Van Laar Model Research Articles

Estimation of excess Gibbs free energy of multicomponent biofuel mixtures of Butan-1-ol using machine learning methods based on modified Raoults law models

In biofuels, the excess Gibbs free energy of mixing is a very important thermodynamic property as it is used in evaluating the efficiency and sustainability in terms of energy conversion. Multiple biofuel systems containing butan-1-ol were examined with oxygenate ether additives such as MTBE and DIPE using isothermal vapour-liquid equilibrium data at different temperatures (298.15K, 313.15K, 318.15K). Two activity coefficient models, Wilson and van Laar model were compared by determining the bubble pressure and vapor mole fractions of each system using Modified Raoults Law and Machine Learning techniques. Besides, mole fractions and activity coefficients were used to identify the excess property. Results showed that Wilson model is appropriate for all the biofuel systems when using the Artificial Neural Network (ANN) resulting in an MSE of 3.2010e-09, 4.6792e-10, 1.6186e-10, and 5.3461e-07. In addition, van Laar model is more acceptable when Rational Quadratic GPR or Fine Tree algorithm were used with an average RMSE of 0.005820.01 and 0.020950.03 respectively. Lastly, the generated data for both activity coefficient models were also used to estimate the systems excess Gibbs free energy of mixing across varying mole fraction of its components.

Impact of the Dicarboxylic Acid Chain Length on Intermolecular Interactions with Lidocaine

Acid–base multicomponent systems have become a popular choice as a strategy to fine-tune the physicochemical properties of active pharmaceutical ingredients. Current prediction tools based on the principles of anticrystal engineering cannot always accurately predict the nature of intermolecular interactions within a multicomponent system. Even small changes in the physicochemical parameters of parent components can result in unexpected outcomes, and many salt, cocrystal, and ionic liquid forms are still being discovered empirically. In this work, we aimed to establish structural consistency in a series of mixtures comprising lidocaine (LID) with decanedioic, undecanedioic, dodecanedioic, and tridecanedioic acids and to explore how length and flexibility of the acid carbon backbone affect the molecular recognition, crystallization, and thermal behavior of the expected binary systems. We found that neat grinding of LID with dicarboxylic acids results in the formation of eutectic phases. The observed eutectic melting points deviated from the ideal eutectic temperatures predicted by the Schroeder van Laar model because of hydrogen bonding between the reacting components within the mixtures. Furthermore, thermal and infrared analysis provided evidence for the possible formation of new phases stemming from partial ionization of the counterions. Besides, the structure of a previously undetermined form I of the tridecanedioic acid was solved by single crystal X-ray diffraction.

A thermodynamic model for feldspars in KAlSi3O8−NaAlSi3O8−CaAl2Si2O8 for mineral equilibrium calculations

AbstractActivity–composition (a‐x) relations for feldspars for petrological calculations in KAlSi3O8−NaAlSi3O8−CaAl2Si2O8 are calibrated using literature data for (i) plagioclase cation exchange experiments at 600 and 700°C, (ii) experimental ternary feldspar pairs at 880 − 900°C, (iii) the alkali feldspar solvus, and (iv) the dry melting loop for plagioclase. The results are tested against the calorimetric heat of solution data and the experimental pressures for plagioclase coexisting with grossular, wollastonite, and quartz. As the aim is to produce a‐x relations suitable for petrological modelling, we do not attempt to model complex structural phenomena in feldspar, except where they appear to contribute significantly to the energetics of high‐temperature mixing. Seven models were investigated, using various formulations of entropy of mixing together with the van Laar model for non‐ideal mixing. The model (4TR) that most satisfactorily reproduces the experimental data is one in which Al and Si partially order onto the four tetrahedral sites, approximated by reducing the tetrahedral site entropy of mixing by a factor of 4. When combined with an ordered albite, this model allows a peristerite gap closing at 600°C at the albite composition. The resulting activity‐composition relations for feldspar should be applicable in petrological phase equilibrium calculations over a large range of geologically relevant pressure and temperature.

