A Fully Differentiable Pore Network for Digital Reconstruction of Porous Media

Abstract

Pore network models are useful for efficiently studying transport processes in porous materials at the pore scale. However, constructing accurate pore network representations is not always straight forward as it involves either complicated image processing or tedious calibration of network properties to experimental data. While network extraction tools are much more accessible today, access to high resolution X-ray tomography images is not nearly as widespread. Researchers of porous materials without access to high resolution microtomography images must therefore rely on calibrating a pore network by manually adjusting pore sizes and constantly checking that it satisfies the properties of the actual material. This paper presents a new strategy for fitting a regular lattice-based pore network to experimental data by using automatic differentiation for gradient descent optimization. The optimization was demonstrated on a data set of carbonate, sandstone, and sandpack materials for which images and experimental information were both available. The optimization of a 10 3 pore network took on average 21 and a half minutes on a GPU and the resulting networks matched the porosimetry curves and permeability in all directions of the actual material very closely. The optimization was then tested on real experimental data in which a final loss of 9.7x10 -4 was achieved. In addition, a workflow was developed for obtaining a stochastic network of arbitrary size from the fitted network. This required a description of the highly specific spatial arrangement of pore sizes found by the optimization, for which a Gaussian Process model was trained.