(106f) Robust and Efficient Algorithm for Optimizing Crude Oil Operations

Scheduling of crude oil is an important and complex routine task in a refinery. It involves crude oil unloading, tank allocation, storage and blending of different crudes, and CDU charging. Optimal crude oil scheduling can increase profits by using cheaper crudes, minimizing crude changeovers, avoiding ship demurrage, and managing crude inventory optimally. However, mathematical modeling of the blending of different crudes in storage tanks results in bilinear terms, which turns the whole problem into a difficult, nonconvex, mixed integer nonlinear program (MINLP).

So far, several efforts (Lee et al., 1996; Li et al., 2002; Moro and Pinto, 2004; and Reddy et al., 2004a,b) in the literature have attempted to solve this MINLP problem. Lee et al. (1996) used reformulation linearization technology (RLT) to turn bilinear equations into linear forms. However, this linearization approximation leads to composition discrepancy (the amounts of individual crudes delivered from a tank to CDU are not proportional to the crude composition in the tank) as shown by Li et al. (2002) and Reddy et al. (2004b). Discretization procedure of Moro and Pinto (2004) leads to discrete values for flow rates and increases problem size to an extent that makes it almost impossible to solve reasonably sized problems. General purpose solver such as DICOPT and the method of Li et al. (2002) require solving one MILP and one NLP iteratively. Reddy et al. (2004a,b) solve a series of MILPs to avoid solving NLP. However, we find that DICOPT as well as the algorithms of Li et al. (2002) and Reddy et al. (2004a,b) fail to get feasible schedules in several examples, although feasible solutions do exist. Moreover, these algorithms still need large solution times for solving large, practical problems. Therefore, no reliable, robust, and efficient algorithm exists in the literature for this real, practical, and very useful problem.

In this paper, we first identify fifteen crude properties that are critical to crude distillation and downstream processing. We enhance the practical utility of Reddy et al. (2004b)'s MINLP formulation by adding appropriate linear blending correlations for these properties. Next, we analyze in detail why Reddy et al. (2004)'s algorithm fails in some cases. We find that progressive fixing of some infeasible combinations of binary variables leads to infeasibility and the algorithm lacks a mechanism to retract from these infeasible combinations. Therefore, we identify a minimal set of binary variables responsible for infeasibility and develop a backtracking strategy using an intelligent integer cut to eliminate the infeasibility and revive the algorithm's progress. We then evaluate the robustness of our improved algorithm using twenty examples of different sizes and with different real life operation features. We also compare its performance with other three algorithms (DICOPT; Li et al., 2002; Reddy et al., 2004b). We find that a general purpose code such as DICOPT fails to solve most problems and is horribly slow in solving the rest. Even the best algorithm of Reddy et al. (2004b) fails to solve several problems. In contrast, our improved algorithm works on all problems and is much more efficient than the other three algorithms. To further increase solution speed, we develop a partial relaxation method in which we relax the integrality restrictions on the binary variables of limited use. Our tests show that the partial relaxation method greatly reduces the computation time and at the same time improves the solution quality for most examples, especially for scheduling problems with horizons as long as 20 days. In addition, we revise Reddy et al. (2004b)'s formulation to ensure practically realistic schedules with limited flow rate changes to the CDUs. In summary, our work takes a great lip in its ability to solve this complex problem reliably and intelligently.

Key words: crude oil scheduling, mixed integer nonlinear programming (MINLP), integer cut strategy, partial relaxation method

References:

(1)Lee, H., Pinto, J. M., Grossmann, I. E., Park, S., Mixed-integer Linear Programming Model for Refinery Short-Term Scheduling of Crude Oil Unloading with Inventory Management, Industrial and Engineering Chemistry Research, 1996, 35, 1630-1641.

(2)Li W. K., Hui, C. W., Hua, B., Zhong, X. T., Scheduling Crude Oil Unloading, Storage and Processing, Industrial and Engineering Chemistry Research, 2002, 41, 6723-6734.

(3)Moro, L. F. L., Pinto, J. M., Mixed-Integer Programming Approach for Short-Term Crude Oil Scheduling, Industrial and Engineering Chemistry Research, 2004, 43, 85-94.

(4)Reddy, P. C. P., Karimi, I. A., Srinivasan, R., A Novel Continuous-time formulation for Scheduling of Crude Oil Operations, Chemical Engineering Science, 2004a.

(5)Reddy, P. C. P., Karimi, I. A., Srinivasan, R., A Novel Solution Approach for Optimizing Scheduling of Crude Oil Operations, AIChE Journal, 2004b, 50, 1177-1197.