(359c) Multiperiod Inventory Pinch Algorithm for Integrated Planning and Scheduling of Oil Refineries

A petroleum refinery plant transforms raw crude oils into more valuable products that can be found almost anywhere such as liquid fuels, plastics, oils, solvents, asphalt, and many chemicals used in production processes across different industries. Oil refineries involve several intertwined complex physical and chemical processes, and they operate in a highly competitive and dynamic market under strict safety, environmental, and governmental regulations. For these reasons, planning and scheduling of refinery operations are very important tasks. Moreover, in order to obtain high quality solutions, integration of planning and scheduling decisions is necessary¹.

Commercial software found in industrial practice to compute production plans for a refinery employ multiperiod models and solve them using linear programming or successive linear programming techniques, e.g. Aspen PIMS, Haverly GRTMPS, and Honeywell RPMS. Nonlinear programming (NLP) algorithms can be found as well, e.g. Aspen PIMS AO. However, in order to avoid intractable problems, such software often use simplified process unit-operation models². Refinery scheduling is usually carried out via interactive simulation (e.g. Aspen Petroleum Scheduler and Haverly H/Sched) with the production plan targets used as constraints. Mixed-integer linear programming (MILP) optimization techniques to solve the scheduling problem represent an opportunity for companies to improve their operations and profits; however, more efficient and reliable MILP models and solution algorithms are required to be developed in order to be applied in practice.

Regarding planning models, current trend is to increase their accuracy by considering their nonlinear nature and developing formulations that can be tractable^2,3,4. For the scheduling problem, several MILP models have been published in the literature for the entire refinery or some of its subsystems^5,6,7. Maravelias and Sung¹ reviewed different strategies to integrate planning and scheduling levels. They discussed the importance of developing more computationally effective models and improving decomposition and iterative algorithms, as well as hybrid methods. Several researchers have formulated full-space models (i.e. simultaneous planning and scheduling), usually as mixed-integer nonlinear programming (MINLP) models, and proposed algorithms to solve them^8,9,10. In general, these models can be solved directly only for a small number of time periods. Various bi-level decomposition algorithms for MILP and MINLP models have been proposed^11,12,13. Castillo-Castillo and Mahalec¹⁴ developed a three-level decomposition approach based on the inventory pinch concept to integrate planning and scheduling decisions in gasoline blending operations, which reduces the number of blend recipes and can handle nonlinear blending rules.

Based on the work by Castillo-Castillo and Mahalec¹⁴, we present a multiperiod inventory pinch algorithm, denoted as â??extended MPIP-C algorithmâ?, to integrate planning and scheduling decisions of an oil-refinery (not only for the gasoline blending section). The original full-space problem is decomposed into three levels: 1) optimization of operating conditions, 2) derivation of an approximate schedule, and 3) computation of a detailed schedule. At the 1^st level, a multiperiod NLP model is formulated, where periods are delineated initially by inventory pinch points of various product pools (e.g. gasoline and diesel). This reduces the number of periods and number of different blend recipes. Various formulations for the processing unit models can be utilized (e.g. fixed yield, multi-mode, or nonlinear). A global optimization algorithm is employed to solve the 1^st level if such model is nonconvex. The 2^nd level is solved via multiperiod MILP model, where periods are delineated by scheduler based on the demand and supply data, and the minimum time requirements to complete major tasks (i.e. blend runs, product tank service). The 3^rd level uses a continuous-time MILP model to determine the exact times to carry out the necessary tasks to meet the targets imposed by the 2^nd and 3^rd level solutions. The 2^nd and 3^rd levels are MILP models since the nonlinear constraints associated with the operating conditions are solved at the 1^st level, and the optimal conditions found at the 1^st level are fixed at the other levels. The algorithm minimizes the total cost comprised by the crude oil cost, production cost, switching cost, and demurrage cost. Switching cost involves blend runs, delivery runs, product changeovers in the swing tanks, and mode transitions in the processing units. The algorithm eliminates infeasibilities found at the 2^nd and 3^rd levels by re-optimizing operating conditions at the 1^st level.

For our case studies, the refinery system consists of a crude distillation unit, a catalytic reformer, a hydrocracker, a fluid catalytic cracking unit, five hydrotreaters, three blenders, and various mixers and splitters. We consider five products and eight quality properties under specification, as well as different demand and supply scenarios. Results show that the extended MPIP-C algorithm computes solutions close to the optimum and in relative shorter execution times than solving the full-space model. Most of the computational time is spent at the 1^st and 3^rd level models. Future work will be to test mathematical decomposition strategies to solve the 3^rd level model (detailed scheduling) more efficiently.

References

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