SRK EOS Research Articles

Measuring the solubility of tacrolimus in supercritical carbon dioxide (binary and ternary systems), comparing the performance of machine learning models with conventional models

The solubility of tacrolimus in a supercritical carbon dioxide (SC-CO2) with and without co-solvent (ternary and binary system) was investigated. The experimental conditions include the temperatures of 308 to 338 K and the pressures of 12 to 30 MPa were considered. The values of tacrolimus solubilization in SC-CO2 in binary and ternary systems were from 0.416 × 10−5 to 1.589 × 10−5 and from 0.389 × 10−4 to 0.875 × 10−4, respectively. The obtained results presented that adding a co-solvent (ethanol) could affect tacrolimus solubility significantly, the mole fraction of tacrolimus in SC-CO2/co-solvent under all experimental conditions was at least 4.9 more than that of SC-CO2 alone. The correlation of the solubility data was achieved by three distinct methods: (1) SRK EoS with van der Waals (vdW2) and Wong-Sandler (WS) as mixing rules, (2) solution theory, (3) empirical and (4) machine learning based models. The analysis of variance (ANOVA) results showed that Sparks et al. (AIC −817.05, and AARD 5.08 %) and Bian et al. (AIC −815.77 and AARD 5.17 %) models could correlate the experimental data of tacrolimus in SC-CO2 with more accuracy, as compared to the other empirical models. Sodeifian and Sajadian model with AARD% and AIC of 2.99 and −726.22, respectively, has acted as the most accurate empirical model in ternary system. The solution theory was able to calculate the solubility for the tacrolimus-SC-CO2-ethanol system with high accuracy (AARD, % 4.85, AIC −701.41, F value 169.70 and Radj 0.9622). Also, the Gradient Boosting model (AARD accurately predicted the outcomes with perfect accuracy for binary and ternary systems. Finally, total (ΔHtotal, 23.21 cal/mol), solvation (ΔHsol, −19.47 cal/mol) and vaporization (ΔHvap, 42.68 cal/mol) enthalpies were obtained by using an energy term in Chrastil and Bartle models.

Experimental measurements and thermodynamic modeling of dissociation pressure of CO2 hydrate in sulfate solutions

Carbon capture and storage (CCS) has been a popular strategy to mitigate climate change and has attracted significant attention from both industry and academia. CO2 can be stored in the form of CO2 hydrate in deeper locations in an ocean, which makes it a potential option for CO2 sequestration. Dissolved salts in the ocean brine can significantly affect the dissociation pressure of CO2 hydrate. Sulfate salts are one of the most common salt species in the oceanic brine. Although various experimental studies have been conducted to investigate the phase behavior of CO2 hydrate in brine, few studies focus on the effect of sulfate salts on the dissociation pressure of CO2 hydrate. In this study, we build an in-house experimental setup to investigate the effect of monovalent and divalent sulfate salts on the dissociation pressure of CO2 hydrate. The dissociation pressure of CO2 hydrate in Na2SO4, K2SO4, MgSO4, and CuSO4 aqueous solutions is measured using the isochoric pressure search method at different concentrations over the temperature range of 274.36–––282.15 K and the pressure range of 1.50–––4.03 MPa. A hybrid methodology incorporating the Soave-Redlich-Kwong Equation of State (SRK EOS), the van der Waals-Platteeuw (vdW-P) model, and the Pitzer model is applied to predict the dissociation pressure of CO2 in sulfate solutions. In addition, the dissociation enthalpies of CO2 hydrate in these sulfate solutions are calculated using the Clausius-Clapeyron equation based on the measured dissociation points. The experimental results show that the dissociation pressure of CO2 hydrate in Na2SO4, K2SO4, and MgSO4 solutions is higher than that in pure water, and the dissociation pressure of CO2 hydrate in sulfate solutions increases with an increasing salt concentration. Conversely, CuSO4 barely affects the dissociation pressure of CO2 hydrate, which is mainly attributed to the lower molar concentration of the ions compared with the other salt solutions and the ion specificity of Cu2+. The prediction results are in alignment with the experimental data measured in this study, which proves the feasibility of the thermodynamic model in predicting the dissociation pressure of CO2 hydrate in sulfate solutions. Additionally, the calculated dissociation enthalpies of CO2 hydrate show a dependence on both temperature and salt concentration. It is also revealed that Cu2+ exhibits ion specificity in affecting the dissociation enthalpy of CO2 hydrate, likely due to its distinct ability to impact the cage occupancy of CO2 hydrate compared with the other ions. These findings enhance our understanding of the impact of sulfate salts on the dissociation behavior of CO2 hydrate and offer valuable insights for CO2 sequestration.

