Comparison of Benedict—Webb—Rubin and back equations of state for use in P—V—T calculations

By means of the available experimental gas and liquid state volumetric data, the relative predictive accuracy of the Benedict—Webb—Rubin and BACK equations was compared at the low, intermediate and critical state range of temperatures and pressures for methane, ethane and ethylene.The average absolute volumetric deviation percent values calculated over the T—P range studied, showed that for both the BACK equation and the simpler Benedict—Webb—Rubin equation their accuracy levels increase when both pressure and temperature decrease; but the BACK equation proves superior for calculations performed at the critical and in the liquid states.     

Bubble pressures and saturated liquid molar volumes of trichlorofluoromethane—chlorodifluoromethane mixtures. Representation of refrigerant-mixtures vapor—liquid equilibrium data by a modified form of the Peng—Robinson equation of state

Experimental vapor—liquid equilibrium data and saturated liquid molar volumes of chlorodifluoromethane—trichlorofluoromethane binary mixtures have been obtained at four temperatures (298.15, 323.15, 348.15 and 373.15 K) using apparatus described previously.The experimental vapor—liquid equilibria are represented well by a modified form of the Peng—Robinson equation of state with one interaction parameter, but the mean deviation between the calculated and experimental densities is 5%.Vapor—liquid data for binary refrigerant mixtures from the literature are treated using the modified form of the Peng—Robinson equation of state with one adjusted interaction parameter in the mixing rule for a. The representation is fair and is not improved by introducing an additional parameter in the mixing rule for b.     

A three-parameter cubic equation of state for asymmetric mixture density calculations

A new three-parameter cubic equation of state of the van der Waals type with one parameter temperature dependent, P = RT/(V − b) − a(T)/[V(V + c) + b(3V + c)], has been developed for representation of liquid volumes (or densities) for asymmetric mixtures such as CO₂C₁₉ and C₁C₁₀. The calculated results are better than those obtained from the two-parameter Peng—Robinson equation, the three parameter Schmidt—Wenzel equation, the volume-translated Soave—Redlich—Kwong equation proposed by Peneloux et al., and the volume-translated Peng—Robinson equation developed in this work. The parameters of the new equation have been generalized in terms of the acentric factor ω and reduced temperature T_r.     

Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state

Stryjek, R. and Vera, J.H., 1986. Vapor—liquid equilibrium of hydrochloric acid solutions with the PRSV equation of state. Fluid Phase Equilibria, 25: 279–290.The PRSV cubic equation of state and a new Margules-type composition-dependent mixing rule previously proposed have been used to correlate vapor—liquid equilibrium data for hydrochloric acid solutions. In total, four adjustable parameters are used for pure hydrogen chloride, pure water and their mixtures. The two binary parameters are determined from azeotropic point data. Results obtained for this highly nonideal system, presenting negative deviations from ideality, are better than those obtained with the modified cubic equation of Gibbons and Laughton.     

Comparison of two hard-sphere reference systems for perturbation theories for mixtures

The Carnahan—Starling equation of state for hard spheres can be extended to mixtures using either a one-fluid theory, or the generalization of scaled-particle (or Percus—Yevick theory) proposed by Boublik and by Mansoori and coworkers. The two reference systems are combined with a perturbation term of the van der Waals form; they are then used to correlate the phase behavior of binary mixtures of nonpolar molecules differing significantly in molecular size. In each case, one adjustable binary parameter (a₁₂) is used to correlate vapor—liquid equilibria over the entire composition range. Predicted Henry's constants and liquid densities for the saturated mixture are compared with experiment. The Boublik—Mansoori hard-sphere-mixture equation is superior to the Carnahan—Starling One-Fluid theory, expecially in the dilute region.     

Vapour—liquid equilibrium T—x measurements by a new semi-micro method

A semi-micro method for determining the boiling temperature of a liquid mixture using a thermistor is described. Boiling temperatures of the binary mixtures n-heptane—toluene, toluene—n-octane and 1-n-octene—n-octane were determined as functions of the composition. The isobaric T—x values were used to compute equilibrium vapour composition by numerical integration of the Duhem—Margules equation. The T—x—y values are presented at 101325, 79993 (or 85326), 53329 and 26664 Pa.     

A note on the temperature dependence of the coordination number

An empirical equation describing the temperature dependence of the coordination number of a molecule in a liquid is examined in terms of Bernal's model for the liquid state. To effect this comparison the non-associated compound n-C₁₁H₂₄ is chosen to represent the temperature span of the empirical equation. Predictions from Bernal's model based on volume expansion and latent heat data are in good agreement with the empirical correlation.     

A new mixing rule—modified conventional mixing rule

The asymmetry of the corrective cohesion parameter a^c against the mole fraction is found out to be a controlling factor of the vapour—liquid equilibrium(VLE) calculations.A new mixing rule which satisfies the asymmetry of a^c and has two adjustable parameters is proposed for systems containing strongly polar substances. Furthermore, it still keeps the functional form of the conventional mixing rule.The parameters of the proposed mixing rule for the MVDW equation of state are correlated by the system temperature and well applied to the ternary systems containing strongly polar substances.     

