近年來，多廠熱交換網路設計研究一直是熱門研究議題之一，不只可使整體能源最小化，也可讓共建合作成本有效的降低，接著，由於各廠獲利可能不平均，因此就發展出利用合作賽局去合理的收益分配。但在多廠熱交換網路設計都是以新建為前提，並不符合實際情況，因此本研究發展出熱交換網路設計翻修，在藉由合作賽局去做合理的分配收益，使得廠際熱整合計畫可行率達到最高。
在本研究中，單廠同步HEN之超結構修改成多廠HEN之設計，並發展出三種翻修情況: (1)單廠HEN中的已存在熱交換器在多廠HEN共建合作時，其可加大熱傳面積已增加其熱傳量; (2)已存在熱交換器除了可加大熱傳面積，也可在廠內移動到其他原始配對上; (3)已存在熱交換器只限用於原廠內，但新購買的熱交換器也可放置在廠內配對上。從上述三種情況可個別求出其最大節省成本費用，接著，在利用其夏普利值與風險夏普利值去合理分配收益。

The heat exchanger network (HEN) is traditionally used for maximum heat recovery in a single chemical plant, while the multi-plant counterparts have been studied in recent years primarily for the purpose of reaping additional energy savings, e.g., see Bagajewicz and Rodera (2002). Since these works focused upon minimization of the total energy cost of the entire site, the resulting arrangements were often infeasible due to the fact that the individual savings were not fairly allocated and therefore not always acceptable to all participating parties.
Jin et al. (2018) developed a rigorous model-based procedure to handle the above benefit allocation problem in the spirit of a cooperative game. The minimum total annual cost (TAC) of every potential coalition was first determined with a conventional MINLP model, while the core and the risk-based Shapley values of all players were then computed to resolve the distribution issues. Although satisfactory results in simple examples were reported, their approach was developed for the grass-root designs only. However, in most cases, the process plants on an industrial park were built to satisfy different market demands arose at various instances and each must have already been equipped with a HEN by the time of its completion. Therefore, the above benefit allocation problem should take shape mainly when a HEN revamp project is called for to facilitate interplant heat integration.
The solution technique taken in the present study is basically the same as that adopted in Jin et al. (2018). Since an existing HEN is present in each plant, a modified objective function, i.e., the extra TAC saving, is utilized in the proposed model formulation. Three HEN revamp strategies are adopted in this work and their configuration rules are summarized below.
Strategy 1: Only the interplant matches are new in the revamp design, while the original matches of each plant are kept unchanged. New heat exchangers can be purchased solely for new matches. Every in-plant match in the revamp design should be housed in an existing heat exchanger for the same match in the original design. If a larger heat-transfer area is called for in the revamp design, then the existing unit can be augmented with a new one in series to fulfil the required heat duty.
Strategy 2: All configuration rules are the same as those in Strategy 1 except that the existing heat exchangers are allowed to be used for other original matches in the same plant.
Strategy 3: All aforementioned restrictions are relaxed.

Furthermore, the HEN configurations have also been analyzed to reduce the risk of plant shutdowns in a coalition. A simple example is provided to demonstrate the feasibility of the proposed allocation and revamp methods.

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