Activity coefficient is a fundamental physical-property value required for the design of separation apparatus. Many models have been proposed for the calculations of activity coefficients. NRTL [1] and UNIQUAC [2] are widely used models for correlations of activity coefficients. A problem of these models is the calculated results of liquid-liquid equilibria for ternary system are usually over estimated from the experimental data when the binary parameters are determined with the constitutive binary systems [3].
The authors have proposed an activity coefficient model which is called CDSAP (Concentration dependent surface area parameter) model [4] to solve the problem. The model is based on the quasi-chemical theory. The surface area parameters in the model depend on partner molecules and concentrations. The parameters in the CDSAP model are surface area parameters (interaction numbers) and energy parameters (interaction energies) between molecules. A demerit in the model is an iterative procedure is necessary for more than 3 component systems, and calculation procedure is slightly complex.
In this study, a new model of excess Gibbs free energy was derived by the sum of the first 2 terms of Taylor series at 0 interaction energy for the excess Gibbs free energy of the CDSAP model. A new model for activity coefficients was derived by the excess Gibbs free energy. The parameters in the new model are (interaction number) x (interaction energies). This means that interaction number and interaction energies cannot be separately determined. The parameters in the new model also depend on partner molecules and concentrations. Any iterative procedures are not necessary in the new model.
The new model was applied to the activity coefficients of Lennard-Jones fluids which were calculated by molecular dynamics simulation [5,6]. The values of (interaction number) x (interaction energies) were obtained by molecular dynamics simulation. The calculated results of activity coefficients by the new model are in good agreement with those of Lennard-Jones fluids without any data fitting.
The new model was also applied to the phase equilibria of real systems. The parameters in the new model were obtained by data fitting to the real systems. The liquid-liquid equilibria for ternary systems and vapor-liquid equilibria for constitutive binary systems are calculated well by the new model with the same parameter set. The calculated results by the new model are much better than those by NRTL and UNIQUAC.
References
[1] H. Renon, J. M. Prausnitz, AIChE J. 14 (1968) 135-144.
[2] D. S. Abrams, J. M. Prausnitz, AIChE J. 21(1975) 116-128.
[3] T.F. Anderson, J.M. Prausnitz, Ind. Eng. Chem. Process Des. Dev. 17 (1978) 561-567.
[4] Y. Iwai,Y, Y.Yamamoto, Fluid Phase Equilibria 337 (2013) 165-173.
[5] Y. Iwai, I. Taniguchi, Y.Tada, Proceeding of 13th International Conference on Properties and Phase Equilibria for Products and Process Design, 22-26 May 2016, Hotel Solverde, Granja-Portugal. [6] Y. Iwai, R. Seki, Proceeding of Joint EMLG/JMLG Annual Meeting 2016, 11-16 September 2016, Platanias-Chania, Crete, Greece.