Hydrate phase equilibria of carbon dioxide/propane gas mixture in concentrated aqueous sodium chloride solutions: Experimental data and prediction

The information on hydrate equilibrium conditions of gas hydrate formers in concentrated NaCl solutions are the prerequisites for hydrate-based desalination methods. Hydrate dissociation conditions for CO2-C3H8 mixture, as a good candidate for this application, were measured for the temperature and pressure ranges of 269–283 K and 0.3–3.4 MPa, respectively using an isochoric pressure-search method. The used gas mixture was a solution of 10 mol% C3H8 + 90 mol% CO2 and NaCl concentrations varied between 8 and 12 wt%. The promoting effect of propane was obviously observed from the experimental data. This promoting effect nearly balanced the inhibitory effect of 12 wt% NaCl. A thermodynamic model was applied to predict the experimental data using SRK, PR, and VPT EOSs. All EOSs had accurate results for prediction of CO2 hydrate equilibrium pressures, with the best result by PR EOS. The overall average absolute percent deviation (AAPD) of PR EOS in pure water and 8 wt% NaCl solution were 5.29 and 3.8 %, respectively. For gas mixture (CO2-C3H8) in pure water, the best accuracy was obtained by using SRK EOS with AAPD of 4.44 %. However, the results of VPT and PR for gas mixture in NaCl solutions, were more accurate than SRK with AAPDs equal to 7.47 and 7.75 %, respectively.

A study on carbon dioxide solubility in the deep eutectic solvent (1 sodium bromide + 6 ethylene glycol): Experimental and modeling by the SRK and CPA EoS

In this study, carbon dioxide solubilities were measured experimentally in the DES composed of 1 NaBr + 6 ethylene glycol at temperatures ranging from 293.2 to 323.2 K and pressures up to 37 bars. The minimum and maximum measured CO2 solubilities (in mole fraction) within the investigated temperature and pressure ranges were 0.0013 and 0.0526, respectively. The measured data were then used to optimize the values of fitting parameters of the Cubic Plus Association, and the Soave–Redlich–Kwong EoSs equations of state. The AARD% values of 3.37 % and 2.52 % for SRK and CPA EoSs, respectively, showed reliable results for both models. However, the SRK EoS could estimate accurate carbon dioxide solubilities only by much larger binary interaction parameters, as compared to the CPA EoS. Also, using the measured data, the values of Henry’s constant, standard enthalpy, standard entropy, and standard Gibbs free energy of dissolution were calculated according to thermodynamic relations. The stronger interactions in the mixture of carbon dioxide with DES by the establishment of new intermolecular bonds (as compared to the pure DES), leads to the liberating of energy upon dissolution. This also results in less disorder and chaos as indicated by analyzing the above-mentioned thermodynamic properties.

Optimized critical parameters for n-alkanes up to C100 for reliable multiphase behavior of hydrocarbon mixture using SRK EOS

