Implementation and Testing of Reduced-Order Models in a General Reservoir Simulation Setting

Reduced-order modeling can lead to computational savings in reservoir management applications when many related models must be simulated, as is the case, for example, in production optimization. In this study, we implement two reduced-order modeling procedures into our in-house simulator AD-GPRS (Automatic Differentiation General Purpose Research Simulator). The methods considered are a POD-Only (proper orthogonal decomposition) technique and a Gauss-Newton with approximated tensors (GNAT) procedure. We believe this to be the first implementation of these methods in a general-purpose reservoir simulation setting. Both approaches entail offline (training runs plus preprocessing) and online (runtime) computations. POD-Only involves expensive online matrix multiplications, which greatly limit the attainable speedup. GNAT, by contrast, entails much less costly runtime computations.
The methods are applied to a 2D oil-water model and to a 3D, four-component, oil-gas compositional case. These models contain 13,000 and 4800 grid blocks, respectively. Some amount of numerical experimentation is required to determine the appropriate POD-Only and GNAT parameters. We show that, using parameters that provide accurate reduced-order model results, POD-Only is actually slower than the full-order AD-GPRS simulations, but GNAT can provide speedup of around 2-3X for the cases considered. More substantial speedup is achieved in some compositional cases for which AD-GPRS encounters numerical difficulties. Speedup could be further enhanced by eliminating the AD-GPRS computations that are not required for GNAT. Application of POD-Only and GNAT on locally refined versions of the original models is, unfortunately, not very successful. This may be due to some of our detailed numerical treatments. This issue should be clarified and, if possible, rectified in future work.