Temperature-independent Binary Interaction Parameter Research Articles

The Effect of Binary Interaction Parameters and Induced Association on the Performance of the PC-SAFT Equation of State: Validation against a Benchmark Database of High-Quality Binary-System Data

The performance of the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) using classical mixing rules, induced-association schemes for mixtures exhibiting cross-association phenomena between two components that do not self-associate, and one regressed temperature-independent binary interaction parameter (kij) per mixture is assessed using a high-quality reference database containing binary-system data for various properties. The binary mixtures that are included in the database are divided into nine categories (Binary Association Codes, BACs) according to their ability to be involved in a hydrogen bond. Grading of the EoS is done by applying an already published procedure with certain modifications that were also published recently. An important feature is the inclusion of a performance indicator, called the “Success Ratio” (SR), that quantifies the percentage of experimental data points which the model can qualitatively reproduce. The original marks of the PC-SAFT EoS when implemented with classical mixing rules, no induced-association scheme, and a kij parameter set equal to zero are recalculated with the modified grading procedure and are directly compared with the new marks obtained in this work. The effect of including induced-association effects in PC-SAFT for mixtures that belong to BAC6, BAC7, and BAC8 (mixtures in which cross-association takes place without both components being self-associating) is also investigated. The effect of regressing cross-association parameters vs regressing kij parameters for mixtures belonging to the BAC6 group (mixtures in which cross-association arises although the two components do not self-associate) is showcased. The final optimized PC-SAFT EoS utilizes classical mixing rules, induced-association effects (using regressed cross-association parameters for some binary systems belonging to BAC6 and a predictive method for BAC7 and BAC8), and one temperature-independent kij parameter per binary mixture (except for binary systems belonging to BAC6 for which cross-association parameters were adjusted). The final average mark of the optimized EoS is 9.3/20.

High-pressure properties of type V Natural Deep Eutectic Solvents: The case of menthol: thymol

This work reports a study on the properties of Menthol: Thymol 1: 1 type V Natural Deep Eutectic Solvent under high pressure conditions (up to 600 bar). The experimental PVT measurements allowed to calculate the most relevant thermophysical properties and its relationships with intermolecular forces and nanostructuring. PC-SAFT equation of state was considered for treating experimental thermodynamic data using a two-components approach, thus leading to a successful prediction of properties considering a single temperature-independent binary interaction parameter. The considered DESs shows atype I global phase behavior, with extremely narrow phase loop and low volatility. Classical Molecular Dynamics simulations provided a detailed nanoscopic picture of the fluid structuring and dynamics upon compression, with results showing minor changes in the nature and extension of hydrogen bonding and the main structural and dynamics features being maintained in the considered pressure range. The combined experimental and modelling study allowed a detailed characterization of the properties of this fluid under high pressure conditions.

Miscibility of Poly(lactide-co-glycolide) in Supercritical fluids

In a polymer based drug delivery system, the polymer material surrounds the drug and delivers the substance to the desired target. Poly(lactide-co-glycolide) (PLGA) is the most widely used control-release system for many drugs with a short half-life, low stability, easy decomposition, and non-toxic side effects. Supercritical fluid (SCF) technology can be used to prepare or micronize drug-loaded particles without additional purification or cleaning procedures. In this work, the liquid–liquid phase transition of PLGA in several supercritical fluids, such as dimethyl ether (DME), CO2, chlorodifluoromethane (HCFC-22), and trifluoromethane (HFC-23), has been investigated. PLGA with a higher content of glycolide in the copolymer backbone shows upper critical solution temperature (UCST)-type phase behavior. Alternatively, in supercritical HCFC-22, lower critical solution temperature (LCST)-type phase behavior has been observed. The ratio of lactide to glycolide in the PLGA copolymer backbone majorly controls the phase behavior including the pressure–temperature (p-T), temperature-polymer weight fraction (T-w), pressure-density (p-ρ), and temperature-density (T-ρ) isopleths. The phase behaviors of PLGA in SCF CO2 and DME change from UCST- to LCST-type behavior with an increase in the lactide content. In contrast, PLGA in SCF HCFC-22 exhibits LCST-type phase behavior for all PLGA copolymers irrespective of the lactide content. Such phase behaviors are described well by the perturbed-chain statistical associating fluid theory (PC-SAFT) in a wide range of temperature (300–395 K) and pressure (3–310 MPa) with temperature-independent binary interaction parameters. In addition, significant differences have been observed in the solubility of PLGA in different SCFs; CO2 being the poorest solvent, and HCFC-22 being the best solvent.

