Temperature-independent Interaction Parameter Research Articles

Thermodynamic representation of ionic liquids phase equilibrium with the PDH-UNIQUAC-NRF model

This article uses four thermodynamic predictive models to calculate the interaction parameters of 4 binary (28 Tie-Line) and 71 ternary (889 Tie-Line) systems. Two specific properties were kept in mind when collecting the systems: 1. A Thiophene (BenzoThiophene) component is contained in all the systems; 2. Ionic liquids are used as the extracting factor.All systems were carried out using UNIQUAC, UNIQUAC-NRF, PDH-UNIQUAC and PDH-UNIQUAC-NRF models. In these models, the long-range contribution is accounted by Pitzer–Debye–Hückel (PDH) equation while the short-range contribution is considered by nonelectrolyte UNIQUAC and UNIQUAC-NRF. The present work inquired phase behavior of 36-types of ILs with various cations (imidazolium, pyrrolidinium, piperidinium, pyridinium, morpholinium phosphonium and Ammonium-Based cations) and various anions (Cl, FeCl4, BF4, B(CN)4, PF6, NTf2, FAP, OAc, DEP, EtSO4, H2PO4, TCM, CH3COO, SCN, TCB, CF3SO3 and MeSO4) in LLE systems. All the temperatures were in the range of 298.15–364.70 K. Therefore, in order to obtain temperature-independent interaction parameters, the adjustable parameter assumed to be as a function of T. This work uses a hybrid optimization approach for computing the interaction parameters. This approach benefits from both the capabilities of Genetic Algorithm (GA) as a global optimization technique while making use of a local search technique like Nelder-Mead Algorithm (NMA). All the interaction parameters for both binary and ternary systems were directly regressed from the experimental data using an optimization program based on two objective functions. Comparison of the results is expressed by root mean square deviation (rmsd) between the experimental and calculated compositions. The applied UNIQUAC, UNIQUAC-NRF, PDH-UNIQUAC and PDH-UNIQUAC-NRF models yielded to quite satisfactory results for ternary and binary systems, with rmsd values of 10.85, 10.54, 10.96 and 10.25 for binary systems, and 20.49, 11.55, 20.50 and 11 for ternary systems respectively. It is demonstrated that the PDH-UNIQUAC-NRF model presents quite satisfactory results.

The Vapor-Liquid Phase Diagram of Pure Methane Using Temperature-Dependent Interaction Parameters: A Monte Carlo Simulation

Adopting temperature-dependent interaction parameters in the Lennard-Jones potential, the vapor-liquid phase diagram of methane was produced using NVT Gibbs Ensemble Monte Carlo technique. Published second virial coefficient data were used to fit a simple two-parameter temperature-dependent model for the interaction parameters. The simulations were carried out in the temperature range 120-190 K. The critical density and temperature were evaluated using Ising-scaling model. Using the temperature-dependent interaction parameters in the simulation has reduced the root mean square deviation by 94.7% compared to the temperature-independent interaction parameters. The evaluated critical temperature was enhanced using temperature-dependent interaction parameters, whereas the simulations using temperature-independent interaction parameters predict a better critical density value

Fluid phase equilibrium prediction of acid gas solubility in imidazolium-based ionic liquids with the Peng-Robinson and the PC-SAFT models

In this research, the solubility of two single gases, hydrogen sulfide and carbon dioxide, in the sixteen ionic liquids ([emim][eFAP], [emim][EtSO4], [emim][OTf], [emim][Tf2N], [bmim][BF4], [bmim][OTf], [bmim][PF6], [bmim][Tf2N], [hmim][PF6], [hmim][Tf2N], [omim][PF6], [omim][Tf2N], [HOemim][BF4], [HOemim][OTf], [HOemim][PF6] and [HOemim][Tf2N]) are modeled using the Peng-Robinson and the PC-SAFT equations of state. For the ionic liquids, the pure component parameters of the PC-SAFT EoS have been obtained by the predictions of the model to both of experimental H2S and CO2 solubility data in ionic liquids as well as experimental liquid density data. Also, the critical properties and acentric factor of the ionic liquids were estimated using the modified Lydersen-Joback-Reid method. In the next step, the temperature-independent interaction parameters between the ionic liquids and the gases for both equations of state were calculated by fitting to the experimental VLE data and the obtained results were analyzed. In most of the studied binary systems, the percent average absolute deviation was lower than 10% that shows good agreement between the experimental and predicted values.

