Vapor-liquid equilibrium predictions of refrigerant mixtures from a cubic equation of state with a G-EoS mixing rule

A modified excess Gibbs energy model which is based on the local composition concept and assigns a single energy parameter per pair of components, is incorporated into the G^E—EoS thermodynamic formalism for vapor-liquid equilibrium (VLE) calculations of simple and complex refrigerant mixtures. One temperature set of data close to 273 K is used to obtain the model's parameters, which are used to extrapolate the VLE at other temperatures and pressures. A one-parameter form of the model based on the Wong-Sandler mixing rule is presented for several simple systems. The physical significance of the model's energy parameter is connected to the preference of the mixture for like to unlike interactions. The model is applied for VLE predictions of the ternary system R14-R23-R13, and the results are compared to calculations using the 3PWS model [H. Orbey. S.I. Sandler, Ind. Eng. Chem. Res. 34 (1995) 2520–2525] and the van der Waals mixing rule. Modelling of a few complex systems with only three data points given at each temperature is shown with a two parameter version of our model on the basis of the Huron-Vidal mixing rule.     

A proposed equation of correlation for the study of thermodynamic properties (density,viscosity, surface tension and refractive index) of liquid binary mixtures

The literature on the physicochemical properties of liquid binary mixtures shows that most such systems exhibit nonlinear behavior. As a result, rigorous data and equations capable of affording a reliable estimate of the behavior of such mixtures are needed.     

Thermodynamics of liquid mixtures of krypton+ethane

The total vapour pressure, the excess Gibbs energy Q^E (at 115.77 K), the excess enthalpy H^E (at 117.0 K) and the excess molar volume V^E (at 115.77 K) are reported for liquid mixtures of krypton and ethane. The results are interpreted in the light of some recent statistical theories of liquid mixtures.     

Study of molecular properties using acoustic non-linearity parameter in the ternary liquid mixtures at different temperatures

The parameters of non-linearity (B/A) of ternary liquid mixtures, namely phenol and o-cresol with dimethyl sulfoxide (DMSO) in carbon tetrachloride have been evaluated at 293.15, 303.15 and 313.15?K. The non-linearity parameter has been computed by three different methods, namely Tong and Dong's method, Beyer's method and Beyer's method using Tong–Dong coefficients. The excess values of non-linearity parameter (B/A)^E have also been evaluated and discussed in the light of intermolecular interactions present in the liquid mixtures. Sehgal's relations for evaluating molecular properties for pure liquids are extended to ternary liquid mixtures.     

Application of Kirkwood-Buff theory of liquid mixtures to water-butanol system

The various integrals over the pair correlation functions G_AA' G_WW, and G_AW were calculated for the t-butanol(A)-water(W) system (0 to 8 mole % alcohol) at 25°C by utilizing the thermodynamic quantities, the isothermal compressibility, partial molal volumes, and vapour pressure and by the application of an inverse procedure for Kirkwood-Buff theory of solutions as suggested by Ben-Naim. It is observed that as functions of concentration G_AA', G_AW, and G_WW have extrema in the concentration range studied. The results are interpreted on the basis of structural changes of solvent water. The behavior of G_AA in the concentration range of 0 to 4 % of t-butanol indicates that the strength of hydrophobic interactions decreases with concentration as x_A increases from 0 to 0.04.     

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.     

A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

Prediction of excess thermodynamic functions and activity coefficients of some polymeric liquid mixtures using a new equation of state

In this work, the excess thermodynamic properties, namely excess molar Gibbs energy, excess molar enthalpy, excess molar entropy, excess molar internal energy, and excess molar Helmholtz energy for four polymer mixtures and blends at different temperatures, pressures, and compositions have been calculated using the GMA equation of state. We have also calculated the activity coefficient for these polymeric mixtures using the GMA equation of state. The values of statistical parameters between experimental and calculated properties show the ability of this equation of state in reproducing and predicting the excess thermodynamic functions and activity coefficients for studied polymeric mixtures.     

Application of the Quartic Hard Chain equation of state to polymer mixtures

The Quartic Hard Chain equation of state proposed by Kubic is a simple model for chain-like molecules. This study considers the application of this equation to polymer solutions. The equation was not found to be a useful predictive model because polymer parameters could not be reliably predicted from pure component properties. However, the equation was found to be a useful empirical form for representing polymer solution data. Because the Quartic Hard Chain equation is applicable to the vapour—liquid equilibria of normal fluids, this method is potentially useful for representing high pressure vapour—liquid equilibria in systems with dissolved polymer.     

