Loop breaking in heat exchanger networks by mathematical programming

In many cases heat exchanger network (HEN) designs require some changes aimed at reduction of units number. This is the case if a rule of division at pinches is applied in designing a HEN as e.g. in pinch analysis approaches. Matches at loops across pinches can be removed and the number of matches in a HEN goes down to the global minimum. Such elimination of units is commonly referred to as loop breaking. Several methods have been suggested for loop breaking. Existing approaches require iterative tedious computations. Moreover, since based on rules from insight into the problem they do not ensure optimal solutions. In this contribution we developed an approach that is based on mathematical programming. The aim is to minimise or to reduce number of units at the condition of minimum energy penalty. The optimisation model consists of relations determining HEN’s topology, heat and mass balances for each heat exchanger (including heaters and coolers) as well as splitters and mixers. Inequalities ensuring feasible heat exchange are included, too. In order to overcome difficulties with solving mixed-integer nonlinear (MINLP) optimisation problem we have decided to impose the condition of linearity for our model. Hence, goal function in optimisation does not account for total cost but the aim is to minimise number of matches and heat load of utilities. Furthermore, flow rates of streams have to be fixed. To relax constraint of fixed flow rates at splitters we have applied a concept of small superstructure that contains all types of arrangements for heat exchangers: parallel, serial and serial–parallel connections. This gives mean to simplify HEN’s topology by replacing parallel arrangement by serial one. Linear optimisation model developed by us accounts for inequality constraints for outlet streams temperatures. We applied EMAT value instead of HRAT. Some new matches can be inserted into a HEN by a designer to make topology changes possible. The optimisation model is of mixed-integer linear type and requires moderate number of binary variables. It can be easily extended in MINLP one that accounts for total cost. In this paper solutions for some literature examples are presented that proved validity of the approach and shows practical merits of the approach.