Thermodynamic Consistency Test Research Articles

Phase equilibrium and separation process of byproduct vinyl acrylate in the ethylene vapor phase method producing vinyl acetate

Vinyl acrylate is one of the byproducts in the ethylene vapor phase method for the production of vinyl acetate (VAc), which not only has a toxic effect on the catalyst but also affects the purity of the product. Currently, phase equilibrium data for vinyl acrylate with water are missing, making the destination of vinyl acrylate in the distillation process uncertain. This has led to a lack of effective removal means, which restricts the optimization of the ethylene vapor phase method. This paper uses a method combining quantum chemistry and molecular dynamics simulation (MD) to investigate the existential form of the water molecule. And based on the ab initio calculation of the first principle, the force field parameters of the special water molecular structure are calculated, and the TIP4P-P force field that can describe the special water structure is established. Using the Gibbs Ensemble Monte Carlo (GEMC) method, the reliability of the improved water molecule force field for modeling the phase equilibrium of a binary system is first verified. Further, vapor–liquid phase equilibrium data for the vinyl acrylate-water binary system at 110 kPa and 150 kPa are calculated and the corresponding x-y and T-x-y phase diagrams are plotted. After performing the thermodynamic consistency test, the phase equilibrium data are fitted to obtain the binary interaction parameters of vinyl acrylate with water. The fitted parameters are applied to the process simulation of the VAc refining process to optimize the conditions and obtain an effective separation scheme for vinyl acrylate. The concentration distribution of vinyl acrylate in the distillation column is investigated, thus clarifying the destination of vinyl acrylate in the distillation process and facilitating the optimization of the ethylene vapor phase method.

New solubility data of Amoxapine (anti-depressant) drug in supercritical CO2: Application of cubic EoSs

The solubility of the anti-depressant drug, Amoxapine drug, in supercritical carbon dioxide has been studied. The experiments were performed by the simple and static procedure at P = 120–300 bar and T(K) = 311, 323, 333, and 343. The drug solubilities (mole fraction) ranged from 0.44 × 10−6 to 7.81 × 10−6. The drug solubilities were modeled, first using two cubic equations of state (Peng-Robinson and Soave-Redlich-Kwong EoSs with van der Waals mixing rule) and additionally by 17 semi-empirical density-based correlations (Stahl et al., Chrastil, Kumar-Johnston, Garlapati-Madras (model I and II), Sung-Shim, del Valle and Aguilera, Adachi-Lu, Ch and Madras, Hezave and Lashkarbolooki, Mendez-Santiago-Teja, Bartle et al., Jafari Nejad et al., Hozhabr et al., Keshmiri et al., Khansary et al. and Sodeifian et al.). The results revealed that cubic EoSs and semi-empirical density-based correlations can be used to obtain satisfactory drug solubility correlations at various temperatures and pressures. Between cubic EoSs, Peng-Robinson EoS (with Akaike Information Criterion is −692.12), and among 17 density-based correlations, the Stahl et al. correlation (with AARD% = 4.16 %, corresponding corrected Akaike Information Criterion is −700.98 and Radj = 0.9963) gave much better accuracy with the experimental data. The thermodynamic consistency test based on Gibbs-Durham's theory was performed by using both cubic EoSs and all experimental data were examined. Furthermore, the solvation, vaporization, and total enthalpies of Amoxapine-CO2 were calculated by Chrastil, KJ, and Bartle et al. correlations.

Assessment and modeling of the isobaric vapor-liquid-liquid equilibrium for water + cyclopentyl methyl ether + alcohol (ethanol or propan-1-ol) ternary mixtures