Activity coefficient models for accurate prediction of adsorption azeotropes

In this study seven adsorption azeotropes involving binary systems and zeolite-based adsorbents were systematically investigated. Pure component isotherms and mixed-gas adsorption data were taken from published literature except for the benzene–propene system on silicalite, which is newly presented in this work using molecular simulations. Experimental adsorbed phase composition and total amount adsorbed of the azeotropic systems were compared with the predictions of several models including: the ideal adsorbed solution theory (IAST), the heterogeneous ideal adsorbed solution theory (HIAST) and the real adsorbed solution theory (RAST) coupled with the 1-parameter Margules (1-Margules) and the van Laar equations. In the latter two models an additional loading parameter was incorporated in the expression of the excess Gibbs energy to account for the reduced grand potential dependency of the activity coefficients in the adsorbed phase. It was found that the HIAST and RAST–1-Margules models were able to predict the azeotropic behaviour of some systems with good accuracy. However, only the RAST–van Laar model consistently showed an average relative deviation below 3% compared to experimental data for both the adsorbed phase composition and the total amount adsorbed across the systems. This modified van Laar equation is therefore preferable in those engineering applications when the location of adsorption azeotropes is required with great accuracy and when there is lack of detailed characterization of the adsorbent that is needed to carry out molecular simulations.

Sequestration of light hydrocarbons in Ionic Liquids at high-pressures: Consistency and thermodynamic modeling

Ionic liquids are applicable in the recovery of valuable products, remotion of polluting agents, and used in many CO2-capture techniques. In this work, high-pressure vapor-liquid equilibria of twenty-one binary mixtures of light hydrocarbons + IL has been modelled with Peng-Robinson/Stryjek-Vera equation of state applying Wong-Sandler mixing rules and van Laar model for the gamma-phi approach and Perturbed Chain-Statistical Associating Fluid Theory equation of state for the phi-phi approach. Critical properties were determined using a group contribution method. Adjustable characteristic pure component parameters were obtained using predicted vapor pressures and saturated liquids densities values. Experimental data, obtained from literature, were subjected to thermodynamic consistency area test. For the thermodynamic modelling, adjustable parameters were fitted between predicted and experimental bubble pressure. Van Laar and interaction parameters were regarded as temperature-dependent. Results obtained for both models, in terms of the main deviations between experimental and calculated pressures, were reasonably satisfactory.

Revisiting the Classic Activity Coefficient Models

A link, established between the classic excess Gibbs free energy expressions and conventional mixture models, allowed the extension of the Margules and van Laar models to multicomponent mixtures. It is shown that the multicomponent form of the classic van Laar model features only one parameter per component in the mixture. It is also a special case of several other models including those due to Wassiljewa and Scatchard. This means that the latter can be seen to be a more general Scatchard–van Laar expression. It is also proven that the composition dependence of the Porter, Margules, van Laar, NRTL, and Wilson are all obtainable as special cases of the weighted double power mean mixture model. The ability of the models to accurately predict ternary performance from knowledge of binary behavior was tested using nine isothermal vapor–liquid data sets. The Wilson-type models performed best in this regard. The extended Scatchard–van Laar model also proved to be effective despite being particularly parameter-sparse.

Solubility of cefixime in aqueous mixtures of deep eutectic solvents from experimental study and modeling

Deep eutectic solvents (DESs) as green cosolvents can be added to water for increasing the solubility of poorly water-soluble drugs. In this study, the solubility of cefixime is studied in three aqueous solutions of DES, including choline chloride+malonic acid, choline chloride+urea, and choline chloride+glucose. The experiments are conducted in the temperature range of 293.15 K to 333.15 K, pressure of 0.1 MPa and different compositions of the DESs. The results show that adding DES to water increases the solubility of cefixime significantly. For instance, adding 6% (mol/mol) of choline chloride+malonic acid to water increases the cefixime solubility by more than 17 times. The DESs of choline chloride+malonic acid and choline chloride+urea are more effective cosolvents compared with the DES of choline chloride+glucose in increasing the mole fraction of cefixime. In addition, the solubility data are successfully correlated with the activity models of NRTL, Wilson and van Laar. The overall AARD% of the NRTL, Wilson and van Laar models in estimating the mole fraction of cefixime in aqueous solutions of the DESs are 3.88, 3.62 and 10.14, respectively.

