**1. Introduction**

With the continuous increase of energy consumption in industrial processes, the energy crisis has further intensified on account of the limited fossil energy reserves. Energy prices are also on the rise at the same time, which drives the pursuit of energy-saving technologies and methods. Heat exchanger networks (HENs) are an inevitable part in processing enterprises for heat recovery. Hot process streams that need to be cooled down and cold process streams that need to be heated up widely exist in process enterprises. Synthesis of HENs is able to obtain HEN structures with reasonable matches between these hot and cold process streams and recover waste heat to the greatest extent. Thus the additional utility consumption will be greatly reduced. On the other hand, utility systems based on steam power cycles are one of the major sources which can export multi-level steam and power to industrial enterprises from a single primary energy source. Energy consumption in utility systems accounts for a large proportion of total industrial energy consumption, which makes it meaningful to improve energy efficiency of utility system. These two parts, the HEN and the utility system, are involved the whole process of energy supply, energy consumption and energy saving. While in implementation, the utility system is usually designed independently with its connections with the processes ignored, so the simultaneous synthesis and optimization of HENs and utility systems should be improved.

Determining the use of utilities is always one important content in HEN synthesis, either within a sequential synthesis method or a simultaneous synthesis method. In pinch technology [1] and the trans-shipment model-based method [2], the consumption of cold and hot utilities is targeted by monitoring of pinch point locations, before designing the network structure in terms of paring hot and cold streams; in the superstructure-based simultaneous method [3], utility consumption is optimized by the trade-off with the capital costs of heat exchangers. Although the study of HEN synthesis has been developed for decades, there are still deficiencies. For example, most previous works on HEN synthesis only used one type of utility at the stream end and assumed that the temperatures of these utilities are able to satisfy all the hot and cold demands, while the fact is that the utility can be in many forms, such as flue gas, steam with different temperatures and hot water. Thus, studies have been launched to investigate the reasonable use of these utilities in HEN synthesis. Costa and Queiroz [4] introduced an extension of the problem table algorithm to optimize and analyze multiple utilities selection and utilization instead of using a grand composite curve. Although the advantages of multi-level utility selection are not analyzed, it is an effective way to optimize multi-level utility utilization with a table algorithm. Salama [5] developed a simple and direct numerical geometry-based technique to target optimal assignment of multiple utilities, but only the heat load was optimized without considering the equipment investment. Shenoy et al. [6] presented a cost-optimal targeting methodology considering the trade-off between energy consumption and equipment investment simultaneously. Optimal selections and loads for multiple utilities were determined based on pinch analysis and the cheapest utility principle. In essence it was still a sequential method, which makes it impossible to achieve a real trade-off between energy and equipment costs. Isafiade and Fraser [7] studied an interval-based MINLP superstructure where the intervals were defined according to the supply and target temperatures of hot or cold process streams. The superstructure model was then applied to HEN synthesis with multi-level available utilities, trading off operating and capital costs for each type of utility. Many nonlinear terms were ignored by mixing split streams at equal temperature, which made the obtained results improvable. Ponce-Ortega et al. [8] developed a stage-wise superstructure that allowed existence of intermediate placement of multiple utilities within each stage. Load and placement of multiple utilities were treated as optimization variables by employing disjunctive programming formulation, rather than regarding utilities as process streams and setting their capacity flowrates as optimization variables. Na et al. [9] proposed a modified superstructure that contained utility sub-stages between adjacent stages. Series utility locations were fixed to facilitate convergence. These studies greatly expanded the design space of the HEN structure and utilization of multiple utilities, but the selection of multiple utilities was mainly based on their price, and the interactions with other systems was not investigated in depth. Zhang et al. [10] explored a new HEN superstructure presentation named the stage-wise chessboard model for management of feasible research regions. A random walk algorithm was employed to lower the calculation load. The problem can be solved faster, but many possible matches are not included in the proposed superstructure because it was equivalent to a stage-wise superstructure with only one stage. Pavão et al. [11] considered the solving difficulty of complex mathematical models resulting from an enhanced stage-wise superstructure which includes the use of multiple utilities at single stream branches. An enhanced meta-heuristic solution method was presented to handle the complex mathematical model, and the superstructure had no difference from the superstructure in Ponce et al. [8] mentioned above. Ma et al. [12] launched multi-objective optimization of interplant HENs operated for multi-periods, which used steam as the heat transfer medium. This research analyzed the conflict between environmental impacts and exchanger investment according to the trade-off between utility consumption and exchanger areas in a case study, but the influence of multi-level steam distribution on the environmental and economic objectives was ignored. Besides, power generation in the utility system was not included in the objective function either, thus the HEN and utility system were not globally integrated.

