Prediction Of Liquid-liquid Equilibria Research Articles

The analysis of liquid–liquid equilibria (LLE) of toluene + heptane + ionic liquid ternary mixture using intelligent models

This paper is to verify the applicability of three intelligence methods including artificial neural network (ANN), support vector machine (SVM) and least square support vector machine (LSSVM) in forecasting the thermodynamic phase behavior of LLE for toluene/heptane/ionic liquid ternary systems. The shuffled complex evolution (SCE), particle swarm optimization (PSO) and genetic algorithm (GA) are employed to acquire the optimal magnitudes of hyper parameters (σ2 and γ) which are embedded parts of SVM and LSSVM models, and the trial and error was employed to obtain the optimal numbers of neuron and layers for ANN intelligent model. Gathering and using 589 liquid–liquid equilibria (LLE) data, the comparison between the capability of applied intelligent models and NRTL thermodynamic model has also been made in giving the phase behavior of ternary system toluene/heptane/ionic liquid. The findings are indicative of a prefect agreement between the estimation from intelligent models and the experimental data. Comparison between these three investigated models reveals that the performance of SCE-LSSVM in prediction of LLE is somewhat better than other intelligent models (i.e., ANN and SVM) in prognosticating LLE behavior in those 40 studied ILs as the coefficient determination (R2) and root mean squared error (RMSE) are respectively 0.9895 and 0.0361 for test sets of data. This is likely due to the existence of structural risk minimization principle of LSSVM which is embodied in SVM algorithm and effectively minimizes upper bound of the generalization error, rather than minimizing the training error.

Measurement and prediction of liquid-liquid equilibria in ternary systems containing water, an organic component, and cyclohexanol

The liquid-liquid equilibria of the four ternary mixtures water + heptane + cyclohexanol, water + toluene + cyclohexanol, water + cyclohexane + cyclohexanol, and water + cyclohexylamine + cyclohexanol were measured at 298.15 K and 323.15 K at atmospheric pressure. The binodal curves were determined by photometric turbidity titration.Our experimental data are compared with the prediction results from both UNIQUAC and NRTL activity coefficient models and the equation of state proposed by Elliott, Suresh, and Donohue (ESD EOS). For this purpose, interaction parameters were determined using binary phase equilibrium data. Due to the sparse amount of binary equilibrium data in literature, the vapour-liquid equilibrium in the binary toluene + cyclohexanol system was determined at 333.15 K and 363.15 K at reduced pressure. When predicting the experimental LLE behaviour of the considered systems, ESD EOS seems to be superior to the UNIQUAC and NRTL approach.

Modelling polylactide/water/dioxane systems for TIPS scaffold fabrication

The representation of liquid–liquid equilibria (LLE) in ternary systems composed by water, 1,4-dioxane and different grades of poly(lactic acid) (PDLLA and PLLA), has been addressed through the PC-SAFT equation of state (EoS), in which the scheme of induced association is used to represent the interaction between solvent (dioxane) and non-solvent (water). The model parameters devoted to the description of pure component properties, as well as those pertinent to the representation of thermodynamic behaviour of solvent/non-solvent mixtures, were tuned on the basis of specific pressure–volume–temperature (PVT) data for the corresponding systems. Only the binary parameters for polymer–solvent and polymer/non-solvent pairs were adjusted to obtain a useful representation of experimental LLE data for the ternary systems. A suitable description of the thermodynamic properties of ternary mixtures was obtained using temperature-independent binary interaction parameters in the range 25–80°C, and the consistency of the approach in the entire composition range was verified against experimental solubility data specifically measured for the polymer/non-solvent pair. The model shows good ability in the description of the thermodynamic properties of the system and it represents a reliable tool for the prediction of LLE also at conditions different from those considered for its set-up. This approach thus represents a useful designing tool for processes, such as thermally induced phase separation (TIPS), used in the preparation of microporous polymeric scaffolds.

