Excess Gibbs Free Energy Model Research Articles

Isothermal vapor–liquid equilibria for the binary system of dimethyl ether (DME) + methyl iodide (CH3I)

Isothermal vapor–liquid equilibrium data for the binary system of dimethyl ether (DME)+methyl iodide (CH3I) were taken with a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated still at five temperatures: 283.15, 293.15, 303.15, 313.15 and 323.15K. This binary mixture system showed negative deviation from the Raoult's law and no azeotrope observance. The equilibrium compositions of vapor and liquid phases and pressures were reported at each temperature. The measured data were correlated with the Peng–Robinson equation of state(PR-EoS) using the Wong–Sandler mixing rules combined with the NRTL excess Gibbs free energy model and Peng–Robinson equation of state (PR-EoS) using the Universal mixing rule (UMR) as well as with the UNIQUAC model. The calculated results with this combination of equations show good agreement with experimental data taken in this study.

Measurement of VLE data of carbon dioxide (CO2) + methyl iodide (CH3I) system for the direct synthesis of dimethyl carbonate using supercritical CO2 and methanol

Isothermal vapor⿿liquid equilibrium data for the binary system carbon dioxide+methyl iodide were measured at temperatures from 283.15 to 323.15K at 10K intervals. Data in the two-phase region were measured by using a circulation-type equilibrium apparatus and gas chromatography. This binary mixture system showed positive deviation from the Raoult's law and no azotrope observance. The experimental data were correlated with the Peng⿿Robinson equation of state (PR-EoS) using the Wong⿿Sandler (W⿿S) mixing rule, which was combined with the nonrandom two-liquid (NRTL) excess Gibbs free energy model and Peng⿿Robinson equation of state (PR-EoS) using the Universal mixing rule (UMR) as well as with the UNIQUAC model. The calculated results with this combination of equations show positive agreement with experimental data taken within this study.

Measurement of VLE data of carbon dioxide + dimethyl carbonate system for the direct synthesis of dimethyl carbonate using supercritical CO2 and methanol

Isothermal vapor–liquid equilibrium data for the binary system of carbon dioxide+dimethyl carbonate (DMC) were measured at 278.15, 283.15, 293.15, 303.15, 313.15, 323.15 and 333.15K using a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated. The equilibrium compositions of vapor and liquid phases and pressures were reported at each temperature. The measured data were correlated with the Peng–Robinson equation of state (PR-EoS) using the Wong–Sandler mixing rules combined with the NRTL excess Gibbs free energy model and the Peng–Robinson equation of state (PR-EoS) using the Universal mixing rule. Calculated results with these equations can be used to estimate the thermodynamic properties of this binary system of CO2 (1)+DMC (2).

Isothermal vapor-liquid equilibria for the binary system of dimethyl ether (CH3OCH3)+ methanol (CH3OH)

Isothermal vapor-liquid equilibrium data for the binary mixture of dimethyl ether (CH3OCH3)+methanol (CH3OH) were measured within the temperature range of 308.15–328.15 K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continuously recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model. The values calculated by the PR-EOS with the W-S mixing rules show good agreement with our experimental data.

10.2478/s11814-009-0334-0

Vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO2)+1,1-difluoroethane (HFC-152a) were measured at five evenly spaced temperatures of (273.15, 283.15, 293.15, 303.15 and 313.15) K by using a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model and the Carnahan-Starling-DeSantis equation of state (CSD EoS). Almost all the calculated values with these two models showed good agreement with the experimental data.

Isothermal Vapor−Liquid Equilibria for the Binary System of Carbon Dioxide (CO2) + 1,1,1,2,3,3,3-Heptafluoropropane (R-227ea)

Isothermal vapor−liquid equilibrium (VLE) data for the binary mixture of carbon dioxide (CO2) + 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) were measured at six evenly spaced temperatures of (278.15, 288.15, 298.15, 308.15, 318.15, and 328.15) K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continuously recirculated. The experimental data were correlated with the Peng−Robinson equation of state (PR-EoS) using the Wong−Sandler (W−S) mixing rules combined with the nonrandom two-liquid (NRTL) excess Gibbs free energy model. The calculated values with the PR-EoS using the W−S mixing rules show good agreement with the experimental data.