HENs have been further integrated with utility systems based on their close interactions. Klemeš et al. [13] studied the simultaneous synthesis of a production process and a utility system

based on pinch analysis methodology in a total site integration, but the optimization was carried out after integration within a single plant was completed in advance. Thus the heat recovery and utility system were not optimized simultaneously. Liew et al. [14] optimized the design and operation of a centralized utility system to adapt to shutdowns or process upsets, making a trade-off between operational adaptability and operating costs. Detailed synthesis of the HEN was not included either. Chen and Lin [15] proposed a MINLP model to design a steam network and heat recovery network simultaneously. Hot and cold utilities were only placed at the stream ends, while steam can be generated within an inner-stage to promote energy synergy among plants. Different from previous total site integrations, the heat demand of the HEN is unknown before the design stage, but this research did not consider the utilization of multiple types of utilities within the inner-stage. Hipólito-Valencia et al. [16] combined an organic Rankine cycle with HEN and converted waste heat into mechanical energy, which provided more inspiration for the combination of HEN and other processes. Goh et al. [17] synthesized a HEN and utility system simultaneously, but the minimum operating cost, hot and cold utility demands were determined in advance through multiple cascade automated targeting, without realizing the overall optimization. Luo et al. [18] integrated a HEN with a utility system, using the sensible heat of steam condensate to heat cold process streams. Besides, waste heat of the hot process streams was recovered to preheat boiler feedwater, but the combination was allocated at stream ends, which limited the optimization space compared with the superstructure considering inner-stage utility utilization. Martelli et al. [19] developed a two-stage sequential synthesis algorithm to solve the nonconvex MINLP problem derived from the simultaneous synthesis of HEN and utility systems. An isothermal mixing assumption was made and the utility systems were set as process streams, which will increase the problem-solving complexity. Elsido et al. [20] have worked on the simultaneous synthesis of utility systems, Rankine cycles and heat exchanger networks. However, their mathematical model was established based on a *p-h* superstructure but not a stage-wise superstructure. The main purpose was proposing an ad hoc bilevel decomposition method to improve solution efficiency but not optimizing the utility utilization through improving the superstructure. The simultaneous optimization of multi-plant heat integration using steam as intermediate fluid described in Chang et al. [21] reflected the utilization of energy within the inner-stage, but the steam used within the inner-stage was generated from process streams, and the utility system was not considered completely here. Huang et al. [22] extended their research to the simultaneous optimization of a heat exchanger network, steam Rankine cycle and organic Rankine cycle, but the steam utilization and ORC evaporator were placed at stream ends, and inner- and inter-stage improvements were not considered in the superstructure.

Research about HEN synthesis and utility system is summarized here. On one hand, improvements have been made to provide more matching possibilities in HENs and obtain HEN configurations closer to an optimal solution. On the other hand, utility systems and HENs were considered simultaneously to strengthen the heat integration. In total site heat integration using the sequential method, the utility system was usually designed after the determination of heating demand, making it unable to obtain the optimal trade-off between equipment investment and operating cost. As for the mathematical programming method which can perform the design of HENs while optimizing the operation of the utility system, either the heaters were placed at stream ends, or the operating parameters and power generation of utility system were not included, even though the utilization of utilities was considered within the inner-stage. Thus, in order to achieve a better network management, an improved superstructure considering multiple utilities utilization within the inner- and inter-stage is presented and integrated with the utility system based on a Rankine cycle. Multiple utilities (steam in different pressure levels) are produced in cascade in the utility system with concurrently power generation. The structure of the HEN and the operation of the utility system are simultaneously influenced by the placement and distribution of multiple utilities, leading to a trade-off among capital costs, fuel costs and power generation profits. It should be noted that steam is not regarded as process stream but rather as an additional heating source in this study, so the established mathematical model corresponding to the special HEN superstructure including inner- and inter-stage heaters is different from previous

formulations, by which the steam in any alternative level can be selected as long as the temperature difference demand is met. Finally, cases are illustrated to show the goals of this paper, demonstrating that multi-level steam selection and utilization within the inner- and inter-stage will provide a larger optimization space for steam distribution, power generation and fuel consumption of the utility system, achieving better economic performance of the whole system.