The three-phase equilibria of water + cyclopentyl methyl ether (CPME) + ethanol or propan-1-ol ternary mixtures are explored from experimental determinations and theoretical modeling at a constant pressure (101.3 kPa), and over 350 K to 356 K. Experimental measurements are performed in a modified Guillespie phase equilibria dynamic cell, which includes an ultrasonic homogenizer. The reliability of the measured three-phase equilibria is validated by employing the Wisniak's L/W thermodynamic consistency test. The measured vapor-liquid-liquid equilibria (VLLE) data at 101.3 kPa are accurately predicted from the phase stability restriction coupled with the multiphase equilibrium criteria. The application of this combined approach is showcased as a thermodynamical tool to explore all possible phase equilibria regions (i.e., one-, two-, and three-phase), providing a robust representation of the multiphase equilibria. Both phase stability and the corresponding multiphase equilibria are calculated using the SAFT-VR-Mie EoS model (statistical associating fluid theory of variable range employing a Mie potential equation of state), where the association and polar nature of pure components and their binary interactions are explicitly considered.No ternary azeotropy is detected within the experimental range of stable VLLE for the water + CPME + ethanol ternary mixture, although the theoretical extrapolation of the experimental conditions using the SAFT-VR-Mie EoS suggests its existence. For the case of the water + CPME + propan-1-ol ternary mixtures, a stable VLLE with a heterogeneous ternary azeotrope is detected from the interpolation of the experimental determinations.The predicted heterogeneous ternary azeotrope supports use of the CPME as a potential entrainer candidate for dehydration of bio-alcohols (e.g., ethanol or propan-1-ol) as well as implying that the distillate products, bio-alcohols (ethanol or propan-1-ol) + CPME mixtures can be directly used as a renewable fuel without the need of additional separation stages.

Vapor-Liquid Equilibrium Measurement of Systems Containing Glycerol for Separation Process of Glycerol as a By-Product of Biodiesel

The most popular technique to produce biodiesel were uses alcohol as a catalyst to transesterify triglycerides. The biodiesel transesterification process has a by-product in the form of glycerol which has a high selling value. Equilibrium data of glycerol and alcohol mixtures is limited in equilibrium conditions and systems which causes the glycerol purification process may not be designed and operated optimally. This research aims to obtain experimentally isobaric vapor-liquid equilibrium of methanol + glycerol binary system at 31.3, 61.3, and 100.8 kPa. A modified Glass Othmer-Still was utilised to carry out the experiment. Refractometer index type Bausch and Lomb ABBE was used to examine the equilibrium composition of the liquid and vapor phases. Using the L-W thermodynamic consistency test method, the experimental data used in this work were shown to be thermodynamically consistent. The experimental data were correlated well with the Wilson, Non-Random Two Liquid (NRTL), and Universal Quasi-Chemical (UNIQUAC) models with absolute average deviation in temperatures (AADT) and that in vapor compositions (AADy) smaller than 0.3% and 0.2%, respectively. The Universal Chemical Functional Group Activity Coefficient (UNIFAC) in predicting VLE the system studied showed good performance giving AADT and AADy smaller than 7.4% and 0.04%, respectively.

Development of the NRTL functional activity coefficient (NRTL-FAC) model using high quality and critically evaluated phase equilibria data. 2

One of the most significant models based on the local composition concept in advanced thermodynamics, is the non-random two-liquid (NRTL) model. Many studies have been conducted to enhance its applicability to various systems. Among these studies, the development of the NRTL model for electrolytic systems, polymer systems, and systems containing special chemical associations has been particularly significant. However, the NRTL model and its developed forms are based on the concept of local composition, and the dependency of these models on the experimental data for regressing NRTL interaction parameters limits their applicability of the NRTL model. Accordingly, to overcome this limitation, the NRTL functional activity coefficient model (NRTL-FAC), which is a group contribution model, was developed (https://doi.org/10.1016/j.fluid.2021.113088). The current study aims to extend the NRTL-FAC model. To achieve this, 15 new main groups have been added to the previous ones, and 266 new interaction parameters have been optimized. A total of 374 isothermal/isobaric VLE data sets, including 7115 data points, were used. The quality of the experimental VLE data was assessed using various thermodynamic consistency tests, including the Herington test, Van Ness test, point test, infinite dilution test, EoS test, and endpoint test. The NRTL-FAC model can accurately predict the VLE of binary systems, with results in good agreement with experimental data at different temperature and pressure ranges. This accuracy was observed for both azeotrope systems and ideal systems with positive or negative deviation from Raoult's law. Unlike the UNIFAC-DMD model, which restricts a portion of its interaction parameters to consortium members, the NRTL-FAC model interaction parameters are publicly accessible. Therefore, the NRTL-FAC model can be confidently used as a preliminary estimate to predict VLE behavior in process design when experimental data is not available.

Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor-Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling.

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker's method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs-Helmholtz equation. Robinson-Mathias, and Peng-Robinson-Stryjek-Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.

