Convergence promotion in the simulation of chemical processes with recycle‐the dominant eigenvalue method

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Abstract
A new method, called the dominant eigenvalue method, is described for promoting the convergence of iterative computations of non‐linear problems, such as chemical processes with recycle. The method is based upon the observation that most iterations eventually approach a geometric progression. In the derivation it is assumed that the iteration can be approximated by a linear matrix difference equation, The iteration continues until the largest eigenvalue of A dominates the solution. It may be used to extrapolate toward the solution before resuming the iteration.The method is applied to the steady‐state simulation of two chemical processes, an alkylation plant and a distillation column. The computation time was reduced by up to a factor of four.

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