Global Optimum Issues on Heat Exchanger Network Synthesis

To date, no published approach to grassroots heat exchanger design has been able to give a solution with the globally minimum cost. One source of the uncertainty of global optimality is the nonlinear programing (NLP) problem used to optimize the final heat exchanger network configuration. This NLP is nonconvex, and consequently has more than one locally optimal solution. As a result of these nonconvexities, conventional solution techniques cannot be guaranteed to reach the global solution. In this paper, an algorithmic approach is presented for overcoming nonconvexities. First, the sources of the nonconvexity are identified, then the sets of constraints and variables are partitioned into subsets, such that the nonconvex formulation is decomposed into convex subproblems. When this approach is applied to the network optimization problem, it is found that partitioning the variables into two subsets: (a) flowrates and (b) temperatures results in a decomposition of the original formulation into two convex subproblems. Using these convex subproblems in the Generalized Benders Decomposition Algorithm gives rise to an approach for determining the globally optimal heat exchanger network. The effectiveness of this approach is demonstrated with an example problem.