Simulation of countercurrent liquid-liquid extraction columns using an accelerated arclength homotopy continuation method

Abstract

In this work, the simulation of both non-equilibrium and non-isothermal liquid-liquid extraction processes was studied through the development of a robust algorithm, based on a new combination, comprising (1) an accelerated arclength homotopy continuation method, with both Broyden updating and asymptotic expansion, and (2) “Inside-Out” strategies. This compelling algorithm managed to exhibit convergence under the mathematical complexity of the rigorous MERSHQ equations (Material balances, Energy balances, Rate equations, Summation constraints, Hydraulic equations and eQuilibrium equations), including drop formation, drop coalescence and drop falling/rising as the accepted transport phenomena in sieve tray extractors.

The proposed method was validated by the simulation of the three well stablished problems: two examples related with experimental tests carried out in an extraction column for the systems water – acetone – toluene and water-acetic acid- methyl-isobutyl-ketone, and one theoretical example related with the recovery of butyric acid from aqueous solutions using xylene as solvent. In all cases, calculations are in good agreement with the experimental or theoretical data.

The algorithm herein developed contributes to new and more efficient computational performance towards the simulation of liquid-liquid extraction processes, as numerical drawbacks such as divergence, requirement of accurate initial estimates are overcome.