(356d) A Solution Strategy for Large-Scale Nonlinear Petroleum Refinery Planning Models

Industrial applications of nonlinear petroleum refinery planning models result in large-scale optimization problems due to the size and complexity of the system. These optimization problems are characterized by their nonlinear nature involving no convex terms (bilinear terms, trilinear terms, etc.). Consequently, the direct implementation of nonlinear optimization solvers (CONOPT, IPOPT, SNOPT, MINOS, KNITRO, etc.) in the solution of these problems can lead to infeasible solution or local optimal solution, depending on the starting point used by the solver (or specified by the user). On the other hand, the global optimization solvers available in the literature (BARON, LINDOGlobal, etc.) fail to solve these practical problems.

In this work, a solution strategy for real work petroleum refinery planning problems is presented. This solution strategy is based on the decomposition of the planning problem in two levels. In the first level, nonlinear terms in the planning model are convexified using the McCormick convex/concave envelopes [1,2] for the bilinear and trilinear terms; the convexified planning model results in a linear programming (LP) problem that can be solved using LP solvers available in the literature (CPLEX, XPRESS, etc.). Results from this LP problem (relaxed solution) are used in the second level as a starting point for the solution of the nonlinear planning model using a local optimization solver. This strategy was implemented for the production planning problem at GRB (ECOPETROL's petroleum refinery located in Barrancabermeja, Colombia) using ECOPETROL's planning model (SIGMA-PLANNING), the results from this strategy were successfully compared with the Distributive Recursion (DR) strategy used in commercial planning tools such as the Process Industry Modeling System (PIMS). The main advantage of this strategy is that the solution of the LP problem provides a good starting point for the solution of the nonlinear optimization problem.

[1] McCormick, G. P. (1976), Computability of Global Solutions to Factorable Nonconvex Programs: Part I - Convex Underestimating Problems. Math. Program. 10, 147 -175.

[2] Maranas, C.D. and Floudas, C.A. (1995), Finding all solutions of nonlinearly constrained systems of equations. Journal of Global Optimization 7(2): 143?182.