Robust optimization formulations for waterflooding management under geological uncertainties

In oil reservoir management, one of the major challenges is the search for the best production plan under geological uncertainties. One way to conduct optimal management of reservoirs under uncertainty is through robust optimization, which uses a set of realizations to approximate some statistics of the reservoir properties. The statistics considered here are the mean and standard deviation of the net present value (NPV). In this work, two different formulations for the optimal robust management of oil reservoirs are considered using a unique objective function. One formulation is also presented in a multi-objective context. All of these are employed to solve two benchmark problems. As all the proposed formulations are very computationally intensive, surrogate models are used for the several function calls required in both optimization and uncertainty propagation. The results obtained by the proposed strategies proved to be efficient for both single and multi-objective problems. For the two studied problems, using 500 and 100 realizations, respectively, the obtained results, when compared with the ones obtained by reactive control strategy, show an increase of mean NPV more than 10% in average. The multi-objective optimization results for both investigated reservoirs show an optimal robust Pareto front that can be used to make a trade-off between the mean of NPV and the mean of water injection. This work shows that surrogate models, a special subset of the full set of reservoir realizations and parallel processing should be used for the application in robust managements of practical reservoir engineering problems.