Modelling of the three phase LLV region for ternary hydrocarbon mixtures with the Soave-Redlich-Kwong equation of state

The prediction of the three phase liquid-liquid-vapour (L2L1V) region for the ternary mixtures ethane + propane + eicosane (C2 + C3 + C20) and methane + ethane + eicosane (C1 + C2 + C20) was performed using the Soave-Redlich-Kwong equation of state. A procedure for finding K- and L-points is presented. It is based on the solution of thermodynamic conditions for the K- and L-point using the Newton iteration technique with carefully chosen starting points. The calculations were performed with all binary interaction parameters set to zero and with binary interaction parameters fitted to vapour-liquid equilibrium data of the binary subsystems. In the latter case for all binary subsystems two adjustable parameters with classical mixing rules were used. The results obtained show only qualitative agreement with experimental data for both sets of interaction parameters.     

Data driven temperature dependence of EOS parameters

Using three kinds of experimental data (p_c, V_c and T_c at the critical state or P_s, V_s^v and V^sL at different temperatures for saturation data) three parameters of the EOS may be directly determined and the temperature dependence of the parameters may be established from thermodynamic conditions of vapour-liquid critical point or vapour-liquid phase equilibria respectively. The principle was demonstrated on the BACK EOS. Examples of argon and n-alkanes were used to demonstrate the idea. It was found, that there are two parameter sets of the BACK equation that satisfy the critical or saturation conditions for certain pure compounds. The BACK equation is able to reproduce experimental Z_c values for compounds above Z_c = 0.2764 (that is, for argon, methane, ethane), but it is improper for higher alkanes. In case of n-alkanes we found that there is no simple function for T dependence of BACK parameters. Parameter values obtained in the way demonstrated may be useful to give initial values for parameter estimation from experimental (e.g., VLE) data.     

Simulation of double retrograde vaporization using the Peng–Robinson equation of state

Double retrograde vaporization is a phenomenon characterized by an unexpected retrograde dew point curve at compositions approaching nearly the pure volatile component (component A) and at temperatures very close to the critical temperature of the more volatile component (Tc_A). On the p–x–y diagram, instead of the single-domed dew point curve in the familiar “single” retrograde vaporization, double retrograde vaporization shows two “domes” at temperatures above but close to Tc_A. At temperatures below but close to Tc_A, the dew point curve has an “S”-shape. This results respectively in quadruple- or triple-valued dew points at a specific composition. In this work, the phenomenon of double retrograde vaporization has been simulated using a cubic equation of state. Both the “double-dome” and the “S”-shape curves for the binary systems (ethane+linalool) and (ethane+d-limonene) were successfully modelled, even without the use of binary interaction parameters. Results are also obtained by optimizing interaction parameters using experimental bubble point data. Even though double retrograde vaporization has rarely been observed in literature, we believe that it is the normal behaviour that always occurs in binary mixtures in which the two components differ largely enough in molecular symmetry to produce a very steep dew point curve. To further verify this generality, simulations were performed on a number of binary mixtures of different families. Double retrograde vaporization was estimated in every system with a steep dew point curve.     

Liquid-liquid equilibria of (cyclohexane + acetonitrile + methylcyclohexane + toluene) and of {(acetonitrile + methylcyclohexane) + benzene or + toluene or + cyclohexane or + chlorobenzene} at 298.15 K

Tie-line results at 298.15 K and atmospheric pressure are reported for (cyclohexane + acetonitrile + methylcyclohexane + toluene) and for {(acetonitrile + methylcyclohexane) + benzene or + toluene or + cyclohexane or + chlorobenzene). The extended UNIQUAC and UNIQUAC equations are used to correlate binary vapour-liquid equilibria and mutual solubilities for 10 mixtures constituting the ternary mixtures and to predict the ternary and quaternary liquid-liquid equilibria by use of only binary parameters.     

