Efficient and robust three‐phase split computations

Abstract

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

Initialization of phase fractions in Rachford–Rice equations for robust and efficient three-phase split calculation

“…We have performed 1395 three-phase equilibrium computations for CO 2 mixing with the acid gas, oil B, Maljamar reservoir oil and Maljamar separator oil [2,4,11,12], and for a gas mixture containing 95 mol% CO 2 and 5 mol% CH 4 mixing with the Bob Slaughter Block oil and North Ward Estes oil [2,[13][14][15]. Some of the points are very close to the phase boundaries and the bicriticals.…”

“…This approach does not require the starting guess of ˇy and ˇz and in principle should always work. In this paper, we significantly improve the work by Haugen et al [4] and make it both robust and efficient. Eq.…”

“…Haugen et al [4] proposed that a sub-triangle is kept if both RR y and RR z have different signs at the three vertices and discard it otherwise. This criterion may keep a sub-triangle not containing the solution and may discard a sub-triangle containing the solution.…”

“…To avoid the confusion, we use the 'starting guess of ˇy anď z ' to represent the input (initial estimate) of the algorithm since the output (solution) will be the 'initial guess of ˇy and ˇz' to start the SSI in three-phase split calculation. Haugen et al [4] proposed the idea of a geometric approach -the two-dimensional (2D) bisection method, to solve Eq. (2).…”

“…A sub-triangle is discarded because RRy has the same signs at the three vertices although it contains the solution using the 2D bisection method by Haugen et al[4].The right-angle side in ˇy direction is only shown within [0.375,0.376] in the upper panel. The sub-triangle is defined by (0.375,0.125), (0.375,0) and (0.5,0).…”