Vapor-liquid equilibrium for the {R-OH + R-palmitate} systems at 50.3 and 101.3 kPa

Fossil sources of energy become focus of many debates due to the pollution caused by them. In this scenario, renewable fuels, as biodiesel, are studied to improve their production efficiency and become more competitive with fossil fuels and even substitute them. Biodiesel, produced by the transesterification reaction, is constituted by a mixture of fatty acid esters and needs to be separated from its reactional solution in order to be commercialized. To improve the separation processes, the thermodynamic behavior of the mixtures involving components of the biodiesel needs to be known. Aiming this, the vapor–liquid equilibrium (VLE) of the methanol + methyl palmitate and ethanol + ethyl palmitate systems was analyzed at 50.3 and 101.3 kPa and the experimental data were submitted to a thermodynamic consistency test and thermodynamic modeling with the Peng-Robinson (PR), Group Contribution Volume Translated Peng-Robinson (GC-VT-PR) and the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equations of state. Experimental data were considered thermodynamically consistent, and the modeling showed good results in terms of the lowest relative deviations of temperature and vapor mole fraction obtained with the GC-VT-PR and PC-SAFT models.

Vapor-liquid phase equilibria, liquid densities, liquid viscosities and surface tensions for the ternary n-hexane + cyclopentyl methyl ether + 1-butanol mixture

Bulk, transport, and surface properties for the n-hexane + cyclopentyl methyl ether + 1-butanol ternary mixture are measured and theoretically predicted. Specifically, the vapor–liquid phase equilibria (VLE) are explored at 94.00 kPa and over 342.8 K to 369.6 K, whereas the liquid densities, the liquid viscosities, and the surface tensions are described over the whole mole fraction range at 298.15 K and 101.3 kPa. The measured data are correlated with the liquid molar fractions using a second-order Redlich-Kister (RK) polynomial and predicted using a molecular-based approach. Specifically, VLE and densities are predicted from the SAFT-VR-Mie EoS. This EoS model is coupled with the free volume theory to calculate the liquid viscosities and the van der Waals interfacial theory to predict the selected surface properties. The parameters of the theoretical approaches only involve pure fluids and binary mixtures information. The experimental VLE data of this ternary mixture passed two thermodynamic consistency tests and exhibited positive deviation from ideal behavior or Raoult's law, where no ternary azeotropic state is detected at the experimental conditions. Liquid densities, liquid viscosities, and surface tensions negatively deviate from the corresponding linear trend, and no ternary stationary points are detected under the explored conditions. The RK polynomials well correlated the experimental information by only using binary contributions. vFrom the theoretical modeling, the used approach (SAFT-VR-Mie-EoS) predicts both dew and bubble points with low deviations without the need of ternary information. Liquid densities, liquid viscosities, and surface tension are reproduced with good agreements, showing deviations of 0.13%, 2.7%, and 4.4%, respectively. Finally, the used EoS coupled to vdW-SGT predicts surface adsorption only for n-hexane and 1-butanol.

New Alpha Functions for the Peng-Robinson Cubic Equation of State.

The alpha function is an important part of the attractive term of cubic equation of state (EoS), which affected the predictive accuracy of thermodynamic properties. In this paper, four new alpha functions (Alpha Function-1 to Alpha Function-4) were proposed for the Peng–Robinson (PR) EoS. The proposed alpha functions and their derivatives satisfied the requirements of the thermodynamic consistency test. The four alpha functions with PR EoS were used to predict the thermodynamic properties of 11 kinds of compounds, the average relative deviation (ARD) of Alpha Function-1 and Alpha Function-2 for the prediction of vapor pressures was 0.57%, and the ARDs of Alpha Function-3 and Alpha Function-4 were 0.44 and 0.38%, respectively. The ARDs of Alpha Function-4 for the estimation of enthalpy of vaporization, liquid volume, and liquid isobaric heat capacity of seven kinds of compounds were 1.46, 7.54, and 7.59%, respectively. The proposed three-parameter alpha functions were more accurate than the two-parameter function for the prediction the vapor pressure and enthalpy of vaporization of pure compounds. However, any alpha function used in the attractive term of PR EoS had great deviations for the estimation of liquid volume and isobaric heat capacity.

