Mathematical modeling of a liquid-liquid phase-transfer catalyzed reaction system.

Abstract

This paper presents a new mathematical model for the dynamics of a liquid-liquid phase-transfer catalyzed batch reaction system. The model is formulated as a system of coupled nonlinear differential and algebraic equations in which the differential equations describe the slow reactions in the organic phase, whereas the algebraic ones describe the rapidly established dissociation equilibria in the aqueous phase and the mass balances of the species. A two-stage optimal parameter estimation method is used to estimate the values of the model parameters, such as the reaction rate constants, the overall mass transfer coefficients, the distribution coefficients, and the dissociation constants, from the experimental data. The reversible reaction between organic-phase benzyl chloride and aqueous-phase sodium bromide, with tetrabutylammonium bromide as a catalyst, was carried out to verify the mathematical model. Simulation results reveal that by the proposed model one can successfully make a correct judgement as to whether the quaternary onium salts in the two phases are in extractive equilibrium. Also, one can explicitly determine the respective contributions of the reaction and the mass transfer to the overall rate. Moreover, the fact that a high-concentration inorganic salt in the aqueous phase salts out the quaternary onium salts into the organic phase and thereby alters the distribution coefficients of the phase-transfer catalysts can be explained by our model.