Non-saturated mixture densities of the binary systems of carbon dioxide and the organic solvents ethanol, acetone, acetonitrile and dimethyl sulfoxide from 6-12 MPa

Mixture density data for the four binary systems consisting of carbon dioxide and the organic solvents ethanol, acetone, acetonitrile and dimethyl sulfoxide are reported. Composition dependent isobaric and isothermal mixture densities from 6−12MPa and 308−333K over the entire composition range in the single-phase region were acquired using a temperature conditioned Coriolis mass flow and density meter. The Non-Random Hydrogen Bonding model with a single, temperature independent binary interaction parameter was used to correlate the mixture density data. Modeled mixture densities showed an averaged deviation < 2% for each binary system. Extensive experimental data also enabled the estimation of the boiling point line of the binary systems within an interval of confidence of 0.05 mole fractions.

Modeling systems relevant to the biodiesel production using the CPA equation of state. Part 2. Systems with supercritical CO2

The CPA EoS is applied to binary mixtures of CO2 with fatty acids and their methyl- or ethyl-esters. The model, using one temperature independent binary interaction parameter, satisfactorily describes the phase behavior of such systems. Correlations of the binary interaction parameters with the number of esters' or acids’ carbon atoms, or with the number of double bonds for compounds with the same number of carbon atoms, were developed in order to make predictions feasible in cases of lack of experimental data. Subsequently, the model was applied for predicting the phase behavior of ternary and multicomponent mixtures. The model rather satisfactorily predicts the vapor-liquid equilibrium of such systems. In accordance with the first part of this series of articles [Tsivintzelis et al. 430 (2016) 75–92], since the binary parameters were optimized solely using experimental data for binary mixtures, CPA results for the ternary and multicomponent mixtures are pure predictions.

Thermodynamic modeling of amino acid solutions: A new perspective on CPA EOS

Abstract The Cubic Plus Association (CPA) equation of state is applied to simultaneously calculate various thermodynamic properties of single aqueous solutions containing amino acids. Likewise, with a new perspective on CPA model, the highly dependency of amino acid solubility on the prevailing pH value is investigated bringing up dissociation/association equilibria. Hence, pure component parameters of 24 organic amino acids are fitted to density, solute activity coefficient, and water activity of their aqueous solutions at ambient conditions, and solely one temperature independent binary interaction parameter is used for each system. Also, two new equations are presented according to optimized parameters of amino acids. To prove the proficiency of applied models, solubility of aqueous solutions is predicted in binary systems at different temperatures and pH values taking into account the dissociation/association equilibria. Subsequently, the optimized parameters of CPA model are applied to reproduce the literature data for various thermodynamic properties including density and solute activity coefficient at other temperatures which range till 333 K. In addition, the effect of pressure on liquid density is checked, and the liquid density of mixed aqueous solutions containing two amino acids is evaluated. Eventually, it can be comprehended that not only the water activity and activity coefficients of aqueous amino acid solutions, but also liquid density and solubility of single solutions are reasonably calculated by CPA EOS over a wide range of temperatures and solute concentration applying dissociation/association equilibria.

Extension of 2C Association Scheme to Polyols Phase Equilibria

The application of the 2C association scheme proposed by De Villiers et al. (Ind. Eng. Chem. Res. 2011 50, 8711–8725) in the association term of cubic plus association equation of state (CPA EoS) is extended to polyol containing systems to correlate the binary and predict the ternary mixtures. First, the CPA parameters of pure components were successfully adjusted by vapor pressure and saturated liquid density experimental data. Then, the performance of the aforementioned scheme is compared to the other classical schemes by modeling the vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) of binary {polyol/small alcohol}, {polyol/water}, {fatty acid ester/small alcohol}, and {polyol/alkane} and ternary {small alcohol/poyol/fatty acid ester} and {small alcohol/water/poyol} mixtures. Applying a simple and robust phase equilibria algorithm proposed by Privat et al. (Comput.Chem. Eng. 2013, 50, 139–151) to binary and ternary systems, the VLE and LLE correlative performance of CPA EoS coupled with various combined schemes are very satisfactory over extensive temperature ranges and shows that each model is within or close to experimental uncertainty. Then, using two temperature-independent binary interaction parameters (BIPs) fitted with binary VLE and LLE data, the predictive performance of different models is further evaluated in ternary systems phase equilibria (LLE and VLE), and acceptable results are achieved at different temperatures. Eventually, it has been demonstrated that 2C scheme exhibits remarkable precision in predicting the VLE and LLE of polyol containing systems.

