**4. Superstructure**

Figure 1 presents the superstructure of the proposed integration problem. All potential configuration alternatives of the HEN are displayed by considering the utilization of steam. For the HEN side, two hot process streams and two cold streams are used to exhibit the features of the stage-wise superstructure. Since the heaters involving steam could be before, after and in parallel with stream-stream heat exchangers, new stages are introduced in the superstructure to fully explore the utilization of steam. It should be noticed that the stages are divided into two types—the inner-stage and the inter-stage—which are alternately arranged. Within each inner-stage, a cold process stream can be split into multiple branches to perform the heat exchange with hot process streams and steam simultaneously. After that, the branches are mixed non-isothermally into a main stream and go into the inter-stage, where only steam is allowed to heat the cold streams. Inter-stage heaters are allowed at both the start and end of cold streams, so the inter-stage number is one more than that of inner-stages. This arrangement could provide much more matching options between cold process streams and steam with limited stages, enriching the configurations of the superstructure. Hot streams are operated in the traditional manner, cooled down by cold process streams within inner-stages and cooling water at stream ends.

**Figure 1.** Superstructure for combined HEN and utility system.

The operation of utility system is in typical Rankine cycle: the highest pressure superheated steam is generated in a boiler through combusting fuel, and then sent into a turbine to generate multi-level superheated steam with turbine condensed steam extracted and condensed at the end, producing power at the same time. The superheated steam needs to be desuperheated by mixing with water from the deaerator before being sent to the HEN as saturated steam. After heating the process streams, the condensed water returns to the deaerator, and splits into two parts after the operation, part is sent to the boiler and evaporated into superheated steam, and the residue is mixed with multi-level superheated steam to obtain saturated steam, finishing a cycle. Although the flowsheet of the utility system is quite certain, the possibilities of steam generation and utilization in the HEN need to be determined within the design.

Based on the presented superstructure, a mathematical model can be formulated to determine the optimal network structures and network parameters. In this work, considering the deaerator is an energy-consuming unit, another system without deaerator is also investigated, e.g., using a chemical deaeration technique. The resultant variation in structure is that part of the condensed water is mixed with the corresponding superheated steam, while the rest flows back to the boiler directly.
