Group‐contribution estimation of activity coefficients in nonideal liquid mixtures

Abstract

and Pratt (1933) contained lower values of holdup (most values were < 10 % ) , and V, was shown to be more nearly constant. At low values of holdup, there is little difference between V, and V,. Generally, V, is believed to be a more useful correlating parameter over a wide range of holdup values. However, neither of the parameters is as accurate as one may desire, and improved correlations, especially those with a theoretical basis, are needed. ACKNOWLEDGMENT This work was sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation. The authors would like to express their appreciation to John S. Taylor, R. 0. Payne, and several students and Directors of the Massachusetts Institute of Technology Chemical Engineering Practice School who made most of the measurements and otherwise assisted in the study.NOTATION a = d p = vc = Vc.f -v d = --Vd,f v, = cm2 of packing surface/cm3 of packing volume diameter of packing, cm superficial velocity of the continuous phase, cm/s superficial velocity of the dispersed phase, cm/s superficial continuous phase velocity at flooding, cm/s superficial dispersed phase velocity at flooding, cm/s characteristic velocity defined by Equation (6), cm/s V, Greek Letters Ap phases, g/cm3 E p = viscosity, poise AVc,01/2 = defined by Equation (5) AV,,01/2 = defined by Equation ( 5 ) Subscripts c, d = continuous and dispersed phases, respectively o = intercept value; flow rate of other phase ap-= superficial slip velocity, cm/s = difference in densities of dispersed and continuous = void fraction of the packing, dimensionless proaching zero A group-contribution method is presented for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method combines the solution-of-functional-groups concept with a model for activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). The resulting UNIFAC model (UNIQUAC Functional-group Activity Coefficients) contains two adjustable parameters per pair of functional groups. AAGE FREDENSLUND, RUSSELL L. JONES, and JOHN M. PRAUSNITZ V IBy using group-interaction parameters obtained from data reduction, activity coefficients in a large number of binary and multicomponent mixtures may be predicted, often with good accuracy. This is demonstrated for mixtures containing water, hydrocarbons, alcohols, chlorides, nitriles, ketones, amines, and other organic fluids in the temperature range 275O to 400OK.

Solid-liquid equilibrium of triolein with fatty alcohols

“…In the present work, solid-liquid equilibrium data on two fatty mixtures, triolein + 1-octadecanol and triolein + 1-hexadecanol, were measured by differential scanning calorimetry (DSC), evaluated with optical microscopy and modeled by resolution of the thermodynamic equilibrium equations using the twoand three-suffix Margules equations, the original UNIFAC (Fredenslund et al, 1975) and the modified UNIFAC-Dortmund model (Gmehling et al, 1993) for calculation of the liquid-phase activity coefficient. An optimization algorithm was implemented in MATLAB for prediction of the melting point.…”

“…According to the UNIFAC model (Equations (6) to (17)) (Fredenslund et al, 1975), the activity coefficient can be written as the sum of a combinatorial contribution C i γ , which accounts for the effects of size and shape, and a residual contribution R i γ , which accounts for interactions among groups. and Q k are the structural parameters for the groups and a nm is the temperature-dependent groupinteraction parameter (Reid et al, 1987).…”

“…The activity coefficients in the solid-liquid equilibrium can be estimated with adjustable models such as the Margules equation or with predictive methods such as the group-contribution UNIFAC model (Fredenslund et al, 1975;Gmehling et al, 1978;Chiavone Filho and Rasmunsen, 2000;Coutinho et al, 2001), both based on the calculation of excess Gibbs free energy.…”

Assessing the reliability of predictive activity coefficient models for molecules consisting of several functional groups

“…The group contribution method UNIFAC and the COSMO-based models are Gibbs excess free energy (G E ) models, which allow the prediction of liquidphase activity coefficients i γ as a function of temperature and composition (Fredenslund et al, 1975). In both families of models the activity coefficient is calculated as the sum of a combinatorial and a residual part:…”

An empirical method to correlate and predict solute distribution in ternary liquid-liquid systems

“…Using a model f or the activity coefficients calculations can be carried out to obtain liquid-liquid compositions (Sørensen et al, 1979b). Two models were used in our calculations: UNIQUAC (Abrams and Prausnitz, 1975) and UNIFAC (Fredenslund et al, 1975). The data, equations, parameters and programs were taken from Sørensen and Arlt (1980) and Magnussen et al (1981).…”