Variable target mass‐exchange network synthesis through linear programming

A mass‐exchange network (MEN) synthesis problem is considered with streams whose target compositions are allowed to vary between upper and lower bounds. The design task is to determine the minimum mass separating agent (utility) cost needed for the transfer of a single component from the rich to the lean streams. The mathematical formulation of this synthesis problem leads to a mixed integer nonlinear program. In this work, we propose a novel formulation of the problem that leads to a linear program. Stream decomposition is employed in attaining this novel linear programming formulation and rigorous proofs are presented which establish that the two formulations have the same solution. The linear programming formulation reduces the complexity of the considered MEN synthesis problem, thus making feasible its solution even for large‐scale problems. Two examples, illustrating the procedure, are presented. Both demonstrate that significant utility cost savings can be achieved over the fixed composition MEN synthesis problem.