High pressure isothermal vapor-liquid equilibria for the binary system of carbon dioxide (CO2)+1,1,1-trifluoroethane (R-143a)

Isothermal vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO2)+1,1,1-trifluoro- ethane (HFC-143a) were measured within the temperature range of 273.15-333.15 K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continu- ously recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EOS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model. The values calculated by the PR EOS with the W-S mixing rules show good agreement with our experimental data.

Prediction of the Selectivity Coefficient of Ionic Liquids in Liquid-Liquid Equilibrium Systems Using Artificial Neural Network and Excess Gibbs Free Energy Models

In this work, the selectivity coefficients of ionic liquids in liquid-liquid systems were correlated and predicted by the NRTL, UNIQUAC, and Wilson-NRF Gibbs free energy models and also by an artificial neural network system. The three thermodynamic models need six binary interaction parameters between solvent(1)-solvent(2), solvent(1)-ionic liquid, and solvent(2)-ionic liquid pairs in obtaining the selectivity of ionic liquid in liquid-liquid systems. Also, the selectivity coefficients of ionic liquids were modeled using an artificial neural network system. In the proposed neural network system, temperature, molecular weight of ionic liquid, molecular weight of solvents, and mole fractions of components (1) and (2) in the solvent-rich phase were considered as input data and the selectivity of ionic liquids in the liquid-liquid system was considered as output. The weights and biases were obtained using the quick propagation (QP) method. A total of 150 experimental data points were used for training and 30 experimental data for testing. The best network topology obtained was one neuron in a hidden layer with five nodes. The average absolute deviation percentages (AAD%) for the results obtained from the neural network system, the NRTL model, the UNIQUAC model, and the Wilson-NRF model are 0.0096, 0.0168, 0.0017, and 0.0178, respectively. Although the artificial neural network gave reasonably good results, the UNIQUAC model can more accurately predict the selectivity of ionic liquids in liquid-liquid equilibrium systems than the other models.

A reliable procedure to predict salt precipitation in pure phases

This article proposes a new procedure to compute solid-liquid equilibrium in electrolyte systems that may form pure solid phases at a given temperature, pressure, and global composition. The procedure combines three sub-procedures: phase stability test, minimization of the Gibbs free energy with a stoichiometric formulation of the salt-forming reactions to compute phase splitting, and a phase elimination test. After the phase splitting calculation for a system configuration that has a certain number of phases, the phase stability test establishes whether including an additional phase will reduce the Gibbs free energy further. The criteria used for phase stability may lead, in some cases, to the premature inclusion of phases that should be absent from the final solution but, if this happens, the phase elimination sub-procedure removes them. It is possible to use the procedure with several excess Gibbs free energy models for liquid phase behavior. The procedure has proven to be reliable and fast and the results are in good agreement with literature data.

High pressure isothermal vapor-liquid equilibria of carbon dioxide+1,1-difluoroethane

Vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO2)+1,1-difluoroethane (HFC-152a) were measured at five evenly spaced temperatures of (273.15, 283.15, 293.15, 303.15 and 313.15) K by using a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model and the Carnahan-Starling-DeSantis equation of state (CSD EoS). Almost all the calculated values with these two models showed good agreement with the experimental data.

Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions

A newly developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software was employed to model the solid and aqueous phase equilibria of calcium sulfate hydrates in electrolyte solutions containing NiSO 4, H 2SO 4, MgSO 4, Fe 2(SO 4) 3, LiCl and HCl from 25 to 90 °C. The MSE model is a variant of an excess Gibbs free energy model for Mixed Solvent Electrolyte systems which takes into account long-range electrostatic interactions from a Pitzer–Debye–Hückel equation, middle-range interactions from a second virial coefficient-type equation and short-range interactions from the UNIQUAC model. The effect of cations with similar anions on the solubility was investigated and it was found that the solubility depends mainly on the anion type while the cation has a minor effect. The effect of acid addition and the acid type was also studied. The addition of both HCl and H 2SO 4 increases the solubility; however H 2SO 4 has a less pronounced effect due to the common ion effect. Furthermore, the effect of phase transitions between different calcium sulfate hydrates was studied. The transformation of CaSO 4 dihydrate to anhydrite results in a significant decrease in the solubility, which complicates the chemistry of the system. Since it is not practical to measure solubility data under all conditions of interest, the model developed and the experimental results obtained serves the purpose of assessing the calcium sulfate scaling potential for a wide variety of complex aqueous industrial streams.

