Binary VLE Research Articles

Critical properties of the N 2 +, CH 4 +, and C 2H 6 + n-alkane mixtures

Stryjek, R., 1993. Critical properties of the N 2 +, CH 4, and C 2H 6 + n-alkane mixtures. Fluid Phase Equilibria, The binary systems formed by N 2, CH 4 and C 2H 6 with alkanes show complex critical behavior as, for some of them, limited mutual solubility are observed. The possibility of cubic equations of state (EOS) for the description of critical fluid behavior of binary mixtures using parameters found from the fit of binary VLE data are object of this study. Rigorous thermodynamic conditions for the calculation of critical state were applied. The modified Redlich-Kwong-Soave EOS was used but for part of systems results have been compared with those obtained using the modified van der Waals and Peng-Robinson (called next PRSV-2) EOS.

Simultaneous representation of vapour-liquid equilibria and excess enthalpies of methanol - hydrocarbons systems using an equation of state

We use the excess functions - equations of state model to represent thermodynamic properties (VLE and H E) of methanol - hydrocarbon binary systems. It is characterized by two conditions: the pure component Helmholtz energies are calculated by equations of state, the exces functions are defined at constant packing fraction. We have chosen a Peng-Robinson-type equation of state and for the excess function the UNIQUAC model in which parameters τ 12and τ 21 are temperature-dependent. This method has been applied to twelve binary VLE in a wide range of temperatures and pressures. The average relative deviation with experiment in bubblepoint pressure is about 1.5 % over 950 data points. We have treated the excess enthalpies of eight binary systems, the average deviation is about 6.4 % over 400 data points.

Thermodynamics of Lewis acid‐base mixtures

AbstractThe associated perturbed‐anisotropic‐chain theory (APACT) has been applied to treat multicomponent mixtures, in which components exhibit Lewis acid‐base interactions. Mixtures of amphoteric molecules (such as alcohols), acidic molecules (such as chloroform), and basic molecules (such as ketones) as well as nonassociating components (diluents) are treated. The acid‐base version of the perturbed‐anisotropic‐chain theory (ABPACT) is a closed form equation of state that takes into account explicitly dispersion interactions, polar interactions, and hydrogen bonding interactions between components that self‐associate or solvate. The equation fits binary VLE mixtures quite accurately. Calculated results also are compared with those obtained from the Peng‐Robinson equation of state, UNIFAC and the original APACT. In all cases where there are mixtures of associating components, the ABPACT gives a better fit of experimental data than these other equations.

The Prediction Of Isobaric Binary Vapour –Liquid Equilibria From Two Isothermal Heat Of Mixing Data

The new modified forms of the Wilsou and the NRTL equations of heat of mixiug data were developed, whose application can be extended to isobaric binary VLE predictions. That was obtained assuming that the two Wilson and NRTL parameters are linear functions of teınpe- rature. Both equations give sufficicnt predictions for systems with max heats of mixing less then 130 cal/ g. mol. Howevcr, the Wilson equation is incapable to describe the heat of mixing data for the system with large heats of mixing, the NRTL equation can overcome this problem, but the quality of the VLE predictions is stili poor.

Vapor-liquid equilibrium calculations for N 2-Ar-O 2 mixtures with modified B-W-R equation of state and a corresponding states principle

Vapor-liquid equilibria for systems containing N 2, Ar, and O 2 are predicted by use of a modified BWR equation of state and a corresponding states principle. The analysis of binary VLE data makes possible the optimization of the binary interaction coefficients and the analysis is extended to the ternary system. Temperature dependence of the binary interaction coefficients as well as the effect of various reference fluids on VLE predictions are evaluated. Results indicate that, with the optimum interaction coefficients, the present equation-of-state approach gives better predictions than the Latimer and the Wilson et al. correlations widely used in the simulation of air separation units. In addition, the present equation-of-state approach can provide enthalpy and entropy data which are consistent with the VLE data.

Prediction of ternary liquid—liquid equilibria from excess enthalpies using a local composition model

Battler J.R. and Rowley, R.L., 1986. Prediction of ternary liquid—liquid equlibira from excess enthalpies using a local composition model. Fluid Phase Equilibria, 25: 129–135. Recently Battler and Rowley reported excess enthalpies over a 30°C temperature range for the constituent binary pairs of six ternary systems exhibiting type I (only one non-consolute pair) liquid—liquid equilibrium. These data have been used to fit parameters in a local composition model for the excess enthalpy (Rowley and Battler). These, in conjunction with binary VLE data available from the literature, were used to determine the liquid—liquid phase behavior of these six systems. Existing local composition models are primarily correlational in nature and cannot be used to predict liquid—liquid equilibria from parameters fitted with VLE or h E data. The method utilized in this work resulted in reasonably good predictions from binary VLE data (at whatever temperature available) and excess enthalpy data over a small temperature range.

Thermodynamic consistency test for binary VLE data

A generalized method for thermodynamic consistency test to binary - isothermal or isobaric - vapor-liquid equilibrium data, based on the isothermal method of Van Ness is proposed. The essential step of the method is to solve the coexistence equation (deduced from the Gibbs-Duhem equation) considering the non--ideality of the vapor phase and possibly the heat of mixing data for the specific system. To calculate the t(x) or P(x) function at equidistant points a cubic spline-polynomial is used rejecting Van Ness' equadratic conditions at the two edges. An algorithm using non-equidistant step sizes - thus without curve fitting - was developed and was applied to systems with complete and limited miscibility as well. The test criteria to be applied to residuals are established on a strict mathematical statistical basis.

