<p>The development of subsurface exploitation projects, including <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\text {CO}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CO</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> storage, relies on extensive numerical simulations in which fluid flow and transport through porous media are, at some stage, coupled with the Biot poroelasticity problem. This coupling is essential, for example, to assess the potential destabilization of faults and the induced seismicity that may follow. Because such high-fidelity simulations are computationally intensive, we explore the use of a surrogate model as an efficient alternative to full-physics computations. Our methodology adopts a data-driven framework based on neural networks, named deep learning reduced order modeling (DL-ROM), to construct a reduced model whose latent space is determined by an autoencoder trained on solutions from full-physics simulations. In this study, we account for uncertain physical parameters (e.g. Young’s moduli, permeabilities, fault transmissibility) alongside operational controls (such as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\text {CO}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CO</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> injection rate) and train the DL-ROM on typical reservoir operation scenarios. We validate the surrogate model on two synthetic cases of underground <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\text {CO}_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>CO</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> storage, each featuring a sloping fault that may be reactivated during injection. High-fidelity reference simulations employ a one-way coupling strategy: flow in the porous medium is treated with a finite-volume commercial code, while the solid mechanics problem is addressed either via a commercial finite-element package or using the multi-point stress finite-volume scheme implemented in the open-source PorePy library, demonstrating the method’s applicability to different workflows. By comparing DL-ROM predictions against standard numerical solutions for unseen parameter combinations during the training, we demonstrate that the reduced model accurately reproduces fault stress states and the key metrics used to evaluate fault ty. Once trained, the DL-ROM is exceedingly fast, making it well suited for multi-query analyses and statistical assessments of fault reactivation risk. Although surrogate models for fault stability have been proposed before, to our knowledge this work represents one of the first applications of a purely data-driven DL-ROM approach in this context.</p>

Enhancing computational efficiency of numerical simulation for subsurface fluid-induced deformation using deep learning reduced order models

期刊论文
发表日期：

2026年3月4日

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E. Ballini,
A. Cominelli,
L. Dovera,
A. Forello,
L. Formaggia,
A. Fumagalli,
S. Nardean,
A. Scotti,
P. Zunino

摘要

The development of subsurface exploitation projects, including $\text {CO}_2$ ${CO}_{2}$ storage, relies on extensive numerical simulations in which fluid flow and transport through porous media are, at some stage, coupled with the Biot poroelasticity problem. This coupling is essential, for example, to assess the potential destabilization of faults and the induced seismicity that may follow. Because such high-fidelity simulations are computationally intensive, we explore the use of a surrogate model as an efficient alternative to full-physics computations. Our methodology adopts a data-driven framework based on neural networks, named deep learning reduced order modeling (DL-ROM), to construct a reduced model whose latent space is determined by an autoencoder trained on solutions from full-physics simulations. In this study, we account for uncertain physical parameters (e.g. Young’s moduli, permeabilities, fault transmissibility) alongside operational controls (such as $\text {CO}_2$ ${CO}_{2}$ injection rate) and train the DL-ROM on typical reservoir operation scenarios. We validate the surrogate model on two synthetic cases of underground $\text {CO}_2$ ${CO}_{2}$ storage, each featuring a sloping fault that may be reactivated during injection. High-fidelity reference simulations employ a one-way coupling strategy: flow in the porous medium is treated with a finite-volume commercial code, while the solid mechanics problem is addressed either via a commercial finite-element package or using the multi-point stress finite-volume scheme implemented in the open-source PorePy library, demonstrating the method’s applicability to different workflows. By comparing DL-ROM predictions against standard numerical solutions for unseen parameter combinations during the training, we demonstrate that the reduced model accurately reproduces fault stress states and the key metrics used to evaluate fault ty. Once trained, the DL-ROM is exceedingly fast, making it well suited for multi-query analyses and statistical assessments of fault reactivation risk. Although surrogate models for fault stability have been proposed before, to our knowledge this work represents one of the first applications of a purely data-driven DL-ROM approach in this context.