Stochastic multi-objective optimization approaches in a real-world oil field waterflood management

Multi-objective differential evolution with hybrid local dynamic search algorithm (HMODE-DLS) and non-dominated sorting genetic algorithm (NSGA-II) are applied successfully in a reservoir sector model of a Middle Eastern real-world oil field under waterflood development. The Pareto solutions of the two objectives of maximum oil production and minimum water production obtained by the two algorithms are analyzed and compared in this study. The sector model consists of four oil producers and three water injectors and it is run for ten years with twenty time-steps of six months each. A total of 140 decision variables are defined as bottom-hole pressures for the four producers and water injection rates for the three water injectors at each time step (i.e. 7 variables by 20 time-steps). The optimal Pareto solution is obtained at 12,600 function evaluations by HMODE-DLS with 70% convergence improvement compared to 42,000 objective evaluations by NSGA-II. Results show that NSGA-II generated more optimum solutions in the lower range (i.e. less than 480 thousand m(3) (Mm(3)) total oil production) whereas, the hybrid MODE-DLS has a more optimum solution in the higher range of the Pareto front. The net flow method (NFM) is usedin this study to select the best optimal solutions from the Pareto front solutions based on the weight of the objective function chosen by the decision-maker. By using the entropy weight criteria, the best optimal solution of high oil production determined is 540.45 Mm(3) at the HMODE-DLS Pareto front. On the other hand, the best optimal solution of low oil production obtained is 469.93 Mm(3) at the NSGA-II Pareto front. The combined optimal Pareto fronts obtained by NSGA-II and HMODE-DLS algorithms offer good spread and diverse solutions for the decision-maker to select and operate the field based on the operation conditions and constraints.