from 1.51% to 0.02%, with a global mean error of 0.48%. A mean error of 0.055% was obtained for the temperature profile of the column, thus demonstrating the effectiveness of the solution and its convergence capacity. The solution based on the Thomas method and the Wang-Henke algorithms coupled to the Runge-Kutta method made it possible to describe the behavior and variables of all stages of the distillation column. Operation at total reflux from start-up avoids wasting product and allows for the stabilization of the state variables, such as temperature and molar composition.

A-priori modelling of density of deep eutectic solvent with cohesion based cubic equation of state

Being an influential thermophysical property, the modelling of densities has been performed over a wide range of temperature from 278.15 K to 373.15 K of 169 different DESs primarily belong to the choline, tetraalkylammonium, menthol, betaine, alanine subcategories having total 1421 experimental datapoints. The models used for the computation of densities are Reid et al. (RR) model, Mchaweh et al. (MH) model, Linear generalized model (LGM), Predictive Soave−Redlich−Kwong (PSRK) equation of state with NSM1 alpha function model (NMPRNSM1), Predictive Soave−Redlich−Kwong (PSRK) equation of state with original derived alpha function model (NMSRK). amongst them the cohesion-based models namely NMPRNSM1 and NMSRK predict densities more precisely than the other models.

Thermodynamic analysis of a semi-lean solution process for energy saving via rectisol wash technology

Currently, it is of great significance to develop energy-saving technologies. Rectisol wash technology is becoming more and more popular in the industrial field due to its excellent performance. In order to reduce the energy consumption, a semi-lean solution process based on the Rectisol wash technology is proposed in this paper. The Cubic-Plus-Association (CPA) and Predictive Soave–Redlich–Kwong (PSRK) property methods are selected for the simulations in Aspen Plus. Two scenarios are proposed for the energy and exergy analysis. Results show that 50% SP3-reflux ratio is the optimal point in both scenarios from the energy view, and the optimal SP3-reflux ratios for scenario 1 and scenario 2 are 40% and 43% from the exergy view, respectively. In addition, the analysis results of related parameters in both scenarios show that increasing the SP1-spitting ratio or decreasing the SP2-spitting ratio has a positive effect on CO2 production; the H2S concentration in CO2 product first increases and then decreases while either ratio increases. The stripping N2 flowrate has a significant impact on the H2S concentration in Claus gas. This paper may guide for further study of the semi-lean solution process and provide a better understanding for Rectisol technology.

Hydrocarbon Dew Point Measurement and Model Evaluation of Synthetic and Real Natural Gases.

Hydrocarbon dew point (HCDP) is one of the most important quality specifications of natural gas. Measuring and predicting the HCDP accurately are essential for the natural gas industry. However, the comprehensive experimental HCDP curve data are still rare, and knowledge about adopting proper prediction models remains unclear. In view of this, HCDP determination work by use of an improved test system and model evaluation based on more than 1000 dew points data have been done to improve the aforementioned dilemma. HCDP curve data of three gravimetrically prepared synthetic natural gases (SNGs) and one real gas (RG) are determined first. Then, one set of data containing 712 dew points from 28 SNGs and 334 dew points from 14 RGs is used to evaluate the performance of eight different HCDP prediction models including Soave–Redlich–Kwong (SRK), SRK–Twu, Peng–Robinson (PR), Twu–Sim–Tassone (TST), predictive SRK (PSRK), GERG-2008, PSRK, and perturbed-chain statistical associating fluid theory (PC-SAFT) models. Considerable prediction deviation of these models in the high-pressure region (pressure above 6.0 MPa) is observed compared to that in the low-pressure region (under 6.0 MPa), and the reasons for that difference are discussed. Evaluation results reveal that among the eight prediction models, GERG-2008 has the best performance (overall average absolute deviation (AAD): 1.44 °C) for SNGs, and PSRK and SRK–Twu fits the experimental data best for RGs (overall AAD: 2.50 °C). Therefore, GERG-2008 is recommended for HCDP prediction of relatively lean gas, whereas PSRK and SRK–Twu are recommended for calculating the HCDP of relatively heavy natural gases in low-pressure and high-pressure regions, respectively.