Phase equilibria of CO2 with components in the light naphtha cut of tyre derived oil

Phase equilibria of CO2+limonene, CO2+1,2,3-trimethylbenzene, CO2+p-cymene and CO2+m-cymene systems were measured to investigate the possibility of extraction of these components from tyre derived oil using supercritical CO2. Measurements were conducted using variable-volume view cells at four temperatures between 313 and 358K, with solute mass fractions ranging from 0.0159 to 0.635. The maximum total solubility pressure measured was 16.5MPa. The phase behaviour of the systems indicated that an increase in system temperature leads to an increase in phase transition pressure at constant composition. The solubility differences between the components increase slightly with the temperature, however a sufficient pressure difference exists for 1,2,3-trimethylbenzene to be isolated at temperature higher than 343K. Experimental data of four binary systems were satisfactory correlated by using the Redlich-Kwong-Soave equation of state, along with Mathias-Klotz-Prausnitz mixing rules, which include two temperature independent binary interaction parameters.

Predicting the Solubility of CO2 in Toluene + Ionic Liquid Mixtures with PC-SAFT

Perturbed-chain statistical associating fluid theory (PC-SAFT) was applied for modeling the vapor–liquid equilibrium of CO2 + toluene + ionic liquid (IL) mixtures and the molar volume of their liquid phases at temperatures between 298.15 K and 333.15 K and at pressures up to 80 bar. ILs used for this study contain the bis(trifluoromethylsulfonylimide) anion ([Tf2N]−) and imidazolium, pyridinium, thiolanium, and phosphonium cations. The pure-IL PC-SAFT parameters were fit to pure-IL liquid density data. Temperature-dependent binary interaction parameters were fit to binary liquid–liquid equilibrium data (i.e., toluene + IL) obtained from the literature and some points measured for this work. Temperature independent binary interaction parameters were fit to vapor–liquid equilibrium data (CO2 + IL, CO2 + toluene) from the literature. The availability of the pure-IL parameters and binary interaction parameters allowed prediction of CO2 solubility in toluene + IL mixtures with an absolute average relative devi...

Application of the modified group-contribution PC-SAFT to nitrile and their mixtures

The modified group-contribution PC-SAFT (NguyenHuynh, Fluid Phase Equilibria2016, 430, 33–46) is applied to simultaneously predict vapor-liquid and liquid-liquid equilibria of nitrile + alkane mixtures (from n-butane to n-hexadecane) using a single temperature-independent binary interaction parameters. Nitriles were considered specific polar and associative compounds. The EoS parameters were regressed on pure compound data and the binary interaction parameter was fitted on liquid-liquid phase equilibrium data of nitrile + n-hexane mixture. The association and dipolar interactions of nitrile in PC-SAFT were investigated with an emphasis on the difficulties in modeling LLE of nitrile + alkanes, water and aromatics binary mixtures.The modeling results were however disappointing when nitrile was studied as unique dipolar or associative compound. It was found in fact that a cross-association interaction between nitrile and aromatic was necessary to accurately calculate the mixtures phase equilibria. The results were finally compared with the induced Polar PC-SAFT EoS.

