An Improved Restarted Adomian-based Solution for the Minimum Reflux Ratio of Multicomponent Distillation Columns

Abstract

An improved version of powerful Adomian decomposition method (ADM), namely Restarted Adomian decomposition method (RADM), has been employed to find the roots of Underwood’s equations. Underwood’s equations frequently appear in the design of multi-component distillation columns and are used to get a quick estimate of minimum reflux ratio. However, due to highly nonlinear nature and presence of singularities, these equations pose convergence-related difficulties. In this communication, it is shown that RADM is not only capable of overcoming these difficulties but also the values of residual errors show that the RADM-based solutions are superior to the recently developed ADM-based solutions as well as to those obtained by using the well-known Newton–Raphson method. Besides, unlike ADM, the proposed RADM does not require convergence accelerators such as Shanks transformation and only few terms are needed to get the accurate results.

Keywords:

• Underwood’s equations
• Adomian decomposition
• Nonlinear algebraic equations
• Shanks transformation

Acknowledgements

The authors are highly indebted to the anonymous reviewers for their valuable suggestions which have really helped in improving the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.