Hierarchical Homogenization With Deep‐Learning‐Based Surrogate Model for Rapid Estimation of Effective Permeability From Digital Rocks

Abstract

AbstractEffective permeability is a key physical property of porous media that defines its ability to transport fluid. Digital rock physics (DRP) combines modern tomographic imaging techniques with advanced numerical simulations to estimate effective rock properties. DRP is used to complement or replace expensive and time‐consuming or impractical laboratory measurements. However, with increase in sample size to capture multimodal and multiscale microstructures, conventional approaches based on direct numerical simulation (DNS) are becoming very computationally intensive or even infeasible. To address this computational challenge, we propose a hierarchical homogenization method (HHM) with a data‐driven surrogate model based on 3‐D convolutional neural network (CNN) and transfer learning to estimate effective permeability of digital rocks with large sample sizes up to billions of voxels. This HHM‐CNN workflow divides a large digital rock into small sub‐volumes and predicts their permeabilities through a CNN surrogate model of Stokes flow at the pore scale. The effective permeability of the full digital rock is then predicted by solving the Darcy equations efficiently on the upscaled model in which the permeability of each cell is assigned by the surrogate model. The proposed method has been verified on micro‐CT scans of both sandstones and carbonates, and applied to the Bentheimer sandstone and a reconstructed high‐resolution carbonate rock obtained by multiscale data fusion. The computed permeabilities of the HHM‐CNN are consistent with the results of DNS on the full digital rock. Compared with conventional DNS algorithms, the proposed hierarchical approach can largely reduce the computational time and memory demand.