Improvements of COSMO-SAC for vapor–liquid and liquid–liquid equilibrium predictions

The COSMO-SAC model has been revised for a better description of the nonideality of liquid mixtures, and thus more accurate predictions of both vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE). Two major modifications are introduced. First, the electrostatic interaction parameter is made temperature-dependent, which is important in LLE predictions for non-hydrogen-bonding systems. Second, the variation in the strength of hydrogen-bonding interactions involving different types of functional groups is treated using separate sigma-profiles. The overall RMS error in LLE predictions of 278 binary mixtures (4281 data points) from the new model is 0.1047, which is 30% lower than that from the original COSMO-SAC (0.1446), 10% lower from that of UNIFAC-LLE (0.1161), and comparable to that from the modified UNIFAC model (0.1048). The accuracy in VLE predictions is also improved. The average deviation in total pressure at a fixed liquid composition is 6.54% and the overall average deviation in vapor phase composition is 2.57% for 1338 binary mixtures, compared to 7.25% and 2.83% from the original model.

Evaluation of COSMO-RS for the prediction of LLE and VLE of water and ionic liquids binary systems

Ionic liquids (ILs) have achieved special and dedicated attention from the scientific community in recent years and a large number of studies involving different features of properties and applications of ILs have been presented. The complete understanding of the phase behaviour of ILs with water is an important issue yet there are few experimental data on their phase equilibria. In this work the predictive capability of COSMO-RS, a predictive model based on unimolecular quantum chemistry calculations, was evaluated for the description of the liquid–liquid equilibria (LLE) and the vapour–liquid equilibria (VLE) of diverse binary mixtures of water and ILs. The effect of the ions conformers on the quality of the predictions was assessed and the quantum chemical COSMO calculation at the BP/TZVP level derived from the lowest energy conformations was adopted. While the LLE predictions degrade with increasing the hydrophilic IL anion character, in general a good qualitative agreement between the model predictions and experimental VLE and LLE data was obtained. COSMO-RS showed to be very helpful as an a priori predictive method in order to find suitable candidates for a certain task or specific applications before extensive experimental measurements.

Liquid–liquid equilibrium correlations using lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of liquid–liquid equilibria (LLE) for binary alcohol and hydrocarbon mixture in a wide pressure range. For hydrocarbon + alcohol mixtures the consideration of a hydrogen-bonding term in the lattice equation of state clearly improves the prediction for vapor–liquid equilibrium (VLE) as shown in previous works, but the prediction of LLE is still in question. In this paper, LLE data for alcohols (methanol and ethanol) + hydrocarbons ( n-hexane to n-hexadecane) were correlated by NLF-HB EOS and results were compared with a cubic equation of state (Peng–Robinson EOS with the T–K Wilson based G E model). Both equations of state showed similar degree of accuracies but with different number of adjustable parameters. The Peng–Robinson EOS based approach requires six temperature dependent coefficients for accurate calculation whereas NLF-HB EOS requires only two temperature dependent coefficients. The effects of varying hydrogen-bonding energies for NLF-HB EOS are discussed.

Application of PC-SAFT to glycol containing systems – PC-SAFT towards a predictive approach

For equations of state of the SAFT type a major limitation is the procedure of obtaining pure compound parameters using saturated vapor pressure and liquid density data. However, for complex compounds such data are often not available. One solution is to develop a group contribution scheme for estimating pure compound parameters from low molecular weight data and extrapolate to complex compounds. For associating compounds this is not trivial since the two parameters for association (association energy and association volume) need to be fixed for a group. In this work, which focuses on glycols, new general pure compound parameters were obtained for PC-SAFT which are able to perform well for both vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE). Linear trends of non-association parameters were obtained with respect to the molar mass. However, identical values for the association parameters were used for all glycol oligomers. This makes it possible to predict the pure compound parameters of other oligomers. With the new estimated parameters the simplified PC-SAFT equation of state has been applied for correlation and prediction of VLE and LLE in mixtures containing glycol oligomers + water, hydrocarbons, aromatic hydrocarbon, methane, N 2 and CO 2. To improve correlations for mixtures containing glycol and aromatic hydrocarbons solvation was explicitly accounted for.

Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols

A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is presented. The phase equilibrium is given by the global minimum of the Gibbs free energy for a system that involves water and organic components. This minimization problem is equivalent to the determination of the convex hull of the corresponding molar Gibbs free energy function. A geometrical notion of phase simplex related to the convex hull is introduced to characterize mathematically the phases at equilibrium. A primal-dual interior-point algorithm for the efficient solution of the phase equilibrium problem is presented. A novel initialization of the algorithm, based on the properties of the phase simplex, is proposed to ensure the convergence to a global minimum of the Gibbs free energy. For a finite termination of the interior-point method, an active phase identification procedure is incorporated. Numerical results show the robustness and efficiency of the approach for the prediction of liquid-liquid equilibrium in multicomponent mixtures.

Modified LIQUAC and Modified LIFACA Further Development of Electrolyte Models for the Reliable Prediction of Phase Equilibria with Strong Electrolytes

The gE model LIQUAC and the corresponding group contribution model LIFAC are widely used for the reliable prediction of vapor−liquid equilibria (VLE), osmotic coefficients, and mean ionic activity coefficients for aqueous systems that contain strong electrolytes up to high concentrations. These models consist of a Debye−Hückel term, a Pitzer type virial equation for the middle-range contribution, and the UNIQUAC, respectively, the UNIFAC term. However, with the variable reference state proposed herein, a reliable prediction of liquid−liquid equilibria (LLE) using the LIQUAC or the LIFAC model is not possible. Because the mean ionic activity coefficient in all existing liquid phases must be predicted reliably, an explicit fixed reference state for the ions had to be introduced for the normalization of the middle-range term. The aim of this work is to modify the LIQUAC and LIFAC model for the prediction of ternary LLE using interaction parameters based on binary datasets. In addition, the results for binary properties could be improved by further changes of the original models. Using a comprehensive database, the interaction parameters for the modified LIQUAC and the modified LIFAC model had to be refitted and the obtained results for the calculated properties of binary and ternary mixtures were finally compared to the results of the original models.

Prediction of Liquid-Liquid Equilibrium Using the Group Solubility Parameter Model

The group solubility parameter (GSP) model was used to analyze the liquid-liquid equilibrium (LLE) of ternary and quaternary systems. The GSP parameters are divided into four dimensions representing the four major intermolecular forces. The values of the parameters were determined by regression using the nonlinear SIMPLEX optimization method to fit the LLE data of 548 ternary and 26 quaternary systems selected from the literature. LLE predictions of 8 ternary systems were then made using the fit parameters. Comparison of the results with predictions using the modified UNIFAC model shows that the GSP model has less adjustable parameters to achieve a similar accuracy and that the parameter values are easily acquired by analysis of available data.

Group‐contribution lattice‐fluid EOS: Prediction of LLE in polymer solutions

AbstractThe modified group‐contribution lattice‐fluid equation of state (GCLF–EOS) was applied to predict liquid–liquid equilibria (LLE) in polymer solutions. The modified GCLF–EOS is a group‐contribution form of the equation of state by Panayiotou and Vera based on the lattice‐hole theory. Group contributions for the interaction energy and reference volume were developed based only on the saturated vapor pressures and liquid densities of low‐molecular‐weight compounds. For a mixture, group contributions for the binary interaction parameter were developed from the binary vapor–liquid equilibria of low‐molecular‐weight compounds. This modified GCLF–EOS model can be applied to predict LLE behavior in polymer solutions with the same group‐contribution parameters as used for predicting the vapor–liquid equilibria. The only input required for the model is the structure of the molecules in terms of their functional groups.

Application of the van der Waals equation of state to polymers III. Correlation and prediction of upper critical solution temperatures for polymer solutions

The van der Waals equation of state is used for correlation (using a single binary interaction parameter) and prediction of liquid-liquid equilibrium in many mixtures including a solvent and a polymer. The equation of state parameters for the polymer are estimated from experimental volumetric data at low pressures. For the solvent, the equation of state parameters are estimated via the classical method, i.e. using the critical properties of the solvent and generalized expressions of the acentric factor. When extended to mixtures, the van der Waals one-fluid mixing rules along with the Berthelot combining rule for the molecular cross energy parameter are used. The arithmetic mean combining rule is used for the cross co-volume parameter. A correction to the Berthelot combining rule which is obtained from vapor-liquid equilibrium data of polymer solutions is used for predicting the upper critical solution temperatures for many different binary polymer solutions, including polar and non-polar systems. The results are remarkably successful. Typically, the difference between the predicted and the experimental upper critical solution temperatures is less than twenty degrees. Further, in all cases, correlation is achieved in an easy and straightforward way without difficulty and excellent results are obtained. Unlike other theories and models, the van der Waals equation of state is capable of predicting the flatness of the coexistence curves, which often occurs in polymer solutions.

