Residual attention U-Net for predicting fluid dynamics and permeability in two-dimensional digital porous rocks

Abstract The prediction of fluid dynamics in porous media, such as sandstone and carbonate found in reservoir rocks, is a crucial aspect of characterizing subsurface fluid storage systems and energy management. Numerical approaches such as the lattice Boltzmann method (LBM) have been used to simulate fluid flow within microscopic pore structures. However, these methods still have limitations in terms of computational efficiency, particularly for complex pore geometries, and require physical parameters that are not always practically available. In response, this study presents a residual attention U-Net (RA-UNet) model to estimate pressure, velocity distribution, and permeability. The model uses two-dimensional rock images obtained from micro-computed tomography scans, trained using labels from LBM simulation results. The predictions show that fluid velocity achieves the highest accuracy in sandstone (MAE: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.24</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for the velocity component in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> </mml:math> direction, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>7.7</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>y</mml:mi> </mml:mrow> </mml:math> direction, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.57</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for the velocity magnitude), while pressure prediction performs best in carbonate rocks (MAE: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.32</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ). Permeability errors are relatively similar across both rock types (MAE: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.61</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ). Although the model performs well in most regions, predicting extreme values and smooth gradients remains challenging, particularly for pressure and velocity distributions. Therefore, the RA-UNet offers a data-efficient alternative to physics-based simulations for image-based flow estimation. Furthermore, it opens opportunities for integrating physical laws through hybrid methods within the framework of digital rock physics.