Liquid—liquid—vapor phase equilibria behavior of certain binary ethane + n-alkylbenzene mixtures

The liquid—liquid—vapor loci for the binary mixtures ethane + n-nonylbenzene, ethane + n-decylbenzene and ethane + n-undecylbenzene were experimentally studied. The pressure, temperature, and compositions and molar volumes of the liquid phases are reported along the loci. n-Nonylbenzene was found to be the first member of the n-alkylbenzene homologous series to exhibit liquid—liquid—vapor immiscibility with ethane. For the three alkylbenzenes studied, the liquid—liquid—vapor loci have the same type of behavior: they extend from a lower critical end point (LCEP) to an upper critical end point (K-point).     

Application of a generalized van der Waals equation of state to several nonpolar mixtures

A generalized van der Waals equation of state, applied recently (Nguyen Van Nhu and Kohler, 1995) to the calculation of excess properties and phase equilibria for the mixture methane + ethane, is now extended to several nonpolar binary mixtures.Improved mixing rules for the van der Waals attractive term and for the correction term are proposed. With these mixing rules, the equation gives good agreement for vapour-liquid and liquid-liquid equilibria over a large temperature range for 29 binary mixtures. The agreement of mixture volumes and cross second virial coefficients is also satisfactory.     

Application of the Wilson—Wegner expansion to represent vapor—liquid equilibrium surfaces of binary and ternary systems from the critical locus to the vapor pressure of the heavier component

The Torquato—Stell modification of the Wilson—Wegner expansion has been used to present and to represent the vapor—liquid equilibrium surfaces of several binary methane—alkane mixtures and one ternary system from the critical locus to the heavier component's vapor pressure within the experimental accuracy of the data. Inconsistent phase compositions are revealed without recourse to equations of state computations. Since the critical point of the mixtures are not precisely known, an isothermal regression analysis of the data is first used to obtain an improved estimate of the critical point of mixtures using the scaled expressions. Then, along isotherms, the phase compositions are analyzed in terms of the reduced proximity to the critical pressure. Subsequently, the entire compositional surfaces are presented in terms of both the reduced proximity to the critical pressure of the mixture and the reduced proximity to the critical temperature of the heavier component.     

Can the speed of sound be used for detecting critical states of fluid mixtures?

The phenomenology of sound speeds in fluid mixtures is examined near and across critical lines. Using literature data for binary and ternary mixtures, it is shown that the ultrasound speed along an isotherm-isopleth passes through a minimum value in the form of an angular (or V-shaped) point at critical states. The relation between critical and pseudo-critical coordinates is discussed. For nonazeotropic fixed-composition fluid mixtures, pseudo-critical temperatures and pressures are found to be lower than the corresponding critical temperatures and pressures. The analysis shows that unstable pseudo-critical states cannot be detected using acoustic methods. The thermodynamic link between sound speeds and isochoric heat capacities is formulated and discussed in terms of p-Vm-T derivatives capable of being calculated using cubic equations of state. Based on the Griffiths-Wheeler theory of critical phenomena, a new specific link between critical sound speeds and critical isochoric heat capacities is deduced in terms of the rate of change of critical pressures and critical temperatures along the p-T projection of the critical locus of binary fluid mixtures. It is shown that the latter link can be used to obtain estimates of critical isochoric heat capacities from the experimental determination of critical speeds of sound. The applicability domain of the new link does not include binary systems at compositions along the critical line for which the rate of change in pressure with temperature changes sign. The new equation is combined with thermodynamic data to provide approximate numerical estimates for the speed of sound in two mixtures of carbon dioxide and ethane at different temperatures along their critical isochores. A clear decrease in the sound speed is found at critical points. A similar behavior is suggested by available critical heat capacity data for several binary fluid mixtures. Using an acoustic technique, the critical temperature and pressure were determined for three different mixtures of methane and propane, and compared with literature data obtained using conventional methods. It is concluded that acoustic-based techniques are reliable to determine, for the most part, critical surfaces of fluid mixtures. The remaining few cases where the present analysis cannot be applied could be tested by the thermodynamic calculation of critical sound speeds using crossover equations of state in conjunction with experimentally determined critical isochoric heat capacities.     