Modeling binary vapor–liquid equilibrium data containing perfluorocarbons using the Peng–Robinson and the PC-SAFT equations of state

In this communication, thermodynamic modeling of twenty four binary systems containing perfluorocarbon compounds is studied using the Peng–Robinson and the PC-SAFT equations of state. Interaction parameters of binary systems were estimated through fitting to experimental equilibrium pressures and vapor phase compositions. Very good results were obtained through using temperature-independent interaction parameter for both equations of state. According to the results, percent deviations in pressure were varying between 0.5 and 7.7 for the PR EoS and 0.2 and 6.5 for the PC-SAFT EoS. Also, percent deviations in vapor phase composition were varying between 0.1 and 6.6 for the PR EoS and 0.1 and 7.4 for the PC-SAFT EoS. Furthermore, when binary system has critical point, phase equilibrium calculations using the PR EoS do not converge through common methods. For solving this problem, a solution is suggested that was absolutely effective on all the studied systems.

Thermodynamic representation of ionic liquids phase equilibrium with the Wilson-NRF model

Ionic liquids (ILs) with their limitless combinations of cations and anions can offer an optimal solvent for a specific purpose especially separation processes such as liquid-liquid extraction (LLE). The present work inquired phase behavior of 32-types ILs with various cations (including imidazolium, pyridinium, piperidinium, morpholinium, pyrrolidinium and phosphonium-based) and various anions (including Cl, FeCl4, BF4, B(CN)4, PF6, NTf2, FAP and alkylsulfates) in LLE systems. Calculation of LLE for 38 binary (220 Tie-Line) and 52 ternary (545 Tie-Line) systems were carried out using Wilson-Non-Random-Factor (Wilson-NRF) model. All the data were in the temperature range of 298.15–408.15K. Therefore, in order to obtain an temperature-independent interaction parameters, the adjustable parameter assumed to be as a function of T as: λij=aij+bij/T. All the interaction parameters either for binary or ternary systems were directly regressed from the experimental data using an optimization program based on two objective functions. All the results were expressed by root mean square deviation (rmsd) between the calculated and experimental compositions (the solubility data from the literature). The applied model had very good satisfactory results for ternary and binary systems with rmsd values of 8.78 and 4.08 respectively. Besides, the effect of cation-type, anion-type and the other organic compound on the model behavior was illustrated. Finally, the results represented that Wilson-NRF model could be satisfying model for evaluation of thermodynamic behavior of various LLE containing ILs.

Phase equilibrium data for potentially hazardous binary mixtures involving dichlorosilane, trichlorosilane and silicon-tetrachloride

Isothermal (vapour+liquid) equilibrium data were obtained for potentially hazardous binary mixtures of (dichlorosilane+trichlorosilane), (dichlorosilane+tetrachlorosilane), and (trichlorosilane+tetrachlorosilane) using an apparatus based on the “static-analytic” method. The apparatus was specially developed and designed to ensure safe measurement of the flammable, toxic, and corrosive components. The (dichlorosilane+trichlorosilane) system was measured at T=(343.04, 353.04 and 363.00)K, and the (dichlorosilane+tetrachlorosilane) system at T=(343.28 and 353.07)K, and the (trichlorosilane+tetrachlorosilane) system at T=(323.17, 333.11 and 343.03)K. The resulting data were correlated with the Peng–Robinson equation of state coupled with the Wong Sandler mixing rule. The model provided accurate description of all isotherms of the binary systems using temperature-independent interaction parameters regressed for all isotherms.

