Hybrid pore-network and lattice-Boltzmann permeability modelling accelerated by machine learning

In this paper, a permeability calculation workflow is presented that couples pore network modeling (PNM) with a Lattice Boltzmann Method (LBM) to benefit from the strengths of both approaches. Pore network extraction is implemented using a watershed segmentation algorithm on 12 three-dimensional porous rock images. The permeabilities of all throats are calculated using the LBM and substituted in the pore network model instead of using the cylindrical formulation for throat's permeability based on the Hagen-Poiseuille equation. Solving the LBM for every throat results in an accurate representation of flow but the algorithm is computationally expensive. In order to minimize the computational costs, LBM is used to model the steady-state incompressible fluid flow through 9333 different throat images and an Artificial Neural Network (ANN) is trained to mimic the trend of throat's permeabilities based on the cross-sectional images. To this end, we extract several morphological features of the throats cross-sectional images and search for the best describing feature. It is found that the averaged distance map of the throat images is highly correlated with the LBM-based permeability of throats to the extent that even a simple empirical correlation can reasonably describe the relationship between these two parameters. Finally, we compare the absolute permeability of samples obtained by full LBM with the presented hybrid method. Results show that the proposed method provides an accurate estimation of permeability with a considerable reduction in the computational CPU time.