Abstract
Network models have proved to be an efficient tool for building data-driven proxy models that match observed production data or reduced-order models that match simulated data. A particularly versatile approach is to construct the network topology so that it mimics the intercell connection in a volumetric grid. That is, one first builds a network of "reservoir nodes" to which wells can be subsequently connected. The network model is realized inside a fully differentiable simulator. To train the model, we use a standard mismatch minimization formulation, optimized by a Gauss-Newton method with mismatch Jacobians obtained by solving adjoint equations with multiple right-hand sides. One can also use a quasi-Newton method, but Gauss-Newton is significantly more efficient as long as the number of wells is not too high. A practical challenge in setting up such network models is to determine the granularity of the network. Herein, we demonstrate how this can be mitigated by using a dynamic graph adaption algorithm to find a good granularity that improves predictability both inside and slightly outside the range of the training data.