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Entropy 2018, 20(6), 452; https://doi.org/10.3390/e20060452

Hybrid Newton–Successive Substitution Method for Multiphase Rachford-Rice Equations

1
School of Energy Resource, China University of Geosciences, Beijing 100083, China
2
Petroleum Engineering, Colorado School of Mines, Golden, CO 80401, USA
*
Authors to whom correspondence should be addressed.
Received: 4 May 2018 / Revised: 2 June 2018 / Accepted: 6 June 2018 / Published: 9 June 2018
(This article belongs to the Section Thermodynamics)
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Abstract

In multiphase (≥3) equilibrium calculations, when the Newton method is used to solve the material balance (Rachford-Rice) equations, poorly conditioned Jacobian can lead to false convergence. We present a robust successive substitution method that solves the multiphase Rachford-Rice equations sequentially using the method of bi-section while considering the monotonicity of the equations and the locations of singular hyperplanes. Although this method is slower than Newton solution, as it does not rely on Jacobians that can become poorly conditioned, it can be inserted into Newton iterations upon the detection of a poorly conditioned Jacobian. Testing shows that embedded successive substitution steps effectively improved the robustness. The benefit of the Newton method in the speed of convergence is maintained. View Full-Text
Keywords: multiphase equilibrium; Rachford-Rice equation; three-phase flash calculation; successive substitution; Newton method multiphase equilibrium; Rachford-Rice equation; three-phase flash calculation; successive substitution; Newton method
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Gao, R.; Yin, X.; Li, Z. Hybrid Newton–Successive Substitution Method for Multiphase Rachford-Rice Equations. Entropy 2018, 20, 452.

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