Data-Driven Modelling with Coarse-Grid Network Models

Interwell network models have been proposed by many authors as a good physics-based alternative to machine-learning methods for building data-driven flow models in subsurface applications. Herein, we suggest an alternative approach, in which a conventional simulator, formulated on top of a very coarse volumetric 3D grid, is used as a data-driven proxy model. What distinguishes this conceptually from standard history matching is that the standard tunable parameters in the simulator (pore volumes, transmissibilities, well-connection factors, initial saturations, relative permeability exponents and scalings, etc.) are calibrated freely without regard to the physical interpretation of the resulting parameter values. In its most basic form, our CGNet models are formulated as a minimal Cartesian grid that covers the assumed map outline and base and top surface of the reservoir. The parameters of the resulting 3D simulation model are then calibrated to match observed well responses. Using simulation cases built on top of public data sets (the Egg model, the Norne field model, etc.), we show that surprisingly accurate proxy models can be developed using grids with a few tens or hundreds of cells, depending upon the geological complexity of the model. For the Norne case, we show that it is important that the proxy model has several vertical layers because of the poor vertical connection inside the true reservoir volume. We also show that starting with a good ballpark estimate of the reservoir volume is a precursor to a good calibration. The resulting CGNet models fit immediately in any standard simulator and are very fast to evaluate because of the low cell count. Compared with an interwell network model like GPSNet (Ren et al., 10.2118/193855-MS), a typical CGNet model has fewer computational cells but a richer connection graph and more tunable parameters. In our experience, CGNet models calibrate better and are simpler to set up to reflect known (or pre-modelled) fluid contacts or geobodies.