A Logic Branch and Bound Algorithm for Petroleum Production Optimization Based on Generalized Disjunctive Programming

A new solution method for solving the real time production optimization (RTPO) problem for a petroleum production system is presented in this thesis. The objective function of the problem maximizes oil production and the RTPO handles decision variables at operational level. Including routing of production flows, lift gas allocation, and pressure configurations of the system. It is aimed to give decision support in a time horizon of days to weeks. Such problems require solution methods able to obtain solutions swiftly, as production planners adjust network components frequently to maintain optimal production.The problem contains binary decision variables combined with nonlinear expressions and is mathematically classified as a nonconvex mixed integer nonlinear problem (MINLP). MINLPs are in general known as computationally expensive and hard to solve to optimality, and when nonconvexities are present, few solvers can guarantee global optimality. The solution method presented deviates from traditional optimization techniques applied to such problems, and introduces logic disjunctions to substitute the binary variables of the MINLP. A specialized branch and bound algorithm (LBB) is developed to utilize the structure of these disjunctions, and as time is of paramount importance for the RTPO, it is aimed to reduce demanded computational effort for the problem. The LBB is given a high degree of user flexibility to be able to tailor the algorithm to different problems.Results of the LBB show substantial variation in solution efficiency when applied to a real petroleum production system. Only when specific problem knowledge is utilized to customize the algorithm to the current system, the algorithm provides solid reduction in computational effort compared to a recognized commercial solver. Also when applied to variations in system structure the LBB clearly outperforms the applied solver, and the effectiveness and robustness of the proposed algorithm when utilizing problem specific knowledge is confirmed. The fact that the LBB provides the same solution to the problem as the applied solver might also indicate that the nonconvexities of the problem are not as complex as expected, and that the solver is in fact able to find the global optimal solution