The prediction of isobaric phase equilibria for non-ideal multicomponent mixtures from heat of mixing data

A method for predicting isobaric binary and ternary vapor—liquid equilibrium data using only isothermal binary heat of mixing data and pure component vapor pressure data is presented. Three binary and two ternary hydrocarbon liquid mixtures were studied. The method consists of evaluating the parameters of the NRTL equation from isothermal heat of mixing data for the constituent binary pairs. These parameters are then used in the multicomponent NRTL equation to compute isobaric vapor—liquid equilibrium data for the ternary mixture. No ternary or higher order interaction terms are needed in the ternary calculations because of the nature of the NRTL equation. NRTL parameters derived from heat of mixing data at one temperature can be used to predict vapor—liquid equilibrium data at other temperatures up to the boiling temperature of the liquid mixture.For the systems studied this method predicted the composition of the vapor phase with a standard deviation ranging from 1–8% for the binary systems and from 4–12% for the ternary systems.     

Calculation of vapour-liquid equilibrium of associated systems by an equation of state

A recently proposed equation of state of the van der Waals type is applied to calculate phase equilibria in hydrogen-bonding, non-electrolytic systems. Association is accounted for by treating alcohols, acids, etc., as mixtures of associated species formed by up to 14 monomers. The method involves essentially one weakly temperature-dependent adjustable parameter per binary system.The calculations cover vapour-liquid equilibrium both at low and elevated pressure in binary systems formed by an associating substance and a non-associating compound such as a hydrocarbon or halogenated hydrocarbon. An attempt has been made to include all experimental data available for these systems in the literature. A number of calculations for ternary systems as well as of liquid-liquid equilibria are included, and a limited number of solvated systems are also treated.Owing to its single adjustable parameter, the method may be used to test existing experimental data and to predict such data.     

Supercritical phase equilibria involving solids

The solubility of solids in supercritical solvents is reviewed in a phenomenological discussion of binary and ternary systems containing one highly volatile component. Solubility and selectivity are greatly determined by the course of the binary critical curves, the ternary critical end-point curves, and the locations of the triple points of the solids. The mean-field lattice-gas model is used to review some important molecular parameters.     

Isothermal vapour-liquid equilibria in the binary and ternary systems composed of 2,2,4-trimethylpentane, 2-methyl-1-propanol, and 4-methyl-2-pentanone

Vapour-liquid equilibrium data in the three binary 2,2,4-trimethylpentane + 2-methyl-1-propanol, 2-methyl-1-propanol + 4-methyl-2-pentanone, 2,2,4-trimethylpentane + 4-methyl-2-pentanone systems, and in the ternary 2,2,4-trimethylpentane + 2-methyl-1-propanol + 4-methyl-2-pentanone system are reported. The data were measured isothermally at 333.15, 348.15 and 364.15 K covering the pressure range 12-100 kPa. The binary vapour-liquid equilibrium data were correlated using the Wilson and NRTL equations by means of a robust algorithm for processing all isotherms together; resulting parameters were then used for calculation of phase behaviour in the ternary system and for subsequent comparison with experimental data.     

Prediction of the salt effect on the vapour-liquid equilibrium of binary mixtures

A salt dissolved in a mixture of volatile components may affect the activities of the components through the formation of associates or complexes. If this interaction is selective, the relative volatility of the volatile components may change drastically and thus facilitate the separation of close-boiling components or even of azeotropic mixtures. A new method for predicting the effect of salt addition has been developed which is based solely on vapour-liquid equilibrium data for the volatile components and solubility data for the binary salt-solvent systems. The procedure can correlate data for various salt and solvent compositions, including saturated solutions. The model may easily be extended to multisolvent-salt systems.     