Application of the Perturbed-Chain SAFT to Phase Equilibria in the Fischer–Tropsch Synthesis

As an alternative route to produce liquid fuels, Fischer–Tropsch synthesis (FTS) has received considerable attention. Phase equilibria have been one of the key issues in the design and operation of not only an FTS reactor, but also relevant downstream processing, e.g., stepwise condensation of FTS products, wastewater treatment, and the recovery of α-olefins. These issues are extremely complex due to a wide spectrum of FTS products and the presence of noncondensable gas, nonpolar components, associating components, and highly polar components. To address these issues, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was evaluated using phase equilibrium data of binary and ternary mixtures containing water, alcohols, hydrocarbons, and noncondensable gases. The parameter values are available via a three-step parametrization strategy established in our previous work [Zheng et al. Ind. Eng. Chem. Res. 2018, 57, 3014]. A couple of popular benchmark models, namely the Soave–Redlich–Kwong (SRK) EoS with the modified Huron–Vidal second-order mixing rule (SRK/MHV2) and the predictive SRK (PSRK) EoS, were selected for comparison to put the performance of the PC-SAFT EoS into perspective. It was found that the PC-SAFT EoS gives reliable correlations/predictions in all the studied cases, whereas the other two models fail to do so. The three models were also employed to simulate hot and cold traps where the stepwise condensation of the reactor effluent occurs. It was found that all three models yield satisfactory results for the paraffin distribution of the liquid stream leaving the hot trap, while the SRK/MHV2 and PSRK models are less accurate for the olefin distribution, particularly at high temperature. It was also found that all three models are capable of predicting the composition of the two liquid streams (namely organic and aqueous) leaving the cold trap except that the SRK/MHV2 model fails to accurately reproduce the distribution of alcohols in the two liquid streams. This study advocates the practical use of the PC-SAFT EoS by its application to a complex, industrially important FTS process and a comprehensive evaluation, together with the two popular benchmark models.

Phase Equilibrium Study of the Ternary System CO2 + H2O + Ethanol At Elevated Pressure: Thermodynamic Model Selection. Application to Supercritical Extraction of Polar Compounds

The purpose of this study is to select an appropriate thermodynamic model among the ones available in commercial process simulators for representing the phase behavior of the carbon dioxide + ethanol + water system. The following versions of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) cubic equations of state (EoS) were considered: Panagiotopoulos-Reid, modified Panagiotopoulos-Reid, Huron-Vidal-NRTL, Modified Huron-Vidal (MHV2-UNIFAC), Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng–Robinson (VTPR). The Polar Perturbed-Chain SAFT EoS deriving from the Statistical Associating Fluid Theory (PPC-SAFT) was also selected for the present investigation. This study highlighted that the optimal thermodynamic models for the application of interest have to be chosen among the VTPR, PSRK and MHV2-UNIFAC EoS. Once identified a suitable thermodynamic model for the CO2 + ethanol + water ternary system, it has been possible then to simulate the extraction process of polar compounds from natural products and to discuss how water influences the process efficiency.

Vapor-Liquid Equilibria Measurements and Modeling of the Isobutane+Butane+Ethanol System

The vapor-liquid equilibria of the isobutane+butane+ethanol system were measured at 313-403 K and the experimental pxy data were compared with the calculation results of the modified Redlich-Kwong (RK) equation of state (EOS) and predictive Soave-Redlich-Kwong (PSRK) EOS. Binary interaction parameters of the modified RK EOS for the butane+ethanol and isobutane+ethanol systems were determined from their binary vapor-liquid equilibrium data, while those for the butane+isobutane were set to zero. The average deviation between the modified RK EOS and experimental data was 0.05.

Selective Encaging of N2O in N2O-N2 Binary Gas Hydrates via Hydrate-Based Gas Separation.

The crystal structure and guest inclusion behaviors of nitrous oxide-nitrogen (N2O-N2) binary gas hydrates formed from N2O/N2 gas mixtures are determined through spectroscopic analysis. Powder X-ray diffraction results indicate that the crystal structure of all the N2O-N2 binary gas hydrates is identified as the structure I (sI) hydrate. Raman spectra for the N2O-N2 binary gas hydrate formed from N2O/N2 (80/20, 60/40, 40/60 mol %) gas mixtures reveal that N2O molecules occupy both large and small cages of the sI hydrate. In contrast, there is a single Raman band of N2O molecules for the N2O-N2 binary gas hydrate formed from the N2O/N2 (20/80 mol %) gas mixture, indicating that N2O molecules are trapped in only large cages of the sI hydrate. From temperature-dependent Raman spectra and the Predictive Soave-Redlich-Kwong (PSRK) model calculation, we confirm the self-preservation of N2O-N2 binary gas hydrates in the temperature range of 210-270 K. Both the experimental measurements and the PSRK model calculations demonstrate the preferential occupation of N2O molecules rather than N2 molecules in the hydrate cages, leading to a possible process for separating N2O from gas mixtures via hydrate formation. The phase equilibrium conditions, pseudo-pressure-composition (P-x) diagram, and gas storage capacity of N2O-N2 binary gas hydrates are discussed in detail.

