Historically, the petroleum industry has used linear programming (LP) to address its planning and optimization needs (Favennec, 2001; Li et al 2005).  The simplicity, robustness and convenience of this approach are tradeoffs for the true optimal and accurate solution to the planning model.  In fact, planning technology is considered well developed and progress is expected in model refinement through the use of nonlinear programming (NLP) (Pelham & Pharris, 1996), which accommodates the use of nonlinear process models.  These improvements are more pressing now with the changing market, increasing demands and limited refining capacities.  This paper is an attempt to address this need with the goal to develop more accurate refinery planning models, using the latest NLP algorithms and implementing more accurate process modeling.  The objectives are to establish the current status of planning models and propose nonlinear process model equations for implementation into a refinery planning model.

Starting with the configuration of a complex refinery, production planning model is designed to determine the types, quantities and mixing strategies for the different crude oils available for purchase, so that the refinery will meet the objective of maximizing profits while satisfying specific demands over a specified time period.  Based on the available information for feedstock, products slate, unit capacities and conditions, the refinery planning model elements are the process units, separators, mixers, product blending and feedstock.  The process units are modeled as a linear function to calculate the yields based on the feed streams.  This approach satisfies the LP modeling requirements.  The focus of this paper is the front end of the refinery, namely the crude distillation unit (CDU).

The CDU yield prediction is modeled using linear functions of the crude feed.   However, it does not reflect true refinery operations where there are different operating modes (such as maximizing naphtha or light distillate, or to meet temporary limitations on utilities or maintenance).  Each mode has its own set of coefficients for yield prediction.  Therefore, the fixed-yield based model does not optimize the yield calculations or allow blending the discrete operating modes for optimum operation.  The swing cut approach addresses this problem by allowing the exact cut or fraction to be optimized or “fine tuned”.  After determining the desired product cuts of the crude, about 5% to 7% of the yield around adjacent fractions of the crude is allowed to change or “swing”, changing the yields so as to improve the objective function (Zhang, 2001, Trierwiler, & Tan, 2001).  The minimum modifications required for the swing cuts approach allow more optimization opportunity and possible blending of different operating modes.  Despite the improvement of the swing cut model, the model does not reflect the nonlinearity of the process, but it provides an incentive to further improve the planning model and calculate more accurate yields.

The CDU model can be upgraded from the linear swing cut equation using an aggregate model approach based on the work of Caballero & Grossmann (1999) for the synthesis of distillation columns.  The principle of their approach is to treat the column sections above and below the feed tray as two integrated heat and mass exchangers.  This aggregate representation, which includes a modest number of nonlinear equations, reflects the nonlinear nature of the process without the increasing computation or complexity of conventional short cut models or rigorous tray-by-tray model (Suphanit, 1999).  Furthermore, this approach can serve as a precursor to more complex nonlinear models.

The aggregate model used applies to a typical distillation column, with a condenser, a reboiler and only top and bottom products.  However, the CDU is a complex distillation column with multiple side streams, side strippers and condensers.  It also depends on steam stripping and uses no bottom reboiler.  Therefore, the aggregate model cannot be applied in its simple format directly to the CDU.  This limitation applies also to the typical Fenske-Underwood-Gilliland (FUG) shortcut model (Suphanit, 1999).  To overcome this limitation, the CDU is represented as a set of simple and thermodynamically equivalent cascaded distillation columns.   The cascaded approach will be used for the aggregate model, as well as future nonlinear modeling approaches.

A key to a successful nonlinear programming model is good initialization.  It helps the model to find a solution and converge.  The initialization schemes are based on the understanding of the problem and foundation principles.  For the CDU aggregate model, the adapted initialization scheme involves two stages, solving an LP model followed by a simple NLP model.  The results of the second initialization stage serve as the initial data for the aggregate model.  The two stage initialization scheme allows the aggregate model to converge and give a solution.  Generating this initialization scheme allowed for analysis of the cascaded columns model and identifying additional constraints.  These constraints are added to the aggregate model to further define the feasible region of the problem.

The developed NLP-based aggregate model for the CDU is integrated into a refinery production planning model.  The results of the new NLP production planning model are compared with the current LP models, namely fixed yield and swing cuts based models.  The benefits of introducing the NLP model are assessed in terms of accuracy, robustness and complexity.

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[2] Favennec, JP. (2001).  Refinery Operation & Management. Editions Technip. Paris.

[3] Li, W.; Hui, C.W.; Li, A.X.  (2005). Integrated CDU, FCC and product blending models into refinery planning.  Computers and Chemical Engineering, 29, 2010-2028.

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[5] Suphanit, B. (1999).  The design of complex distillation systems, PhD Thesis.  UMIST. Manchester.

[6] Trierwiler, D.; Tan, R.L. (2001) Advances in crude oil LP modeling. Hydrocarbon Asia, 8, 52-58

[7] Zhang, J.; Zhu, X.X.; Towler, G.P. (2001). A simultaneous optimization strategy for overall integration in refinery planning.  Industrial & Engineering Chemistry Research, 40, 2640-2653.