An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids

Abstract

In this study, an efficient iterative algorithm is devised to handle a nonlinear equation arising in estimation of thermodynamic properties at supercritical conditions. The approach is based on a synergistic combination of the classic Newton-Raphshon algorithm and the Adomian decomposition method. We demonstrate that the proposed method enjoys a higher degree of accuracy while requiring fewer iterations to reach a specific solution compared to that by the Newton-Raphson algorithm. To illustrate the efficiency of the aforementioned solution technique, several numerical examples are provided. The proposed method has been easily implemented in computer codes to provide parametric, not just numeric, solutions to the model equations. Consequently, one can derive other thermodynamic properties, which have not been treated parametrically to date, based on our new combined approach.

Keywords:

• Adomian decomposition method
• Adomian polynomials
• Iterative scheme
• Quintic EOS
• Supercritical fluids
• Thermodynamic properties

Acknowledgments

The authors would like to express their sincere gratitude to the editors and reviewers of Chemical Engineering Communications whose comments and suggestions have indeed improved the quality of this article.

Notes

¹Ideal gas assumption is taken as the initial guess for both methods.

²Measured in seconds. The simulations have been performed on a PC with a 2.66 GHz processor and 2.00 GB of RAM.

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