Evaporation of pure and blended droplets of diesel and alcohols (C2–C9) under diesel engine conditions

ABSTRACTAn improved multicomponent evaporation model was developed to study the evaporation characteristics of the pure diesel and alcohol (C2–C9) as well as their blended droplets. In this model, the Predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) was employed to evaluate the vapor–liquid equilibrium for pure and blended droplets. The results indicated that the model predictions agree very well with the experimental measurements. The evaporation characteristics of different pure alcohol droplets were analyzed, and the influence of the addition of alcohols in diesel on the evaporation behavior of droplets under various conditions was discussed.

Prediction of phase equilibrium conditions for gas hydrates formed in the presence of cyclopentane or cyclohexane

In this work, we predicted the hydrate formation conditions for the pure and mixed gas systems of CH4, N2, O2 and CO2 in the presence of cyclopentane or cyclohexane. Chen-Guo model coupled with the predictive Soave-Redlich-Kwong (PSRK) group contribution method was used to calculate the three-phase equilibrium, and the UNIFAC model was employed to calculate the activity coefficient of the liquid phase. The pressure-corrected Henry’s law was employed to calculate the mole fraction of gas components existing in the aqueous phase except water. The prediction results and the percent of Absolute Average Deviation for the calculated hydrate formation pressures and temperatures were presented. It was found that the results predicted in this work agree well with those reported in the literature. Cyclopentane and cyclohexane in aqueous phase was assumed to evaporate into the gas phase and may change the gas components and the corresponding mole fractions in the gas phase. However, the results showed that the concentration variation of cyclopentane or cyclohexane has slight impact on the hydrate formation thermodynamics.

Modeling of the Thermodynamic Equilibrium Conditions for the Formation of TBAB and TBAC Semiclathrates Formed in the Presence of Xe, Ar, CH4, CO2, N2, and H2

The solid phase model of Paricaud1 is used, in conjunction with the predictive Soave–Redlich–Kwong (PSRK) equation of state,2 to correlate the thermodynamic equilibrium conditions of TBAB and TBAC semiclathrates formed in the presence of pure gases. Unlike many previous modeling efforts, the current approach does not neglect the solubility of the gas in the aqueous phase or the presence of water in the vapor phase. Rather, the solubility of the gas and molar fraction of water in vapor phase are computed from a flash calculation. Furthermore, the new approach also computes the Langmuir constants from the Kihara potential rather than from the square well potential or from an empirical correlation. The new modeling approach is applied to TBAB and TBAC semiclathrates that are formed in the presence of Xe, Ar, CH4, CO2, N2, and H2. For all of the gases, new Kihara potential parameters were regressed from the experimental data. It was found that the new approach was able to correlate the experimental data to a ...

P–T–x Measurements for 1,1,1,2-Tetrafluoroethane (R134a) + N,N-Dimethylacetamide (DMA) and N-Methyl-2-pyrrolidone (NMP)

The present study concerns p–T–x phase equilibria measurements involving two working fluid pairs (refrigerant + organic solvent), namely, 1,1,1,2-tetrafluoroethane (R134a) + N,N-dimethylacetamide (DMA) and, 1,1,1,2-tetrafluoroethane + N-methyl-2-pyrrolidone (NMP), using the static–analytic method at temperatures varying between 303 and 353 K. The experimentally measured data were successfully correlated using the Peng–Robinson equation of state (PR-EoS) in combination with Huron–Vidal mixing rule, and the nonrandom two-liquid activity coefficient model (NRTL), contrarily to the predictive Soave–Redlich–Kwong (PSRK) group contribution equation of state which failed to reproduce accurately enough such data.

Prediction of CO2 solubility in ionic liquids using the PSRK model

The predictive Soave–Redlich–Kwong (PSRK) model was applied to predict CO2 solubility in imidazolium-based ionic liquids containing bis(trifluoromethylsulfonyl)imide [Tf2N], tetrafluoroborate [BF4], and hexafluorophosphate [PF6] anions. The UNIFAC PSRK matrix was extended to include these new groups. Binary interaction parameters were obtained by regressing experimental vapor–liquid equilibrium data available in the literature. Experimental data were subjected to a consistency test, and only consistent data were considered during the regression. The model predictions showed satisfactory agreement with the experimental data at pressures up to 5MPa, with an overall root mean square deviation (RMSD) of 0.31. The prediction ability of the model was tested for ionic liquids containing long alkyl chains, exhibiting an overall RMSD of 0.40. The results indicated that the PSRK model provides a reasonable prediction of CO2 solubility in ionic liquids at pressures not in the vicinity of the critical pressures of CO2 and ionic liquids.