MODELACIÓN DEL EQUILIBRIO LÍQUIDO-VAPOR DEL SISTEMA CLOROFORMO-METANO USANDO VAN LAAR Y PENG ROBINSON

Mathematical modeling of the phase balance is the basis of the description of distillation, used to refine products of purchasing potential. The ability to understand, model and predict the balance of phases is necessary for the design of industrial separation processes. The purpose of this article is to present the thermodynamic model and the methodology described step by step, for the construction of the bubble and dew curves, of the chloroform-methanol system. Matlab programs adequately predicted the azeotrope, using Peng’s cubic equation Robinson and the Van Laar model. Finally, the simulations were compared with Aspen Hysys and validated with experimental data reports reported in the literature, with error rates below 5 %.

Liquid balance - steam for methanol mixing - Benzen using the Peng Robinson and Van-Laar models

This paper is related to the procedure for calculating curves dew point and bubble point of a binary system, consisting of the methanol and benzene mixture to 45°C, using the Peng-Robinson cubic equation to calculate the fugacity coefficient of gas i in the mixture, and Van Laar model to calculate the activity coefficient of component i in the liquid mixture. Then a comparison between the theoretical data with the experimental data and later with the commercial simulator Hysys-Aspen, which applies the model of Wilson. The simulation was validated with experimental data,in addition to comparing the results with a commercial simulator.

Investigation of molecular interactions in binary liquid mixture: Measurements and correlation through thermo physicochemical study

Density (ρ)/acoustic speed (u) of sound have been experimentally measured over the complete mole fraction on (dimethyl carbonate + diisopropyl ether) mixture at T = (308.15/313.15/318.15) K and atmospheric pressure. Investigational data have been used to gauge excess molar volume /partial molar volume/excess partial molar volume/excess values of intermolecular free length/isentropic compressibility/acoustic impedance/isobaric thermal expansion coefficient/isothermal compressibility/surface tension. Extended Langmuir model pertinent to surface tension was applied to check the depth of penetration of molecular interactions between molecules. The excess values were fitted to Redlich-Kister equation and subsequently standard deviations are evaluated from coefficients. The departures of computed excess properties were explored in terms of molecular interactions. Experimental excess molar volume in the existing adventure was correlated by Prigogine–Flory–Patterson (PFP) theory/Soave-Redlich-Kwong (SRK) CEoS/Peng-Robinson (PR) CEoS at 308.15 K. Theoretical excess chemical potentials are computed and correlated by Margules/Porter/Wilson and VanLaar models at 308.15 K. Furthermore, vital thermodynamical potential derivatives are worked out at all temperatures through physicochemical properties rather calorimetric experiments. Contemporary study also consists of estimation and correlation of cohesive energy ΔA, Van der Wall's constants (a, b), distance of closest approach (d) by Hartmann–Balizar and Ballou non-linear equations at all temperatures.

Measurement and correlation of (vapour–liquid) equilibrium for binary mixtures composed of 1-(ethoxymethoxy)-propane with ethanol and 1-propanol at 101.33 kPa

Experimental vapour–liquid equilibrium (VLE) for binary mixtures composed of 1-(ethoxymethoxy)-propane with ethanol and 1-propanol at 101.33kPa was measured. The experimental data of saturated vapour pressure for 1-(ethoxymethoxy)-propane was measured. The measurements were performed using an improved Rose equilibrium still. Two binary systems present a minimum boiling azeotropes at 101.33kPa, in which the azeotropic temperature and composition are 351.45K and 95.98mol% (ethanol) and 369.44K and 81.30mol% (1-propanol), respectively. The VLE experimental values were correlated with the help of the NRTL, Wilson, and van Laar models for which the binary interaction parameters are reported. The results showed that the measurements have a good correlation under the NRTL and Wilson models about two binary systems, respectively. The thermodynamic consistency of the VLE experimental data was checked using the traditional area test and the direct test methods.

Phase stability conditions of clathrate hydrates for methane + aqueous solution of water soluble organic promoter system: Modeling using a thermodynamic framework

A thermodynamic model is presented for predicting the phase stability conditions of clathrate hydrates for methane+water-soluble organic promoter aqueous solution. A new equation is then proposed to estimate the enthalpy of hydrate dissociation for methane+aqueous solution of water-soluble organic promoter using Genetic Programming (GP) and Teaching–Learning-Based Optimization (TLBO) evolutionary algorithm. The model reliably predicts the hydrate dissociation conditions for methane+aqueous solutions of tetrahydrofuran, 1,3-dioxolane, 1,4-dioxane and acetone. The van Laar model is used to calculate the activity coefficient of water in aqueous solution of water-soluble organic promoter. About 30% of the reported experimental data were used for finding the empirical relationships to estimate the enthalpy of hydrate dissociation and the remaining 70% was used to test the accuracy and the predictive capability of the correlation. The average absolute error for methane hydrate dissociation temperatures was found to be 0.33K, which indicates the accuracy of the model.

