Graph network surrogate model for subsurface flow optimization

The optimization of well locations and controls is an important step in the design of subsurface flow operations such as oil production or geological CO 2 storage. These optimization problems can be computationally expensive, however, as many potential candidate solutions must be evaluated. In this study, we propose a graph network surrogate model (GNSM) for optimizing well placement and controls. The GNSM transforms the flow model into a computational graph that involves an encoding -processing -decoding architecture. Separate networks are constructed to provide global predictions for the pressure and saturation state variables. Model performance is enhanced through the inclusion of the single-phase steady-state pressure solution as a feature. A multistage multistep strategy is used for training. The trained GNSM is applied to predict flow responses in a 2D unstructured model of a channelized reservoir. Results are presented for a large set of test cases, in which five injection wells and five production wells are placed randomly throughout the model, with a random control variable (bottom -hole pressure) assigned to each well. Median relative error in pressure and saturation for 300 such test cases is 1-2%. The ability of the trained GNSM to provide accurate predictions for new (geologically similar) permeability realizations is demonstrated. Finally, the trained GNSM is used to optimize well locations and controls with a differential evolution algorithm. GNSM-based optimization results are comparable to those from simulation -based optimization, with a runtime speedup factor of 36. Much larger speedups are expected if the method is used for robust optimization, in which each candidate solution is evaluated on multiple geological models.