Synthesis of Mass-Exchange Networks: A Mathematical Programming Approach

This chapter shows how optimization techniques enable designers to simultaneously screen all mass-separating agents (MSAs), even when there are no process MSAs, determine the minimum operating cost (MOC) solution and locate the mass-exchange pinch point, determine the best outlet composition for each MSA, and construct a network of mass exchangers with the least number of units that realize the MOC solution. The objective is to minimize the cost of MSAs that can remove pollutant from waste streams in a thermodynamically feasible manner. Because the flow rates of the MSAs are not known, the objective function as well as the material balances around composition intervals have to be written in terms of these flow rates. The solution of the optimization program determines the optimal flow rate of each MSA. The target compositions are only upper bounds on the outlet compositions and it may be necessary to optimize the outlet compositions. A shortcut method of optimizing the outlet composition is the use of “lean substreams.” Theoretically, an infinite number of substreams should be used to cover the whole composition span of each MSA. However, in practice, few substreams are needed. On the CID, the various substreams are represented against their composition scale. Having identified the values of all the flow rates of lean streams as well as the pinch location, now the number of mass exchangers for an MOC solution can be minimized.