Improving Monte-Carlo and Molecular Dynamics Simulation Outcomes Using Temperature-Dependent Interaction Parameters: The Case of Pure LJ Fluid

The main proposition of this work is that introducing temperature-dependent interaction parameters (TDIP) instead of using temperature-independent interaction parameters (TIIP) may lead to improvement in the prediction of phase equilibrium properties such as vapor liquid equilibria, and transport properties e.g., self-diffusivity. Published second virial coefficient data was used to fit a simple two parameter temperature-dependent model for the collision diameter and well depth. This fitting procedure reduces the Root Mean Square Deviation (RMSD) between the experimental and predicted second virial coefficients by tenfold compared to the best TIIP and by 15 fold with the literature values. The vapor–liquid coexistence curve for argon was simulated in the NVT Gibbs ensemble in the temperature range: 110–148 K. The critical temperature and density were determined using the Ising-scaling model. The TDIP simulations produce, in general, a more accurate phase diagram compared to the diagram generated using TIIP. RMSD is reduced by 42.1% using TDIP. Also, there was no significant difference between the results obtained using TDIP and the highly accurate and computationally demanding phase diagrams based on three body contributions implementing Axillrod–Teller correction. Self-diffusivities of atomic argon were evaluated using the mean square displacement or the Einstein method using equilibrium molecular dynamics (MD) at a pressure of 13 bars and a temperature range from 90 K up to 135 K in the isobaric, isothermal NPT ensemble. TDIP, in general, produces more accurate self-diffusivities than the values computed by TIIP simulations. RMSD is reduced by about 64% using the temperature-dependent parameters.

Thermodynamic modelling of miscibility in (InAs) x (GaAs)1−x solid solutions

Current methods used to model the solution thermodynamics of III–V compound semiconductors involve the use of the valence force field as the molecular model and the regular solution model (with the temperature independent interaction parameter and underlying assumption of random mixing) as the engineering model. In this study, excess free energy models (with three or less adjustable parameters) are investigated to predict the solid–solid miscibility of (InAs) x (GaAs)1− x . The models investigated include the Porter/one-constant Margules (OCM) model, the two-constant Margules (TCM) model and the non-random two liquid (NRTL) model. These models are fit to excess free energy values derived from free energy change of mixing (variation with composition) data available from molecular simulations at different temperatures. The parameters in all the models have been found to be temperature dependent. The coexistence compositions are best predicted by the NRTL model, indicating the need to consider non-random mixing effects present in these solid solutions. The TCM model predicts better equilibrium composition data as compared to the OCM model.

Vapor–liquid equilibrium measurement and thermodynamic modeling of binary systems (methane + n-tetradecane)

The vapor–liquid equilibrium (VLE) data for binary system of methane+n-tetradecane at four temperatures T=295, 324, 373, and 448K were measured using a designed pressure–volume–temperature (PVT) apparatus. The phase composition and density and viscosity of saturated liquid phase were measured for pressures up to 10MPa. The experimental VLE data were compared with the modeling results obtained using the Peng–Robinson and Soave–Redlich–Kwong equations of state. Two approaches, a single temperature-independent interaction parameter and temperature-dependent interaction parameter, were considered to fit the generated experimental data.

Liquid–liquid equilibria for ethyl esters + ethanol + water systems: Experimental measurements and CPA EoS modeling

The knowledge and the capacity to describe the liquid–liquid equilibria of systems composed of fatty acid ethyl esters, ethanol and water are crucial for an adequate design of the biodiesel washing units found in the ethylic biodiesel production processes. Since limited data is available for systems of this kind, in this work measurements were carried out for fatty acid ethyl esters+ethanol+water systems containing some of the fatty acid ethyl esters most commonly found in biodiesels: ethyl linoleate+ethanol+water at 313.15K, technical grade ethyl oleate+ethanol+water at 298.15K and ethyl palmitate+ethanol+water at 298.15, 308.15 and 333.15K. The experimental data were predicted with the Cubic-Plus-Association equation of state (CPA EoS). Using temperature independent interaction parameters, obtained from binary data, this equation of state was able to provide a very good prediction of the phase diagrams of the studied systems, with average global deviations of only 3.09%.

Experimental study and phase equilibrium modeling of systems containing acid gas and glycol

In this work, we study phase equilibria of systems containing acid gases and glycols. The acid gases include carbonyl sulfide (COS), hydrogen sulfide (H2S), and carbon dioxide (CO2) while glycols include monoethylene glycol (MEG), diethylene glycol (DEG), and triethylene glycol (TEG). A brief literature survey on the solubility of the acid gases and hydrocarbons in glycols is presented. New experimental solubility data mainly for COS and some limited data for H2S in glycols from 276 to 333K and at elevated pressures are reported. Experimental measurements have been carried out using the “static-synthetic” method. The reliability and repeatability of the experimental work are demonstrated. The experimental solubility data for COS and glycols, from this work, and those for H2S and CO2 from the literature are modeled using the cubic-plus-association (CPA) equation of state (EoS). CPA parameters for pure components and binary systems are reported. Satisfactory correlations have been achieved using temperature-independent interaction parameters. Various modeling strategies and alternatives using CPA are tested and the results are critically evaluated. The variations and trends in the values of binary interaction parameters are discussed for the different systems studied.

