Analytical Solution Of Groups Research Articles

Prediction of Phase Equilibria and Transport Properties Using ASOG and PRASOG Group Contribution Methods: A Review

Half century has passed since the first version of Analytical Solution of Groups (ASOG) model was proposed. Now the ASOG model is well known as a group contribution method as well as UNIFAC. Although the ASOG model was designed for prediction of vapor-liquid equilibrium around the atmospheric pressure, the applications are extended to not only the phase equilibria in the wide temperature and pressure ranges but also the transport properties. The function forms in the ASOG model, basically composed of Flory-Huggins equation and Wilson equation, can be applied for the prediction of the phase equilibria (vapor-liquid, liquid-liquid, solid-liquid and vapor-solid) and the transport properties (kinematic viscosity, thermal conductivity) of the mixtures with some modifications.

Estimation of kinematic viscosities and thermal conductivities for liquid mixtures using ASOG-VLE, ASOG-VISCO and ASOG-ThermConduct models

We present an estimation of the kinematic viscosities and thermal conductivities for liquid mixtures using the analytical solutions of groups (ASOG) contribution method. Two procedures were examined to estimate these properties using the excess properties. First method is a use of the vapor-liquid equilibria as equilibrium property. Optimization of the Eyring constant k was also done from the experimental data of the kinematic viscosities or thermal conductivities. Second one is a determination of the interaction parameters in the excess Gibbs energy model, that is, activity coefficient model, from these experimental transport property data. Estimated results of these properties at low pressure by the two procedures, i.e., ASOG-VLE + kvisco or kTC and ASOG-VISCO or ASOG-ThermConduct were given, and the estimation accuracies were discussed. Estimation of the kinematic viscosities by the ASOG-VISCO was extended to the binary systems containing carbon dioxide expanded liquid at high pressure.

Thermodynamic Behavior of the Phase Equilibrium of Ethyl Acetate + Ethanol + Water Systems at Atmospheric Pressure: Experiment and Modeling

The fluid phase behavior of liquid–liquid equilibrium (LLE) is an important piece of the separation processes in chemical engineering, mainly for solvent extraction or liquid–liquid extraction. In this work, experimental studies were carried out in the LLE of a ternary system composed of water, ethanol, and ethyl acetate at four different temperatures at atmospheric pressure. A two-step procedure was done for each temperature in the experimental stage. First, the construction of the binodal curve of the ternary system, and second, the determination of the tie-lines (LLE). For the tie-lines, because the configuration of the binodal curve and the refractive index of the liquid phases at equilibrium were known, their compositions were determined. The LLE experimental data were evaluated through the method developed by Marcilla and collaborators. The gamma–gamma approach was used for the modeling, by using the analytical solutions of groups (ASOG), the nonrandom two-liquids (NRTL), and the universal quasichemical (UNIQUAC) models. Results of the thermodynamic modeling were compared with the experimental values, and the deviations of the compositions of the lighter phase were very low for the thermodynamic models used.

Prediction of liquid-liquid equilibria of multicomponent fatty systems using the ASOG method

Purification steps, as solvent extraction, play an important role in biodiesel and edible oil processing. Their continuous improvement relies on predictive tools for computing liquid-liquid equilibria (LLE), and among these tools, group contribution methods, such as the UNIQUAC Functional-group Activity Coefficients (UNIFAC) method and its variants, and the Analytical Solutions of Groups (ASOG) method, are commonly used. In this work the ASOG method was evaluated for predicting LLE of 372 multicomponent fatty systems from the literature. The ASOG method, although quite unexplored, in particular for fatty systems, performed satisfactorily well, resulting in a global deviation of 9.27%. The Solution Structure of Isoactivity Equations (SSIE), a recently published procedure for computing LLE based on the solution of the isoactivities was adopted as the calculation strategy. The predictive capacity of the ASOG method was also improved by means of readjustment of interaction parameters related to functional groups of fatty acid (COOH), ester (COO), aldehydes (COH), water (H2O), and unsaturation (CC). The new parameters allowed prediction of solubility of fatty acid, alcohol and aldehyde in both fatty and solvent phases more precisely, diminishing deviations between calculated and experimental compositions.

