In this study, the authors propose the use of a deep-learning (DL) reduced-order surrogate model that can lower computational costs significantly while maintaining high accuracy for data assimilation or history-matching (HM) problems. The fundamental component is the Embed-to-Control Observe (E2CO) DL architecture. It serves as a reduced-order model mimicking the trajectory piecewise linearization (TPWL) coupled with proper orthogonal decomposition (POD) to simulate subsurface flow by using blocks of neural networks trained with the snapshots generated from a high-fidelity model or simulator.
Methodology, Results, and Discussion
An initial section of the complete paper outlines the theories, methods, and mathematical equations that support the proposed E2CO-HM. These subsections of the complete paper include discussions of POD-TPWL formulation and E2CO-HM formulation. In this section of the synopsis, the authors describe the synthetic reservoir model, SPE10, used to apply the E2CO-HM-based approach and discuss the results obtained.
Reservoir Model. A section of the oil/water SPE10 benchmark model with grid dimensions 60×60×4 was used in the proposed E2CO-HM. This channelized reservoir model consists of four layers with permeability values measured in mD for each layer.
