A new solution technique is proposed here for a specific kind of separation-network synthesis (SNS) problem, using Branch-and-Bound (B&B) framework and linear programming (LP). The suggested method determines effectively the structure and flowrates of the optimal separation network.
The method is illustrated by the solution of an SNS problem introduced in (Kovacs et al., 1995). The aim is to produce three pure product streams from two three-component feed streams with minimal cost. The rigorous super-structure of the problem is given by (Kovacs et al., 1995). The term itself was defined by Kovacs et al. (1999). The main idea is that it can be proved that the rigorous super-structure contains at least one optimal structure. The mathematical programming model generated from this rigorous super-structure is non-linear.
The goal of the present work is to determine the optimum of the aforementioned model effectively. The proposed method handles the splitting ratios of the dividers as intervals. A B&B method operates on these intervals. A branching step split one of the intervals. The bounding function approximates the concave cost functions of the separators. This function can be determined by solving LPs. The solution of the non-linear problem can be determined with arbitrary precision.