Modelling the VLE properties using van der Waals-type equation of state

The vapour–liquid equilibrium (VLE) properties of polar and non-polar fluids have been modelled by the use of two modified van der Waals (vdW)-type equations of state (EOSs). In this article, a revised method is applied to the above-mentioned EOSs to improve the representation of VLE properties of different class of fluids. In this respect, the repulsion parameter b is considered to be temperature dependent and also a temperature-dependent revision factor α(T) is introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration to reproduce the vapour pressure (P^s) of pure liquids. The present method is also extended to represent the VLE properties of binary mixtures containing noble gases, refrigerants and hydrocarbons. This method outperforms the original vdW-type EOSs in predicting the VLE and pressure-volume-temperature (PVT) properties of 22 pure substances and 7 binary mixtures.     

A new development of equation of state for square-well chain-like molecules with variable width 1.1 ≤ λ ≤ 3

A new equation of state (EOS) for square-well chain molecules and their mixtures with variable well-width range (SWCF-VR-EOS) has been developed based on the sticky-point model for chemical association. Two important modifications have been made. Firstly, a new dispersion contribution to the Helmholtz function of monomers due to square-well potential with variable well-width range of 1.1 ≤ λ ≤ 3 was established by combining the second-order perturbation theory and Chiew's PY2 approximation of the integral equation. Secondly, the contribution of chain formation to the Helmholtz function is divided into two parts: One is from the hard sphere, and the other is from the effect of square-well potential described via the nearest-neighbor and next-to-nearest-neighbor residual cavity correlation functions (CCFs). The predicted compressibility factors and vapor–liquid coexistence curves for square-well fluids as well as for their mixtures are in good agreement with simulations. The new EOS has been applied to real non-associating fluids and the corresponding mixtures by adopting one-fluid mixing rule. The pVT and vapor–liquid equilibria (VLE) can be correlated satisfactorily. The model parameters for some homologous compounds are found to be linear with the molar mass indicating that the pVT and VLE of those homologous compounds can be predicted even if no accurate data are available.     

A New Modified van Laar Model for Associating Mixtures

In this study, a modification is presented for van Laar model (van der Waals mixture theory) for association mixtures. The molecular association effects are considered in van der Waals mixture theory by adding two new steps to van Laar cycle. The excess Gibbs free energy function and corresponding activity coefficient equations are derived for presented model. In addition to general case when both components are associating fluids, model simplified for two interesting cases: (i) only one fluid is associating, (ii) two fluids are associating but only self-associated species exist in the mixture. This model also is used for VLE calculations for 16 different binary mixtures in which one or both components are associating fluids. Results of the presented model show satisfactory improvement over the nonassociating case for vapor liquid equilibrium (VLE) prediction.     

The potential of head-space gas chromatography for VLE measurements

Head-space gas chromatography (HS-GC) is thought to allow the performance of (vapour + liquid) equilibrium (VLE) measurements in a fast and automated way. However, two decades after the first applications of HS-GC for this purpose, the potential of this technique is not fully developed yet. Measurements of isothermal VLE and activity coefficients of mixtures can be obtained in a high throughput scenario. However, several considerations have to be taken into account before starting the analysis, such as the equilibration time or the minimum sample volume and the GC response factors. These aspects can strongly influence on the validity of the results and should therefore be determined for each mixture.In this paper, four azeotropic mixtures of interest in the pharmaceutical and chemical industry, i.e., (ethylacetate + water), which forms a heterogeneous azeotrope, (ethylacetate + isooctane), (acetonitrile + toluene) and the ternary mixture (acetonitrile + toluene + tetrahydrofuran), are considered to show the potential of HS-GC for VLE measurements. The thermodynamic analysis of VLE data leads to activity coefficients for the mixtures at (35, 50, and 70) °C. In addition, the experimental data are compared with thermodynamic models and data from the literature, when available.     

Correlation,verification and prediction of vapour–liquid equilibria using equation of state with association term: II. Alcohols + non-aliphatic hydrocarbons

An equation of state with association term was used to correlate all available binary VLE data sets for mixtures of alkanols with non-aliphatic hydrocarbons. The self association of alkanols was described using a uniform set of parameters. The cross association between alkanols and aromatic compounds was taken into account. The verification of the VLE data for mixtures of alkanols and non-aliphatic hydrocarbons is described and recommended data are given.The method of prediction of the VLE in the investigated mixtures is described. The recommended data were compared with the results of the prediction.     

