Hybrid approach of using bi-objective genetic programming in well control optimization of waterflood management

A new hybrid optimization approach is proposed by applying bi-objective genetic programming (BioGP) algorithm along with NSGA-II algorithm to expand the diversity of the Pareto solutions and speed up the convergence. The novel methodology is used in two distinct cases: the benchmark model for the Brugge field and a Middle Eastern oil-field sector model. The Brugge field includes twenty producing wells and ten injecting wells, but the real sector model has three injectors and four producers. The two primary objectives applied are to optimize the total volume of produced oil and reduce cumulative produced water. In the optimization process, the injection rate (q_wi) and the bottom-hole pressure (BHP) are the control parameters for injection and producing wells, respectively. The hybrid technique of applying BioGP guided NSGA-II in the Brugge field model demonstrated a 50% acceleration in the convergence speed when compared to the NSGA-II solution. The calculated Pareto solutions for the Middle-Eastern sector model by the proposed methodology at various generations exhibited better diversity and convergence in comparison to the NSGA-II solutions. The highest cumulative produced oil of 550.45 × 10³ m³ is obtained by the proposed hybrid methodology in comparison to the NSGA-II's highest cumulative of 522 × 10³ m³. The two solution points A′ and B′ achieved using the BioGP guided NSGA-II have lower WOR by 17% and 15%, respectively, than A and B solutions established by NSGA-II alone. Pareto solution ranking is performed using the net flow method (NFM) and the best optimum solution determined for BioGP guided NSGA-II is 532.38 × 10³ m³ oil using equal-based weight compared to 505.44 × 10³ m³ using the entropy-based weights of 41% oil & 59% water. Overall, the optimal Pareto solutions achieved by the proposed methodology of using BioGP guided NSGA-II algorithm has better diversity with improvement in convergence speed in comparison to the NSGA-II.