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• The liquid and vapor branches of the coexistence curve of nitrogen, ethylene and sulfur hexafluoride are obtained in analytically closed form. • The critical exponents of the order parameter and reduced coexistence-curve diameter are regressed from high-precision data and compared with scaling predictions. • Index functions (effective exponents) defined by the Log–Log slope of the order parameter and diameter indicate the onset of the critical scaling regime. • The crossover from the ideal power-law scaling regime of the coexistence curve to the triple point is modeled with Index functions. Analytic closed-form expressions are obtained for the liquid and vapor saturation densities defining the coexistence curve. The densities are modeled with broken power laws and Weibull distributions. Specifically, the coexistence curves of nitrogen, ethene and sulfur hexafluoride are derived, without the use of perturbative expansions, based on high-precision data extending from the triple point into the critical regime. The analytic continuation of the vapor branch below the triple point decays exponentially at low temperature. The order parameter and coexistence-curve diameter of the fluids are assembled from the regressed liquid and vapor branches of the coexistence curve, and the critical power-law scaling of these quantities is examined. The scaling exponents of the order parameter and the reduced diameter are regressed and compared with the calculated critical exponents of the 3D Ising universality class. Index functions representing the Log−Log slopes (temperature-dependent effective exponents) of the liquid and vapor densities, order parameter and diameter are used to determine the onset of the ideal power-law scaling regime and to illustrate the slope evolution of these quantities in the subcritical regime. [Display omitted] [ABSTRACT FROM AUTHOR]

With the emerging application of near-critical fluid, the subject of equation of state (EoS) covering the critical point is of great significance as the thermodynamic behavior of fluids near the critical point is different. Although many different EoSs are available for fluids at the moment, the ones which can give good quantitative results are still rare. Therefore, it is essential to have a suitable model for proper prediction of fluids behavior and their thermodynamic properties near the critical region. In this study, the crossover translation, which applies the asymptotic behavior of fluids and scaling laws near and far from the critical point, was used. Thermodynamic properties including density, vapor pressure and isochoric heat capacity of fifteen pure components in the saturated state and single-phase region on different isotherms were investigated near the critical point by Soave-Redlich-Kwong (SRK) equation of state and crossover SRK EoS and the results were compared with experimental data. According to the results, crossover SRK EoS predicted all of the mentioned properties with quantitative accuracy. The average absolute percent deviation (AAPD) of the saturated liquid density, saturated vapor density, density on isotherms, vapor pressure and isochoric heat capacity based on crossover SRK EoS were 0.0060,0.1287, 0.0171, 0.057 and 2.53, respectively. [ABSTRACT FROM AUTHOR]

Abstract Recently, hydrophobic deep eutectic solvents (DESs) were proposed as interesting solvents for biorefinery processes, such as the production of 5-hydroxymethylfurfural (HMF) from glucose in an aqueous environment. Physicochemical property data of hydrophobic DES + water/HMF systems are of utmost importance for process design. In this work, density and vapor pressure of eight different hydrophobic DESs, as well as water solubility and HMF solubility in these DESs were experimentally determined. The solubility was modeled using the pseudo-pure component approach within the framework of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). New pure-component parameters for the eight hydrophobic DESs were obtained by fitting to measured density and vapor-pressure data, instead of to density data only. Based on these new pure-component parameters for the DESs, the solubilities of water and of HMF in the hydrophobic DESs were modeled in good agreement with the experimental data at 298 K and atmospheric pressure. [ABSTRACT FROM AUTHOR]

• A new semi-empirical vapor density model for pure compounds. • Range of validity: triple point temperature to critical temperature. • The model can predict vapor pressure data from vapor density data. • The model allows thermodynamic consistency checks of vapor density data. In chemical engineering, surrogate functions are commonly used in modeling thermodynamic properties of pure compounds because they are often more accurate than equations of state. In 2020, we presented a semi-empirical model describing the vapor density from the reduced triple point temperature to about a reduced temperature of 0.97 with only one temperature-dependent term. However, in many cases the temperature range up to critical temperature is necessary. Therefore, the existing semi-empirical model was extended by another temperature-dependent term. This allows the vapor density to be described from the triple point temperature up to the critical temperature. This model has the additional advantage that it can predict the vapor pressure data from vapor density data. Therefore, this model can also be used for thermodynamic consistency testing. This is not possible with conventionally known surrogate models for describing vapor density. The model was successfully tested using fluoromethane (R41) and difluoromethane (R32) as examples. [Display omitted]. [ABSTRACT FROM AUTHOR]