The Soave-Redlich-Kwong equation of state (SRK EOS) is widely used for phase behavior simulation of hydrocarbon mixtures. However, its applicability and reliability are limited for heavier hydrocarbon mixtures and reservoir fluids. This research presents optimized critical temperatures (TC), critical pressures (PC), and acentric factors (ω) parameters for n-alkanes up to C100 for improved volumetric and compositional multiphase behavior predictions.Parameters TC, PC, and ω for C7 to C100 are optimized using Particle Swarm Optimization (PSO) to match the density as well as vapor pressure data. Average absolute relative deviations (AARDs) achieved are 1.9% and 2.4% respectively for density and vapor pressure matches, corresponding values for the unoptimized case are 53.23%, and 3.90% respectively. The case of optimization of ω only to match vapor pressure has AARD of 2.0% in comparison to 3.90% from unoptimized values.Binary interaction parameters (BIPs) are optimized by matching upper critical end point (UCEP) for CO2, CH4, C2, and C3 binaries with n-alkanes with their optimized TC PC ω, optimized ω (and unoptimized TC and PC) only, and unoptimized TC PC ω values cases. It is found that optimized TC PC ω is correctly able to show the presence of three-phases for all 23 ternary hydrocarbon mixtures.

Phase Equilibrium and Density of CO2 + Acetic Acid Systems from 308.15 to 338.15 K and 15 to 45 MPa.

Using a high-pressure phase equilibrium apparatus and vibrating-tube densimeter, phase transition pressures of CO2 (1) + acetic acid (2) binary systems with x2 = 0.000, 0.107, 0.163, 0.222, and 1.000 were measured under temperatures from 308.15 to 338.15 K. Besides, the densities at the same composition and temperature under pressure from 15 to 45 MPa were also detected, and the volumes of mixing (ΔVm) were calculated. Three prediction models (SRK EOS, PC-SAFT EOS, and TS model) were introduced to predict and correlate the density of binary systems, which was found to have positive relationships with temperature and acetic acid concentration and a negative relationship with pressure. Thereinto, the variation trend of CO2 density with pressure tends to be flat under high pressure, and which of acetic acid density increased linearly with pressure. ΔVm are negative, and their absolute value increases with the increase of temperature and the decrease of pressure. The work herein could provide a theoretical guide and basic data for supercritical CO2 extraction technology and CO2 application in oil field development.

Chemistry of Reservoir Fluids in the Aspect of CO2 Injection for Selected Oil Reservoirs in Poland

Worldwide experiences related to geological CO2 storage show that the process of the injection of carbon dioxide into depleted oil reservoirs (CCS-EOR, Carbon Capture and Storage—Enhanced Oil Recovery) is highly profitable. The injection of CO2 will allow an increasing recovery factor (thus increasing CCS process profitability) and revitalize mature reservoirs, which may lead to oil spills due to pressure buildups. In Poland, such a solution has not yet been implemented in the industry. This work provides additional data for analysis of the possibility of the CCS-EOR method’s implementation for three potential clusters of Polish oil reservoirs located at a short distance one from another. The aim of the work was to examine the properties of reservoir fluids for these selected oil reservoirs in order to assure a better understanding of the physicochemical phenomena that accompany the gas injection process. The chemical composition of oils was determined by gas chromatography. All tested oils represent a medium black oil type with the density ranging from 795 to 843 g/L and the viscosity at 313 K, varying from 1.95 to 5.04 mm/s. The content of heavier components C25+ is up to 17 wt. %. CO2–oil MMP (Minimum Miscibility Pressure) was calculated in a CHEMCAD simulator using the Soave–Redlich–Kwong equation of state (SRK EoS). The oil composition was defined as a mixture of n-alkanes. Relatively low MMP values (ca. 8.3 MPa for all tested oils at 313 K) indicate a high potential of the EOR method, and make this geological CO2 storage form more attractive to the industry. For reservoir brines, the content of the main ions was experimentally measured and CO2 solubility under reservoir conditions was calculated. The reservoir brines showed a significant variation in properties with total dissolved solids contents varying from 17.5 to 378 g/L. CO2 solubility in brines depends on reservoir conditions and brine chemistry. The highest calculated CO2 solubility is 1.79 mol/kg, which suggest possible CO2 storage in aquifers.

