Physics-Informed AI Modeling and Forecasting in Porous Media
Abstract
Numerical simulation in porous media relies on the discrete representation of equations that have been derived from first principles and conservation laws. In many practical applications, the scope of these equations can be insufficient to realistically describe the dynamics of flow in complex porous media induced by sudden changes in boundary conditions and force terms (e.g., wells, aquifers). Nevertheless, the increasing affordability for collecting and storing large volumes of data is enabling possibilities to gain new insights and discover elusive physical relations missing from existing simulation models.
In this work, we propose a novel class of combined physics-based and data-driven models, namely physics-informed AI models, to reconstruct and discover spatiotemporal trends observed in challenging porous media scenarios. These models are designed to learn and identify new relationships from monitoring data as well as providing explainable interpretations of the underlying phenomena. In this respect, the proposed approach differs from traditional data-driven approaches that strictly relies on black-box solutions. We focus our attention on porous media applications characterized by extreme permeability contrasts and geometries as those induced by arbitrary channels or fractures. To that end, we assume that complex flows can reliably be decomposed into a sequence of spatiotemporal coherent structures through an extended dynamic mode decomposition approach. Using sparse elastic net type of regressions on a generic form of the PDE governing the process, we can also derive coefficients that best describe the underlying phenomena. We illustrate the capability of our framework on both single- and two-phase flow models, and investigate performance implications of these models for optimizing well geometries and locations under uncertainty. Results illustrate tangible opportunities for performing forecast on relevant environmental and energy applications.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.H34B..01K
- Keywords:
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- 1805 Computational hydrology;
- HYDROLOGY