Proxy Models Accelerated Using Physics-Based Reduced-Order Model

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This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 228142, “Acceleration of Data-Driven Proxy Models Using Physics-Based Reduced-Order Model: Pseudosteady-State-Based Simulation,” by Koki Nakano, SPE, Chin-Hsiang Chan, SPE, and Akhil Datta-Gupta, SPE, Texas A&M University. The paper has not been peer-reviewed.

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Injecting CO2 into subsurface formations for large-scale geological carbon sequestration requires rapid and reliable reservoir-pressure estimation for storage integrity and minimization of potential seismic activities. Although various machine- and deep-learning models have been proposed for this purpose, these models typically require numerous reservoir simulations to generate adequate training data, which can be computationally expensive and potentially can offset the acceleration in pressure prediction. This work uses a novel pseudosteady-state-based simulation (PSS-SIM) to significantly reduce training-data-generation cost while maintaining high-performance predictions of data-driven proxy models for near-real-time monitoring and control of carbon sequestration projects.

Methodology

Pseudosteady-State Pressure Contour.

The applicability of fast marching method (FMM)-based simulation has been demonstrated in unconventional oil and gas reservoir and enhanced geothermal applications, both of which are characterized by lower permeability. While FMM-based simulation has been applied successfully to low-permeability reservoirs, this method has limitations with regard to applications for high-permeability reservoirs, which are typical for carbon capture and storage (CCS) applications. The diffusive time of flight (DTOF) is insufficient for capturing pressure distribution in high-permeability reservoirs accurately because it fails to properly incorporate the influence of both internal and external boundary conditions. As an alternative spatial coordinate for high-permeability reservoirs, PSS pressure was developed. Under PSS conditions, the pressure drops uniformly throughout the reservoir, which mathematically is referred to as the pressure derivative with respect to time being uniform across the reservoir. In this condition, the pressure-profile shape in space is steady and the pressure change is linear in time. The complete paper includes several establishing equations for this approach.

Computing the PSS pressure typically takes several minutes per million cells, whereas calculating DTOF requires only a few seconds using FMM. The PSS pressure calculation needs to be performed only once before running the simulation. Therefore, if the overall simulation time is sufficiently long, the preprocessing time becomes negligible. However, because the reduced-order model significantly shortens the simulation time by orders of magnitude, reducing the preprocessing time also is necessary to maintain efficiency. Using an advanced matrix solver, the PSS calculation can now be completed in under a minute per million grid cells, compared with several minutes in previous applications.