Vapour-liquid equilibria. II. The ternary system methanol-chloroform-acetone at 313.15 and 323.15 K

Total vapour pressure measurements made by the modified static method for the ternary systems methanol-chloroform-acetone and constituent binaries at 313.15 and 323.15 K are presented. The different expressions of G E suitable for correlation of these data are tested. A prediction of ternary VLE from binary data is examined. The possibility of predicting the binary and ternary VLE at one temperature using VLE data at another temperature and H E data is investigated. Accuracy of prediction of H E from two ( P, x) isotherms is also studied. Our results are compared with literature data.

On statistical principles in reduction of thermodynamic data

Estimation of the parameters in mathematical models describing physical phenomena is often performed using a fairly simple empirical criterion. Alternatively, the parameter estimation may be performed using a more sophisticated criterion based on statistical considerations. The principle of maximum likelihood, M.L., offers the most appealing possibility for optimum parameter estimation. However, the application of this principle requires that the statistical distribution of the observations is known and that the observations are subject to random errors only. Furthermore, no systematic errors should be introduced by the model for which the parameters are estimated. In cases where the requirements are fulfilled the M.L. estimator gives the best estimates of the parameters in question. Most of the models used (e.g. models for physical properties of pure or mixed fluids) do not represent the connection between the observed variables within experimental accuracy. For models of this type the use of a criterion based on the M.L. principle reduces to an empirical procedure for weighting the available information. The possibility of detecting systematic errors by means of data reduction using the M.L. principle has been somewhat exaggerated. It is not possible to detect the source of systematic errors in the observed variables by means of the M.L. principle. This is due to the fact that the principle is based on the assumption of random errors. The M.L. principle offers a valuable tool in the limiting case of parameter estimation in a perfect model based on observations which are subject to random errors only. It does not, however, give any hope for estimation of reliable model parameters based on systematically erroneous data. Furthermore, it is not possible to give any general guidelines based on statistical considerations for reliable parameter estimation in models which are not capable of representing the connection between the true values of the observed variables. This paper gives a short survey of the principle of M.L. It is discussed how the principle may be applied to data evaluation and to the estimation of model parameters. The M.L. principle is exemplified by parameter estimation for an equation of state using binary VLE data. It is furthermore shown how the computation time may be reduced by economic use of the available information.

Industrial applications of cubic equations of state for VLE calculations, with emphasis on H 2 systems

The use of the Soave and Joffe-Zudkevitch modifications of the Redlich-Kwong and the Peng-Robinson equations in vapor-liquid equilibrium calculations is examined generally and then specifically for H 2-containing binaries and ternaries. Several procedures for handling H 2 are also examined. Although the Joffe-Zudkevitch modification gives the best fit of the binary VLE data, all cubic equations of state examined give similar predictions for cryogenic ternary systems. However, the Joffe-Zudkevitch modification retains its advantage for high-temperature ternary systems. Improved prediction of ternary VLE data may require adjustment in the binary interaction constants.

A continuous linear association model for determining the enthalpy of hydrogen-bond formation and the equilibrium association constant for pure hydrogen-bonded liquids

This article presents a new method for determining the enthalpy of hydrogen-bond formation and the equilibrium association constant for pure liquid compounds. The method is based on an association model, derived from Flory's theory of mixtures of polymers. The experimental data needed are the vapour pressures of pure liquids as a function of temperature. Pure-liquid association constants may be used to correlate binary VLE data with the UNIQUAC associated-solution theory, reducing the number of adjustable parameters and making the theory consistent with the theoretical requirement that the association parameters be independent of the nature of the inactive solvent.

Calculation of ternary vapor-liquid-liquid equilibria for design of three-phase distillation

For the design of distillation of systems showing azeotropic behaviour and two liquid phases, VLLE data must be represented with high accuracy. Until now, sufficiently accurate methods for both VLE and LLE have not been available. A new method for ternary systems is presented using as accurate a representation as possible of the excess Gibbs energy and an experimental co-existence curve. For computation of a distillation process, a co-existence curve for constant saturation pressure is required. The excess Gibbs energy is calculated by NRTL or modified UNIQUAC using parameters based only on binary VLE data. Both ternary VLE and LLE are represented by the new method with sufficient accuracy for design.

A new method of parameter adjustment and diagnostic checks on gamma models used in vapor—liquid equilibrium calculations

A procedure based on the maximum likelihood principle applied to the general case when all variables are subject to random error has been developed for the estimation of parameters in thermodynamic relationship (gamma) models (eqns 2–5) from binary VLE x- T- P data sets. A high precision dynamic ebulliometry technique has been used to measure isobaric VLE in toluene-cyclohexane and methylcyclohexane- n-heptane system. Geometrical interpretation of the maximum likelihood principle for the VLE problem has led to plotting κ i s -distances (eqn 13) which are used as diagnostic checks on the models applied.

Simultaneous representation of binary VLE, LLE and H E data using the UNIQUAC model

Simultaneous representation of binary VLE, LLE and H E data using the UNIQUAC model

Single-Set Treatment of All Available Binary System VLE Data Leads to Simplified Correlation Procedures

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSingle-Set Treatment of All Available Binary System VLE Data Leads to Simplified Correlation ProceduresHal Ozkardesh, Ramanathan R. Tarakad, and Stanley B. AdlerCite this: Ind. Eng. Chem. Fundamen. 1978, 17, 3, 206–209Publication Date (Print):August 1, 1978Publication History Published online1 May 2002Published inissue 1 August 1978https://doi.org/10.1021/i160067a011RIGHTS & PERMISSIONSArticle Views55Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (410 KB) Get e-Alerts