EXPERIENCE WITH ADOPTING ONE-PARAMETER IMBEDDING METHODS TOWARD CALCULATION OF COUNTERCURRENT SEPARATION PROCESSES

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Abstract
The one-parameter imbedding method (also called homotopy or continuation) was adopted toward solution of large sets of nonlinear algebraical equations describing counter-current separation processes. Different imbedding functions were tested on a spectrum of difficult distillation problems ranging from distillation of hydrocarbons to strongly nonideal distillation problems. For the one-parameter imbedding functions studied in this report the classical Newton-Raphson Formula can be easily generated after an appropriate selection of the control parameters. Two different approaches were used to solve the homotopy equations: i) marching integration, ii) sequential use of the Newton-Raphson method. The one-parameter imbedding technique represents a trade-off between robustness and computation time. The algorithm is more robust than the Newton-Raphson technique, however, the computational time is usually higher. A combination of the one-parameter imbedding and the Newton-Raphson approach seems to be a very efficient method, the solution is approached by the one-parameter imbedding technique and the Newton-Raphson method is used to finish the iteration process. Geometrical interpretation of convergence is presented.