Using Graph Neural Networks to Predict the Permeability of Porous Media

The permeability of porous media is often calculated using correlations or computationally expensive simulations. Several methods have been developed which use neural networks to predict porous media properties, but little work has been done on the development of a model that can handle porous media at the representative elementary volume (REV) scale. This work describes the framework for developing a graph neural network (GNN) to predict the permeability of porous media based on representative pore networks extracted from the structures, rather than representative structure volumes. This allows for consistent input sizes for the neural network, irrespective of the average pore size, which is more difficult when the entire voxelized structure is the model input. A GNN was trained to predict the permeability of porous media based on lattice Boltzmann method (LBM) simulations of the flow through the structures. The GNN showed a good agreement with the LBM simulations over samples with permeabilities spanning several orders of magnitude. The GNN was able to outperform the Carman-Kozeny equation with a mean squared error (MSE) for the unseen testing dataset of 0.00190 and a mean absolute error (MAE) of 0.0302 compared to an MSE of 1.125 and an MAE of 0.783 for the Carman-Kozeny equation, when comparing against the LBM ground truth. The inference time of the GNN alone was several orders of magnitude faster than the LBM simulations, and nearly 10 times faster when including the pore network extraction time needed for the GNN. This work demonstrates the potential of using GNNs to predict the permeability of representative porous media, and the benefits of using model architectures that take pore networks as the inputs.