The biofuels 2-methylfuran and 2,5-dimethylfuran, derived from furfural and 5-hydroxymethylfurfural, have a high potential to be used as clean and sustainable energy resources. As a consequence, investigating the properties of these compounds using molecular simulations is getting more important. In this work, we evaluated the widely used force fields OPLS-AA, GAFF and CHARMM27 regarding their ability to correctly reproduce the thermodynamic properties of these bio-masses and bio-fuels. We therefore performed Gibbs Ensemble Monte Carlo and molecular dynamics simulations to compute liquid density and vapor liquid equilibria properties of these bio-compounds. Subsequently, the obtained results are compared with experimental data and correlations by the PC-SAFT equation of state. Notably, the reported data create a basis for selecting an appropriate model or modifying the available force fields for further investigations. [ABSTRACT FROM AUTHOR]

Abstract: Configurational-biased Gibbs ensemble Monte Carlo simulations were performed to obtain the phase behavior of the homologous series of primary alcohols from ethanol to 1-heptanol. Molecular interactions in these systems are modeled by a newly developed exp-6 potential in combination with a Coulombic intermolecular potential. Some of exp-6 potential parameters required to describe these alcohols were taken from the previous literature data reported for methanol and n-alkanes. The oxygen''s potential parameters were optimized to fit the coexistence curve of these alcohols to the experimental data. Simulated values of saturated liquid and vapor densities, vapor pressures and critical constants of the alcohols are in good agreement with experimental data. The efficiency of the new model in the prediction of binary phase diagram of water/ethanol and n-hexane/1-propanol mixtures is also evaluated. The calculated mole fractions in the vapor and liquid phases of these binary mixtures also show satisfactory agreement with the experimental data. [Copyright &y& Elsevier]

Abstract: An equation of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) has been applied to model 35 pure associating and non-associating fluids and 15 binary mixtures. The pure components consist of alkanes, alcohols, water, aromatics and polar or multi-polar compounds like ammonia and H2S. In contrast to other attempts which have used the SAFT-VR model for various thermodynamic calculations using the square-well or Yukawa potentials, the short-range dispersion interactions have been accounted for here using the Sutherland potential, while hydrogen bonding interactions are explicitly taken into account as in other versions of the SAFT approach. The Sutherland potential is particularly useful for modeling the interactions among multi-polar species. Model parameters for the pure components have been optimized by fitting available experimental data on vapor pressure, saturated vapor density and saturated liquid density for temperatures ranging from near the triple point up to reduced temperatures of 0.9. The effect of several simplifying assumptions aimed at reducing the number of model parameters has been investigated, and the resulting trends in parameters has been discussed. Binary interaction coefficients have been obtained for the binary systems by fitting experimental data on vapor–liquid equilibrium pressure and phase concentrations. Results have been compared to those obtained using other versions of the SAFT-VR model. [Copyright &y& Elsevier]

Abstract: The thermodynamic and dielectric properties of the simple point charge extended (SPC/E) water model are examined over wide temperature and density range by means of molecular dynamic simulations. Accurate analytical thermodynamic and dielectric equations of state for the SPC/E pair-potential are presented. Parameterizations cover a broad range of high temperature states including the critical region. The critical point parameters of SPC/E water were determined to be ρ c =0.276g/cm3, T c =640.25K and p c =164.37 bar. The value of the static dielectric constant of SPC/E water at its critical point was calculated to be 5.35, which compares remarkably well with the corresponding experimental value of 5.36. Analytical thermodynamic and dielectric equations for the saturated liquid and vapor densities are also given. [Copyright &y& Elsevier]

Abstract: In this study a temperature-dependent function of the attractive term, called the alpha function, and the critical compressibility factor (ζ c) of the ER (Esmaeilzadeh–Roshanfekr) equation of state have been modified to improve the performance of equation of state. The ER EOS is a new three-parameter equation of state that was developed in 2006 with special attention to application for reservoir fluids. Using these modifications, saturated liquid density, saturated vapor density and vapor pressure of pure components are calculated more accurate than the ER equation of state. The average absolute deviations of the predicted saturated liquid density, saturated vapor density and vapor pressure of pure components with the modified ER (mER) are 0.95%, 1.17% and 1.20%, respectively. Also, the mER, the ER and the Peng–Robinson (PR) equation of state are used to predict dew point pressure for six gas condensate mixtures and bubble point pressure for five LNG mixtures. In order to have an unbiased comparison between these equations of state, van der Waals mixing rules are used without using any adjustable parameters (k ij =0). The results show that the mER EOS predicts the dew point pressure and bubble point pressure with best accuracy among the other EoSs. [Copyright &y& Elsevier]

