Machine learning assisted relative permeability upscaling for uncertainty quantification

Abstract

Traditional two-phase relative permeability upscaling entails the computation of upscaled relative permeability functions for each coarse block (or interface). The procedure can be extremely time-consuming especially for cases with multiple (hundreds of) geological realizations as commonly used in subsurface uncertainty quantification or optimization. In this paper, we develop a machine learning assisted relative permeability upscaling method, in which the flow-based two-phase upscaling is performed for only a small portion of the coarse blocks (or interfaces), while the upscaled relative permeability functions for the rest of the coarse blocks (or interfaces) are quickly computed by machine learning algorithms. The upscaling procedure was tested for generic (left to right) flow problems using 2D models for scenarios involving multiple realizations. Both Gaussian and channelized models with standard boundary conditions and effective flux boundary conditions (EFBCs) are considered. Numerical results have shown that the coarse-scale simulation results using the newly developed machine learning assisted upscaling are of similar accuracy to the coarse results using full numerical upscaling at both ensemble and realization-by-realization levels. Because the full flow-based upscaling is only performed for a small fraction of the models, significant speedups are achieved.