Application of multi-criterion robust optimization in water-flooding of oil reservoir

• A robust multi-objective optimization is presented to reduce the sensitivity.
• The optimization is done for cases when no measurement is available.
• Three dedicated objective functions are formulated to cover this situation.
• The ranking scheme is based on NPV of Base Case.
• Robust optimization shows better results in comparison with single non-robust optimization.

Most of the reported robust and non-robust optimization works are formulated based on a single-objective optimization, commonly in terms of net present value. However, variation of economical parameters such as oil price and costs forces such high computational optimization works to regenerate their optimum water injection policies. Furthermore, dynamic optimization strategies of water-flooding often lack robustness to geological uncertainties. This paper presents a multi-objective while robust optimization methodology by incorporating three dedicated objective functions. The goal is to determine optimized and robust water injection policies for all injection wells. It focuses on reducing the sensitivity to the uncertainty in the model and objective function parameters when no measurement information is assumed to be available. This work also, utilizes a derivative-free Evolutionary Multi-objective Optimization (EMO) procedure in the form of a Non-dominated Sorting Genetic Algorithm (NSGA) which attempts to find a robust Pareto-optimal solution without a priori knowledge of the reservoir dynamic models. Some modifications have been introduced to the original NSGA-II code to handle the constraints of the optimization problem. The comparative test studies clearly demonstrate superiority of the proposed methodology to give optimal robust solutions under geological uncertainties with much less standard deviations and variances. Furthermore, the optimization results demonstrate less sensitivity to the imposed time-varying economical parameters such as operation costs and oil price, revealing non-dependency of the introduced multi-objective functions.