Abstract
Optimizing the objectives of long-term reservoir management typically requires a high number of forward reservoir simulations. Two important remedies to reduce the runtime (and make the optimization problem manageable) are model reduction/upscaling and efficient computation of gradients. Adjoint methods are generally considered to be the most efficient means for obtaining gradients. Furthermore, there has been much interest in reduced-order modelling (e.g., based on POD) for reservoir management optimization. Very promising results have been reported for models with somewhat limited complexity. Application to industry-standard cases is inhibited in part by the invasive nature of the approach with respect to simulator code, and the fact that the number of required basis functions is correlated with the degree of nonlinear dynamics. In this work, we utilize ideas from POD to compute upscaled transmissibilities for a coarse model, rather than using the method directly to build a basis for the fine-scale state space. The proposed coarsening strategy takes as input any number of fine-scale states (pressure fields from e.g., a previous simulation), and produces a coarse-scale model calibrated to the specific flow scenario(s) dictated by the input. We argue that compared to traditional general-purpose upscaling approaches, much more aggressive coarsening can be applied in this type of scenario-specific upscaling. Utilizing a fully-implicit, threephase, black-oil simulator with adjoint capabilities, we investigate the performance of our methodology by optimizing the net-present-value (NPV) for a real-field model. We consider multiple coarsening strategies and coarsening factors, and conclude that for the model considered, at least two orders of magnitude speed-up can be achieved whilst retaining sufficient accuracy.
