A New Modeling and Global Optimization Approach for Scheduling of Crude Oil Operations

Scheduling of crude oil operation is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of refinery turnover (Kelly and Mann, 2003). Moreover, blending with cheaper crudes can significant increase profit margins. 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 many bilinear terms, which transforms the problem into a difficult, nonconvex, mixed integer nonlinear program (MINLP).

The crude oil scheduling problem has received considerable attention with researchers developing different models based on discrete- (Lee et al., 1996; Li et al., 2002; Reddy et al. 2004a) and continuous-time representations (Jia and Ierapetritou, 2003; Reddy et al., 2004b; Moro and Pinto, 2004; Karuppiah et al., 2008; Saharidis et al., 2009; Mouret et al., 2009). While the models of Lee et al. (1996), Karuppiah et al. (2008), Saharidis and Ierapetritou (2009), and Mouret et al. (2009) only considered single jetty, Li et al. (2002) incorporated multiple jetties. All of these models (Li et al., 1996; Li et al., 2002; Karuppiah et al. 2008; Saharidis and Ierapetritou, 2009; Mouret et al., 2009) allowed one tank feeding one CDU at one time and vice versa. Reddy et al. (2004a,b) included a single buoy mooring (SBM) station, multiple-parcel vessels, brine settling, crude segregation, multiple tanks feeding one CDU at one time and vice versa. Besides all operational features of Reddy et al. (2004a), Reddy et al. (2004b) incorporated multiple jetties. Li et al. (2007) extended the model of Reddy et al. (2004b) for fifteen important volume-based and weight-based crude property indices. It is important to note that no continuous-time models exist that incorporate all of the aforementioned realistic features.

To address this non-convex MINLP problem, researchers developed some special algorithms such as linearization approach (Lee et al., 1996), the iterative decomposition algorithm (Li et al., (2002), rolling horizon algorithm (Reddy et al. 2004a,b) and the improved rolling horizon algorithm with backtracking and partial relaxation strategies (Li et al., 2007). The linearization approach of Lee et al. (1996) led to composition discrepancy where the amount 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). Iterative decomposition algorithm, and rolling horizon algorithm may fail to find feasible schedules although feasible solutions do exist as mentioned by Li et al. (2007). Although the improved rolling algorithm with backtracking and partial relaxation strategies successfully solved all tested twenty examples, it cannot guarantee global optimality. General purpose solvers such as DICOPT and BARON also fail to get feasible schedules in several examples, although feasible solutions do exist. Recently, Karuppiah et al. (2008) developed an outer approximation algorithm to optimize crude oil scheduling operations globally. They generated cutting planes from spatial decomposition of the crude oil network and added them to the MILP relaxation from McCormick convex and concave envelope to reduce computational time. The MILP relaxation provided a valid lower bound and solving a nonconvex NLP provided an upper bound. They solved MILP relaxation and NLP iteratively until the lower and upper bounds converged to within a specified tolerance.

In this paper, we develop a novel unit-specific event-based continuous-time MINLP formulation for this problem. We incorporate realistic operational features such as single buoy mooring (SBM), multiple jetties, multi-parcel vessels, single-parcel vessels, crude blending, brine settling, crude segregation, multiple tanks feeding one CDU at one time and vice versa. In addition, we also consider fifteen important volume-based or weight-based crude property indices. We exploited recent advances in piecewise-linear underestimation of bilinear terms (Meyer and Floudas, 2006; Karuppiah and Grossmann, 2006; Bergamini et al., 2008; Saif et al., 2008; Wicaksono and Karimi, 2008; Gounaris et al., 2009; Misener and Floudas, 2009; Pham et al., 2009; Hasan and Karimi, 2010; Misener and Floudas, 2010; Misener et al., 2010) within a branch-and-bound algorithm for global optimization. Several examples from Li et al. (2007) are used to illustrate the capability to reach global optimality of the branch-and-bound algorithm with piecewise-linear underestimation.

