Approximating the minimum reflux ratio of multicomponent distillation columns based on the Adomian decomposition method

The Underwood's equations are very famous as they provide a shortcut method for evaluating the minimum reflux ratio of a multicomponent distillation column. In this paper, a semi-analytical tool for finding the roots of a practical form of the Underwood's equations is devised based on a reliable mathematical technique known as the Adomian decomposition method. Despite the discontinuities inherently present in the Underwood's equations, the proposed strategy rapidly yields highly accurate results without any difficulties. In contrast to many previous algorithms, the current method is robust and does not impose the need for any initial guess in course of solution. It is also shown that the proposed scheme can optionally be equipped with a nonlinear convergence accelerator known as the Shanks transform to become much more computationally efficient. Two multicomponent distillation problems are chosen and solved by the present approach for the sake of exemplification. (c) 2013 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.