Optimal control of polymer flooding based on simultaneous perturbation stochastic approximation method guided by finite difference gradient

• An optimal control model was proposed to design injection scheme of polymer flooding.
• A modified optimization method was developed and compared with two common algorithms.
• Efficiency and effectiveness of the proposed method was validated by a case study.
• The net present value of polymer flooding increased by 11.67% after optimization.
• Optimum polymer injection amount increased with oil price until it reached stable.

The paper established an optimal control model of polymer flooding, which involves the incremental cumulative net present value as objective function, the injection concentration and volume size in each slug of every injector as control variables, and the limitation of polymer concentration and injection amount as boundary constraints. An improved simultaneous perturbation stochastic approximation method guided by finite difference gradient was then proposed. It adjusted the ratio among perturbation steps of different control variables during iterations according to the finite difference gradient. The case study showed the improved algorithm needed much fewer simulations for convergence. Compared with uniform injection scheme, the allocation amount of polymer solution in well groups with strong vertical heterogeneity was increased and the incremental cumulative net present value increased by 11.64% after optimization. The paper finally investigated the effect of crude oil price on the optimum injection amount of polymer solution for a given reservoir.