Prediction of liquid-liquid equilibria in ternary mixtures from binary data

Liquid-liquid equilibria in type-I and type-II ternary mixtures are predicted from binary data alone by two methods: (1) Statistical Associating Fluid Theory (SAFT) which models molecular association based on the first-order perturbation theory developed by Wertheim; (2) a hybrid model in which a modified form of the Panagiotopoulos-Reid mixing rule is applied to the physical contribution terms of SAFT. The proposed mixing rule reduces to the original Panagiotopoulos-Reid mixing rule for binary mixtures while simultaneously satisfying the invariant condition when a component is divided into sub-components and hence is consistent for application to multicomponent systems. Although the Panagiotopoulos-Reid mixing rule provides accurate representation of phase equilibria in type-II ternary systems, the prediction of ternary phase behavior in type-I systems is not satisfactory. The association model, however, predicts phase behavior in both type-I and type-II ternary mixtures quite accurately. The significance of inclusion of hydrogen bond acceptor groups on aromatic rings, due to the presence of π-electrons, is elucidated in the representation of phase equilibria in binary and ternary mixtures.

Thermodynamics of aqueous poly(ethylene glycol)-dextran two-phase systems using the consistent osmotic virial equation

Abstract In this work we present a thermodynamic model for the prediction of the liquid-liquid phase behavior of aqueous poly(ethylene glycol) (PEG) - dextran two-phase systems. The model is based on the McMillan-Mayer solution theory (1945) and results in thermodynamically consistent expressions for the chemical potentials of the solutes derived from the osmotic virial equation (COVE). Applying the COVE, we have examined the predictability using a complete and reliable data- base of liquid-liquid equilibrium (LLE) and vapor-liquid equilibrium (VLE) data. As a result of this examination, we were able to demonstrate the essential influence of the molecular-weight distribution of polydisperse polymers on the LLE predictions. Accounting for the polydispersity in our calculations, the prediction of the compositions as well as the molecular-weight distributions in the coexisting phases is in good agreement with our experimental results, as illustrated for the system PEG 3000 + dextran 110000 + water at 293.15 K. It should be stressed, that these calculations are true predictions, since the LLE were calculated using model parameters determined from VLE measurements alone.

Liquid-liquid equilibria for ternary systems of cyclohexane-water and C1 to C3 alcohols: data and predictions

Abstract Plackov D. and Stern I., 1992. Liquid-liquid equilibria for ternary systems of cyclohexane-water and C 1 to C 3 alcohols: data and predictions. Fluid Phase Equilibria , 71:189-209. Liquid-liquid equilibrium (LLE) data are presented for the systems cyclohexane-water-methanol cyclohexane-water-ethanol, cyclohexane-water-1-propanol and cyclohexane-water-2-propanol at 25° C. The data presented for the system cyclohexane-water-methanol are more accurate than those previously published. In addition conflicts in the previously published data for the systems cyclohexane-water with methanol, ethanol and 2-propanol have now been resolved. The applicability of the semiempirical models NRTL, UNIQUAC, Hiranuma's modification of the Wilson equation and Bevia et al., together with the UNIFAC group contribution method in LLE predictions of the studied systems is also examined. The semiempirical models tested give quantitative results only for the systems cyclohexane-water with methanol and ethanol, while giving poor results for the systems with 1-propanol and 2-propanol. UNIFAC gives quantitative results for all systems studied.

