熱交換器網路(heat exchanger network, HEN)在運行一段時間後，會因為熱傳表面結垢使得熱傳效率降低而增加了能源成本。在過去的研究中，Cheng and Chang (2016)曾提出具單一規格備件的熱交換器網路清洗排程，雖然可以有效補足熱交換器清洗時損失的熱傳量，但是在正常未清洗操作時，HEN仍會受結垢影響而須耗費額外能源成本。因此在建構熱交換器網路時，常常會引入裕度設計來對抗正常操作時的結垢問題，而Sun et al. (2008)即提出在引入裕度的熱交換器增設可控制旁路以調節熱傳量，同時增加熱交換器網路操作的彈性及穩定性。而Yi and Chang (2016)則是在熱交換器網路清洗排程的數學規劃模式中同時考慮多規格備件以及裕度設計，有效的減少熱交換器網路的正常操作以及清洗時的總成本。然而，前述研究針對裕度、旁路、備件及輔助單元仍未有適當的規劃配置。在本研究我們修改已存在的MINLP模式，並且分兩階段求解。首先分析且決定裕度與相應旁路的恰當位置，再引入輔助單元及備件讓熱交換器網路每一流股皆能達到目標溫度。在相應最適解中，我們可以得到最佳清洗排程、備件及輔助單元數目及相應熱傳面積、引入裕度大小等。最後，以兩個案例驗證所提方法之可行性與有效性。

Fouling develops in almost every heat exchanger in a heat-exchanger network (HEN) during operation. This inevitable deterioration in heat-transfer efficiency obviously raises the hot and cold utility consumption levels of HEN. To address this practical issue for a given process, it is necessary to introduce extra refinements into the traditional design in order to accommodate a cleaning schedule.
In this study, the optimal cleaning schedule, with the support of spares and heat-transfer area margins, is determined by solving a generic mathematical programming model. A particular binary variable in the model formulation represents the option to select the corresponding spare, while the heat-transfer area of each chosen unit and the corresponding bypass flowrates are real variables.
The use of a spare eliminates (or reduces) the energy loss caused by removing and cleaning a heat exchanger in HEN during normal operation. The importance of a spare is obvious if this unit is exccessively large. In addition, the size of spare should be compatible with that of the unit it replaces. To address these issues, the proposed model incorporates two heuristic rules for properly placing the spares into cleaning schedules.
In order to reduce the total utility cost as much as possible, the purposes of embedding area margins and bypasses into HEN should be to introduce additional heat-transfer capacities into one or more unit and to shift heat loads strategically along paths and loops via bypasses. Based on this observation, the present work adopts a two-stage computation method for synthesis of optmal cleaning schedules. The first identifies the aforementioned candidate units for margin placement and the corresponding bypasses by considering two fictitious scenarios. One is concerned with the conventional operation without the defouling actions, while the other takes place after removing a chosen unit from HEN. The candidate units and corresponding bypass locations are then determined by ranking the total utility costs in these scenarios.
By solving the modified model in the second stage, one should be able to obtain the optimal cleaning schedule, the optimal spare replacement strategy, the time-dependent flowrates of bypasses, the heat transfer areas of all margin-embedded heat exchangers, the heat transfer areas of spares, and the utility consumption rates. Finally, this thesis reports the optimization results of three examples to demonstrate the feasibility and effectiveness of the proposed approach.

1.Akpomiemie, M. O. and R. Smith (2015). "Retrofit of heat exchanger networks without topology modifications and additional heat transfer area." Applied Energy 159: 381-390.

2.Alsadaie, S. and Mujtaba, I. (2017). "Dynamic modelling of Heat Exchanger fouling in multistage flash (MSF) desalination. " Desalination, 409, pp.47-65.

3.Cheng, K.Y. and C.T. Chang (2016). "Model based approach to synthesize spare-supported cleaning schedules for existing heat exchanger networks." Computers and Chemical Engineering.(accepted)

4.Escobar, M., J. O. Trierweiler and I. E. Grossmann (2013). "Simultaneous synthesis of heat exchanger networks with operability considerations: Flexibility and controllability." Computers and Chemical Engineering 55: 158-180.

5.Fan, J., J. Li., L. Liu., Y. Zhung., J, Du (2014). "Simultaneous optimization of areas and cleaning schedule for heat exchanger networks." Chinese Journal of Chemical Engineering
65(11): 4484-4489.

6.Georgiadis, M. C., L. G. Papageorgiou and S. Macchietto (1999). "Optimal cyclic cleaning scheduling in heat exchanger networks under fouling." Computers & Chemical Engineering 23: S203-S206.

7.Lavaja, J. H. and M. J. Bagajewicz (2004). "On a new MILP model for the planning of heat-exchanger network cleaning." Industrial & Engineering Chemistry Research 43(14): 3924-3938.

8.Linnhoff, B. and E. Hindmarsh (1983). "The pinch design method for heat exchanger networks." Chemical Engineering Science 38(5): 745–763.

9.Luo, X. L., L. Sun and J. F. Zhang (2008). "Optimal design of bypass location on heat exchanger networks." Journal of Chemical Industry and Engineering(China) 59(3):
646-652. (in Chinese)

10.Luo, X. L., C. K. Xia and L. Sun (2013). "Margin design, online optimization, and control approach of a heat exchanger network with bypass." Computers and Chemical Engineering 53: 102-121.

11.Markowski, M. and K. Urbaniec (2005). "Optimal cleaning schedule for heat exchangers in a heat exchanger network." Applied Thermal Engineering 25(7): 1019-1032.

12.Sanaye, S. and B. Niroomand (2007). "Simulation of heat exchanger network (HEN) and planning the optimum cleaning schedule." Energy Conversion and Management 48(5): 1450-1461.

13.Smaïli, F., D. K. Angadi, C. M. Hatch, O. Herbert, V. S. Vassiliadis and D. I. Wilson (1999). "Optimization of Scheduling of Cleaning in Heat Exchanger Networks Subject to Fouling." Food and Bioproducts Processing 77(2): 159-164.

14.Sun, L., J. H. Chi and X. L. Luo (2008). "The analysis of the overdesign and the
bypass design for the heat exchanger." Computers and Applied Chemistry 25(11):
1369–1373.

15.Sun, L., X. L. Luo., B. Q. Hou and Y. J. Bai (2013). "Bypass selection for control of heat exchanger network." Chinese Journal of Chemical Engineering 21(3): 276-284.

16.Sawanya, B., K. Siemanond (2016). "Heat exchanger network design with foulingeffects." Computer Aided Chemical Engineering, 38,pp. 1701-1706.

17.Tian, J., Wang, Y. and Feng, X. (2016). "Simultaneous optimization of flow velocity and cleaning schedule for mitigating fouling in refinery heat exchanger networks. " Energy, 109, pp.1118-1129.

18.Xiao, F., J. Du., L. Chen., L. L. Liu., P. J. Yao (2009). "Simultaneous optimization of synthesis and cleaning schedule for flexible heat exchanger networks." Chinese Journal of Chemical Engineering 60(10): 2530-2535.

19.Yi K. T.(2016). "HEN design refinements to accommodate cleaning schedules via spare and margin allocations." MS Thesis, National Cheng Kung University, Tainan, Taiwan.