Volumetric studies on binary mixtures of surfactants N,N′-bis(dimethyldodecyl)-1,2-ethanediammonium dibromide and 1-dodecyl-3-methylimidazolium bromide in aqueous solutions

The micellization of the binary mixed surfactants comprising of the Gemini surfactant N,N′-bis(dimethyldodecyl)-1,2-ethanediammonium dibromide and 1-dodecyl-3-methylimidazolium bromide has been studied by measurements of density. The apparent molar volumes were calculated for various surfactant concentrations and used to determine the critical micelle concentrations of the mixed surfactants at various compositions. An attractive effect was suggested by negative deviations of the experimental CMC values from the ideal ones. The Margules equation was applied to evaluate the micelle compositions, the activity coefficients of both components, and the excess molar Gibbs free energies of the mixed micelles. The stability of mixed micelles was shown to be enhanced as compared to those formed by single surfactants from the negative values of the excess Gibbs free energy. The comparison of the results obtained from the volumetric and ITC measurements indicated a reasonable good accordance with each other and confirmed the reliability of both methods for investigation on the properties of the mixed micelles.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Correlation of thermodynamic modeling and molecular simulations for liquid-liquid equilibrium of ternary polymer mixtures based on a phenomenological scaling method

In our previous study [S.Y. Oh, Y.C. Bae, J. Phys. Chem. B 114 (2010) 8948-8953], we presented a new method to predict liquid-liquid equilibria in ternary simple liquid mixtures by using a combination of a thermodynamic model and molecular simulations. As a continuation of that effort, we extend our previously developed method to ternary polymer systems. In the simulations, we used the dummy atoms to calculate the pair interaction energy values between the polymer segments and the solvent molecules. Furthermore, a thermodynamic model scaling concept is introduced to consider the chain length dependence of the energy parameters. This method was applied to ternary mixtures incorporating low to high molecular weight polymers. The method presented here well described the experimental observations using one or no adjustable parameters.     

A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.     

Liquids and liquid mixtures: Deduction of the BGY equation considering the angular distribution function

The Born→Green→Yvon equation for molecular fluid has been deduced considering the orientational distribution functions. The isotropic and anisotropic parts of the distribution function have been separated. The expressions deduced can be used in the case of mixtures and for the non-central type of intermolecular potential energy.     

Application of 1-1 modification of van der waals equation of state for saturated binary liquid mixtures

The Law-Lielmezs (L-L) modification of Van der Waals equation of state has been extended to include four hydrocarbon-hydrocarbon binary liquid mixtures for the saturated liquid-vapour equilibrium states. The values of the characteristic mixture p_m and q_m parameters have been calculated, and a relation between the values of these parameters and the molecular weight of binary mixture has been established. The proposed relation is compared with the results obtained by the use of Lielmezs, Howell and Campbell, and Soave 1980 modifications of the Redlich-Kwong equation of state.     

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.     

Thermodynamic study of (anthracene + phenanthrene) solid state mixtures

Polycyclic aromatic hydrocarbons (PAH) are common components of many materials, such as petroleum and various types of tars. They are generally present in mixtures, occurring both naturally and as byproducts of fuel processing operations. It is important to understand the thermodynamic properties of such mixtures in order to understand better and predict their behavior (i.e., fate and transport) in the environment and in industrial operations. To characterize better the thermodynamic behavior of PAH mixtures, the phase behavior of a binary (anthracene + phenanthrene) system was studied by differential scanning calorimetry, X-ray diffraction, and the Knudsen effusion technique. Mixtures of (anthracene + phenanthrene) exhibit non-ideal mixture behavior. They form a lower-melting, phenanthrene-rich phase with an initial melting temperature of 372 K (identical to the melting temperature of pure phenanthrene) and a vapor pressure of roughly lnP/Pa = −2.38. The phenanthrene-rich phase coexists with an anthracene-rich phase when the mole fraction of phenanthrene (x_P) in the mixture is less than or equal to 0.80. Mixtures initially at x_P = 0.90 consist entirely of the phenanthrene-rich phase and sublime at nearly constant vapor pressure and composition, consistent with azeotrope-like behavior. Quasi-azeotropy was also observed for very high-content anthracene mixtures (2.5 < x_P < 5) indicating that anthracene may accommodate very low levels of phenanthrene in its crystal structure.     

A new density-dependent mixing rule for the SRK equation of state

A new procedure for obtaining density-dependent mixing rules is applied to the Soave-Redlich-Kwong equation of state. The result is a one-parameter local-composition mixing rule which adequately represents the nonidealities possible in dense fluid mixtures but approaches the classical mixing rule at low densities. A three-parameter version of the mixing rule is also presented which allows for the local-composition effect in the low density limit. The expressions are tested with the Soave-Redlich-Kwong equation of state. Results for vapor-liquid and gas-liquid systems are discussed.     

Coherent thermodynamic model for solid,liquid and gas phases of elements and simple compounds in wide ranges of pressure and temperature

Thermodynamic modeling of fluids (liquids and gases) uses mostly series expansions which diverge at low temperatures and do not fit to the behavior of metastable quenched fluids (amorphous, glass like solids). These divergences are removed in the present approach by the use of reasonable forms for the “cold” potential energy and for the thermal pressure of the fluid system. Both terms are related to the potential energy and to the thermal pressure of the crystalline phase in a coherent way, which leads to simpler and non diverging series expansions for the thermal pressure and thermal energy of the fluid system. Data for solid and fluid argon are used to illustrate the potential of the present approach.