• H 2 S solubility in five carboxylate-based ionic liquids including, [emim][Ace], [bmim][Ace], [hmim][Ace], [emim][Lac] and [emim][Pro] have been thermodynamically modeled. • RETM and mHKM-CPA EoS were implemented to calculate the liquid and vapor phase concentrations, respectively. • RETM constants were optimized utilizing fitting the model to the experimental solubility data. • Some physical properties of five investigated ILs were estimated through modified Lydersen-Joback-Reid method. • Simultaneous employing the RETM and CPA presents the excellent overall AADs% equal to 4.41 for 317 H 2 S solubility data. • A comparison between the used model and SRK-CPA EoS was made. The results show that the mHKM-CPA EoS reduced the AAD% by 2/3 (65%). In current work, mHKM-CPA EoS together with the RETM was employed to correlate H 2 S absorption into five carboxylate ionic liquids, including 1-ethyl-3-methylimidazolium acetate ([emim][Ace]), 1-butyl-3-methylimidazolium acetate ([bmim][Ace]), 1-hexyl-3-methylimidazolium acetate ([hmim][Ace]), 1-ethyl-3-methylimidazolium lactate ([emim][Lac]) and 1-ethyl-3-methylimidazolium propionate ([emim][Pro]). The RETM proposes a chemical reaction between IL and H 2 S so that the liquid phase concentrations may be obtained by solving the model. Moreover, mHKM-CPA EoS contributes to VLE calculations. In the model, H 2 S considered as associating component with 4 association sites while the ILs assumed as non-self-associating compounds with one electron donor/acceptor sites. Fourteen adjustable variables of mHKM-CPA EoS for pure components were calculated using experimental liquid density and vapor pressure data. Afterward, binary systems were correlated by applying RETM. Indeed, two nested loops calculate the liquid phase, total pressure, and vapor phase concentrations, respectively. The parameters of the pure ILs were calculated with maximum AAD% below 0.3. Moreover, the binary results present 4.41 as the overall AAD% for 317 data points. Furthermore, a comparison between the results of the used model with those of the SRK-CPA was performed to show the capability of the mHKM-CPA EoS. As the outputs show, the model has a good ability to correlate the H 2 S solubility in the ILs concerning the classic SRK-CPA EoS. [Display omitted] [ABSTRACT FROM AUTHOR]

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 (T C), critical pressures (P C), and acentric factors (ω) parameters for n-alkanes up to C 100 for improved volumetric and compositional multiphase behavior predictions. Parameters T C , P C , and ω for C 7 to C 100 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 CO 2 , CH 4 , C 2 , and C 3 binaries with n-alkanes with their optimized T C P C ω, optimized ω (and unoptimized T C and P C) only, and unoptimized T C P C ω values cases. It is found that optimized T C P C ω is correctly able to show the presence of three-phases for all 23 ternary hydrocarbon mixtures. [ABSTRACT FROM AUTHOR]

• A new EOS parameterization method based on global minimization has been developed • The P ρ T data were used to reparameterization of the SAFT-HR EOS for 60 pure compounds • New parameters were applied to predict the thermodynamic properties • VLE, critical point, and 2nd-order thermodynamic derivative properties were predicted • The results of the PρT-SAFT-HR and SAFT-HR for all systems is compared The lack of a transparent and universal parameterization method is one of the main problems in developing SAFT-type equations of state and it's an obstacle in their way of becoming an industrial equation of state. Usually, vapor-pressure and saturated liquid density data with a local optimization algorithm are used to parameterize SAFT-type equations of state. In addition to the ambiguity in the data selection process, using a local optimization method reduces the accuracy of the estimated parameters. Therefore, in this paper, a new method for calculating the adjustable parameters of SAFT or any equations of state with several parameters is presented. By providing a clear and explicit data selection procedure, including data categorization, comparison, and validation, integrated with the use of a combination of global and local optimization methods, the new methodology achieves the best possible parameters set for the equation of state. The proposed computational program for fitting parameters is based on the use of the Differential evolution algorithm as the main process and the Levenberg-Marquardt algorithm as the post-process along with applying one (or two) hyperparameter. Afterward, a wide range of pressure-temperature-density data has been used to estimate the parameters of 60 non-associating and associating pure compounds. Then, the SAFT equation of state with the new parameters, so-called PρT-SAFT-HR, is applied to predict pressure (P), temperature (T), density (ρ), vapor-pressure (P s a t), saturated vapor density (ρ v a p s a t), saturated liquid density (ρ l i q s a t), critical point, isochoric heat capacity (c v), isobaric heat capacity (c P), speed of sound (u), isothermal compressibility (κ T), and isobaric thermal expansivity (α P). All properties are calculated with the PρT-SAFT-HR equation of state, and the results are compared with experimental data and SAFT-HR and the average absolute percentage deviation is reported for all of them. In total, 19460 experimental and pseudo-experimental data were used to reparameterization the SAFT equation of state, and more than 74,000 data were validated to calculate thermodynamic properties. The results showed a significant improvement in predicting second-order thermodynamic derivative properties. In general, PρT-SAFT-HR performs better than SAFT-HR, and in some cases, such as pressure, speed of sound, isothermal compressibility, and isobaric thermal expansivity, the results have been significantly improved, and the average absolute deviation of PρT-SAFT-HR has been much less than SAFT-HR. [Display omitted] [ABSTRACT FROM AUTHOR]

