A comprehensive global optimization approach for the synthesis of heat exchanger networks with no stream splits

The mathematical programming approach for the synthesis of heat exchanger networks provides a powerful, and versatile framework for the simultaneous optimization of energy consumption, area, and stream matches. Nevertheless, nonconvexities introduced by the logarithmic mean temperature difference (LMTD), the heat transfer equation, the energy balances for mixers or splitters, and the concave area cost functions to mathematical models often give rise to multiple local optimum solutions. In this paper a rigorous global optimization method is presented for the synthesis of heat exchanger networks under the simplifying assumption of no stream splitting. We present a new class of approximating planes that bound the LMTD from above, and a convex mixed integer nonlinear programming (MINLP) model that is linearly constrained, and predicts lower bounds for the minimum total annual cost of the network. This convex MINLP model is embedded within a branch and bound algorithm that performs a spatial search in the domain of the network temperatures. The solution of the lower bounding MINLP model also provides a set of promising network configurations that are globally optimized to search for the global optimum network configuration and operating conditions. This last set of global nonlinear programming (NLP) problems is solved by applying a specialized version of the branch and contract algorithm proposed by Zamora and Grossmann (1996b) for the global optimization of problems with bilinear and linear fractional terms.