Prediction of liquid-liquid equilibria and of enthalpies of mixing in alkanoic acid anhydride + n-alkane mixtures using DISQUAC

Abstract Kehiaian, H.V., Gonzalez, J.A., Garcia, I., Escarda, R., Cobos, J.C. and Casanova, C, 1991. Prediction of liquid-liquid equilibria and of enthalpies of mixing in alkanoic acid anhydride + n -alkane mixtures using DISQUAC. Fluid Phase Equilibria, 69: 91-98. The liquid-liquid equilibrium (LLE) data from the literature on acetic anhydride + heptane and our molar excess enthalpies measured previously, H E , of butyric or heptanoic anhydrides + n -alkanes (hexane through tetradecane) are examined on the basis of the DISQUAC group-contribution model. These experimental data, along with structure-property relationships derived from the properties of related classes of carbonylic compounds, were used to estimate the interaction parameters for symmetrical or asymmetrical carboxylic acid anhydride [CH 3 (CH 2 ) u -1 -CO-O-CO-(CH 2 )[ v -1 CH 3 ] + alkane [CH 3 (CH 2 ) m -2 CH 3 ] mixtures. The anhydride (CO-O-CO group)/alkane (CH 3 or CH 2 groups) interaction parameters are the same for the anhydrides of all the carboxylic acids ( u, v > 1), except for acetic acid anhydride ( u, v = 1). The model describes consistently H E , LLE and the vapor-liquid equilibrium diagram of acetic anhydride + cyclohexane.

Liquid—liquid equilibria for ternary systems of cyclohexane-water and butanols. Data and predictions

Liquid—liquid equilibrium (LLE) data are presented for the systems cyclohexane-water- 1-butanol, cyclohexane-water-2-butanol, cyclohexane-water-2-methyl-2-propanol and cyclohexane-water-2-methyl-1-propanol at 25°C. The applicability of four semiempirical models—the NRTL and UNIQUAC models, Hiranuma's modification of the Wilson equation (Hiranuma-Wilson) and the model of Bevia et al.—together with the UNIFAC group contribution method, in LLE predictions of the systems studied is also examined. The best predictions were derived by the UNIFAC method, while the Hiranuma-Wilson approach gave the best results among the semiempirical models tested.

Prediction of liquid-liquid equilibria with UNIFAC: a critical evaluation

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTPrediction of liquid-liquid equilibria with UNIFAC: a critical evaluationParag A. Gupte and Ronald P. DannerCite this: Ind. Eng. Chem. Res. 1987, 26, 10, 2036–2042Publication Date (Print):October 1, 1987Publication History Published online1 May 2002Published inissue 1 October 1987https://doi.org/10.1021/ie00070a018RIGHTS & PERMISSIONSArticle Views1102Altmetric-Citations32LEARN 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 (691 KB) Get e-Alerts Get e-Alerts

Local-composition models and prediction of binary liquid-liquid binodal curves from heats of mixing

The temperature dependence of several local-composition models has been studied in conjunction with the Gibbs-Helmholtz identity. Binary heat-of-mixing data at temperatures near but above the critical solution temperature have been used to fit parameters obtained from excess-free-energy models in conjunction with the Gibbs-Helmholtz equation. These models, if the temperature dependence is adequate, should allow prediction of liquid-liquid equilibria (LLE) from the fitted parameters. The NRTL, UNIQUAC, and modified NRTL and UNIQUAC models (modified by inclusion of temperature-dependent parameters) seldom provide even qualitatively correct LLE predictions. A new local-composition model due to Wang and Chao (1983) yields reasonably good predictions for some systems but incorrect results for others. Reasons for these model inadequacies are discussed in terms of a local-composition model for the excess enthalpy which can be used to predict binodal curves accurately, including reasonably accurate values for the critical solution temperature, if reference excess-free-energy data at higher temperatures are available from VLE maesurements.

An expression for activity coefficients of liquid mixtures based on the local surface composition.

Based on the energy of mixing with local surface fractions and the Gibbs-Helmholtz equation, a new activity-coefficient equation, referred to as SILS (Simple Local Surface Fractions), is derived. The SILS equation contains only two interaction parameters for a binary system, and it is applicable to both miscible and partially miscible systems. This equation can be generalized to multicomponent systems without any additional parameter. Correlation of binary vapor-liquid equilibria and prediction of ternary vapor-liquid and liquid-liquid equilibria using only binary experimental data are made by means of the SILS equation. The SILS and modified UNIQUAC equations assure almost the same accuracy when applied to calculating vapor-liquid equilibria. Furthermore, the SILS equation is found to give better accuracy than the modified UNIQUAC equation for prediction of liquid-liquid equilibria.