The theory of Perturbed Chain Statistical Associating Fluid (PC-SAFT) is largely applied in many industrial fields. It requires three parameters: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By convention, they are determined by fitting vapor pressure and liquid density data. However, the shortage behind these parameters adopted by their respective authors is that they give excessive values of critical temperatures and critical pressures, which are crucial to forecasting vapor-liquid critical pressure and composition of the mixture at high pressures and temperatures. In this paper, a new approach is proposed to evaluate PC-SAFT parameters of different substances from diverse chemical families. Good fits of saturation pressure and vapor densities values of 94 pure substances are obtained, with an overall AARD of 0.89% and 1.50% respectively. The proposed method requires as input the critical pressure (P c), the critical temperature (T c), and the acentric factor (ω). By using these parameters, PC-SAFT estimates with accuracy the critical properties of pure compounds as well as the successful prediction of vapor-liquid equilibria for many non-associating binary systems at critical regions including mixtures containing ammonia, comparing with other literature values. But the limitation of this method is reflected in underestimated liquid densities. [ABSTRACT FROM AUTHOR]

Two issues of energy and environment cannot be separated in energy utilization systems. Using the working fluids in the thermal systems has to be highly attained due to these fluids may affect to the energy efficiency, global warming, and ozone depletion. Trans-1,3,3,3-tetrafluoropropene (HFO-1234ze(E)) was developed to address the issue. This fluid can replace the use of R-134a which is available in commercial market. Reliable thermodynamic equation of state (EOS) for HFO-1234ze(E) plays important role on optimization and design of refrigeration and thermal power systems. Helmholtz EOS is used as base of mathematical model because it is able to easily derive all thermodynamic properties and reliable to represent for a wide range of fluid phase. A new EOS was developed with a genetic algorithm combined with regression. The EOS represents thermodynamic properties of HFO-1234ze(E) with average absolute deviation (AAD) of 0.043% for the ideal gas isobaric specific heat, 0.084% for the liquid density, 0.39% for the vapor density, 0.096% for the vapor pressure, 0.11% and 1.0% for the saturated liquid and vapor densities. The caloric properties can be represented within AAD of 13%, 1.5%, and 5.4% for the isochoric, isobaric, and saturated specific heats, respectively, and the ADD of the speed of sound is 0.12% for liquid phase and 0.063% for vapor phase. The EOS also has proper behavior of the second and third virial coefficients and has proper extrapolation trend for the caloric and PVT properties. The EOS can be applied for temperature up to 600 K and pressure up to 100 MPa. [ABSTRACT FROM AUTHOR]

The experimental data on density and vapor pressure for nonaqueous solution of ionic liquids are important not only for the design and optimization of chemical processes, but also from the theoretical perspective to predict physical properties and modeling under different conditions. In this study, the vapor pressure for nonaqueous solutions of the ionic liquid, 1-ethyl-3-methylimidazolium ethyl sulfate [EMIM][ES] in some polar organic solvents, i.e. 1-propanol, ethanol and methanol, in dilute region of the ionic liquid concentration were measured by the use of isopiestic method at 298.15 K. In this regard, the Perturbed Chain Statistical Association Fluid equation of state (PC-SAFT) is used for prediction of the vapor pressure and density of the investigated systems. The obtained results from the PC-SAFT equation of state provide reliable and accurate predictions with the absolute average deviations (AAD), 0.01 and 0.084 for density and for vapor pressure , respectively. [ABSTRACT FROM AUTHOR]