Thermodynamic modeling of ternary systems containing imidazolium-based ionic liquids and acid gases using SRK, Peng-Robinson, CPA and PC-SAFT equations of state

In this study, the cubic and the associative equations of state are applied to model the VLE data of ternary systems containing ionic liquids. In the first section, the simultaneous solubility of CO2 and H2S in the ionic liquids [omim][Tf2N], [omim][PF6] and [bmim][PF6] is modeled and the selective absorption of CO2/H2S is investigated at the temperatures T/K = (303.15 and 343.15) and the pressures P/MPa = (0.1 and 1). According to the obtained results, the percent deviations in pressure were varying between 6.0 and 10.8 for the SRK EoS, 6.0 and 10.6 for the PR EoS, 2.6 and 9.6 for the CPA EoS and 3.4 and 6.1 for the PC-SAFT EoS. Also, percent deviations in vapor phase composition were varying between 3.1 and 4.9 for the SRK EoS, 3.3 and 4.9 for the PR EoS, 3.1 and 7.0 for the CPA EoS and 3.8 and 4.9 for the PC-SAFT EoS. In the selectivity calculations, at high ionic liquid concentrations, the cubic models predict the selectivity drop; while the associative models present increasing trend. In the second section, the CO2 solubility in ethanol and [emim][Tf2N] as well as the mixture of ethanol and [emim][Tf2N] is modeled and the experimental points were tested for thermodynamic consistency. According to the obtained results, the percent deviation in pressure of the ternary systems was 3.9 for the SRK EoS, 3.9 for the PR EoS, 3.8 and 4.0 for the CPA EoS and 3.1 and 3.2 for the PC-SAFT EoS. In the same temperature and pressure, the CO2 solubility decrease when the concentration of ethanol increases, and the proposed models can describe this phase behavior.

Screening of HFCs and Fluoroethers as Alternatives to R134a Using SRK EoS

The volumetric and thermodynamic properties of fluorinated ethers such as trifluoromethyl-1-H-pentafluoroethylether, F-oxetane, 2-H-heptafluoropropane, pentafluorodimethylether, F-methyl methyl ether, perfluorodoxolane, pentafluorodimethoxymethane and HFCs such as trifluoroethane, heptafluoropropane, difluoroethane, pentafluoropropane, ethyl fluoride as alternatives to replace R134a have been predicted using SRK equation of state over the temperature range from − 25 °C to + 55 °C. Theoretical analysis is carried out using ten-point vapour compression cycle for screening of candidate refrigerants. The results of analysis have been used to ascertain standard refrigeration parameters in respect of each of the candidate refrigerants. The analysis indicates that the performances of difluoroethane, ethyl fluoride, pentafluorodimethylether and F-oxetane are better than that of R134a.

Implementation of electrolyte CPA EoS to model solubility of CO2 and CO2 + H2S mixtures in aqueous MDEA solutions

Abstract The electrolyte version of SRK plus association equation of state (eSRK-CPA EoS) was employed to correlate CO2 solubility in MDEA aqueous solutions. The applied model comprises the classic form of CPA EoS including SRK EoS plus Wertheim association term in addition to MSA theory and Born terms so that the two last terms are responsible for the long-range interactions. A reaction-containing bubble pressure computation technique comprising two nested loops was utilized to model the systems. The internal loop, calculates the liquid phase concentrations via reaction, mass and charge balance equation solving, whereas, the vapor phase concentrations will be obtained in the external one. 470 experimental data were used to correlate binary subsystems and the H2O + MDEA + CO2 ternary system. Since, there not exist any binary VLE data for MDEA + CO2 subsystem, two fitting scenarios were applied. At the first scenario, the binary interaction parameter was assumed equal to zero, while, in second approach the parameter was obtained through ternary system correlation. Both scenarios show very good accuracy in that the Absolute Average Deviation percentages (AAD) obtained were 19.12% and 18.85%, respectively. Also, to show the efficiency of the used model, a comparison between our results and those of the best-known models was made. Finally, having model parameters for H2S solubility from our previous work [A. Afsharpour, Petroleum Science and Technology 35 (3) (2017) 292-298], simultaneous solubility of CO2 + H2S mixtures in MDEA solutions was predicted using the eSRK-CPA EoS with no new optimizable parameters. As the results show, the applied model has a good performance for correlation and prediction of acid gas solubility in a wide range of pressures, temperatures, acid gas loadings, and MDEA concentrations.

