Distillation calculation by use of conjugated gradient method.

概要

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Distillation calculation by the nonlinear optimization technique is proposed. This method has the following objective function: φ(t) = Σwj(Xj-1)2)2→min.where t denotes the temperature vector, wj the weight factor and Xj=Σxj(i), and xj(i) is obtained by solving the tridiagonal matrix by making the component material balance for a given t. The temperature vector is corrected by the conjugated gradient method suggested by Fletcher and Reeves. From three numerical examples related to the separation of nC5 and nC6 fraction from nC5-nC9 mixture at atmospheric pressure, that of C2 fraction from C2-C3 mixture at high pressure and extractive distillation, it has been confirmed that the proposed method provides a stable solution as compared with the matrix methods by Amundson et al. and Saito et al., it retains the simplicity of the matrix method, and the storage required for the main array in this method is obviously less than that for the original gradient method by Naphtali et al.