High pressure solubility of methane in the ionic liquid 1-hexyl-3-methylimidazolium tricyanomethanide

In this paper, new experimental measurements of methane (CH4) solubility in the ionic liquid (IL) 1-hexyl-3-methylimidazolium tricyanomethanide ([hmim][TCM]) are presented. The solubility data were obtained using a synthetic method based on bubble-point pressure measurements for concentrations ranging from (2–10) CH4 mole% and within a temperature range of (293–363K) and pressures up to 10MPa. The results obtained in this work were compared with those obtained for other ILs. The IL [hmim][TCM] was found to show the lowest CH4 solubility, which is desired for application of this IL as gas sweetening solvent (low co-absorption of hydrocarbons). Moreover, the CH4 solubility was compared to the CO2 solubility in the same IL, showing that [hmim][TCM] can selectively absorb CO2 from natural gas. The experimental solubility data of CH4 in [hmim][TCM] were accurately modeled using the PR-EoS with only one temperature-independent binary interaction parameter.

Representation of phase behavior of ionic liquids and their mixtures using various forms of cubic-two-state equation of state

In this work, in addition of Soave-Redlich-Kwong (SRK) equation of state, two other alternative cubic models such as Peng- Robinson (PR) and Cubic Square Well (CSW) EoSs are combined with the Two-State Association Model (TSAM) and the new forms of the Cubic-Two-State equation of state (CTS EoS) as PR-TS and CSW-TS are presented. In the beginning, the present models are used to correlate the saturated vapor pressure and liquid density of pure water, alcohols and phenol. The models are also employed to predict vapor molar volume and second virial coefficients of pure compounds to explore the predictability of the different type of the CTS models. Also, the liquid density of different pure ionic liquids (ILs) at various temperatures from 298.15 K up to 500 K and pressure from 0.1 MPa up to 59.59 MPa is correlated and the parameters of the CTS models are obtained. Following successful application of the models for the pure components, using one temperature independent binary interaction parameter, the SRK-TS and PR-TS models are applied to predict the vapor-liquid equilibrium of the several binary mixtures consists of IL with non-association and association components at various temperatures from 298.15 K up to 363.15 K and pressure from 0.09 kPa up to 216 kPa. The results of the SRK-TS and PR-TS models for pure and binary systems containing ILs are in very good agreement with experiments and also are compared with various equations of states that show better results. In overall for the systems that are presented in this work, the PR-TS model shows slightly better results with respect to the SRK-TS model specially in prediction, and PR-TS and SRK-TS models present superiority with respect to the CSW-TS EoS.

Phase equilibrium of CCS mixtures: Equation of state modeling and Monte Carlo simulation

To understand the role played by the impurities (such as N2, Ar, H2, CO, SO2, O2 and NO) during the processes of Carbon Dioxide Capture and Storage (CCS), it is essential to know the thermodynamic properties of the CO2-impurities mixtures under the conditions of CO2 capture, transport and storage. Considering the variety of composition of these gas mixtures, it is necessary to have at one’s disposal suitable models to predict their thermodynamic properties. In this work, two thermodynamic models: the E-PPR78 (Enhanced Predictive Peng-Robinson, 1978) and the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) models, are applied for describing the phase equilibria properties of 77 binary CCS mixtures containing CO2, gas impurities (SO2, O2 and NO), water and hydrocarbons. Our research results indicate that both models are able to accurately predict the phase behavior of binary CCS mixtures. It was however necessary to adjust the binary interaction parameters (kij,PC-SAFT) within the PC-SAFT model to improve the prediction accuracy. Compared to the PC-SAFT model with one temperature-independent binary interaction parameter, the E-PPR78 model normally shows better prediction accuracy for the investigated systems. In addition, to extend the experimental database which was built for the evaluations of Equation-of-State (EoS) modeling, the Monte Carlo (MC) simulation method is employed in this work to generate phase-equilibrium data of a few CCS mixtures deemed as insufficiently described by experimental measurements reported in the open literature.

A simple model for temperature-independent kij of the PR-vdW model for mixtures containing HCs, HFCs, PFCs, HFOs, CO2, RE170 and R13I1

The purpose of this paper is to establish a simple model for temperature-independent binary interaction parameter kij of the PR-vdW model (Peng-Robinson equation of state with van der Waals one-parameter mixing rules). The model was proposed as kij = wjki + wikj (i ≠ j). In the present model, every pure component was considered to have a constant contribution ki to kij, constant wi is the contribution coefficient of component j mixing with component i. kij can be determined by summing the contribution coefficient of each pure component times its contribution. By regressing the vapor-liquid equilibrium (VLE) data of binary mixtures, 119 kij were obtained and used to optimize the constant contribution ki and contribution coefficient wi. kij of 351 binary systems were predicted and used to describe the VLE data of binary and ternary mixtures. Better performs could be found in the present model than the available models on VLE description of the mixtures.