Solubility of carbon dioxide in methanol from 213.15 K to 273.15 K: Measurement and modeling

The isothermal solubility data of carbon dioxide in methanol were measured at temperatures from 213.15 K to 273.15 K and pressures from vacuum up to 3.3450 MPa. The experimental method was a static analytical method with liquid sampling using a heated sample cylinder coupled to a gas chromatograph for analysis. The SRK EOS with the vdW one-fluid mixing rule was used to describe the equilibrium behavior of the vapor phase in the system for carbon dioxide + methanol binary mixture. The equilibrium behavior of the liquid phase was separately described by the NRTL and Wilson activity coefficient models. The measured data were separately correlated with SRK-vdW-NRTL and SRK-vdW-Wilson models. The calculated results indicate that the SRK-vdW-NRTL model predicts false liquid-liquid splitting, and the SRK-vdW-Wilson model not only matches well with the measured data but also predicts optimally VLE data of the system from 213.15 K to 273.15 K.

The CPA EoS application to model CO2 and H2S simultaneous solubility in ionic liquid [C2mim][PF6

ABSTRACTThe CPA EoS was utilized for solubility modeling of pure CO2 and H2S and their mixture in [C2MIM][PF6]. The model is comprised of SRK EoS in addition to Wertheim's association term. Up to now, several associating models such as SAFT variants have been successfully applied to such systems. Considering the complexity and time consuming nature of SAFT EoSs, CPA can be a good alternative due to its accuracy and simplicity with respect to the SAFT.The AAD % for binary systems including H2S+ IL and CO2+ IL are 11.78, 10.40 respectively. Moreover, the ternary system show AAD% equal to 16.51.

Thermal and Transport Properties for the Simulation of Direct-Fired sCO2 Combustor

The direct-fired supercritical CO2 (sCO2) cycle is currently considered as a zero-emission power generation concept. It is of interest to know how to optimize various components of this cycle using computational tools; however, a comprehensive effort in this area is currently lacking. In this work, the behavior of thermal properties of sCO2 combustion at various reaction stages has been investigated by coupling real gas CHEMKIN (CHEMKIN-RG) (Schmitt et al., 1994, Chemkin Real Gas: A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, University of Iowa, Iowa City, IA) with an in-house premixed conditional moment closure code (Martin, 2003, “The Conditional Moment Closure Method for Modeling Lean Premixed Turbulent Combustion,” Ph.D. thesis, University of Washington, Seattle, WA) and the high-pressure Aramco 2.0 kinetic mechanism. Also, the necessary fundamental information for sCO2 combustion modeling is reviewed. The Soave–Redlich–Kwong equation of state (SRK EOS) is identified as the most accurate EOS to predict the thermal states at all turbulence levels. Also, a model for the compression factor Z is proposed for sCO2 combustors, which is a function of mixture inlet conditions and the reaction progress variable. This empirical model is validated between the operating conditions 250–300 bar, inlet temperatures of 800–1200 K, and within the currently designed inlet mole fractions, and the accuracy is estimated to be less than 0.5% different from the exact relation. For sCO2 operating conditions, the compression factor Z always decreases as the reaction progresses, and this leads to the static pressure loss between inlet and exit of the sCO2 combustor. Further, the Lucas et al. and Stiel and Thodos methods are identified as best suitable models for predicting the viscosity and thermal conductivity of the sCO2 combustion mixtures.