Keywords: refinery, crude oil scheduling, mixed-integer nonlinear programming (MINLP), non-convex, global optimization, piecewise linear, branch and bound

References

Bagajewicz, M. A review of recent design procedures for water networks in refineries and process plants, Computers and Chemical Engineering, 2000, 24, 2093-2113.

Gounaris, C. E., Misener, R., Floudas, C. A. Computational comparison of piecewise-linear relaxations for pooling problems, Industrial and Engineering Chemistry Research, 2009, 5742-5766.

Hasan, M. M. F., Karimi, I. A. Piecewise linear relaxation of bilinear programs using bivariate partitioning, AIChE Journal, 2010, DOI: 10.1002/aic. 12109.

Jia, Z., Ierapetritou, M. G., Kelly, J. D. Refinery short-term scheduling using continuous time formulation: crude oil operations, Industrial and Engineering Chemistry Research, 42, pp. 3085-3097. 2003.

Karuppiah, R., Grossmann, I. E. Global optimization for the synthesis of integrated water systems in chemical proesses, Computers and Chemical Engineering, 2006, 30, 650-673.

Karuppiah, R., Furman, K. C., Grossmann, I. E. Global optimization for scheduling refinery crude oil operations, Computers and Chemical Engineering, 2008, 32, 2745-2766.

Kelley, J. D., Mann, J. L. Crude oil blend scheduling optimization: An application with multi-million dollar benefits-Part 1, Hydrocarbon Processing, 2003, 82, 6, 47-51.

Kelley, J. D., Mann, J. L., Crude oil blend scheduling optimization: An application with multi-million dollar benefits-Part 2, Hydrocarbon Processing, 2003, 82, 7, 72-79.

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(5), 1630-1641.

Li, J., Li, W. K., Karimi, I. A., Srinivasan, R. Improving the robustness and efficiency of crude scheduling algorithms, AIChE Journal, 2007, 53 (10), 2659-2680.

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.

Meyer, C. A., Floudas, C. A. Global optimization of a combinatorially complex generalized pooling problem, AIChE Journal, 2006, 52(3), 1027-1037.

Misener, R., Floudas, C. A. Advances for the pooling problem: Modeling, global optimization, and computational studies, Applied and Computational Mathematics, 2009, 8(1), 3-22.

Misener, R., Floudas, C. A. Global optimization of large-scale generalized pooling problems: Quadratically constrained MINLP models, Industrial and Engineering Chemistry Research, 2010. Forthcoming.

Misener, R., Gounaris, C. E., Floudas, C. A. Mathematical modeling and global optimization of large-scale extended pooling problems with the (EPA) complex emissions constrains, Computers and Chemical Engineering, 2010, DOI: 10.1016/j.compchemeng.2010.02.014.

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.

Mouret, S., Grossmann, I. E., Pestiaux, P., A novel priority-slot based continuous-time formulation for crude-oil scheduling problems, Industrial and Engineering Chemistry Research, 2009, 48, 8515-8528.

Pham, V., Laird, C., El-Halwagi, M. Convex hull discretization approach to the global optimization of pooling problems, Industrial and Engineering Chemistry Research, 2009, 48, 1973-1979.

Reddy, P. C. P., Karimi, I. A. Srinivasan, R., A novel continuous-time formulation for scheduling of crude oil operations, Chemical Engineering Science, 2004a, 59, 1325-1341.

Reddy, P. C. P., Karimi, I. A. Srinivasan, R. A novel solution approach for optimizing scheduling of crude oil operations, AIChE Journal, 2004b, 50(6), 1177-1197.

Saharidis, G. K. D., Ierapetritou, M. G. Scheduling of loading and unloading of crude oil in a refinery with optimal mixture preparation, Industrial and Engineering Chemistry Research, 2009, 48, 2624-2633.

Saif, Y., Elkamel, A., Pritzker, M. Global optimization of reverse osmosis network for wastewater treatment and minimization, Industrial and Engineering Chemistry Research, 2008, 47 (9), 3060-3070.