Feasible and locally optimal designs in the class of homogeneous, countercurrent, processing networks: two-component, non-sharp separations

Abstract A methodology is presented for finding feasible or locally optimal designs in the class of homogeneous, countercurrent, processing networks performing two-component, non-sharp separations. The advantage of the methodology developed here is that given a set of independent performance criteria (specifications such as network separation factor, beneficiation ratio or recovery), a feasible or locally optimal countercurrent network design meeting those criteria can be found in one step. In the methodology, graph-theory was used to obtain explicitly the exact network responses of specific countercurrent networks. These responses were used to formulate the linear recursion equations whose solution gives the expressions for the countercurrent network responses which are a function of the stage transfer functions for two-component, non-sharp separations. These expressions are also functions of the network variables n and c. These expressions, together with the set of independent design criteria, were solved simultaneously for n and c using the Levenberg-Marquardt algorithm for systems of constrained, nonlinear equations. The network variables n and c embody the coded network design information which is used to find the feasible network design which satisfies the set of independent performance criteria.