Prediction Of Vapor-liquid Equilibria Research Articles

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Knowledge of vapor-liquid equilibria is essential for chemical process design. Development of algebraically simple cubic equations of state, particularly Peng-Robinson and Soave-Redlich-Kwong equations of state has encouraged vapor-liquid equilibria calculation using the equation of state approach. To extend applicability to complex mixtures, several modifications to these equations of state were proposed. Also, many new mixing rules have been developed besides the already existing ones that incorporate excess free energy models. Some of these EoS/GE models are found to be applicable to complex systems in which the components can be highly polar, differ vastly in size or may be forming association. In spite of a large number of publications on this field, this subject is still open for further research. In this article, an overview on the work done using the most successful of the cubic equations of state, i.e., Peng-Robinson and Soave-Redlich-Kwong equations of state is presented. In the later part of this article, VLE predictions (using these two equations of state) of some interesting systems like water/hydrocarbon mixtures, polymer solutions, electrolyte solutions and refrigerant mixtures are discussed. The objective is to present the available information for ready reference that will prove to be useful from a designers point of view. It is seen from the existing literature that with a proper choice of equation of state and mixing rule based on the available knowledge on the properties of the system of interest, VLE of highly complex systems can be predicted with accuracy. Several comparative studies that are cited here (and discussed) will help the designer to pick-up the right combination for the system under investigation.

Potential applications of artificial neural networks to thermodynamics: vapor–liquid equilibrium predictions

The associative property of artificial neural networks (ANNs) and their inherent ability to “learn” and “recognize” highly non-linear and complex relationships finds them ideally suited to a wide range of applications in chemical engineering. Dynamic Modeling and Control of Chemical Process Systems and Fault Diagnosis are the two significant applications of ANNs that have been explored so far with success. This paper deals with the potential applications of ANNs in thermodynamics — particularly, the prediction/estimation of vapor–liquid equilibrium (VLE) data. The prediction of VLE data by conventional thermodynamic methods is tedious and requires determination of “constants” which is arbitrary in many ways. Also, the use of conventional thermodynamics for predicting VLE data for highly polar substances introduces a large number of inaccuracies. The possibility of applying ANNs for VLE data prediction/estimation has been explored using the back propagation algorithm. The methane–ethane and ammonia–water systems have been studied and the VLE predictions have been found to be accurate to within ±1%. Preliminary results confirm exciting possibilities of ANNs for applications to thermodynamics of mixtures. Advantages and limitations of this application are also discussed. An heuristic approach to reduce the trial and error process for selecting the “optimum” net architecture is discussed.

Numerical Analysis and Vapor Concentration Measurement on the Evaporation Process of Multi-component Fuel.

In previous multi-dimensional modeling on spray dynamics and vapor formation, single component fuel with pure substrance has been analyzed to assess the mixture formation process. Then it shold be expected that the evaporation process could be performed for the multi-component fuel such as actual Gasoline and Diesel gas oil. In this study, vapor liquid equilibrium prediction was conducted for multi component fuels such as 3 and 10 components mixed solution with ideal solution analysis and non ideal solution analysis. And the computation of distillation characteristics was conducted for the steady state fuel conditions to understand the evaporation process. As a result, calculated distillation characteristics is consistent well with experiment results. Further the vapor concentration was measured for the analysis of the binary fuel spray using IR absorption measurement method.

A study on ternary vapor-liquid equilibria for the system heptane/methylcyclohexane/toluene at 101.325kPa

The isobaric separation of multicomponent mixtures by distillation require reliable vapor-liquid equilibrium data. Since the experimental determination of multicomponent vapor-liquid equilibrium data is laborious and time consuming there is a need to use a predictive method for the liquid phase activity coefficients. The estimated vapor-phase compositions are dependent on the predictive thermodynamic method used. The ternary vapor-liquid equilibrium data for the system, heptane/ methylcyclohexane/ toluene at 101.325 kPa have been chosen to compare the abilities of the three-suffix Margules and the UNIQUAC Equations in the prediction of isobaric ternary vapor-liquid equilibria with parameters estimated from the corresponding binary vapor-liquid equilibria compositions taken from the literature. The predictions with the three-suffix Margules equations was found to be little superior with overall root mean square deviations of ±0.0047 whereas the UNIQUAC equations could predict the ternary vapor compositions with overall root mean square deviations of ± 0.0061.

