(356c) 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.