Mathematical model of the liquid membrane extractive column. Sensitivity to operating parameters

Abstract

The extraction-back extraction column of low concentration species by means of an organic closed loop flow, considered as liquid membrane, was modelled then simulated, using some simplifying assumptions. The main hypotheses are: the aqueous phase is perfectly mixed, the drops of the organic phase are lumped into a plug-flow inner cylinder co-axial with the aqueous phase, and the organic phases under the sieve and on the top of the column are perfectly mixed also. The dynamic model of the extraction-back extraction column is, then, applied to the recovery of the hydrocarboxylic acids. The mathematical model, reduced through orthogonal collocation to a system of ordinary differential equations, was solved using a self-adaptive (RK)-type method. Its validation was done based on batch experimental data; the optimal model parameters (the specific mass transfer coefficients for both extraction and back-extraction zones), ensuring the agreement with the experiment, were found by means of a modified genetic algorithm technique. Then, a sensitivity analysis was done, to grasp the behaviour of the system with respect to the main operating parameters - the organic flow in the closed loop, the partition coefficient and the buffer volume.