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO 2-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.

Prediction of Vapor−Liquid Equilibria at Low and High Pressures from UNIFAC Activity Coefficients at Infinite Dilution

A modified procedure of using the Huron−Vidal mixing rule based on UNIFAC activity coefficients at infinite dilution (HVID) at low pressures is shown to be useful for making vapor−liquid equilibrium (VLE) predictions for polar and nonpolar systems at low and high pressures. Four cases were considered: (a) symmetric polar systems; (b) systems containing alkanols and hydrocarbons; (c) systems containing acetone and hydrocarbons; (d) hydrocarbon mixtures. Prediction of both low- and high-pressure VLE for binary systems is good. The HVID model, using UNIFAC ‘93 activity coefficients at infinite dilution, performs satisfactorily in the VLE predictions of ternary systems also.

Prediction of Vapor−Liquid Equilibria with the LCVM Model: Systems Containing Light Gases with Medium and High Molecular Weight Compounds

The LCVM model (Boukouvalas et al., 1994) is applied to the prediction of vapor−liquid equilibria (VLE) for a variety of binary, ternary, and multicomponent mixtures involving gaseous components (CH4, H2S, C2H6, C3H8, and CO2) with medium and high molecular weight hydrocarbons and/or polar compounds. New interaction parameters (CH4/−CH2O−, CH4/−OCCOH, and CH4/gases) are evaluated, and some existing ones (H2S/−CH2−, CH4/ACH, CH4/ACCH2, and C2H6/ACCH2) are reevaluated by using additional data. Very satisfactory results are obtained in all cases, even for asymmetric systems, where the MHV2 model (Dahl et al., 1991) fails. Of special interest are the successful results for the multicomponent systems that involve up to 24 components, including a H2S-rich sour gas mixture. LCVM is, thus, a powerful model for the prediction of VLE for a broad range of binary and multicomponent systems.

Vapor-liquid equilibrium predictions of refrigerant mixtures from a cubic equation of state with a G E-EoS mixing rule

A modified excess Gibbs energy model which is based on the local composition concept and assigns a single energy parameter per pair of components, is incorporated into the G E —EoS thermodynamic formalism for vapor-liquid equilibrium (VLE) calculations of simple and complex refrigerant mixtures. One temperature set of data close to 273 K is used to obtain the model's parameters, which are used to extrapolate the VLE at other temperatures and pressures. A one-parameter form of the model based on the Wong-Sandler mixing rule is presented for several simple systems. The physical significance of the model's energy parameter is connected to the preference of the mixture for like to unlike interactions. The model is applied for VLE predictions of the ternary system R14-R23-R13, and the results are compared to calculations using the 3PWS model [H. Orbey. S.I. Sandler, Ind. Eng. Chem. Res. 34 (1995) 2520–2525] and the van der Waals mixing rule. Modelling of a few complex systems with only three data points given at each temperature is shown with a two parameter version of our model on the basis of the Huron-Vidal mixing rule.

VAPOUR LIQUID EQUILIBRIA IN STRONG ELECTROLYTE SOLUTIONS BY THE CORGC EQUATION OF STATE

Abstract The capability of chain-of-rotalor group contribution equation of state (CORGC EOS) in prediction of vapour-liquid equilibria for electrolyte solutions is discussed. A new approach is considered in which salt is considered as a single component and therefore, there is no ion in the solution. The interaction parameters between water and 50 salts are determined and reported. The parameters are temperature dependent and thus, vapour-liquid equilibria calculations can be achieved at moderate temperature. The percent average absolute deviation for prediction of vapour pressure and osmotic coefficient for 50 aqueous solutions are equal to 0.89 and 16.7, respectively. Comparison between the calculated results and experimental data has been performed.