A non-recycle flow still for the experimental determination of vapor–liquid equilibria in reactive systems

Experiments for the determination of vapor–liquid equilibrium (VLE) data with a Non-Recycle Flow Still (NFS) are described. Due to short residence times, the NFS is especially suited for systems with thermally unstable components and for reactive mixtures. VLE data of the latter are necessary for modeling reactive distillation processes. With the NFS isobaric data both at atmospheric and at reduced pressure can be gained. The potential of this technique is demonstrated and validated with the well-known, non-reactive systems methanol–ethanol and ethanol–water. The other (mainly reactive) binary mixtures investigated stem from two esterification systems (methyl formate and ethyl acetate production) and one etherification system (tert-amyl methyl ether production). The NRTL equation is used for modeling of the VLE data. The data acquired with the NFS are compared with literature data (whenever possible) or with results of group contribution methods.     

Generalized interaction parameters in cubic equations of state for CO2—n-alkane mixtures

Five equations of state (including one recently proposed by the authors) have been applied to the calculation of vapour—liquid equilibrium (VLE) of CO₂—n-alkane mixtures. Interaction parameters for several systems have been obtained through regression analysis of experimental VLE data. These parameters have been correlated in terms of the temperature and the acentric factor of the hydrocarbon for three equations of state and for all systems. It is concluded that while all equations perform more or less with the same degree of accuracy, there are some advantages in using one or another for different VLE calculations.     

Potential of thermodynamic tools (group contribution methods, factual data banks) for the development of chemical processes

Reliable knowledge of the thermophysical properties of pure compounds and their mixtures in the whole composition and a wide temperature and pressure range is a vital prerequisite for the computer aided synthesis, design and optimization of chemical processes. At the beginning of the development of thermodynamic models, the main interest was directed to the development of predictive g^E-models for vapor–liquid equilibria (VLE) of subcritical compounds. Today group contribution equations of state are available which can also handle supercritical compounds, very asymmetric systems and even systems with strong electrolytes. These sophisticated models together with factual data banks (e.g. the Dortmund Data Bank) are powerful software tools for the reliable development of chemical processes and other applications of industrial interest. In this paper, the status of the different approaches and important applications of industrial interest using thermodynamic information derived from factual data banks or by using sophisticated predictive thermodynamic models will be presented.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

Phase equilibria study of Lennard–Jones mixtures by an analytical equation of state

The recently developed equation of state (EOS) for Lennard–Jones mixtures [Y. Tang, B.C.-Y. Lu, Fluid Phase Equilibria 146 (1998) 73.] is further investigated in this work for describing phase equilibria of these mixtures. The investigation covers vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE) and vapor–vapor equilibria (VVE) over a wide range of temperatures, pressures and molecular characteristic parameters. Results from the van der Waals one-fluid (VDW1) theory are included for comparison. The newly proposed theory performs very well for VLE and LLE and the performance is better than the VDW1 theory; but both theories yield only qualitative results for VVE. It is also found that one system should exhibit VLLE, which was not noticed in previous investigations. Results from two other perturbation theories are also compared in some cases.     

Vapour-liquid equilibria. I. An apparatus for isothermal total vapour pressure measurements: Binary mixtures of ethanol and t-butanol with n-hexane, n-heptane and n-octane at 313.15 K

A static apparatus for the determination of total vapour pressure isotherms of mixtures is described. The apparatus works without a null manometer, and degassing of samples is done without freezing. VLE data for six binary mixtures of ethanol and t-butanol with n-hexane, n-heptane and n-octane are reported and compared with literature data. References to other VLE data obtained using this apparatus are also given.     

用二元交互作用函数预测高压下多组分体系的气液平衡

用和体系的状态有关且满足不变性条件的二元交互作用函数,结合F函数修改的立方状态--方程FRKS方程,预测高压下多组分体系的气液平衡.选择15个三元体系及其组分二元系来检验方法的可行性,这些体系覆盖了从简单的接近理想溶液行为的体系到高度非理想体系.计算结果表明,该方法不仅能相当精确地关联各种类型二元系的气液平衡,而且能在仅用组分二元系参数的条件下较准确地预测所考察的所有三元体系的气液平衡     

A new modification of the UNIQUAC equation including temperature dependent parameters

The UNIQUAC equation was modified by introduction of a linear temperature dependence of the volume and surface area parameters, r_i and q_i. The slope of r_i and q_i functions were found to be the same for hydrocarbons and pyridine. The modified equation was used for prediction of vapor–liquid equilibria (VLE) in binary mixtures of hydrocarbons and pyridine with hydrocarbons as well as for the prediction of the excess enthalpy (H^E) in binary mixtures formed by pyridine with aliphatic alkanes. The results obtained were compared with predictions by UNIFAC and further with UNIQUAC equation and its modification involving temperature dependant coordination number z. The proposed temperature dependence of the r_i and q_i parameters enables prediction of the VLE at various temperatures and leads to reasonable values of H^E. The necessary input reduces to one set of isothermal VLE data. One set of UNIQUAC interaction parameters u_ij is sufficient for representation of VLE in a wide range of temperature and to obtain a reasonable prediction of H^E.     