Calculation of the solid solubilities in supercritical carbon dioxide using a new G ex mixing rule

The aim of this study is to develop a new EOS/G ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO 2, by using six mixing rules, namely, the Wong–Sandler (WS) rule, the Orbey–Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide. The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO 2.

Towards the development of theoretically correct liquid activity coefficient models

We propose a general approach for developing liquid activity coefficient models based on the concept of local composition that satisfy at least two important physical conditions: (1) the total number of neighboring molecules around one molecule of species A must be a constant at any temperature for all possible mixture compositions, and (2) the number of pairs between any two species A –B determined from the local composition of B around A must be the same as that of A around B. Most commonly used liquid activity coefficient models (such as UNIQUAC) satisfy condition (1) but fail to meet condition (2), and thus are considered as fundamentally flawed. We propose a general formulation for the local composition equation containing a symmetric function of species A and B which ensures condition (2) be always satisfied. We show that the composition and temperature dependence of the symmetric functions can be completely obtained from condition (1), resulting in a new class of excess Gibbs free energy models. It is found that such a model can quantitatively reproduce the results of Monte Carlo simulation for various types of lattice fluids, while conventional models are merely qualitative. Furthermore, such a model is more accurate than the UNIQUAC model in correlating experimental data, especially in the dilute regime. Therefore, models developed based on this approach are theoretically sound and potentially applicable to a broader range of conditions.

Measurement and modeling of osmotic coefficients of aqueous solution of ionic liquids using vapor pressure osmometry method

Osmotic coefficients of binary mixtures containing an ionic liquid, (1-butyl-3-methylimidazolium tetrafluoroborate, [BMIm]BF 4, 1-ethyl-3-methylimidazolium ethyl sulfate, [EMIm]ES, and 1-butyl-3-methylimidazolium methyl sulfate, [BMIm]MS) with water were measured until about 3 molal concentrations using vapor pressure osmometry method (VPO) at temperature ranges 298.15–328.15 K and modeled using different electrolyte excess Gibbs free energy models including electrolyte non-random two liquids (NRTL), modified NRTL (MNRTL), mean spherical approximation NRTL (MSA-NRTL), non random factor (NRF), and extended Wilson models. The results show that osmotic coefficient data increase with increasing temperature. The calculated standard deviations of the studied systems show that the applicability of these models for the correlation of VLE properties of ionic liquid solutions. The average standard deviations for the models have the order σ( ϕ) MNRTL < σ( ϕ) Wilson < σ( ϕ) NRTL < σ( ϕ) MSA-NRTL < σ( ϕ)NRF. The results show MNRTL model is able to reproduce experimental osmotic coefficients of aqueous solution of studied ionic liquids with good precision.

Bilevel optimization formulation for parameter estimation in vapor–liquid(–liquid) phase equilibrium problems