Phase equilibrium and dissociation enthalpies of CO2/cyclopentane hydrates in presence of salts for water treatment and CO2 capture: New experimental data and modeling

The applications of clathrate hydrates on carbon dioxide capture and desalination is an attractive and growing subject within the hydrate community. While many promoters exists to overcome the numerous issues of hydrate-based technologies (mostly how to mild the operating conditions and improve the kinetics), there is a need to find a guest that could be recovered easily. That is why cyclopentane (CP), an organic molecule not miscible into water that can form hydrates under atmospheric pressure at 7 °C, has been studied widely in the literature. However, its behavior in forming mixed hydrates with CO2 in presence of salts is still not well understood. This work is an effort to investigate the thermodynamics of mixed CO2/CP hydrates to fulfill the gap in this field from a thermodynamic point of view. In this effort, new equilibrium data of mixed CO2/CP hydrates in the presence of salts (NaCl-KCl, MgCl2, CaCl2 which are among the main factors of hard water) have been obtained under different concentrations and pressures. Final dissociation points and as well as intermediate metastable points were obtained. Furthermore, thermodynamic consistency tests have been performed on our data and literature data to discuss their reliability. This test is important to question the idea of thermodynamic equilibrium since we suspect from a previous work the formation of several hydrate structures. Finally, three modeling approaches were considered: van der Waals and Platteeuw (vdW-P) approach, Hu-Lee-Sum (HLS) correlation, and ice melting point method derived from HLS proposition. Results showed a greater inhibition effect of cation Ca2+ compared to Mg2+ and that vdW-P method can predict equilibrium temperature within 0.2 °C uncertainty.

The mechanism explosion of separating binary azeotropic system with intermediate-boiling-point solvent based on vapor–liquid equilibrium experiment, quantum chemical calculation and molecular dynamics simulation

For the extraction distillation process, the choice of entrainer is very important. Usually, the boiling point of the entrainer is higher than that of any of the components to be separated, while the mechanism of separation of azeotropic system with intermediate-boiling-point solvent as entrainer is not common. Taking the azeotrope of n-heptane and isopentyl alcohol as an example, the intermediate-boiling-point solvent of butyl acetate was determined as the entrainer. The experimental data of vapor–liquid equilibrium for the two systems of n-heptane isoamyl alcohol and n-heptane butyl acetate were analyzed. After the thermodynamic consistency test, the binary interaction parameters of three models were obtained by correlating and regressing the experimental data. The possibility and mechanism of the extraction of azeotropic system by the intermediate-boiling-point solvent were analyzed from the aspects of σ-profile, interaction energy and charge density by the principle of quantum chemistry and molecular dynamics. The results showed that the tendency of hydrogen bond between the intermediate-boiling-point solvent and the azeotropic system was different: one component interacted with each other in the form of hydrogen bond, and the other had no hydrogen bond. The mechanism of the intermediate-boiling-point solvent as the entrainer to separate azeotropic system was verified in the extractive distillation process.

VLE measurement of binary systems containing imidazolium ionic liquids and water or ethanol

Experimental VLE data for binary systems of ethanol or water with three 1-ethyl-3-methylimidazolium ionic liquids (ILs) containing different anions were measured at normal pressure using the Siwoloboff procedure. ILs selected in this study were those that appear to be suitable for the ethanol−water mixture separation by extractive distillation. Measured vapor–liquid equilibria were described by the extended Raoult's law with components activity coefficients calculated using the NRTL equation. Detailed analysis of the VLE data is presented in form of equilibrium diagrams, variation of activity coefficients with mixture composition and thermodynamic consistency tests. Experimental t–x data were measured within a wider range of the binary mixture compositions and compared to those found in literature. Boiling point temperature measurement of binary mixtures (adapted Siwoloboff procedure) provided comparable results to those obtained applying conventional methods of VLE estimation (circulation method, ebulliometric measurement, etc.). Reliability and thermodynamic consistency of experimental data obtained using the adapted Siwoloboff procedure for high ILs’ content (high temperature) were affected by the accuracy of the temperature measurement. However, the trend of these experimental data is useful for VLE description in concentration regions where usually only coarse extrapolation is applied. Experimental data obtained for a wide binary mixture composition range (IL content of more than 70 mole%) seem to be more suitable for binary and ternary VLE description in separation equipment simulations, e.g. extractive distillation columns.