Measurement,correlation and estimation of binary vapor—liquid equilibria for alcohol—chlorobenzene systems

Experimental VLE of chlorobenzene—1-pentanol binary mixtures are determined at 101.08 kPa. Also, the activity coefficients at infinite dilution (γ^∞) for some alcohol—chlorobenzene systems are determined from ebulliometric measurements. The Wilson equation is tested for 10 binary alcohol—chlorobenzene systems. The results show that this model represents the data well. There is good comparison between experimental γ^∞,s and γ^∞,s computed from Wilson parameters. Further, the VLE data for the above-mentioned mixtures are estimated by the UNIFAC method.     

Prediction of ternary vapor–liquid equilibria for 33 systems by molecular simulation

A set of molecular models for 78 pure substances from prior work is taken as a basis for systematically studying vapor–liquid equilibria (VLE) of ternary systems. All 33 ternary mixtures of these 78 components for which experimental VLE data are available are studied by molecular simulation. The mixture models are based on the modified Lorentz–Berthelot combining rule that contains one binary interaction parameter which was adjusted to a single experimental binary vapor pressure of each binary subsystem in prior work. No adjustment to ternary data is carried out. The predictions from the molecular models of the 33 ternary mixtures are compared to the available experimental data. In almost all cases, the molecular models give excellent predictions of the ternary mixture properties.     

Isobaric vapor-liquid equilibria of the methanol,methyl acetate and methyl acrylate system at atmospheric pressure

Isobaric vapor-liquid equilibrium (VLE) data were determined at atmospheric pressure for the binary and the ternary mixtures of methanol, methyl acetate and (stabilized) methyl acrylate. The thermodynamic consistency of the data for the three binary mixtures was tested via Herington analysis. The experimental VLE data were reduced and binary parameters for four activity coefficient models, such as Margules, Wilson, NRTL and UNIQUAC, were fitted. The four models with their best-fitted parameters were used to predict the ternary vapor-liquid equilibria. A comparison of model performances was made by using the criterion of average absolute deviations in boiling point and in vapor-phase composition.     

Isothermal vapor–liquid equilibria and excess molar volumes for the ternary mixtures containing 2-methyl pyrazine

Isothermal vapor–liquid equilibrium (VLE) data at 353.15 K and excess molar volumes (V^E) at 298.15 K are reported for the binary systems of ethyl acetate (EA)+cyclohexane and EA+n-hexane and also for the ternary systems of EA+cyclohexane+2-methyl pyrazine (2MP) and EA+n-hexane+2MP. The experimental binary VLE data were correlated with common g^E model equations. The correlated Wilson parameters of the constituent binary systems were used to calculate the phase behavior of the ternary mixtures. The calculated ternary VLE data using Wilson parameters were compared with experimental ternary data. The experimental excess molar volumes were correlated with the Redlich–Kister equation for the binary mixtures, and Cibulka’s equation for the ternary mixtures.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

The prediction of vapor—liquid equilibrium from heat of mixing data for binary hydrocarbon—ketone mixtures

The method of Hanks et al. for predicting vapor—liquid equilibrium (VLE) from heat of mixing (h^E) data was successfully applied to binary hydrocarbon—ketone mixtures. The LEMF model for the excess free energy was found to be the most adequate to correlate experimental g^E and h^E data simultaneously for these mixtures. The predicted vapor-liquid equilibrium values were compared to experimental values and good agreement was found. The dependence of the accuracy of the VLE data predictions on the experimental uncertainties of heat of mixing data and on the set of parameters obtained by fitting these data to the algebraic equation for h^E is discussed.     

Room temperature ionic liquids and their mixtures—a review

Room temperature ionic liquids are salts that are liquid at room temperature and their use as catalysts and catalytic support has been studied extensively. They are also being considered as “green solvents” for various separation processes. Recent measurements reported on the properties of pure ionic liquids and their mixtures, including gas and liquid solubility in common organic solvents will be reviewed. While some property values are in good agreement, some show large differences. These values will be compared and reasons for the discrepancies will be conjectured. Since traditional approaches to predicting the properties of fluid liquids require extensive LLE and VLE measurements, alternative predictive methods need to be explored. The predictions of the properties of mixtures of ionic liquids using COSMOtherm, an approach based on unimolecular quantum chemical calculations of the individual molecules, will be presented.