Abstract In this work we discuss the successful application of our previously developed automated scenario reduction approach applied to life-cycle optimization of a real field case. The inherent uncertainty present in the description of reservoir properties motivates the use of an ensemble of model scenarios to achieve an optimized robust reservoir development strategy. In order to accurately span the range of uncertainties it is imperative to build a relatively large ensemble of model scenarios. The size of the ensemble is directly proportional to the computational effort required in robust optimization. For high-dimensional, complex field case models this implies that a large ensemble of model scenarios which albeit accurately captures the inherent uncertainties would be computationally infeasible to be utilized for robust optimization. One of the ways to circumvent this problem is to work with a reduced subset of model scenarios. Methods based on heuristics and ad-hoc rules exist to select this reduced subset. However, in most of the cases, the optimal number of model realizations must be known upfront. Excessively small number of realizations may result in a subset that does not always capture the span of uncertainties present, leading to sub-optimal optimization results. This raises the question on how to effectively select a subset that contains an optimal number of realizations which both is able to capture the uncertainties present and allow for a computationally efficient robust optimization. To answer this question we have developed an automated framework to select the reduced ensemble which has been applied to an original ensemble of 300 equiprobable model scenarios of a real field case. The methodology relies on the fact that, ideally, the distance between the cumulative distribution functions (CDF) of the objective function (OF) of the full and reduced ensembles should be minimal. This allows the method to determine the smallest subset of realizations that both spans the range of uncertainties and provides an OF CDF that is representative of the full ensemble based on a statistical metric. In this real field case application we optimize the injection rates throughout the assets life-cycle with expected cumulative oil production as the OF. The newly developed framework selected a small subset of 17 model scenarios out of the original ensemble which was used for robust optimization. The optimal injection strategy achieved an average increase of 6% in cumulative oil production with a significant reduction, approximately 90%, in the computational effort. Validation of this optimal strategy over the original ensemble lead to very similar improvements in cumulative oil production, highlighting the reliability and accuracy of our framework.

We propose a novel adaptive, adjoint-based, iterative multiscale finite volume (i-MSFV) method. The method aims to reduce the computational cost of the smoothing stage of the original i-MSFV method by selectively choosing fine-scale sub-domains (or sub-set of primary variables) to solve for. The selection of fine-scale primary variables is obtained from a goal-oriented adjoint model. An adjoint-based indicator is utilized as a criterion to select the primary variables having the largest errors. The Lagrange multipliers from the adjoint model can be interpreted as sensitivities of the objective function value with respect to deviations from the constraints. In case of adjoining the porous media flow equations with Lagrange multipliers, this implies that the multipliers are the sensitivities of the objective function with respect to the residuals of the flow equations, i.e., to the residual error that remains after approximately solving linear equations with the aid of an iterative solver. This allow us to recognize at which locations the solution contains more errors. More specifically, we propose a modification to the i-MSFV method to adaptively reduce the size of the fine-scale system that must be smoothed. The aim is to make the fine-scale smoothing stage less computationally demanding. To that end, we introduce a goal-oriented, adjoint-based fine-scale system reduction criterion. We demonstrate the performance of our method via single-phase, incompressible flow simulation models with challenging geological settings and using a history-matching like misfit objective function as the goal. The performance of the newly introduced method is compared to the original i-MSFV method. We investigate the adaptivity versus accuracy of the method and demonstrate how the solution accuracy varies by varying the number of unknowns selected to be smoothed. It is shown that the method can provide accurate solutions at reduced computational cost. The proof-of-concept applications indicate that the method deserves further investigations.

In this work, we discuss the application of stochastic optimization approaches to the OLYMPUS case, a benchmark challenge which seeks the evaluation of different techniques applied to well control and field development optimization. For that matter, three exercises have been proposed, namely, (i) well control optimization; (ii) field development optimization; and (iii) joint optimization. All applications were performed considering the so-called OLYMPUS case, a synthetic reservoir model with geological uncertainty provided by TNO (Fonseca 2018). Firstly, in the well control exercise, we successfully applied an ensemble-based approximate gradient method in a robust optimization formulation. Secondly, we solve the field development exercise using a genetic algorithm framework designed with special features for the problem of interest. Finally, in order to evaluate further gains, a sequential optimization approach was employed, in which we run one more well control optimization based on the optimal well locations. Even though we utilize relatively well-known techniques in our studies, we describe the necessary adaptations to the algorithms that enable their successful applications to real-life scenarios. Significant gains in the expected net present value are obtained: in exercise (i) a gain of 7% with respect to reactive control; for exercise (ii) a gain of 660% with respect to a initial well placement based on an engineering approach; and for (iii) an extra gain of 3% due to an additional well control optimization after the well placement optimization. All these gains are obtained with an affordable computational cost via the extensive utilization of high-performance computing (HPC) infrastructure. We also apply a scenario reduction technique to exercise (i), with similar gains obtained in the full ensemble optimization, however, with substantially inferior computational cost. In conclusion, we demonstrate how the state-of-the-art optimization technology available in the model-based reservoir management literature can be successfully applied to field development optimization via the conscious utilization of HPC facilities.