8An approach for optimising the cleaning schedule in heat exchanger networks (HENs) subject 9 to fouling is presented. This work focuses on HEN applications in crude oil preheat trains 10 located in refineries. Previous approaches have focused on using mixed-integer nonlinear 11 programming (MINLP) methods involving binary decision variables describing when and 12 which unit to clean in a multi-period formulation. This work is based on the discovery that 13 the HEN cleaning scheduling problem is in actuality a multistage optimal control problem 14 (OCP), and further that cleaning actions are the controls which appear linearly in the system 15 equations. The key feature is that these problems exhibit bang-bang behaviour, obviating the 16 need for combinatorial optimisation methods. Several case studies are considered; ranging 17 from a single unit up to 25 units. Results show that the feasible path approach adopted is 18 stable and efficient in comparison to classical methods which sometimes suffer from failure 19 in convergence. 20 is achieved through process turndown, increased utility consumption with affiliated surge 32 in greenhouse gas emissions until operation requirements such as temperature and pump-33 around targets are met, or in extreme cases plant shutdown. The reduction of production 34 rates and increased energy consumption lead to economic losses which are more significant 35 in larger networks of heat exchangers that require long continuous operational times between 36 to a mixed integer linear programming (MILP) model (Georgiadis and Papageorgiou, 2000). 56Stochastic optimisation frameworks using distinctive modifications of simulated annealing al-57 gorithms have been implemented (Smaïli et al., 2002a) as well as heuristic schemes composed 58 2 of a set of movements according to a greedy rationale (Gonçalves et al., 2014). 59 This problem has been addressed in the literature through extending the formulation 60 of the general cleaning scheduling problem in a multitude of ways. Rodriguez and Smith 61 (2007) combined the conventional cleaning scheduling problem with optimisation of operating 62 conditions such as wall temperature and flow velocity in a comprehensive mitigation strategy 63 while Ishiyama et al. (2010) considered the addition of the problem of controlling the desalter 64 inlet temperature by using hot stream bypassing within a PHT fouling mitigation strategy 65 based on heat exchanger cleaning. 66 Certain formulations include constraints set by pump-around operation (Smaïli et al., 67 2002a) and pressure drop (Smaïli et al., 2001), while both thermal and hydraulic impacts of68 fouling were considered by Ishiyama et al. (2009b) where variable throughput and control 69 valve operation are implemented on the cleaning scheduling problem. 70 A cleaning operation will ideally remove all fouling deposits from a heat transfer surface. 71 In practice the effectiveness of a cleaning operation depends on the nature of the deposit and 72 the method of cleaning. Ishiyama et al. (2011) presen...

This article presents a novel approach to optimise scheduling and production planning to meet seasonal demand in an industrial process using decaying catalysts, based on its formulation as a multistage mixed-integer optimal control problem (MSMIOCP). Unlike existing methodologies, the MSMIOCP formulation allows to solve this problem as a standard nonlinear optimisation problem without combinatorial optimisation methods, which can be advantageous in providing reliable, robust and e cient solutions. Using this formulation, four case studies of this problem, di↵ering in reaction or deactivation kinetics, are investigated. Two di↵erent solution implementations are used, each having their own relative advantages. The first implementation demonstrates a bang-bang behaviour for the linear scheduling controls, consistent with a theoretical analysis, but faces integration problems and does not always produce high quality solutions. The second implementation, while not demonstrating the bang-bang property, always produces high quality solutions and shows the advantages of the MSMIOCP formulation over existing methodologies.

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