Activity coefficients and excess Gibbs energy functions of acetophenone with 1,2-dichloroethane and 1,1,2,2-tetrachloroethane binary mixtures by using NRTL, UNIQUAC, UNIFAC and VAN LAAR models at a local atmospheric pressure of 95.3 kPa

Bubble point temperatures of pure liquids (Acetophenone, 1,2-dichloroethane and 1,1,2,2-tetrachloroethane) and their liquid mixtures were measured over complete composition range at a local atmospheric pressure of 95.3 kPa using a Swietoslawski-type ebulliometer. The data were then correlated with Antoine's equation. From the data activity coefficients and Gibbs energies were calculated. The systems showed a positive deviation from Raoult's law which suggests the presence of the dispersal forces acting between component molecules in the liquid mixture. NRTL, UNIQUAC, UNIFAC and VAN LAAR models have also been applied and good results were obtained. Molecular interactions between the unlike molecules in the binary liquid mixtures are discussed.

ChemInform Abstract: Fluid‐Mineral Equilibria and Thermodynamic Mixing Properties of Fluid Systems

AbstractReview: 44 refs.

Modeling of gas–solid equilibrium of binary systems aided by Frankenstein PSO

Binary systems containing supercritical CO 2 + hydrocarbons were used for modeling gas–solid equilibrium by a combined method including a thermodynamic model and a meta-heuristic algorithm. The Peng–Robinson (PR) equation of state was used in the classical solubility equation. In addition, Wong–Sandler (WS) mixing rules were used, and the van Laar model (VL) was included in order to evaluate the excess Gibbs free energy that appears in these mixing rules. Then, a variant of particle swarm optimization (PSO), called Frankenstein PSO (FPSO) was implemented for minimizing the difference between calculated and experimental solubility values. The results showed that the FPSO algorithm is a very powerful tool for parameter estimation on the PR-WS-VL model with good performance and accuracy, and considerably low deviations. Therefore, values calculated by the combined method (PR-WS-VL + FPSO) are considered accurate enough for physical and engineering calculations, among other uses.

Growth mechanism and magnetic and electrochemical properties of Na0.44MnO2 nanorods as cathode material for Na-ion batteries

Nanorods of Na0.44MnO2 are a promising cathode material for Na-ion batteries due to their large surface area and single crystalline structure. We report the growth mechanism of Na0.44MnO2 nanorods via solid state synthesis and their physical properties. The structure and the morphology of the Na0.44MnO2 nanorods are investigated by X-ray diffraction (XRD), scanning and tunneling electron microscopy (SEM and TEM), and energy-dispersive X-ray (EDX) techniques. The growth mechanism of the rods is investigated and the effects of vapor pressure and partial melting of Na-rich regions are discussed. The magnetic measurements show an antiferromagnetic phase transition at 25K and the μeff is determined as 3.41 and 3.24μB from the χ–T curve and theoretical calculation, respectively. The electronic configuration and spin state of Mn3+ and Mn4+ are discussed in detail. The electrochemical properties of the cell fabricated using the nanorods are investigated and the peaks in the voltammogram are attributed to the diffusion of Na ions from different sites. Na intercalation process is explained by one and two Margules and van Laar models.

Phase equilibrium and excess Gibbs energy functions of acetophenone with 1,1,2-trichloroethene and cyclohexane binary mixtures by using NRTL, UNIQUAC, UNIFAC and VANLAAR models at a local atmospheric pressure of 95.3 kPa

Boiling points of pure liquids and their binary mixtures are measured over the entire range of composition at a local atmospheric pressure of 95.3kPa. The experiments were carried by using a Swietoslawski-type ebulliometer. Vapor pressures of the pure components were computed using Antoine's equation. The activity coefficients and Gibbs energies were calculated for both the binary mixtures under investigation. Excess Gibbs energy values were found to be positive in both the binary systems. Both the binary systems were observed to be positive deviation from Raoult's law due to the dispersal forces acting between the component molecules in the liquid mixture. NRTL, UNIQUAC, UNIFAC and VAN LAAR models have also been applied successfully to both of the binary mixtures presented here. The results are discussed in terms of molecular interactions between the unlike molecules in the binary liquid mixtures.