Measurement and equation of state prediction of vapor–liquid equilibrium and physical properties for the system methane + n-octadecane

The vapor–liquid equilibrium (VLE) data for binary system of methane + n-octadecane at four temperatures T = (323, 348, 398, and 448) K were measured using a designed pressure–volume–temperature (PVT) apparatus. The phase composition and density and viscosity of saturated liquid phase were measured for pressures up to 10 MPa. The experimental VLE data were compared with the modeling results obtained using the Peng–Robinson and Soave–Redlich–Kwong equations of state. Two approaches, a single temperature-independent interaction parameter and temperature-dependent interaction parameter, were considered to fit the generated experimental data.

Vapor–Liquid Equilibrium Measurements for the Ternary Systems of CO2 + n-Hexane + n-Decane and CO2 + n-Octane + n-Decane

The experimental vapor–liquid equilibrium (VLE) data for two ternary systems containing CO2 + n-alkane + n-decane were measured using an online static–analytic apparatus with a movable ROLSI sampler. The studied CO2 + n-hexane + n-decane and CO2 + n-octane + n-decane systems were measured at temperatures of (312.89, 342.50, and 376.20) K and (313.59, 344.28, and 373.49) K, respectively. The Peng–Robinson equation of state was used to predict the VLE data of the ternary systems from the temperature–independent interaction parameters of the binary systems.

Vapor−Liquid Equilibrium Data for the Nitrogen + Dodecane System at Temperatures from (344 to 593) K and at Pressures up to 60 MPa

A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers has been used to obtain new vapor−liquid equilibrium data for the N2 + C12H26 system over the temperature range from (344 to 593) K and at pressures up to 60 MPa. Equilibrium phase compositions and vapor−liquid equilibrium ratios are reported. All of the measured vapor−liquid equilibrium data were subject to a thermodynamic consistency test of high-pressure vapor−liquid equilibrium data involving the calculation of the vapor-phase composition from the isothermal pressure liquid phase composition data. The consistency test showed that most of the data are thermodynamically consistent. The new results were compared with solubility data reported by other authors. The comparison showed that the vapor−liquid equilibrium data obtained in this study are in good agreement with those reported in the literature. The experimental data were modeled with the PR (Peng−Robinson) and PC-SAFT (perturbed-chain statistical associating fluid theory) equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results of the modeling indicated that the PC-SAFT equation of state represents better the measured data of the N2 + C12H26 system over the whole temperature, pressure, and composition range studied.

Phase Equilibria of Mixtures Containing Glycol and n-Alkane: Experimental Study of Infinite Dilution Activity Coefficients and Modeling Using the Cubic-Plus-Association Equation of State

In this work, we report the infinite dilution activity coefficients for four n-alkanes (n-pentane, n-hexane, n-heptane, and n-octane) in monoethylene glycol in the temperature range from 298 to 334 K and at atmospheric pressure. Experimental data were measured using a previously described inert gas stripping technique. The new experimental data are compared with the literature data whenever possible. The experimental infinite dilution activity coefficients of several alkanes from n-pentane to n-hexadecane in monoethylene glycol, diethylene glycol, triethylene glycol, and tetraethylene glycol previously reported in the literature, along with the data measured in this work have been modeled using the cubic-plus-association (CPA) equation of state (EoS). Satisfactory results have been obtained using temperature-independent interaction parameters. Useful remarks are presented about the application of infinite dilution activity coefficient data for estimating binary interaction parameters of the CPA EoS for the description of whole vapor-liquid equilibria. Furthermore, the variation in the values of the interaction parameters is discussed for different glycol systems.

