(26b) Deterministic Global Optimization Approach to Midterm Planning of an Industrial Integrated Petroleum-Petrochemical Facility

Refining processes transform petroleum into a wide range of valuable products, from fuels to petrochemicals. Profitability of this industry relies on key activities such as crude oil evaluation, petroleum allocation, fuel blending and selection of optimal operational windows. Linear representations for refinery planning operations tend to under- or overestimate production rates and products quality, making questionable the effectiveness of optimization based approaches^1–3. Recently, refining process accuracy has been improved via metamodeling^4–6 and empirical correlations⁷. Also, complex petroleum supply chains can be represented by a 3-tuple composed of a mixer – process unit – splitter⁸ linked between them. Despite the notorious advantage of achieving a better process representation, the presence of non-convexities leads to obtain local or suboptimal solutions. In terms of strategies for addressing this problem, heuristic-based algorithms^9,10 have been applied to find near optimal solutions, while deterministic global optimization methods³ ensure a mathematical global optimum. However, applying these approaches for a real-size problem is challenging owing to process integration between petroleum – petrochemical technologies, competition for intermediate raw materials and the multiple grades of commodities to produce. In addition, if process models are represented by non-linear expressions, the chance of finding a local solution is significant.

Herein, we formulate a Mixed-Integer Quadratically-Constrained Quadratic Program (MIQCQP) to solve within a certain global optimality gap a midterm supply-chain problem for a full-scale integrated refinery – petrochemical complex in the context of the Colombian hydrocarbon market. Our approach clusters the refinery topology into subprocesses according to their functionality. For each cluster, a relaxed model (MILP) based on generalized¹¹ and piecewise McCormick envelopes is formulated. The number of partitions (NP) for the discretized variables inside the cluster change dynamically, while variables that do not belong to the cluster are not discretized. The MILP solution provides a Lower Bound (LB) for the original problem. Then, fixing the binary variables obtained from the relaxed model solution, the original MIQCQP is transformed into a quadratic problem (QP) which provides an Upper Bound (UB). If the UB is improved, Optimality-Based Bound Tightening (OBBT)¹² is applied to reduce the domain for the variables belonging to the cluster. This procedure is repeated until a stopping criteria is met, such us reaching maximum runtime, exploring all clusters or obtaining and optimality gap less than epsilon.

The methodology was tested through five cases studies that recreate typical planning scenarios for the Colombian hydrocarbon industry. The model has about 6975 equations, 35104 nonlinear terms derived from bilinear and trilinear expressions, 9592 and 279 continuous and discrete variables respectively. Results show that commercial solvers for deterministic global optimization^13,14 get stuck at a local optimum solution with an optimality gap above 50%, on average. Furthermore, there is no improvement in the UB if the CPU time is increased from 2 to 6 hours. In contrast, we found a better UB for all the case studies with a maximum runtime of 1.3 hours on average. This demonstrates that clustering decomposition is a promising solution strategy for problems of that scale. Future work will incorporate the Reformulated Normalized Multiparametric Disaggregation Technique¹⁵ for comparison with the piecewise McCormick envelopes.

References

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