Framework for correlating the effect of temperature on nonelectrolyte and ionic liquid activity coefficients

A power‐law expression is proposed for correlating the temperature dependence of infinite‐dilution activity coefficients ( ) for nonelectrolyte solute–solvent binary pairs and for pairs including an ionic liquid: , where θij = 0 for Lewis–Randall ideal solutions, θij = 1 for classic enthalpy‐based Scatchard–Hildebrand regular solution and van Laar models, and −5 < θij < 5 for most real binaries. The exponent θij is a function of partial molar excess enthalpy ( ) and entropy ( ) such that . Real binaries are classified into seven types corresponding to distinct domains of and θij. The new method provides a framework for correlating phase‐equilibrium driven temperature effects for a wide variety of chemical and environmental applications. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3675–3690, 2014

Fluid-mineral equilibria and thermodynamic mixing properties of fluid systems

The paper presents a review of an experimental method to quantitatively constrain thermodynamic mixing properties of fluid systems at high temperature T and pressure P. The method is based on bracketing equilibrium parameters of simple fluid-mineral reactions. Experimental data obtained with this technique for the H2O-CO2, H2O-N2, and H2O-H2 binary systems were utilized to calculate mixing parameters corresponding to the simplified van Laar model W12VL, according to which the equation for the integral excess Gibbs free energy of a binary mixture Gex is Gex =X1X2W12VL/(X1V10 + X2V20), where Xi is the mole fractions of the components, and Vi0 are pure species molar volumes at given P and T (in cm3). The W12VL for the three mixtures correspond to 202, 219, and 331 kJ cm3/mol. The empirical correlation \(W_{H_2 O - X}^{VL}\) (kJ cm3/mol) = 887.012 QX − 16.674, where Q = Pc (critical pressure, bar)/Tc (critical temperature, K) for gas X (where X = CH4, CO, H2S, O2, Ar, and NH3) is used to evaluate the van Laar parameters for a number of petrologically important water-gas mixtures. The H2O-H2 system is characterized by the greatest positive deviation from the ideal mixing and can thus decompose into two immiscible fluid phases under the P-T parameters typical of deep lithospheric zones. The exsolution of the H2O-CO2 and H2O-N2 systems is expected to occur only under high pressure and low temperature. This combination of parameters may be expected only in the environments of cold subduction. Salts (highly soluble simple salts and/or silicates) should significantly expand the exsolution regions in petrologically important fluids.

Phase equilibria modeling of binary systems containing ethanol using optimal feedforward neural network

A comprehensive understanding of vapor liquid equilibrium (VLE) data is one of the most important information for designing and modeling of process equipment. Because, it is not always possible to completely carry out experiments at all of the possible operational temperatures and pressures range, generalized thermodynamic models, e.g. equations of state are constructed for computing of required VLE data. In this work, artificial neural network (ANN) was used to derive predictive models of bubble point pressure and vapor phase composition of binary ethanol (C2H5OH) mixtures. In the neural network model, it is assumed that the considered VLE data depend on critical properties, acentric factor, normal boiling point, liquid phase composition of the solutes, and temperature. The proposed ANN model has been constructed and trained with VLE experimental data of nine different binary systems containing C2H5OH collected from various literatures. Optimal configuration of the ANN model has been determined using minimizing the average absolute relative deviation percent (%AARD), mean square errors (MSE) and the maximizing the correlation coefficient (R2) between observed and predicted VLE data with the ANN model. By using this procedure a two-layer ANN model with twenty-three hidden neuron has been found as an optimal topology. The accuracy of our optimal two layers ANN model has been compared with the Peng–Robinson cubic equation combined with Wong–Sandler (WS) mixing rules including a Van Laar (VL) model for the excess Gibbs free energy. Comparison with available literatures data and Peng–Robinson equation of state confirm that the present ANN model is more accurate and superior than the other published works. The sensitivity errors analysis clarify that our ANN model could predict vapor phase composition and bubble point pressure of all of the nine binary ethanol systems with %AARD of 1.52% and 2.59% respectively. The study demonstrates that the neural network model is a good alternative method for the estimation of VLE properties of the binary system containing C2H5OH.