Phase equilibria of systems containing aromatic oxygenated compounds with CH4, CO2, H2, H2S, CO and NH3: Experimental data and predictions

The present work proposes an analysis of the solubility of a number of important gases in some representative oxygenated molecules of bio-oils. New experimental equilibrium (VLE, LLE, VLLE) data are presented for binary and ternary systems containing the oxygenated compounds m-cresol, 2-ethylphenol and 2,3-benzofuran in the presence of methane and carbon dioxide. The data were obtained using PVT cells. These data and additional systems with phenol were compared with predictive or semi-predictive approaches as the GC-PPC-SAFT (Group Contribution-Polar Perturbed Chain-Statistical Associating Fluid Theory), PSRK (Predictive Soave–Redlich–Kwong) equations of state and molecular simulation. The predicted values showed to be consistent with both new and existing experimental data. The use of the predictive binary interaction parameter with GC-PPC-SAFT makes it possible to have accurate calculations, in particular with regard to the risk of liquid–liquid phase split in the presence of high pressure CO2. Vapor–Liquid equilibria for these oxygenated compounds were calculated for systems considering other small compounds important in hydrotreatment as hydrogen, CO, H2S and NH3. When no data exist, the different predictive approaches were used in order to evaluate the effect of the gas type or that of the solvent on the gas solubility.

Densities of Six Commercial Ionic Liquids: Experiments and Prediction Using a Cohesion Based Cubic Equation of State

Ionic liquids (ILs) are eco-friendly solvents due to their low vapor pressure. Properties such as density should be known as it affects the mass transfer rates. Due to its limitless combinations, it is impractical to measure densities experimentally. For the first time, the cohesion factor in the cubic equations of state (CEOS) is used to predict the densities of six commercial ILs, namely, 1-ethyl-3-methylimidazolium methane sulfonate [EMIM][MeSO3], 1-ethyl-3-methylimidazolium acetate [EMIM][Ac], 1-ethyl-3-methylimidazolium thiocynate [EMIM][SCN], 1-ethyl-3-methylimidazolium ethyl sulfate [EMIM][EtSO4], Tris(2-hydroxyethyl)-methylammonium methyl sulfate [TEMA][MeSO4], and trihexyl(tetradecyl) phosphonium bis(2,4,4-trimethylpentyl) phosphinate [TDTHP] [Phosph]. CEOS models such as predictive Soave–Redlich–Kwong (PSRK) coupled with cohesion factor gave better results when compared to the correlations such as Reid et al. (RR), Mchaweh et al. (MH), and the linear generalized model (LGM). In this work the PSRK equation of state (EOS) with the derived NSM1 alpha function and PSRK with original SRK alpha function were used for the prediction. PSRK EOS model with NSM1 alpha function and PSRK EOS with original SRK alpha function proved very accurate with average minimum deviation of 0.02 % to 0.44 % and 0.29 % to 0.66 % from experimental values for six ILs, respectively.

Extension of the VTPR Group Contribution Equation of State: Group Interaction Parameters for Additional 192 Group Combinations and Typical Results

Today development, design, and optimization of the various processes is carried out with the help of process simulators. The reliability of the results mainly depends on the quality of the thermodynamic model and the model parameters used. While gE models can be applied for calculation of the phase equilibrium behavior of multicomponent systems using only binary experimental data, group contribution methods like UNIFAC or modified UNIFAC Dortmund allow prediction of the required thermophysical properties using only a limited number of group interaction parameters. For systems containing supercritical components equations of state like Soave–Redlich–Kwong or Peng–Robinson or group contribution equations of state (GCEOS) like the predictive Soave–Redlich–Kwong (PSRK) or the volume-translated Peng–Robinson group contribution equations of state (VTPR) can be applied. In different papers it was already shown that VTPR is a very powerful thermodynamic model. In this paper new group interaction parameters for 192 group combinations are presented, so that the actual matrix now contains group interaction parameters for 252 group combinations. In this paper predicted results of the VTPR group contribution equation of state are compared with the results obtained using modified UNIFAC Dortmund or the PSRK method.