Correlation and prediction of liquid–liquid equilibria for alcohol/hydrocarbon mixtures using PC-SAFT equation of state at high pressure up to 150 MPa

In this paper, we present a systematic study of the ability of the PC-SAFT equation of state to predict of liquid–liquid equilibria (LLE) for alcohol/hydrocarbon mixtures at high pressure on the basis of LLE data at 0.1 MPa. The adjustable temperature-independent binary interaction parameters, kij, in the PC-SAFT model were determined from LLE data at 0.1 MPa. The new proposed parameters set for methanol and ethanol with the two-site association scheme reproduce vapor pressures and liquid density with the same accuracy of PC-SAFT original parameters but show a better representation of the LLE data. In addition to using pure component PC-SAFT parameters derived from the standard method of fitting to liquid density and saturated vapor pressure, the new PC-SAFT parameters set for methanol and ethanol are determined from experimental association energy. The new association energy parameter of methanol and ethanol shows better agreement with the experimental results at approximately 298 K compared to all previously published PC-SAFT parameters.Different binary methanol + hydrocarbon and ethanol + hydrocarbon systems at high pressure up to 150 Mpa were tested using the PC-SAFT. LLE calculations and prediction show good agreement with experimental data for almost considered systems.

Phase equilibria of 3-methylstyrene, 4-methylstyrene, alpha-methylstyrene and a methylstyrene mixture in supercritical CO2

Phase equilibria of 3-methylstyrene, 4-methylstyrene, alpha-methylstyrene and a methylstyrene mixture (mainly 3-methylstyrene (60%mol) and 4-methylstyrene (40%mol)) in supercritical CO2 were measured using high-pressure variable-volume view cells based on the static synthetic method. The systems were investigated between 308 and 353K, with mass fractions of solute ranging continuously from 0.0275 to 0.65 and pressures up to 15MPa. The experimental data shows a linear relationship between the phase transition pressure and the system temperature at constant composition. When the solubilities are compared, the methylstyrene isomers show little yet significant differences between them with the methylstyrene mixture being the most soluble. As the temperature increases, a decrease in the difference between the phase transition pressures of the methylstyrene structural isomers were observed. Lastly, the experimental data were correlated with the Peng-Robinson cubic equation of state using one temperature-independent binary interaction parameter and satisfactory results were obtained in both low and high solute concentration regions.

Measurement and modelling of interfacial tension in methane/water and methane/brine systems at reservoir conditions

It is well established that the presence of salt in the aqueous phase raises the interfacial tension (IFT) of gas–water systems when compared to the case of pure water under the same pressure and temperature conditions. However, experimental data for gas–brine systems is still scarce, in particular at high pressure and high temperature (HPHT) conditions. In this communication, IFT data for methane with distilled water were experimentally determined using the pendant drop and bubble rise methods for temperatures ranging from (311–473) K and pressures up to 92 MPa and the results compared against literature data. Moreover, for the first time, the effect of NaCl on the IFT of the methane–water system was investigated in solutions with a maximum salinity of 10 wt% at HPHT conditions.The Cubic-Plus-Association equation of state (CPA EoS) along with the Debye–Hückel activity model was used to describe the effect of salt in the phase behaviour of the methane–water system and bulk properties used to compute the IFT of the studied systems with the Density Gradient Theory (DGT). The modelling results showed that by using only bulk phase properties and one temperature independent binary interaction parameter adjusted to the methane–water system, the DGT was able to predict the impact of NaCl on the IFT with remarkably low deviations from measured values. Furthermore, the impact of the fluids microstructure and the distribution of molecules across the interface on the IFT were evaluated with the DGT.

