Benjamin C.-Y. Lu

Surface tension of aqueous electrolyte solutions at high concentrations - representation and prediction

Abstract A calculation method was developed for representing and predicting surface tension of aqueous electrolyte solutions over a wide range of concentrations, up to 36 m. Based on the Gibbs dividing surface concept, the Langmuir adsorption equation was adopted for modeling the surface excess of electrolyte(s). The activities of electrolytes in the aqueous solutions were calculated by the Pitzer equation. The surface tensions for 45 aqueous single-electrolyte systems at a single temperature were used to correlate the model parameters, and the correlation yields an overall average absolute percentage deviation (AAPD) of 0.47. Surface tensions for 23 aqueous inorganic electrolyte systems are available at several temperatures. Application of these model parameters to extrapolate surface tensions of these systems to different temperatures yields an overall AAPD of 0.91. The proposed method was successfully applied to predict surface tensions for an aqueous binary electrolyte system containing a free acid (HNO 3 ) and its salt (KNO 3 ), which have opposite effects on surface tension with an increase in their concentrations, with an overall AAPD of 1.87. The predicted surface tensions for additional 11 binary and five ternary mixed-electrolyte aqueous systems indicate an overall AAPD of 1.69.

A molecular model for representing surface tension for polar liquids

Abstract An expression based on molecular thermodynamic considerations was developed for representing surface tensions of pure polar liquids and their mixtures. Contributions to surface tension from hard spheres, dispersion, and polar–polar interactions were considered and assumed to be additive in the development. The Davis theory (J. Chem. Phys. 62 (1975) 3412, Adv. Chem. Phys. 49 (1982) 357) and the simplified radial distribution function expression of Xu and Hu (Fluid Phase Equilibria 30 (1986) 221) were adopted in the model development. Two pair-potential parameters, size and energy, were used for each pure fluid. In addition, one adjustable parameter was used for each binary system, but two adjustable parameters were required for binary systems containing water. The average absolute percentage deviations obtained for arbitrarily selected 22 pure polar compounds, 12 non-aqueous binary polar systems and four binary aqueous systems (excluding ethanol + water and 1-propanol + water) are 0.59, 0.58 and 2.40, respectively. In addition, the proposed approach was extended to mixtures containing polar and non-polar compounds with reasonably good results. Feasibility of the proposed model for predicting surface tension for multicomponent (ternary) mixtures was demonstrated.

On the application of cubic equations of state: Analytical expression for α/Tr and improved liquid density calculations

Abstract An analytical equation has been developed for the quantity α/ T r , in the subcritical region of pure fluids for the van der Waals type cubic equations of state, and expressed as a function of the ratio P r / T r and Ω ac . A new approach using an exact fit of two saturated liquid densities was adopted to determine two of the cubic equation parameters. The calculated densities for pure liquids in subcooled conditions or at saturation as well as for mixtures at saturation conditions were much improved on those obtained from the linear volume-translation technique.

A simplified perturbed hard chain theory equation of state for phase equilibrium calculations for polar fluid mixtures

Abstract A simplified perturbed hard chain theory (PHCT) equation of state was proposed for vapor—liquid equilibrium calculations for highly non-ideal mixtures containing one or more polar components. In the proposed expression, Z involves three terms. The Z (repulsion) term is based on the expression of Carnahan-Starling for hard spheres. The Z (attractive non-polar) term follows the expression of Alder et al. but simplified as suggested by Gmehling, Liu and Prausnitz. In the formulation of the third term, the Z (polar) term, the multipolar expressions of Gubbins and Twu were adopted but much simplified. The adjustable parameters were evaluated for a variety of pure fluids, including water, acetone, alcohols, acids, esters and a number of hydrocarbons. Average absolute percent deviations in the calculated vapor pressures and saturated liquid densities for these substances are 0.67 and 1.68, respectively. The calculated vapor—liquid equilibrium values for non-polar—polar and polar—polar mixtures are in good agreement with the experimental values and are comparable with the results obtained from more elaborated versions of the PHCT equation.

On the determination of minimum reflux ratio for a multicomponent distillation column with any number of side-cut streams

Abstract The proposed method is general for an ideal multicomponent distillation column with one feed, but with any number of side-cut liquid streams, in addition to the distillate and bottoms. In the derivation, the location and number of pinch points, the analysis of the column, the influence of the presence of the side-cut streams on the characteristic equation and its roots, and the degress of freedom are determined. The calculation procedure together with sample calculation are presented using a hypothetical ten-component mixture to illustrate the numerical evaluation.

Density-dependent local-composition mixing rules for cubic equations of state

Abstract A computer simulation technique (Monte Carlo method) using 256 particles was carried out to determine the local compositions of the “LB 2” model mixture, and the local composition ratio τij (r) was found to be density dependent. A mole fraction dependence was introduced in this work instead of the density dependence and used to develop the Wilson type and Renon-Prausnitz type mixing rules for the parameters “a” and “b” of the van der Waals equation. However, the calculated vapor-liquid equilibrium values indicate that strong density dependence of local composition mixing rules is not generally necessary in VLE calculations using cubic equations of state.

Temperature Dependence of the Cohesion Parameter for Calculating Binary VLE Values for Systems Containing Helium and Neon

The temperature functions for representation of the cohesion parameter “a” of the van der Waals type cubic equations of state have been analyzed in both the subcritical and supercritical regions. The most suitable values of Ωac (=acPc/R2T c 2 ) for representation of vapour pressures of alkanes are found to be 0.4484 and 0.4254 for the Soave and the exponential functions, respectively. These results indicate that the Soave function is better suited for the Peng-Robinson equation; and the exponential functions, for the van der Waals, Redlich-Kwong and Soave-Redlich-Kwong equations. In the vapor-liquid equilibrium (VLE) calculations for systems containing helium and neon, which have very low critical temperatures, binary data have been used to determine the optimal value of Ωa (=aPc/R2T c 2 ) in the supercritical region. The temperature functions developed for these two gases have been successfully applied to VLE calculations for eight helium-containing, three neon-containing and helium-neon systems.

Effect of Cohesion Parameter on VLE Calculations

Vapor-liquid equilibrium (VLE) values are frequently calculated by means of cubic equations of state. The general form of these equations can be expressed in terms of the summation of a repulsive term, containing a covolume parameter “b”, and an attractive term, containing a cohesion parameter “a”.

Evaluation of Mixing Rules for VLE Calculations

Recently, the performance of several cubic equations of state has been evaluated1 for their representation of vapor-liquid equilibrium (VLE) values for 27 binary systems, including hydrocarbon-hydrocarbon, nitrogen-hydrocarbon, hydrogen sulfide-hydrocarbon and carbon dioxide-hydrocarbon mixtures. VLE values for some of the systems were reported at cryogenic temperatures. The cubic equations investigated include the Redlich-Kwong (RK) equation2 as modified by Soave3 (SRK), the Peng-Robinson (PR) equation4, the Martin equation5 as modified by Joffe6, the three-parameter RK equation7 and the four-parameter (ALS) equation8 proposed by Adachi et al., and the van der Waals equation9 with its parameter “a” considered temperature dependent (MVDW)1. The calculated results indicate that for the normal fluid mixtures tested, the MVDW equation can achieve the same satisfactory results for VLE calculations as those obtained from the other five cubic equations. In the calculation, the following set of mixing rules (MR I) was used in all the six equations of state: