HENS Unchained: MILP Implementation of Multi-Stage Utilities with Stream Splits, Variable Temperatures and Flow Capacities

Abstract

In this paper, we present an extended heat exchanger synthesis superstructure (HENS) formulation to consider streams with variable temperatures and flow capacities using mixed-integer linear programming (MILP). To keep the problem tractable and to leverage the potential of state-of-the-art MILP solvers, piecewise-linear models with logarithmic coding are used. Allowing for variable utility parameters within a feasible technical range, instead of a priori defined ones, removes limitations of the HENS. Increasing the utility’s degree of freedom offers advantages when sensible heat from, for example, flue gas, thermal oil, or water is used. Moreover, utilities are no longer limited to single-stage heat transfer without stream splits at the stream ends, generating opportunities for efficiency enhancement. We consider three representative case studies to evaluate the performance of the unchained HENS method. Our results show that representing utilities as streams in the HENS optimization problem leads to lower total annual costs (TAC). Significant cost savings arise due to more efficient utility placement, heat transfer, and smaller heat exchanger areas. The results indicate that this method can lead to cheaper and more resource-efficient HEN and thus positively contribute to the environment.