Solution of MEN synthesis problems using MINLP: Formulations of the Kremser equation

摘要

One way of solving mass exchange network (MEN) synthesis problems is to formulate the synthesis task as a mixed integer non-linear programming problem. The solution of this optimisation problem delivers the desired MEN. In most cases, the objective function of the optimisation problem is the total annual cost. Assuming linear phase equilibrium relations, capital investment calculations of staged mass exchangers are most commonly based on the Kremser equation. Discontinuous functions, such as the Kremser equation, are difficult to formulate in an MINLP model. A new method is suggested for overcoming the difficulties arising from the discontinuity of the Kremser equation. Our new method is reliable and faster than the big-M, multi-M, simple logic, and convex-hull formulations applied for this particular problem. Our method is tested on a small and a large MEN synthesis problem. The solutions for four well-known MEN synthesis problems are also presented.