In industrial processes, the stream parameters of the heat exchanger network (HEN) synthesis problem can vary during different periods. As a result of the change in inlet and outlet temperatures and the flow rates of the streams, the optimal HEN and the optimal heat transfer areas of the heat exchangers can be different in each period. In our previous work, the standard HEN synthesis for minimum utility consumption was extended to consider varying stream parameters, where bypasses at the heat exchangers are used to ensure the exit streams meet the expected outlet temperatures. This requires optimization of the total annualized cost based on the maximal heat transfer areas of the heat exchangers for each period. Minimum approach temperature is applied to ensure that the areas of the heat exchangers stay within reasonable limits in the solution network. Since minimum approach temperature affects both the structure of the HEN and the total annualized cost, its value needs to be determined during the optimization procedure. The current work proposes a procedure for HEN synthesis which determines the best, n-best, or all feasible HENs for all periods considering variable approach temperature. The proposed method extends the P-graph-based HEN synthesis method for determining all feasible networks in all periods. Three case studies are used to demonstrate the application of the proposed method. The case studies show that while the commonly applied minimum approach temperature of 10 °C does indeed gives near-optimal results, some problems need different values, such as 25 °C or 30 °C.

Heat exchanger networks in real industrial processes often have to be designed for varying parameters of the process streams that renders multiperiod heat exchanger network synthesis essential in industrial realization. However, three standing issues must be considered in the synthesis procedure. (1) The generated network should be efficient in all periods, preferably consuming minimum utility. (2) This network should also be structurally as simple as possible for minimizing the investment cost and making the process controllable. Furthermore, (3) all or the n-best networks that fulfilled the first two principles must be considered for the selection of the most preferred industrial realization. The method proposed in the current work satisfies all three requirements simultaneously; it has been the only known method with these properties. The method primarily relies on the formerly developed P-graph-based heat exchanger network synthesis procedure. Three case studies demonstrate the application of the proposed method.