A new viscosity model based on Soave-Redlich-Kwong equation of state

In this study based on the Soave-Redlich-Kwong equation of state (SRK EOS), a new viscosity model for light hydrocarbons, CO2 and N2 has been proposed. The proposed model can be applied in both liquid and gas phases and in high and low ranges of pressure and temperature. The optimal values of the parameters in the proposed model are determined by using the Genetic algorithm and generalized in term of acentric factor. The performance of the proposed model has been compared with the performance of Peng-Robinson EOS-based viscosity model of Guo et al. (2001), the Peng-Robinson EOS-based viscosity model of Fan and Wang (2006) and the Lohrenz-Bray-Clark (LBC) method. In order to have a fair comparison, the binary interaction coefficients in the mixing rules are set to zero. The results of calculations for seventeen pure components (6449 data), thirty eight binary mixtures (2772 data), ten simple and twenty complex mixtures (74 data) show the superiority of the proposed model compared to the other viscosity models.

Modeling H2S and CO2 solubility in ionic liquids using the CPA equation of state through a new approach

In this communication, the solubility of two single gases, hydrogen sulfide and carbon dioxide, in the fourteen ionic liquids ([emim][eFAP], [emim][EtSO4], [emim][OTf], [emim][Tf2N], [bmim][BF4], [bmim][PF6], [hmim][PF6], [hmim][Tf2N], [omim][PF6], [omim][Tf2N], [HOemim][BF4], [HOemim][OTf], [HOemim][PF6] and [HOemim][Tf2N]) are modeled using the CPA EoS through a new approach. First, the critical temperature of ionic liquids was estimated using modified Lydersen-Joback-Reid method. Then, Using the CPA EoS, the pure parameters of ionic liquids were obtained through optimization on both of H2S and CO2 solubility data in ionic liquids as well as experimental liquid density data of ionic liquids. In next step, the interaction parameters between the ionic liquids and H2S as well as the ionic liquids and CO2 were calculated. Using the obtained pure parameters of the ionic liquids and the interaction parameters, the vapor-liquid equilibrium data were tested for thermodynamic consistency. Also, the proposed systems were modeled by the SRK EoS and the obtained results were compared by the obtained ones by the CPA EoS. For all the studied systems, the percent average absolute deviation (AAD %) was lower than 10% that shows good agreement between the experimental and calculated values.

Vapor–Liquid Equilibrium for Methanol + Methyl Palmitate near the Critical Temperature of Methanol

The vapor–liquid equilibrium for a methanol + methyl palmitate system was measured using a flow-type method at a pressure range of 1.86–8.81 MPa and a temperature range of 493–543 K, which is near the critical temperature of methanol (512.64 K). The mole fractions of methyl palmitate in the vapor phase were nearly zero, and the errors were also close to zero at all temperatures. The measuring errors of the liquid phase were slightly higher than those of the vapor phase. The Soave–Redlich–Kwong equation of state (SRK EOS), the Peng–Robinson equation of state (PR EOS), and the Cubic-Plus-Association equation of state (CPA EOS) combined with the Adachi–Sugie (AS) mixing rule were employed to correlate the measured data. The correlated results are consistent with the measured data. Because of their accuracy and concise calculation, the SRK and PR EOSs are better choices for correlating the methanol + methyl palmitate system when considering the accuracy and conciseness of calculating.

Developing a new model for the determination of petroleum fraction PC-SAFT parameters to model reservoir fluids

In this work, PC-SAFT, an equation of state based on perturbation theory, is applied to predict the reservoir fluids phase behavior. PC-SAFT parameters for pure components have previously been assessed, but they cannot be determined for petroleum fractions with unspecified components and composition. In order to remove this difficulty and making use of PC-SAFT model in the reservoir fluids simulations, a new approach is studied which leads to appearing generalized correlations for the estimation of PC-SAFT parameters for petroleum cuts and plus fractions using only their molecular weight and specific gravity, without the essential need for the characterization of petroleum fractions in different homologous hydrocarbon families. The proposed technique is then validated with the reliable experimental PVT data of reservoir fluids, including saturation pressure and differential liberation test (oil formation volume factor, soluble gas oil ratio, and liquid phase density) for 10 oil samples. Subsequently, available experimental data are compared to results calculated by PC-SAFT model for all existing samples. Afterwards, a comparison between PC-SAFT model and two widely used cubic equations of state (PR and SRK EOS) was also conducted. The results demonstrated PC-SAFT model estimation capabilities and ease of use as an effective tool for describing the phase behavior of reservoir fluids in a wide range of scales and applications. Moreover, the effect of parameter tuning process on reduction of error values was investigated and acceptable results were obtained.