Simulation of mass transfer in hollow fiber used for concentration of juices by osmotic distillation

A bi-dimensional diffusion mathematical model is proposed to study mass transfer in hollow fiber used for the concentration of juices by osmotic distillation (OD). The mathematical model was solved using the Finite Volume Method (FVM). The mass fraction at the boundaries was calculated by using the Functional-group Activity Coefficients (UNIFAC) method for the juice and by the Analytical Solutions Of Groups (ASOG) method for the brine. Calculated results were compared to an analytical solution for a case of mass diffusion in a cylinder with mass flow boundary condition. An algorithm to find the effective diffusion coefficient of gas through the membrane is proposed. To show its usefulness, different velocities were applied over the fiber surface to study the bi-dimensional effects that this velocity field has on the mass transfer inside the fiber. The results showed a maximum error of 5.6% when compared to experimental results.

Measurements and Modeling of VLE Data for Butyl Acetate with 2-Propanol or 2-Butanol. Binary Systems at 0.15 and 0.6 MPa

Isobaric vapor–liquid equilibrium is measured at 0.15 and 0.6 MPa for binary mixtures of butyl acetate with 2-propanol and 2-butanol. The experimental data are reported and the thermodynamic consistency is verified by using the point-to-point test. Prediction of these binary systems was obtained by employing the analytical solutions of groups (ASOG) and the different versions of UNIQUAC functional-group activity coefficients (UNIFAC) group contribution models. The perturbed chain-statistical associating fluid theory (PC-SAFT) equation of state has been used to reproduce experimental data.

Experimental Vapor–Liquid Equilibria Data of Methyl Acetate or Ethyl Acetate with 2-Butanol at 0.3 MPa and 0.6 MPa. Quality Assessment and Predictions

Isobaric vapor–liquid equilibria for the binary system methyl acetate + 2-butanol at 0.3 MPa and 0.6 MPa and ethyl acetate + 2-butanol at 0.3 MPa and 0.6 MPa have been determined. Thermodynamic consistency was checked. The Redlich–Kister and Herington area tests were employed. The Point test, Area test and Infinite dilution test (PAI) of Kojima et al. and the point-to-point test of Van Ness et al. were also applied. The different criteria for validation were considered, and all systems showed an acceptable quality. The results of global and individual deviations on experimental data calculated by using the Fredenslund et al. routine are shown. The different versions of the unique functional group activity coefficient (UNIFAC) and analytical solution of groups (ASOG) predictive group contribution models were applied. The experimental data were also correlated with the Peng–Robinson equation applying quadratic mixing rules.

Ebulliometric Determination and Prediction of Vapor–Liquid Equilibria for Binary Mixtures of Ethanol and Ethyl Hexanoate

The objective of this study is to measure vapor–liquid equilibria (VLE) data for an ethanol + fatty acid ethyl ester (FAEE) system. VLE data for the binary system ethanol + ethyl hexanoate were determined at pressures of (40.00 to 101.3) kPa using an ebulliometer, which could compensate for vapor hold-up. The hold-up compensable ebulliometer was designed for this study, and the experimental apparatus and procedure were verified by measuring the VLE data for ethanol + p-xylene at pressures of (40.00 to 101.3) kPa. The densities at 298.15 K for pure components investigated in this study were also measured by a densimeter. The experimental VLE data of the two binary mixtures, ethanol + p-xylene and ethanol + ethyl hexanoate, were represented by the Wilson and nonrandom two-liquid (NRTL) models. The analytical solutions of groups (ASOG) and modified universal functional activity coefficient (UNIFAC, Dortmund) group contribution models were also used to predict the VLE behavior of these binary mixtures. The VL...

Application of the Unified Functional Activity Coefficient (UNIFAC) and Analytical Solution of Groups (ASOG) for the Calculation of Mutual Solubilities in Water Systems of Alkanes, Arenes, and Alkanols

The recommended solubilities taken from the International Union of Pure and Applied Chemistry/National Institute of Standards and Technology (IUPAC-NIST) Solubility Data Series were used as testing data for the prediction of the solubilities in water systems of alkanes, arenes, and alkanols with various versions of unified functional activity coefficient (UNIFAC) and analytical solution of groups (ASOG) methods. It was strongly confirmed that parameters aimed at the prediction of vapor–liquid equilibria (VLE) are not applicable for predictions of liquid–liquid equilibria (LLE) in the water systems. The average relative error of the predicted solubility for alkane–water systems is equal to hundreds or even thousands of percent. For arene–water and alkanol–water systems it is usually about 100 %. Much better accuracy can be obtained with parameters adjusted to the solubility data. The UNIFAC version developed by Voutsas and Tassios, VT-UNIFAC, predicts mutual solubilities in alkane–water systems with an ave...