Relationship between the density of supercritical CO_2 + ethanol binary system and its critical properties

The solvent strength and selectivity of supercritical fluids (SCF) can be greatly enhanced by addition of one or two entrainers into the system. The amount of entrainer added is usually less than 5% (mole fraction). However, even with such slight amount, solubility of organic solutes has been observed to increase by several orders magnitude[1]. Therefore, critical pressure and tem-perature data of these supercritical fluid + cosolvent systems are imperative for the reasonable design of effici…     

近临界下HZSM-5催化的甲苯歧化反应

用高压观测池通过可视观测确定了苯、甲苯和对二甲苯等二元系及三元系的临界性质以及甲苯歧化反应混合物临界性质随着反应进程的变化规律；在此基础上，分别研究了近临界区以及高温下以HZSM-5为催化剂的甲苯歧化反应。结果发现，在近临界区甲苯歧化反应的对二甲苯选择性最高，随温度的升高甲苯转化率明显增加，对二甲苯选择性下降。高温下压力对对二甲苯选择性没有影响，转化率随压力升高而提高。     

Wetting of the container wall as a critical-point phenomenon. III. Wetting by contacting conjugate solutions of ternary systems

In the ternary systems benzene-ethanol-water and ethyl acetate-ethanol-water, the contact angles of the meniscus between two immiscible liquid phases (i.e., conjugate solutions) and a solid substrate tend toward 90° as compositions approach the consolute point at a constant temperature; just as, in a binary system, the contact angles between the corresponding three phases have been shown (in the previous paper of this series) to tend toward 90° as the temperature approaches the critical point. The quantitative expression for the variation of the contact angle with the concentration of the cosolvent in the vicinity of the consolute point in a ternary system also bears a formal mathematical resemblance to that found for the corresponding variation of the contact angle with temperature in a binary system.     

Calculating binary and ternary multiphase equilibria: extensions of the integral area method

The area method was proposed in 1992 to calculate binary and ternary 2-phase equilibria. In its integral form, the method provides both the necessary and sufficient conditions required for the determination of the global minimum reduced Gibbs energy of mixing (Φ). The method has since been applied to the calculation of both pure component and ternary multiphase equilibria in a differential form. However, the extension of the original (2 point) integral area method to the direct calculation of both binary and ternary multiphase equilibria has not been completed. Direct 3 point and modified 2 point search methods have therefore been developed here and used to estimate the phase compositions of a representative binary vapour-liquid-liquid system. The 2 point area method principle has been extended and applied to the calculation of ternary multiphase equilibria using a net volume approach. However, this volume method was found to fail due to an underlying inconsistency in the bounding of the integrated Φ surface by the trial 3-phase region. A new method is proposed that overcomes this problem by minimising the area of intersection between a tangent plane and the Φ surface. This new method has successfully calculated the 3-phase compositions of two simple test systems from a variety of initial mixture starting points.     

A new equation for correlation of vapour-liquid equilibrium data of strongly non-ideal mixtures

A new equation for correlation of the thermodynamic excess functions of mixing, based on considerations of geometrical shape is proposed. Use of this equation for the correlation of heat of mixing data and vapour-liquid equilibrium data is proposed. The possibility of predicting multicomponent vapour-liquid equilibrium from binary data by using the proposed equation is shown. The equation is especially useful for correlating the excess functions of strongly non-ideal systems and for checking thermodynamic consistency of vapour-liquid equilibrium data.     

Critical points of adsorbed phases using a 2D lattice gas equation of state

The types of critical phase diagrams for adsorbed binary mixtures that can be predicted by an equation of state (EOS) based on a two-dimensional lattice gas theory are investigated. The search for critical point conditions was done using the Hicks and Young algorithm, switching to the Heidemann and Khalil algorithm in the close of vicinity of a critical point. We observed that the model can predict critical points that represent the conditions in which a vapor-like and a liquid-like adsorbed phases collapse. The critical diagrams were classified using an analogy with the van Konynenburg and Scott scheme for classifying the critical behavior of binary bulk mixtures. The original classification scheme is based on the critical lines on the pressure–temperature plane; we used a straightforward extension based on the critical lines on the spreading pressure–temperature plane. Five of the six types of phase behavior classified by von Konynenburg and Scott were observed using this thermodynamic model. The transitions between the types of phase diagram were also observed in temperature–mole fraction projections. These results extend previous observations that suggested the possibility of very interesting phase behaviors for adsorbed mixtures. However, experimental data would be necessary to confirm the predicted types of critical diagrams.