Straightforward determination of attenuation factor and treatment of nonphysical values for the Newton-Raphson method. An application to distillation system.

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  • AN APPLICATION TO DISTILLATION SYSTEM

Abstract

For solving a set of simultaneous non-linear algebraic equations the Newton-Raphson method is a powerful mathematical tool. If the number of unknown variables is not large and an appropriate initial set of variables is used, no problem occurs. But if the number of variables is extremely large, overcorrection often takes place in the course of calculation and the calculation fails to converge. To adjust these overcorrections, several techniques have been proposed.<br> In distillation problems, the number of unknown variables is generally very large. For this reason we have frequently met problems which never converge even if the above-cited techniques are applied. To solve such difficult problems, two techniques are newly presented in this report. The first is a straightforward determination of an optimum attenuation factor to reduce the scalar value of corrections. The second is a mapping technique, by which physically nonadmissible values can be converted into admissible ones. Solving numerical examples of distillation problems, it was shown that simultaneous usage of the techniques presented is useful for the Newton-Raphson method.

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