Solid-Liquid Equilibrium of Xylose in Water and Ethanol/Water Mixture

This work deals with the study of thermodynamical models for the solid-liquid equilibrium (SLE) and comparing its performance with experimental data. The xylose solubility in the xylose-water and xylose-water-ethanol systems has been measured using a variant of the isothermal method. A total of 12 experiments were performed in a 100 mL glass jacketed crystallizer with helix-type agitator by changing the temperature from 0 to 60°C. The solution was mixed during 72 h with an IKA Labortechnic, RW 20.n agitator at 450 rpm. Later, the experimental and reported results were fitted using the prediction models based on the vapor-liquid-equilibrium (UNIFAC (Universal Functional Activity Coefficient), ASOG (Analytical Solutions of Groups) and GSP (Group Solubility Parameter); semi-empirical models based on the vapor-liquid-equilibrium (VLE) (UNIQUAC (Universal Quasi Chemical), Wilson and NRTL (Non Randon Two Liquid)) on the solid-liquid-equilibrium, and empirical model with fitted parameters (Nývlt, λh, Margules with 1 and 2 parameters). The results showed that the UNIQUAC model with fitted parameters can describe the SLE with reasonable accuracy (1.28 and 3.36% for binary and ternary systems, respectively). The average deviation was the arithmetic mean of the deviations. On the other hand, the other methods resulted in poor agreement with the system’s behavior presenting systematic deviations from the experimental data.

Density, Refractive Index, Speed of Sound at 298.15 K, and Vapor−Liquid Equilibrium at 101.3 kPa for Binary Mixtures of Methanol + Ethyl Lactate and 1-Propanol + Ethyl Lactate

Density, refractive index and speed of sound at 298.15 K, together with isobaric vapor−liquid equilibria data (VLE) at 101.3 kPa are reported for two binary mixtures, methanol + ethyl lactate and 1-propanol + ethyl lactate. Excess molar volumes on mixing were determined from the experimental data and consequently fitted with Redlich−Kister polynomials. VLE experimental data were tested by Dechema test, which proved their thermodynamic consistency. The activity coefficients were correlated with the Margules, van Laar, UNIQUAC, NRTL, and Wilson equations. The Analytical Solutions of Groups and Universal quasichemical Functional group Activity Coefficients models were also used for the prediction. Investigated binary systems did not show any azeotrope.

Vapor–liquid equilibria for binary mixtures containing ethyl tert butyl ether (ETBE) + (p-xylene, m-xylene and ethylbenzene) at 101.3 kPa

Isobaric vapor–liquid equilibria data at 101.3 kPa were reported for the binary mixtures ethyl tert butyl ether (ETBE) + (p-xylene, m-xylene and ethylbenzene). VLE experimental data were tested for thermodynamic consistency by means of a modified Dechema test and was demonstrated to be consistent. The activity coefficients were correlated with the Margules, van Laar, UNIQUAC, NRTL, and Wilson equations. The Analytical Solution Of Groups (ASOG) model also was applied for prediction.

Prediction of vapor–liquid equilibrium for systems containing hydrofluoroethers using ASOG group contribution method

Owing to extend the applicability of analytical solution of groups (ASOG) to the systems composed of the hydrofluoroethers, hydrofluorocarbons, and the solvents, its group pair parameters of CF 2/CH 2, CF 2/O(HFE), CF 2/O(ether), and CF 2/OH have been newly determined using 10 binary vapor–liquid equilibrium data at 101.3 kPa. The group pair parameters relating CHF 2, CH 2F, and CHF groups were assumed to equate to those containing CF 2 group. The vapor–liquid equilibria at 101.3 kPa were predicted with good accuracy using the determined parameters for 11 binary systems constituted by the hydrofluoroethers and alcohols.

Measurement and correlation of infinite dilution activity coefficients of bis(2,2,2-trifluoroethyl)ether in dodecane or alkanol

Infinite dilution activity coefficients of bis(2,2,2-trifluoroethyl)ether in dodecane or alkanol (1-octanol, 1-decanol or 1-dodecanol) were measured in the temperature region 10–40°C using the gas stripping method. The experimental results were correlated by the modified analytical solution of groups (ASOG) method previously proposed.