A rigorous method is proposed for parameter estimation in thermodynamic models used for predicting vapor–liquid and vapor–liquid–liquid equilibrium of binary mixtures. Typically, vapor–liquid(–liquid) equilibria are modeled using asymmetric models, i.e., an excess Gibbs free energy model for the liquid phase and an equation of state for the vapor phase. Parameter estimation for asymmetric models is a nontrivial task. The existence of spurious additional liquid splits predicted by the models, but not observed experimentally, must be excluded and the capability of the models to predict homogeneous or heterogeneous azeotropes accurately is crucial. The proposed formulation for parameter estimation in this class of nonideal phase equilibria is based on bilevel optimization with nonconvex lower-level programs. The bilevel formulation proposed can reliably estimate model parameter values that can be employed to correlate the correct (experimentally measured) number of phases, phase splits and azeotropes and can distinguish between heterogeneous and homogeneous azeotropes. Using the bilevel formulation multiple minimization problems are solved globally: the upper level program (minimization of the discrepancy between measured and predicted values for the species compositions in each phase) that yields the best possible thermodynamic description of the systems studied, and several lower-level programs per experiment that enforce thermodynamic stability and correlation of the correct number and type of phases and phase splits. Examples from the literature are given, in which conventional parameter estimation methods yield significant qualitative and quantitative errors in the prediction of the phase behavior using the NRTL, UNIQUAC and Wilson models.

Bilevel optimization formulation for parameter estimation in liquid–liquid phase equilibrium problems

Excess Gibbs free energy models contain parameters which for a given mixture are estimated from measurements of phase-splits. Local composition models are very flexible and can accurately predict complex phase behavior. However, in many cases it has been reported that use of local composition models leads to prediction of more phase splits or more phases than measured, modeling homogeneous azeotropes as heterogeneous, etc. Here, a formulation is proposed that addresses these limitations of current parameter estimation methods. The formulation is based on a bilevel program, i.e., an optimization problem embedded in another one. Minimizing the error between model predictions and measurements gives the upper-level program. The lower-level programs are given by the minimization of the Gibbs free energy, or equivalently the satisfaction of the Gibbs tangent plane criterion. Each of the experiments is cast as a separate lower-level program. Additional requirements on the phase behavior of the system, such as enforcing the correct number of phase splits and the correct number of phases in each phase split, are similarly formulated as additional lower-level programs. Global optimization techniques are necessary even to obtain a feasible point since the lower-level programs are nonconvex. The proposed formulation is applied to problems from the literature, in which inappropriate fitting of the parameters of the non-random two-liquid (NRTL) model to experimental data has been reported to result in significant model errors, such as the prediction of an additional spurious phase split. The discussion is restricted to binary mixtures, however, the formulation can in principle be applied also to multicomponent mixtures.

Densities and Viscosities of the Ionic Liquid [C 4mim][PF 6]+ N, N-dimethylformamide Binary Mixtures at 293.15 K to 318.15 K

Viscosities and densities for 1-butyl-3-methylimidazolium hexafluorophosphate ([C 4mim][PF 6]) and N, N-dimethylformamide (DMF) binary mixtures have been measured at the temperature range from 293.15 K to 318.15 K. It is shown that the viscosities and densities decrease monotonously with temperature and the content of DMF. Various correlation methods including Arrhenius-like equation, Seddon et al.'s equation, Redlich-Kister equation with four parameters, and other empirical equations were applied to evaluate these experimental data. A model based on an equation of state for estimating the viscosity of mixtures containing ionic liquids were proposed by coupling with the excess Gibbs free energy model of viscosity, which can synchronously calculate the viscosity and the molar volume. The results show that the model gives a deviation of 8.29% for the viscosity, and a deviation of 1.05% for the molar volume when only one temperature-independent adjustable parameter is adopted. The correlation accuracy is further improved when two parameters or one temperature-dependent parameter is used.