Prediction of vapor-liquid equilibria for acetic acid aqueous solutions containing salt

A calculation method to predict the salt effect on the vapor-liquid equilibria of acetic acid aqueous solutions is proposed. In the developed method, the nonidealities of the liquid phase are considered by employing the vapor pressure models of electrolyte solutions (Shiah and Tseng, Fluid Phase Equilibria, 90 (1994) 75–85; Jaques and Furter, AIChE J., 18 (1972) 343–346) to describe the ion-ion and ion-solvent interactions and the Tan's modified Wilson or NRTL model (Tan, Chem. Eng. Res. Des., 65 (1987) 355–366; Tan, Trans. Ind. Eng. Chem., 68 (1990) 93–103)) to describe the solvent-solvent interactions. The chemical theory model is applied to the vapor phase to describe the deviations from ideal gas behavior caused by dimerization of acetic acid. The data required by this method are the equilibrium constant of dimerization in the vapor phase, the vapor pressure of aqueous electrolyte solutions and the solvent-solvent interaction parameters in the liquid phase activity coefficient model. No ternary parameter is required. The proposed method has been used to predict the VLE of five saltacetic acidwater systems for salt concentrations varying from zero to saturation. The calculated results agree well with the experimental ones reported in literatures, with the overall absolute deviations of vapor phase compositions being 1.00% if the modified Wilson model is employed, and 1.64% if the modified NRTL model is used to describe the solvent-solvent interactions. For the bubble point temperatures, the overall mean deviations are 0.99 K if modified Wilson model is used and 1.34K if modified NRTL model is used.

A comparison of various cubic equation of state mixing rules for the simultaneous description of excess enthalpies and vapor-liquid equilibria

Recent new mixing and combining rules for cubic equations of state (EOS) have extended the range of such equations to the accurate description of the vapor-liquid equilibria (VLE) of highly nonideal mixtures. However, the simultaneous correlation and/or prediction of vapor-liquid equilibrium (VLE) and liquid mixture excess enthalpies ( H ex) by either activity coefficient models or equations of state has been a difficult problem in applied thermodynamics. In this communication, we re-examine this problem using a modified version of the Peng-Robinson equation of state and the two-parameter van der Waals one-fluid, Wong-Sandler and modified Huron-Vidal mixing rules. For comparison, the direct use of activity coefficient models is also considered. In each case a temperature dependence of the model parameters is introduced in an attempt to represent simultaneously VLE and H ex behavior. Four highly nonideal binary mixtures (2-propanol + water, methanol + benzene, benzene + cyclohexane, and acetone + water) are considered. The results indicate that while all the models can accurately correlate VLE and H ex data separately, attempting to predict the values of one property with parameters obtained from the other does not give satisfactory results with any model. Also, we find that the simultaneous correlation of both VLE and H ex with the EOS models at one temperature is possible, but extrapolations to other temperatures with parameters obtained in this way did not result in accurate predictions of either VLE or H ex. The main problem appears to be that the excess free energy (activity coefficient) models used are not capable of representing both VLE and H ex over a range of temperatures, and so equations of state that incorporate these free energy models have the same shortcoming.

Comparative study of mixing rules for cubic equations of state in the prediction of multicomponent vapor-liquid equilibria

Some common volume-independent mixing rules and the problems associated with them are reviewed. Reported experimental data of a highly non-ideal quaternary mixture and all its constituent binaries and ternaries are used for adjusting binary interaction parameters and comparing the performance of each mixing rule in predicting vapor-liquid equilibria (VLE). The parameters in each mixing rule were obtained fitting experimental binary data only. The ternary and quaternary VLE calculations were then used to test the capability of the mixing rules to predict multicomponent VLE. It is shown that the VLE of those systems can be adequately reproduced with a cubic equation of state using Wong and Sandler's mixing rule with Wilson's excess Gibbs energy function thanks to its simultaneous correction of several inconveniences. It is also shown that mixing rules should be tested with multicomponent mixtures.