High-Pressure Vapor−Liquid and Solid−Gas Equilibria Using a Peng−Robinson Group Contribution Method

In this paper, the new excess Gibbs energy mixing rule, which coupled with the consistent form with the quadratic composition dependence of the second virial coefficient and the excess Gibbs energy ( ) at standard zero pressure, has been developed. This proposed mixing rule, combining a Peng−Robinson equation of state with the analytical solutions of groups (ASOG) group contribution method, provide a Peng−Robinson group contribution method (PRASOG). The PRASOG model has predicted the high-pressure vapor−liquid equilibria (VLE) for binary systems containing alcohols, acetone, and water using the available ASOG group pair parameters determined at low pressure with good accuracy. The ASOG parameters have also been shown for 31 group pairs relating to two gas groups, CO2 and CH4, which indicate potential for global warming, using binary experimental high-pressure VLE data in the temperature range 200−600 K. High-pressure VLE have then been correlated for 56 binary systems containing carbon dioxide and/or meth...

Mass transfer properties of osmotic solutions. I. Water activity and osmotic pressure

In this review paper data on water activity, solute activity and osmotic pressure of”; binary and multi‐component osmotic solutions are provided. The Characteristics of the osmotic solutions are needed for the optimization of mass transfer during osmotic process, and for the improvement of final product quality. The vant Hoff equation and Gibbs Duhem theorem are commonly used to estimate osmotic pressure and solute activity. Water activities can be easily estimated through experimental determination of the freezing point depression. The possibilities of the group contribution models such as the Analytical Solution of Groups (ASOG) approach are also explored. The future needs especially in the case of multicomponent solutions consisting of electrolyte and non‐electrolyte mixtures are pointed out.

Correlation of Infinite Dilution Activity Coefficients of 1- and 2 Alkanols in Tetradecane and Hexadecane Using Modified ASOG.

ASOG (Analytical Solution of Groups), which is widely applied to predict the liquid-phase activity coefficients of solutions, is extended to be capable to distinguish isomers. The Flory-Huggins (FH) part is examined by using the infinite dilution activity coefficient data of n-alkane binary mixtures and an empirical equation is proposed to modify the number of carbons contained in the n-alkanes. The concept of effective carbon number is adopted to apply the empirical equation to components other than n-alkanes. To evaluate the number of group, in the group interaction part, the contact probability is introduced, in which a steric hindrance factor is incorporated. The present model can give a good correlation for the infinite dilution activity coefficients of 1- and 2-alkanols in tetradecane and hexadecane.

Use of analytical solutions of groups (ASOG) contribution method to predict water activity in solutions of sugars, polyols and urea

ASOG (Analytical Solutions of Groups) group contribution method was used to predict water activities in solutions of carbohydrates, polyalcohols and urea. Water activities for the systems water‐fructose, water‐fructose‐urea and water‐glucose‐urea at 25°C were measured with an electric hygrometer. A set of new ASOG groups was considered and their interaction parameters calculated by numerical non‐linear regression of published and measured experimental data. aw Values predicted by the proposed method agree with experimental data within 0.1–0.9%.

Thermodynamic Analysis of a Continuous Distillation Processes Using ASOG Group Contribution Methods for Excess Enthalpy and Excess Entropy

A thermodynamic analysis based on the second law of thermodynamics has been applied to the separation of binary and ternary systems by continuous distillation. Previously developed analytical solution of groups (ASOG) group contribution methods were used for estimating phase equilibria and liquid-phase excess enthalpy and excess entropy. Thermodynamic efficiency of the distillation processes was studied as a function of reflux ratio. An incorporation of a heat recovery system was also tested. In the studied cases, a heat recovery system showed almost no effect on the thermodynamic efficiency of the processes. A maximum of the thermodynamic efficiency was observed at the minimum reflux ratio.

Prediction of excess enthalpy by using thirty-one ASOG groups

Excess enthalpy is predicted by the analytical solution of groups (ASOG) contribution method. The group interaction parameters have been determined for 157 group pairs consisting of 31 groups, including water. The temperature range of experimental data used for parameter estimation was 288-348K. By using the ASOG model, excess enthalpies are predicted for binary, ternary, quaternary, and quinary systems. The example predictions for 608 systems show that the average deviation of calculated excess enthalpy is 13.5% and 14.7% for binary and multicomponent systems, respectively