Hierarchical homogenization with deep-learning-based surrogate model for
rapid estimation of effective permeability from digital rocks
Abstract
Effective permeability is a key physical property of porous media that
defines its ability to transport fluid. Digital rock physics combines
modern tomographic imaging techniques with advanced numerical
simulations to estimate effective rock properties. Digital rock physics
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 workflow (HHM-CNN) divides the large digital rock into
small sub-volumes and predicts the sub-volume 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 is verified on micro-CT data of both sandstones and
carbonates as well as the reconstructed high-resolution digital rock
obtained by multiscale data fusion. The computed permeabilities of our
proposed hierarchical approach are consistent with the results of the
DNS on the full digital rock. Compared with conventional DNS algorithms,
the proposed hierarchical approach can largely reduce the computational
time and memory demand.