Novel Mathematical Approaches for the Structural Synthesis of Heat Exchanger Networks

Abstract

This work presents new systematic approaches for the synthesis of heat exchanger networks (HENs) relying on efficient optimization models. The basic idea consists of partitioning the process streams into a set of nonoverlapping substreams with variable temperatures ranges and exchanging heat among such hot and cold substreams. The problem objective is to synthesize the configuration of the HEN featuring either minimum utility usage or minimum total cost, even if stream splitting is required. First, a mixed-integer linear programming (MILP) model is introduced to systematically find the detailed structure of HENs reaching the minimum utility usage (MUU) target with the minimum number of units. Isothermal mixing of the stream branches is assumed, and a fixed minimum approach temperature (ΔTmin) is arbitrarily chosen. The model is then generalized to minimize the HEN total cost, including the capital cost, by considering the minimum approach temperature as a new problem variable. As a result, nonlinearities arise in the objective function, leading to a mixed-integer nonlinear (MINLP) formulation. The MINLP also includes nonlinear constraints when nonisothermal mixing is allowed. Both simultaneous approaches have been validated by efficiently solving 45 benchmark examples from the literature. Compared to previous contributions, savings of up to 37% in the total costs have been achieved.