A new look at the Rachford-Rice equation

Leibovici, ClaudeF.; Neoschil, Jean

doi:10.1016/0378-3812(92)85069-k

Cited by 49 publications

(29 citation statements)

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“…In such a case, the bisection method provides a simple and robust solution. 12 The bisection method is very inexpensive and is guaranteed to converge fast for the solution to the two-phase Rachford-Rice equation. As a whole, the combination of stability analysis (for both phase stability testing and obtaining an initial estimate of the equilibrium ratios), successive substitution, and the Newton method is both efficient and robust.…”

Section: Introductionmentioning

confidence: 99%

Efficient and robust three‐phase split computations

2010

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The combination of successive substitution and the Newton method provides a robust and efficient algorithm to solve the nonlinear isofugacity and mass balance equations for two-phase split computations. The two-phase Rachford-Rice equation may sometimes introduce complexity, but the Newton and bisection methods provide a robust solution algorithm. For three-phase split calculations, the literature shows that the computed three-phase region is smaller than measured data indicate. We suggest that an improved solution algorithm for the three-phase Rachford-Rice equations can address the problem. Our proposal is to use a two-dimensional bisection method to provide good initial guesses for the Newton algorithm used to solve the three-phase RachfordRice equations. In this work, we present examples of various degree of complexity to demonstrate powerful features of the combined bisection-Newton method in threephase split calculations. To the best of our knowledge, the use of the bisection method in two variables has not been used to solve the three-phase Rachford-Rice equations in the past. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: [2555][2556][2557][2558][2559][2560][2561][2562][2563][2564][2565] 2011

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Section: Introductionmentioning

confidence: 99%

Efficient and robust three‐phase split computations

2010

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“…(40) for bounds of the WA window, denoted L-WA, and of the WA␣ window, denoted L-WA␣). Several previous works (Leibovici and Neoschil, 1992;Michelsen and Mollerup, 2004;Kocak, 2011;Li et al, 2012) used the mid-interval as starting point and this option was added for comparison (related to intervals = ˛k +1 − ˛k and to the WA solution window). As opposed to the similar in nature Rachford-Rice equation, using the quasi-convex function and switching to the convex function if an iterate goes out of bounds (FGH) does not improve the convergence speed.…”

Section: Influence Of the Initial Guessmentioning

confidence: 99%

“…Leibovici and Nichita (2010) (in a way similar to Leibovici and Neoschil, 1992 for the Rachford-Rice function) proposed the modified function…”

Section: A First Bound For a Solution Windowmentioning

confidence: 99%

Rapid and robust resolution of Underwood equations using convex transformations

Nichita¹,

Leibovici²

2014

Computers & Chemical Engineering

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“…(1) would become zero for values of c ¼ À1= K i À 1 ð Þ . This is likely to cause critical issues during massive computer simulation of actual industrial fractionators or oil reservoirs where the RRA needs to be iterated many, many times (typically several million times in practise) [2]. Traditional root-finding algorithms such as the Newton-Raphson method and its variants are not well suited for solving such multi-constituent chemical processes resulting in complex algebraic system models due to their reliance on a priori suitable guesses to initiate their repetitive iterations, because strongly nonlinear systems are well-known for extreme sensitivity to even a very small change of input, e.g., the so-called butterfly effect intrinsic to the Lorenz oscillator system, that dramatically alters the output; see Table 7 for an exemplar of characteristic N-R performance in a similar case.…”

Section: Introductionmentioning

confidence: 99%