Improvement of predictive Soave–Redlich–Kwong (PSRK) equation of state for representing volumetric properties of carbon dioxide-expanded organic solvents

In this study, the volume translation correction is applied to the predictive Soave–Redlich–Kwong (PSRK) equation of state (EOS) for improving the prediction accuracy of liquid densities of carbon dioxide (CO2)-expanded organic solvents. A total of 23 CO2-expanded organic solvents including hydrocarbons, ketones, and esters are considered in our calculation. By applying the original PSRK EOS, the prediction accuracy of liquid density is only qualitative and the average deviation is about 15%. When applying the translated volumes proposed by Péneloux and Rauzy (1982) and Lin et al. (2006), significant improvements in prediction accuracy are obtained and the average deviation is reduced to 4% and 6%, respectively. To further enhance the predictive accuracy, one attempt has been made in this study to consider the translated volume of CO2 and organic solvent separately. With Péneloux and Rauzy's translated volume for organic solvent, an alternative translated volume for CO2 is developed and adopted. With this approach, satisfactory predicted results are obtained especially at higher pressures and the average deviation can be further reduced to 3%. The volume-translated PSRK EOS discussed in this study provides a simple, empirical and totally predictive approach to accurate representation of liquid densities of CO2-expanded organic solvents.

High pressure phase equilibrium measurements for binary systems CO2 + 1-pentanol and CO2 + 1-hexanol

This work reports phase equilibrium measurements for the systems CO2(1)+1-pentanol(2) and CO2(1)+1-hexanol(2). Experiments were carried out using a high pressure variable-volume view cell with operating temperatures ranged from 303.15K to 373.15K and pressures up to 17.05MPa for the system CO2+1-pentanol, and 303.15K to 353.15K with pressures up to 16.2MPa for the system CO2+1-hexanol. The CO2 molar fractions were ranged from 0.3987 to 0.9192 for the system CO2(1)+1-pentanol(2) and from 0.3926 to 0.9800 for the system CO2(1)+1-hexanol(2), respectively. Only vapor–liquid (VL) phase transitions were observed for the system CO2(1)+1-pentanol(2), while for the system with 1-hexanol(2) vapor–liquid (VL), liquid–liquid (LL) and vapor–liquid–liquid (VLL) phase transition were observed. The experimental data sets were modeled using the Peng–Robinson equation of state with a classical van der Waals quadratic mixing rule (PR-vdW2) and with Wong–Sandler (PR-WS) mixing rule, and they were compared with predicted values using the Predictive Soave–Redlich–Kwong (PSRK) equation of state. PR-WS model provided a better fitting to experimental data for both systems modeled.

Simulation of the multicomponent distillation of spearmint essential oil by a predictive Soave-Redlich-Kwong equation of state and comparison with experiments

In this study, enrichment in major component of spearmint oil has been studied by continuous multicomponent distillation. A mathematical model was evaluated to predict the enrichment by multicomponent distillation of spearmint oil. The aim of the work was to obtain simulation data to compare with experimental data of spearmint oil enriching. The simulation model is based on bubble point method ,the Wang-Henke algorithm and predictive Soave-Redlich-Kwong (PSRK) equation. In this method, MESH equations are solved and a diagonal matrix method for solving equations is used. The model was validated by experimental data obtained from a pilot-plant system, where a continuous distillation column with trays of one to five numbers has been used. The simulation was able to predict satisfactory the experimental data. The results of simulation and experiments show that the major component of spearmint essential oil is enriched from 31% to 62.04% by the distillation column with five trays. The results show that the addition of a tray to the distillation column with a low number of trays, have more effective relative to add a tray to the distillation column with higher trays. The results indicate that increasing of reflux ratio from 2 to 3 increases separation of the major component from 62.04% to 67.04%.

Generalized PSRK Model for Prediction of Liquid Density of Ionic Liquids

Abstract A simple and generalised expression for adjustable parameter for pure ionic liquids in conjunction with predictive-Soave- Redlich-Kwong (PSRK) approach is presented for prediction of pure IL density. The proposed expression is based on the correlation developed by Nasrifar and Moshfeghian for perfection of saturated liquid density for pure compounds. The generalized expression uses acentric factor and mass connectivity index of pure ionic liquids. A set of 47 pure ionic liquids with 735 data points and 4 different cohesion functions were used in the study. The results were compared with linear generalized model (LGM) developed by Valderrama to check appropriateness and accuracy of expression presented. It was found that the compound specific PSRK approach gives very accurate predictions and generalized expression is at par with LGM model. Further study would include use of other cohesion factor models.