A modification to the Peng–Robinson-fitted equation of state for pure substances

In this work we present two modifications to the Peng–Robinson-Fitted equation of state where pure component parameters are regressed to vapor pressure and saturated liquid density data. The first modification (PR-f-mod) is a method that enhances the equation of state pure component property predictions through simple temperature dependent pure component parameters. In the second modification (PR-f-prop) we propose a temperature dependency for co-volume b in the repulsive parameter of the EoS, and revise the temperature function in the attractive term. The agreement with experimental data for 72 pure substances, including highly polar compounds, is remarkably good. We obtain average absolute deviations in saturated liquid density of less than 1% for all substances studied.     

Vapor—liquid equilibrium measurements for the methanol—acetone system at 372.8, 397.7 and 422.6 K

A static high pressure equilibrium facility has been used to obtain P − x − y measurements for the methanol—acetone binary for the three isotherms 372.8, 397.7 and 422.6 K. These measurements show that maximum pressure azeotropic behaviour exists at each of these temperatures. The data obtained have been correlated satisfactorily using the three suffix Margules equation. A comparison has been made between the information resulting from this study and the high pressure data of Griswold and Wong. Parameters of the three suffix Margules equation have been correlated with temperature over the range 285–425 K using additional vapor—liquid equilibrium and excess enthalpy data available in the literature. These correlations have been used to predict isobaric behavior. Auxiliary expressions have been developed which relate azeotropic pressure and composition to temperature.     

Description of cyclopropane with Backone equation of state

This paper aims to accurately describe the thermodynamic properties of Cyclopropane with a molecular based BACKONE equation of state. The parameters of the BACKONE equation of state found by fitting to experimental vapor pressures and liquid densities are the characteristic temperature T ₀, characteristic density ρ₀, anisotropy factor α, and reduced quadrupolar moment Q*². The values of these parameters are 393.9583 K, 6.076139 mol/L, 1.295445, and 0.699483, respectively. The average absolute deviation between experimental values and those derived from BACKONE EOS is 0.29% for vapor pressures, 0.75% for saturated liquid densities. The prediction power of the BACKONE equation of state are investigated. It is shown that the uncertainties of values derived from the BACKONE equation of state are within 0.90% for isobaric densities in the liquid phase and 2.0% for enthalpy of evaporation.     

Phase equilibrium calculations of highly polar systems

It is well known that highly polar and hydrogen bonding mixtures pose a serious challenge to equations of state. In the present report it is shown that excellent correlations and predictions of complex systems can be achieved when the van der Waals mixing rules are properly associated with an equation of state. In this report the proper form of the van der Waals mixing rules is used with the Peng—Robinson equation of state to predict the vapor—liquid equilibrium properties of water—ketone, water—alcohol, alcohol—ketone, and other complex mixtures, which exhibit either positive or negative azeotropy, with an accuracy which was not achievable by the original form of Peng—Robinson equation of state of mixtures.     

Characterization and gas permeation of polycarbonateliquid crystal composite membrane

Polymer/liquid crystal composite membranes were cast from a 1,2-dichloroethane solution of polycarbonate (PC) and N-(4-ethoxybenzylidene-4'-n- butylaniline) (EBBA). The mixing state of the polymer/liquid crystal composite membrane was investigated on the basis of differential scanning calorimetry, x-ray, density, sorption isotherm and sorption—desorption studies and also by electron microscopic observations. EBBA molecules in the composite membrane exist in an almost molecularly dispersed state up to an EBBA fraction of 30 wt%, and in the case of EBBA fractions above 30 wt% form a crystal domain as the mutual continuous phase among the network of polycarbonate fibrils. The composite membrane containing EBBA of 60 wt% can be handled as a homogeneous medium when considering gas permeation.The diffusive permeability coefficient to water reveals a distinct jump in the vicinity of the crystal—liquid crystal phase transition temperature of EBBA. The permeability coefficients, P, to hydrocarbon gases increases 100-200 times over several degrees in the phase transition temperature range. P for hydrocarbon gases decreases with increasing number of carbon atoms below the phase transition temperature, but increases with increasing number of carbon atoms above it. These results suggest that the permeation process is predominantly controlled by diffusion mechanism below the transition temperature of EBBA, while the solubility factor significantly affects gas permeation above it.     

Liquid—liquid equilibria for the methanol—toluene—n-octane and methanol—toluene—n-hexane systems at 25°C

Ternary liquid—liquid equilibrium data have been measured for the methanol—toluene—n-octane and the methanol—toluene—n-hexane systems at 25°C. The results have been correlated using a modified Wilson equation.     

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.     

A perturbed hard-sphere equation of state for alkali metals

A perturbed hard-sphere equation of state, employing a basic frame proposed by Eslami [H. Eslami, J. Nucl. Mater. 336 (2005) 135–139] has been developed for alkali metals. Following the approach introduced by Ihm et al. [G. Ihm, Y. Song, E.A. Mason, J. Chem. Phys. 94 (1991) 3839–3848], the temperature dependence of the parameters a and b has been fitted to liquid density data for potassium. The scaling parameters that are used to reduce the temperature are the temperature and density at normal boiling point. The important improvement is to omit the adjustable parameters, the well depth and the location of the minimum of pair potential, which are required to apply the earlier equation of state of Eslami. The present EoS, which can be used without fitting parameters, reproduces the volumetric behavior of liquid alkali metals with a very good accuracy. Six hundred and ninety four data points at different pressures and temperatures are examined and the average absolute deviation of predicted liquid density data compared to experiment is 1.41%.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.