Vapor–liquid equilibrium data for the nitrogen + n-octane system from (344.5 to 543.5) K and at pressures up to 50 MPa

A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers has been used to obtain new vapor–liquid equilibrium data for the N 2 + n-octane system over the temperature range from (344.5 to 543.5) K and at pressures up to 50 MPa. Equilibrium phase compositions and vapor–liquid equilibrium ratios are reported. The new results were compared with solubility data reported by other authors. The comparison showed that the solubility data reported in this work at 344.5 K are in good agreement with those determined by others at 344.3 K. The experimental data were modeled with the PR and PC-SAFT equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results from the modeling effort showed that the PC-SAFT equation was superior to the PR equation in correlating the experimental data of the N 2 + n-octane system.

Vapor−Liquid Equilibrium Data for the Nitrogen + n-Decane System from (344 to 563) K and at Pressures up to 50 MPa

A static-analytical apparatus with visual sapphire windows and pneumatic capillary samplers has been used to obtain new vapor−liquid equilibrium data for the N2 + C10H22 system over a wide temperature range from (344 to 563) K and at pressures up to 50 MPa. Equilibrium phase compositions and vapor−liquid equilibrium ratios are reported. The experimental data were modeled with the PR (Peng−Robinson) and PC-SAFT (perturbed-chain statistical association fluid theory) equations of state by using one-fluid mixing rules and a single temperature-independent interaction parameter. Results from the modeling effort showed that the PC-SAFT equation was superior to the PR equation in correlating the experimental data of the N2 + C10H22 system over the whole temperature, pressure, and composition range studied.

The phase diagram of the Lennard-Jones fluid using temperature dependent interaction parameters

The forces of interaction between argon atoms can be described by the Lennard-Jones potential model. It is hypothesised that the use of temperature dependent interaction parameters, instead of using temperature independent interaction parameters, may lead to improvement in the prediction of the vapour–liquid coexistence curve. Published second virial coefficient data were used to fit a simple two-parameter temperature dependent model for the collision diameter and well depth. Vapour–liquid coexistence curve for argon was simulated in the NVT Gibbs ensemble Monte Carlo technique. The simulations were carried out using each of the temperature independent and temperature dependent parameters in the temperature range: 110–148 K. The critical temperature and density were determined using the Ising-scaling model. The results using temperature dependent parameters produce, overall, a more accurate phase diagram compared to the diagram generated using temperature independent interaction parameters. The root mean square deviation is reduced by 42.1% using temperature dependent interaction parameters. Also, there was no significant difference between the results obtained using temperature dependent interaction parameters and the highly accurate and computationally demanding phase diagrams based on three body contributions.

Phase equilibrium calculations for multi-component polar fluid mixtures with tPC-PSAFT

The truncated Perturbed-Chain Polar Statistical Associating Fluid Theory (tPC-PSAFT) is applied to a number of different mixtures, including binary, ternary and quaternary mixtures of components that differ substantially in terms of intermolecular interactions and molecular size. In contrast to most other SAFT versions, tPC-PSAFT accounts explicitly for polar forces. Three pure-component parameters are required for non-polar and non-associating compounds, two additional parameters characterize the association contribution and one parameter is needed to account for polar interactions. The experimental dipole and/or quadrupole moment and/or polarizability of the component are used to calculate polar interactions. Using a temperature-independent interaction parameter k ij for each binary system, tPC-PSAFT provides accurate prediction of multi-component phase behavior over a wide range of conditions.

Phase behavior of polymer mixtures with nonadditive hard-sphere potential

The phase behavior of a binary mixture of homopolymers in which macromolecules are composed of tangent hard spheres was studied. The interaction of unlike units is characterized by the contact distance (1/2)(σA + σB)(1 + Δ), where σ i is the diameter of the ith sphere (unit) and Δ is the nonadditivity parameter. The effect of nonadditivity was taken into account by means of the perturbation theory relative to the additive system (Δ = 0) considered earlier (Polymer Science, 47, 2146 (2005)) in terms of the Percus-Yevick approximation. The theoretical consideration presented is completely analytical. It was found that a polymer mixture experiences phase separation with an increase in pressure; the two-phase region extends with an increase in both the size ratio between the units α = σA/σB and the length of the chain per se. Closed phase diagrams were first predicted for athermal mixtures; such diagrams appear at Δ < 0 and certain values of α. It was shown that the thermodynamics of an incompressible mixture of hard-chain molecules at α = 1 follows the Flory-Huggins theory with the temperature-independent interaction parameter. Phase separation in polymer solutions with the nonadditive hard-sphere potential was also analyzed.