96/04269 A method for the prediction of vapour-liquid equilibria of refrigerant mixtures at low and moderate pressure

96/04269 A method for the prediction of vapour-liquid equilibria of refrigerant mixtures at low and moderate pressure

Prediction of vapor-liquid equilibria at high pressures using activity coefficients at infinite dilution

A modified procedure of using the Huron-Vidal mixing rule based on available activity coefficients at infinite dilution at low pressures is shown to be useful for making vapor-liquid equilibrium predictions for non ideal mixtures at high temperatures and pressures. We compare the performances of this mixing rule (called HVID model), coupled with the SRK equation of state and a reduced UNIQUAC model, with those of two other equation of state mixing rules, one by Dahl and Michelsen (MHV2) and another by Wong and Sandler (WS). Six binary systems are used in this study, and we find that the errors in the predicted pressure with the new mixing rule are, on the whole, less than those obtained when using the MHV2 model. Compared with the WS mixing rule, the HVID model performs slightly better.

The performance of EoS/G E models in the prediction of Vapor-Liquid Equilibria in asymmetric systems

An extensive comparison of four EoS/G E models: LCVM, MHV2, PSRK and Wong-Sandler in the prediction of Vapor-Liquid Equilibria (VLE) in asymmetric systems is presented and demonstrates that only LCVM yields satisfactory results.

Prediction of vapor-liquid equilibria in polymer solutions using EOS-group contribution model consistent with the second virial coefficient condition

Prediction of vapor-liquid equilibria in polymer solutions using EOS-group contribution model consistent with the second virial coefficient condition

Simulation of binary refrigerant mixture vapor-liquid equilibria using a quasi-regular nonrandom fluid theory and local composition mixing rules

A new model and a novel approach are presented for correlation/prediction of refrigerant mixture phase equilibria. The excess Gibbs free energy in binary halogenated alkane mixtures is described by a recently proposed two-liquid theory with a regular solution reference for mixtures of nonpolar species. The single g E model parameter, obtained by correlating near-ambient binary vapor-liquid equilibria (VLE), is used in Wong-Sandler mixing rules in the Peng-Robinson-Stryjek-Vera equation of state to predict binary VLE at elevated temperatures. This model is applied to the tetrafluoromethane-chlorotrifluoromethane (R14-R13), tetrafluoromethane-trifluoromethane (R14-R23), and the trifluoromethane-chlorotrifluoromethane (R23-R13) binary systems. The one-parameter quasi-regular g E model provides good correlation of VLE for the binary systems at near ambient conditions. However, successful prediction of high temperature VLE depends on the accuracy of the g E model, the consistency of the EOS mixing rule model, and the method used to solve the model equations and associated material balances.

Prediction of vapor-liquid equilibrium for polymer solutions by a group-contribution Redlich-Kwong-Soave equation of state

The aim of this work is to apply a group-contribution cubic equation of state to vapor-liquid equilibria calculations of polymer-solvent mixtures. The model is based on a Redlich-Kwong-Soave equation of state with Huron-Vidal mixing rules where infinite-pressure activity coefficients are predicted by a UNIFAC-type model. An original procedure for estimating the equation-of-state parameters of the polymer is developed: experimental activity data of solvents in banary systems with the same polymer are used to fit parameter b (actually, b/MW) of the polymer, so that only one value of polymer density is needed to calculate parameter a at the temperature of interest. To show the potential of the proposed approach, a table of parameter b values is provided for six polymers, and several examples are presented both for nearly athermal and for polar polymer solutions. The model is able to correlate equilibrium pressure and solvent activities of the data base with good accuracy. The proposed method is then applied to predict solvent activities of systems not included in the fitting procedure with satisfactory results in all cases.

Evaluation of a model for the prediction of phase equilibria from general molecular parameters I: Vapour-liquid equilibria and enthalpy at low pressures

A model (AGAPE), based on consideration of the properties of whole, rather than segments of, molecules, that allows the prediction of phase equilibria in terms of two general physical parameters is presented. One of the parameters is a geometric (or entropic) parameter while the other is an energetic parameter (a net unlike molecular pair interaction energy). Two procedures are presented for estimating these parameters. The first employs ab initio calculations based on the generalised London potential theory which needs only pure component molecular and atomic parameters; the second uses a single experimental vapour-liquid equilibria (VLE) data point. The range of each procedure is explored together with the results of the application of the model (a multicomponent version of which is presented) to the prediction and correlation of VLE and enthalpy data for several binary mixtures. Satisfactory results were obtained.