Improvements for a fully consistent description of the new semi-empirical vapor density model for pure compounds

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.

Vapor-liquid equilibrium in methanol + water system and modeling from 298.15 to 373.15 K

Vapor-liquid equilibrium (VLE) relationships are needed in the solution of many engineering problems. The required data can be found by performing an experiment. But such measurements are not so easy, even for binary systems. The fundamental idea of a solution- of- groups model is to utilize existing phase equilibrium data for predicting phase equilibria of systems for which no experimental data are available. The popular predictive method of industries called the UNIFAC (Universal Quasi-Chemical Functional Group Activity Coefficient) group contribution model has been found to be successful to represent the available experimental data of VLE for wide variety of mixtures at various values of temperatures and pressures. In this work, the vapour-liquid equilibrium (VLE) for the methanol (1) + water (2) system has been investigated at temperatures ranging from 298.15 K to 373.15 K. The VLE data of methanol (1) + water (2) mixture for this temperature range have been also regressed using UNIFAC model available in data pro ii. The thermodynamic consistency test of experimental data such as point test has been also performed. The phase equilibrium data generated in this work are relatively good in agreement with previous data reported in the literature.

Three-dimensional condensation in a vertical channel filled with metal foam using a pseudo-potential lattice Boltzmann model

In this study, three-dimensional condensation in a domain filled with metal foam is investigated using the lattice Boltzmann method for the first time. A recently proposed two-phase pseudo-potential lattice Boltzmann model is extended to 3D phase-change problems by adding the energy equation with the Peng–Robinson equation of state. The phase-change model is validated using the thermodynamic consistency test, Laplace law, contact angle test, and D2-law. To provide accurate pore-scale analysis, both the flow and energy equations are discretized with the D3Q27 model. Moreover, the metal foam cell structure is reconstructed by implementing the Lord Kelvin model on the mesh nodes. The results are reported in terms of condensation modes, droplet nucleation, growth and removal, heat flux on the walls and mass flow rate of the discharged condensate. Furthermore, the effects of the Jakob number (in range of Ja=0.06 to 0.24) and cell size (S=16,32, and 64) are investigated regarding the condensation process, average heat flux, and mass flow rate. The condensation curve under constant temperature boundary condition is presented for different configurations. It is shown that the model is capable of simulating convection heat transfer along with different condensation modes, including dropwise and filmwise modes. Our results revealed that the onset of nucleation and mode transition occurs at lower Jakob values as the metal foam cell size is increased. Also, it is shown that at a fixed configuration, increasing the Jakob number affects the condensate mass flow rate more than heat flux. The results of this study could be useful in the design of phase-change heat exchangers with metal foam construction.

Experimental investigation and modeling of vapor-liquid equilibria for Bi–Zn and Bi–Sn–Zn systems at 10 Pa

For the Bi–Zn and Bi–Sn–Zn systems, vacuum distillation experiments were carried out at 10 Pa. The results show that the content of Zn for the Bi–Zn system in the vapor phase could reach more than 0.999 mol fraction in vacuum distillation. The VLE (vapor-liquid equilibrium) data were correlated using the Tsuboka-Katayama's modification of the Wilson equation (T-K-Wilson). The correlation showed good agreement with experimental data. Thermodynamic consistency tests of experimental data for the binary and ternary systems were presented by the Van Ness method. The results demonstrate that VLE phase diagram is reliable for predicting the process of vacuum distillation for the systems. It provides an efficient way to guide the separation and purification of crude Zn in vacuum metallurgy

Development of the NRTL functional activity coefficient (NRTL-FAC) model using high quality and critically evaluated phase equilibria data. 1

The non-randomness two-liquid model (NRTL) has been used successfully in chemical engineering to calculate phase equilibria. Different forms of the NRTL model have been developed, including original NRTL, electrolyte NRTL (e-NRTL), polymer NRTL and segment based NRTL (NRTL-SAC). The mentioned forms of the NRTL model are correlative so that they require experimental data to regress the NRTL interaction parameters, which in turn, limit the application of the NRTL models. In the current study, therefore, the NRTL functional activity coefficient (NRTL-FAC) model was developed based on the high-quality experimental vapor-liquid equilibrium (VLE) data. The quality of experimental data were checked using different thermodynamic consistency tests, including Herington test, Van Ness test, point test, infinite dilution test, EOS test and endpoint test. Of the available VLE data, 2938 isothermal/isobaric data sets including 46,651 data points were used in the development of the model. Besides, 137 molecules with 50 main groups were used to develop the NRTL-FAC model. The Stavermann-Guggenheim term was also used to account the combinatorial contribution of the NRTL-FAC model. The good agreement between the predicted results by the NRTL-FAC and the experimental VLE data is encouraging. The present model performs superior to the previous versions of the UNIFAC model.

