Efficient and robust three‐phase split computations

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 Rachford–Rice equations. In this work, we present examples of various degree of complexity to demonstrate powerful features of the combined bisection‐Newton method in three‐phase 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. © 2010 American Institute of Chemical Engineers AIChE J, 2011