Extraction of alcohols from water with 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Ethanol production in the U. S. has increased 36% between 2006 and 2007 (J. M. Urbanchuk, Contribution of the Ethanol Industry to the Economy of the United States, LECG, LLC, Renewable Fuels Association, 2008) in response to a growing demand for its use as a commercial transportation fuel. 1-Butanol also shows potential as a liquid fuel but both alcohols require high energy consumption in separating them from water. 1-Butanol, in particular, is considered an excellent intermediate for making other chemical compounds from renewable resources, as well as being widely used as a solvent in the pharmaceutical industry. These alcohols can be synthesized from bio-feedstocks by fermentation, which results in low concentrations of the alcohol in water. To separate alcohol from water, conventional distillation is used, which is energetically intensive. The goal of this study is to show that, using an ionic liquid, extraction of the alcohol from water is possible. Through the development of ternary diagrams, separation coefficients are determined. The systems studied are 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide/ethanol/water, which exhibits Type 1 liquid–liquid equilibrium (LLE) behavior, and 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide/1-butanol/water, which exhibits Type 2 LLE behavior. Based on the phase diagrams, this ionic liquid (1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) can easily separate 1-butanol from water. It can also separate ethanol from water, but only when unreasonably high solvent/feed ratios are used. In addition, we use four excess Gibbs free energy (gE) models (NRTL, eNRTL, UNIQUAC and UNIFAC), with parameters estimated solely using binary data and/or pure component properties, to predict the behavior of the ternary LLE systems. None of the models adequately predicts the Type 1 system, but both UNIQUAC and eNRTL aptly predict the Type 2 system.

Modeling Liquid−Liquid Equilibrium of Ionic Liquid Systems with NRTL, Electrolyte-NRTL, and UNIQUAC

Characterization of liquid−liquid equilibrium (LLE) in systems that contain ionic liquids (ILs) is important in evaluating ILs as candidates for replacing traditional extraction and separation solvents. Although an increasing amount of experimental LLE data is becoming available, comprehensive coverage of ternary liquid-phase behavior via experimental observation is impossible. Therefore, it is important to model the LLE of mixtures that contain ILs. Experimental binary and ternary LLE data that involve ILs can be correlated using standard excess Gibbs energy models. However, the predictive capability of these models in this context has not been widely studied. In this paper, we study the effectiveness with which excess Gibbs energy models can be used to predict ternary LLE solely from binary measurements. This is a stringent test of the suitability of various models for describing LLE in systems that contain ILs. Three different excess Gibbs free energy models are evaluated: the non-random two-liquid (NRTL) model, the universal quasi-chemical (UNIQUAC) model, and the electrolyte−NRTL (eNRTL) model. In the case of eNRTL, a new formulation of the model is used, based on a symmetric reference state. To our knowledge, this is the first time that an electrolyte excess Gibbs energy model has been formulated for and applied to the modeling of multicomponent LLE for mixtures that involve ILs. Ternary systems (IL, solvent, co-solvent) that exhibit experimental phase diagrams of various types have been chosen from the literature for comparison with the predictions. Comparisons of experimental and predicted octanol−water partition coefficients are also used to evaluate the models studied.

Vapor–liquid equilibrium measurements and correlations for the binary mixture of difluoromethane + isobutane and the ternary mixture of propane + isobutane + difluoromethane

Hydrocarbons such as propane (R-290), n-butane (R-600), and isobutane (R-600a) are expected candidates for CFC, HCFC, and HFC alternative working fluids for refrigerators and heat pump systems. Hydrocarbons (HCs) are environmentally acceptable refrigerants; however, most HCs have the problem of flammability. In order to maintain the safety of home refrigerators and air-conditioners, mixing a small amount of HFCs with HCs may be effective. In our previous study, the vapor–liquid equilibrium (VLE) measurements for the binary mixtures of R-290 + R-600a and the difluoromethane (R-32) + R-290 have already been performed. This study measured the VLEs of the binary mixture of R-32 + R-600a and the ternary mixture of R-290 + R-600a + R-32. Based on the experimental data, the VLEs for three binary mixtures were correlated by using the cubic equations of state with the conventional mixing rule, and the appropriate binary interaction parameters were determined for each binary mixture. For the R-290 + R-600a and R-32 + R-290 mixtures, the correlations were successful. For the R-32 + R-600a mixture, however, because of a relatively high nonideality, the accuracy of correlation was less than that for the other two mixtures. By applying the mixing rule based on the excess Gibbs free energy model, the accuracy was well improved. Moreover, by using the binary interaction parameters for each binary mixture the prediction of the VLE for the R-290 + R-600a + R-32 mixture was tested, and predicted bubble-point pressures were compared with the experimental values. The accuracy of this prediction was at similar level to the VLE correlation for the R-32 + R-600a mixture.