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

• An efficient method for calculating the roots of the Underwood's equations.
• Roots are found accurately by fast-converging series without computational difficulty.
• Unlike prior works, the scheme is semi-analytical and does not need a first guess.
• The method is much superior to the Newton–Raphson algorithm in terms of robustness.

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.