Solubility Modeling of N-CBZ Derivatised Amino Acids in Supercritical Carbon Dioxide

The experimental solubility of CBZ (Carbobenzoxy) derivatized amino acids namely N-CBZ valine, N-CBZ proline, N-CBZ aspartic acid in supercritical carbon dioxide were correlated by Soave-Red- lich-Kwong Equation state based on fugacity determination and group contribution method using extrapolated critical parameters and mixing rules and other two different empirical models proposed by Yu (1994) and Gordillo-coworkers (1999). The SRK EOS prediction showed very high deviation of % AARD of 9% - 59%. The Yu model had three derivatized amino acids with average absolute deviation from 2.04, 8.17, 10.96, while the Gordillo model had 0.245, 1.067 and 1.144 for CBZ-valine, CBZ-proline and CBZ-aspartic acid successively. The correlated values had better fit with Gordillo model. The predictive capability and applicability for these amino acid derivatives for both the models demonstrated with correlation coefficient around 0.99 for all the experimental solubility observed.

Are the reservoir fluid compositional grading data reliable?

Outlier detection in compositional grading data of a reservoir fluid is the main objective of the present study. The experimental data of a petroleum reservoir fluid including the mole fractions of the fluid components at different depths (from around 1000 to about 1400m) and at constant temperature of 361.15K are investigated. The utilized algorithm applies the basis of a mathematical approach, in which the statistical Hat matrix, Williams plot, and the residuals of a compositional grading model results bring about the probable outliers detection. The range of applicability of the applied model and quality of the existing experimental data are also investigated. The reported results of a previously developed model using the Soave–Redlich–Kwong equation of state (SRK EoS) with Peneloux volume correction are employed to evaluate the compositional analysis of the species in different depths of the fluid column. It is interpreted from the obtained results that the applied model for estimation of the compositional gradients has wide ranges of applicability. In addition, we may conclude that there is no outlier or probable doubtful datum in the investigated experimental datasets.

Critical properties and acentric factors of ionic liquids

Since most ionic liquids (ILs) decompose before reaching their critical state, the experimental measurement of their critical properties are not possible. In this study, the critical temperatures, critical pressures and acentric factors of ten commonly investigated ILs were determined by making an optimum fit of the calculated vapor-liquid equilibrium data of binary mixtures of CO2+IL to the experimental values found in literature. For this purpose, the Peng-Robinson equation of state (PR EoS) and the differential evolution optimization method were used. The ILs considered were 1-ethyl-3-methylimidazolium hexafluorophosphate ([emim][PF6]), 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide ([emim][Tf2N]), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]), 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide ([bmim][Tf2N]), 1-hexyl-3-methylimidazolium tetrafluoroborate ([hmim][BF4]), 1-hexyl-3-methylimidazolium hexafluorophosphate ([hmim][PF6]), 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide ([hmim][Tf2N]), 1-octyl-3-methylimidazolium tetrafluoroborate ([omim][BF4]) and 1-octyl-3-methylimidazolium hexafluorophosphate ([omim][PF6]). To evaluate the ability of the determined parameters in predicting the phase behavior of systems other than the systems that were used for parameter optimization, both sets of parameters obtained in this work and that of Valderrama et al. were used to predict bubble-point pressures of CHF3+[bmim][PF6] (by using the PR EoS and the Soave-Redlich-Kwong equation of state. The bubble-point pressures of CO2+IL systems optimized in this study by the PR EoS were also determined using the Soave-Redlich-Kwong equation of state (SRK EoS). In addition, liquid densities of pure ILs were predicted using a generalized correlation proposed by Valderrama and Abu-Shark. In all cases, the various predicted properties of these ten ILs, were in better agreement with the experimental data, using the critical properties and acentric factor obtained in this study, compared to the values suggested by Valderrama et al.