Isobaric vapour-liquid equilibrium data for the binary systems of polyoxymethylene dimethyl ethers with methanol, methylal and ternary system of methylal + methanol + polyoxymethylene dimethyl ethers at 50.0 kPa

Polyoxymethylene dimethyl ethers (PODEn) are excellent diesel blending components that can reduce pollution compared to conventional diesel. In this work, isobaric vapour-liquid equilibrium (VLE) data for the two binary systems of (methanol + PODE3), (methylal + PODE3) and ternary system of (methylal + methanol + PODE3) at 50.0 kPa were measured in an Ellis equilibrium still. The thermodynamic consistency of the experimental data was checked by the Herington area method and Van Ness method. All systems passed thermodynamic consistency test. The UNIFAC and NRTL models were applied to correlate the experimental data, the root-mean-square deviation (RMSD) and the average absolute deviation (AAD) for the temperature (T) and the molar fraction of the vapour phase (y1) were obtained. The results demonstrate that the UNIFAC model is more accurate than the NRTL model for the studied systems. Therefore, the UNIFAC model can predict the VLE data of PODEn systems accurately. The VLE phase diagrams of studied systems were obtained and they were useful for the separations of PODEn.

Influence of thermodynamically inconsistent data on modeling the solubilities of refrigerants in ionic liquids using an artificial neural network

In this work, a general thermodynamic consistency test is applied to analyze phase equilibrium data (PTx) for binary refrigerant and ionic liquid mixtures. The Valderrama-Patel-Teja (VPT) equation of state and the Kwak and Mansoori (KM) mixing rules are employed to correlate the solubility data of several refrigerants in different ionic liquids, and the Gibbs-Duhem equation is employed to check the thermodynamic consistency of six hundred forty-two experimental data points. The main purpose of this work is to analyze the influence of experimental data that are declared thermodynamically inconsistent on modeling the solubilities of refrigerants in ionic liquids using an artificial neural network. The results obtained via the test are classified into three categories: thermodynamically consistent, not fully consistent and thermodynamically inconsistent. Subsequently, a multilayer perceptron is trained to predict solubility in three cases: i) learning with isotherms that are declared thermodynamically consistent; ii) learning with isotherms, including those that are declared thermodynamically consistent and those that are not fully consistent; and iii) learning with all isotherms, even those that are declared thermodynamically inconsistent. For each case, the architecture, input combination and number of parameters necessary to achieve reasonable predictions are determined. The results show that the use of thermodynamically consistent and not fully consistent data is sufficient for finding an artificial neural network with a reasonable number of parameters.

Modification of Peng–Robinson Cubic Equation of State with Correction of the Temperature Dependency Term

Equations of state (EoSs) have always been one the most interesting field of study for scientists and engineers, due to their extensive applications in various industries and scientific research. Accordingly, scientists have extensively studied useful modifications of the original EoSs. In this study, the temperature dependent part of the Peng–Robinson cubic equation of state is modified. The new dual parameter α-function is able reproduce the vapor pressure data accurately for a large variety of pure components. Mono-atomic and di-atomic molecules, hydrocarbons, polar and associating compounds are well represented by the Peng–Robinson–Saali equation of state with negligible deviation with experimental data. Moreover, the thermodynamic consistency test of P–T–x solubility data based on the fundamental Gibbs–Duhem equation, for binary mixtures including acid gases (CO2 and H2S)/polar and associating solvents at low and high pressure were also investigated. The proposed EoS coupled with a three-parameter binary interaction term, namely the Panagiotopoulos–Reid mixing rule, was used in order to present the PR–Saali EoS as a versatile equation for analyzing thermodynamic consistency of experimental data. Modeling processes were carried out by using MATLAB 2018a.