A Black-Box Stencil Interpolation Method to Accelerate Reservoir Simulations

摘要

The present work aims at predicting space-time pressure solutions via a novel non-intrusive reduced order simulation model. The construction of low-dimensional spaces entails the combination of the Discrete Empirical Interpolation (DEIM) method with a suitable regressor such as artificial neural network to accurately approximate the pressure solutions arising in an IMPES formulation. Two basic assumptions are key in the present work: (a) physics invariance and, (b) stencil locality. The first one allows for coping with the curse of dimensionality associated with the training of a lower-dimensional surrogate model. The second assumption enables to significantly reduce the input parameter space and therefore, infer the global solution from local mass conservation principles. These assumptions are inspired in the discretization of PDEs governing the flow in porous media and serve as a powerful vehicle to generate physics-based surrogate models at a low computational cost. Hence, without explicit or little knowledge of simulation equations and numerical schemes, a sequence of pressure solutions or initial guesses can be obtained from inexpensive solutions of reduced order models (ROMs). Numerical examples are provided to illustrate the potentials of the present approach.