PC-SAFT predictions on mixtures of 1-alkyl-3methylimidazolium-bis(trifluroromethanesulphonyl)amide with hydrocarbons, alcohols and aqueous systems using a correlative based binary interaction parameter

The current work proposes a PC-SAFT (perturbed chain-statistical associated fluid theory) based temperature independent binary interaction parameter (kij) expressed as a function of carbon atoms in a solute molecule and chain length of cation for the ionic liquid (IL), 1-alkyl-3methylimidazaolium bis(trifluroromethanesulphonyl)amide ([Cnmim][Tf2N]). A total of nine binary mixtures comprising of mixtures of ILs with hydrocarbons, alcohol and water were investigated in this study. Initially the PC-SAFT parameters from liquid densities and vapor pressures along with the correlated binary interaction parameter were used to predict the vapor liquid equilibria (VLE) for nine systems. The absolute average deviation (AAD) for the three systems was found to be 3%, 4% and 3% respectively. Further the effect of alkyl chain length of cation, alcohol, hydrocarbon and temperature were also studied and compared using the correlated binary interaction parameter. In comparison with the results obtained from COSMO-RS, UNIFAC and PC-SAFT–UNIFAC methods, the PC-SAFT parameters with the correlated interaction parameter gave an average AAD of 4%.This is lesser as compared to the COSMO-RS model (∼9%) and the PC-SAFT version (∼5%) which uses liquid density to regress the parameters. The transferability of the correlated binary interaction parameters have also been demonstrated on another system namely [C4mim][BF4]–alcohol system albeit with limited success.

Application of the perturbed chain-SAFT equation of state for modeling CO2 solubility in aqueous monoethanolamine solutions

CO2 removal by treatment of acid gases by aqueous alkanolamines is a very significant operation from industrial and environmental point of view. To attain a comprehensive thermodynamic model of the CO2–MEA–H2O in a wide range of temperature and CO2 partial pressures, Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) EOS is applied to predict the absorption of carbon dioxide by MEA (MonoEthanolAmine). In order to find the best association scheme for MEA in PC-SAFT EOS, three pure parameter sets for MEA in the 2B, 3B and 4C association schemes are determined in temperature range 303.15–443.15K. Temperature independent binary interaction parameters have been adjusted in the VLE calculation for three schemes of MEA and two schemes of water. Binary VLE calculations show the 3B scheme for MEA and the 4C scheme for water indicate the best prediction in the MEA–H2O system. Excess enthalpy data for aqueous MEA are predicted by kij, which has been adjusted in VLE calculations. The 3B scheme for MEA and the 4C scheme for water also are used to find CO2 solubility in the ternary system of CO2–MEA–H2O system. Ideal Smith–Missen algorithm has been applied to find the concentration of all species in chemical equilibrium. Results show the 3B association scheme for MEA and the 4C association scheme for water in PC-SAFT EOS have better agreement with binary and ternary experimental data. PC-SAFT EOS is able to anticipate the CO2 solubility in the CO2–MEA–H2O system without any regression in the ternary system. The CO2 solubility in ternary system is compared to e-NRTL as a common thermodynamics model. The average absolute partial pressure deviations for PC-SAFT and e-NRTL are calculated around 36% and 42%, respectively.

Modelling polylactide/water/dioxane systems for TIPS scaffold fabrication

The representation of liquid–liquid equilibria (LLE) in ternary systems composed by water, 1,4-dioxane and different grades of poly(lactic acid) (PDLLA and PLLA), has been addressed through the PC-SAFT equation of state (EoS), in which the scheme of induced association is used to represent the interaction between solvent (dioxane) and non-solvent (water). The model parameters devoted to the description of pure component properties, as well as those pertinent to the representation of thermodynamic behaviour of solvent/non-solvent mixtures, were tuned on the basis of specific pressure–volume–temperature (PVT) data for the corresponding systems. Only the binary parameters for polymer–solvent and polymer/non-solvent pairs were adjusted to obtain a useful representation of experimental LLE data for the ternary systems. A suitable description of the thermodynamic properties of ternary mixtures was obtained using temperature-independent binary interaction parameters in the range 25–80°C, and the consistency of the approach in the entire composition range was verified against experimental solubility data specifically measured for the polymer/non-solvent pair. The model shows good ability in the description of the thermodynamic properties of the system and it represents a reliable tool for the prediction of LLE also at conditions different from those considered for its set-up. This approach thus represents a useful designing tool for processes, such as thermally induced phase separation (TIPS), used in the preparation of microporous polymeric scaffolds.