We present an efficient workflow that combines multiscale (MS) forward simulation and stochastic gradient computation - MS-StoSAG - for the optimization of well controls applied to waterflooding under geological uncertainty. A two-stage iterative Multiscale Finite Volume (i-MSFV), a mass conservative reservoir simulation strategy, is employed as the forward simulation strategy. MS methods provide the ability to accurately capture fine scale heterogeneities, and thus the fine-scale physics of the problem, while solving for the primary variables in a more computationally efficient coarse-scale simulation grid. In the workflow, the construction of the basis fuctions is performed at an offline stage and they are not reconstructed/updated throughout the optimization process. Instead, inaccuracies due to outdated basis functions are addressed by the i-MSFV smoothing stage. The Stochastic Simplex Approximate Gradient (StoSAG) method, a stochastic gradient technique is employed to compute the gradient of the objective function using forward simulation responses. Our experiments illustrate that i-MSFV simulations provide accurate forward simulation responses for the gradient computation, with the advantage of speeding up the workflow due to faster simulations. Speed-ups up to a factor of five on the forward simulation, the most computationally expensive step of the optimization workflow, were achieved for the examples considered in the paper. Additionally, we investigate the impact of MS parameters such as coarsening ratio and heterogeneity contrast on the optimization process. The combination of speed and accuracy of MS forward simulation with the flexibility of the StoSAG technique allows for a flexible and efficient optimization workflow suitable for large-scale problems.@en

The goal of reservoir management is to make decisions with the objective of maximizing the value creation from oil or gas production. To achieve this, models that preserve geological realism and have predictive capabilities are being developed and used. These models are commonly calibrated using assisted-history-matching (AHM) methods which, in general, will lead to reduced uncertainty in the predicted production. Although uncertainty assessment and reduction are often elements of high-quality decision making, they are not value-creating. Value can only be created through decisions, and any decision changes resulting from AHM should be modeled explicitly. Recently, there has been a surge in the application and understanding of value-of-information (VOI) work flows for reservoir management. In this text, we present a comparison of existing work flows and note the differences between them. After this, we introduce a practically driven approach, referred to as “drill and learn,” with elements and concepts from existing work flows to quantify the value of learning (VOL). VOL can be used as a metric to quantify the potential of such work flows and the strategies obtained. Ensemble methods [ensemble smoother with multiple data assimilation (ES-MDA) and stochastic simplex approximate gradient (StoSAG)] are used for the history matching and optimization. The results presented are obtained by applying the proposed drill-and-learn work flow on a realistic synthetic case. Sensitivities to the amount of information obtained before a closed-loop exercise is performed are also investigated. We show the benefit of performing the closed-loop approach to quantify the VOL to modify field-development decisions, which leads to a mature and robust decision-making framework.@en