Interpretable pressure-dependent permeability modeling for confined gas transport in complex nano-porous media

Abstract

Estimating permeability in complex nano-porous media is difficult because of strong heterogeneity and a wide range of pore sizes. Shale is a prominent example, and it is the focus of this work. Experimental measurements are slow, particularly because apparent gas permeability is pressure-dependent due to gas slippage in nano-porous media and must be measured at several pressures. Direct numerical simulation is an alternative but requires high-resolution SEM or FIB-SEM imaging, digital-rock reconstruction, and substantial computational resources per sample. In this work we use a data-driven workflow to uncover the relationship between apparent gas permeability and the morphological and network-theoretic descriptors of the pore space. Over 5,000 2D porous-media images are generated at 1 nm resolution, and gas transport is modeled with the lattice Boltzmann method on high-performance computing resources. A large set of descriptors including porosity, pore-size distribution, morphology, and network-theoretic descriptors are extracted from each sample. Feature selection is followed by symbolic regression, which produces interpretable and physically consistent correlations for permeability with R2=0.95. The correlation is then coupled with a power-law Knudsen correction to obtain a pressure-dependent, white-box apparent-permeability model. We apply this model end-to-end on a sample of Mowry shale, covering SEM imaging, stitching, segmentation, reconstruction, and permeability prediction, and compare it with LBM simulations across two orders of magnitude in pressure. Without parameter tuning, the model underpredicts the simulated permeability by a typical factor of 3.3, and it remains more accurate than black-box models applied to the same sample. The workflow offers a route to estimating apparent permeability in shale at a fraction of the cost of direct simulation.