An improved algorithm for solving the mass balance equations in multistage separation processes

Abstract

Abstract The reliability and efficiency of any method of solving the equations that describe multicomponent, multistage, counter‐current separation processes depend on the accuracy and efficiency of the algorithm that is employed to solve the component mass conservation (CMC) equations. Previous investigators have shown that ordinary Gaussian elimination is very efficient for solving the CMC equations when they are expressed in tridiagonal form. The present work, however, demonstrates that this procedure is subject to excessive round‐off error under certain conditions. In such cases, the error can be reduced to insignificant levels by using a newly developed algorithm based on recursion formulas derived specifically to treat the tridiagonal system of CMC equations.