A multiscale study of the retention behavior and hydraulic anisotropy in deformable porous media

Abstract

The following proceeding presents a multiscale approach to investigate the hydraulic anisotropy and retention behavior in porous materials involving deformation effects. Concerning the former, single-phasic fluid flow simulations using the lattice Boltzmann method (LBM) are initially accomplished at the pore-level geometry of Bentheimer sandstones provided by X-ray microscopy at several degrees of compression to compute the intrinsic permeability. Due to the anisotropic nature of the Bentheimer sandstones, favored pore channels for fluid flow are witnessed within the domain. Therefore, it is important to understand the alteration of the preferred flow paths at each degree of compression. In this regard, we propose a new upscaling approach between the LBM and the macroscopic Theory of Porous Media (TPM) to accurately compute the macroscopic hydraulic structural tensor, which plays a crucial role in the calculation of the deformation-dependent anisotropic specific permeability. As for the latter, the Shan-Chen (SC) model of the LBM is applied at each strain level to model biphasic fluid flow via the unsaturated porous domain. Herein, the retention curves of the drainage and imbibition processes of each deformed state are computed. In turn, the comparison among the results shows the effect of variation of the strain degree on the retention behavior.

A machine‐learning supported multi‐scale LBM‐TPM model of unsaturated, anisotropic, and deformable porous materials

“…Therefore, a suitable size of the RVE of 350 × 350 × 350 voxels is determined. 46 The size of the dataset for the ML model includes 2286 datapoints, whereby each datapoint corresponds to an increment of the pressure gradient on the porous domain. Herein, the LB model assigns for each strain degree several increasing increments of the pressure gradient of the fluid across the porous domain to calculate the resulting average velocity of the fluid.…”

“…For the selection of the suitable RVE size of the geometry of the Bentheimer Sandstones, the reader is referred to our work in ref. [46]. For visualization of the output of LB simulations, exemplary results are shown in Figure 1.…”

“…For more details regarding the LBM simulations and related discussions, such as the effect of deformation on hysteresis or the air‐entry value, the reader is referred to our work in ref. [46].…”

“…For discussions regarding the effects of deformation on the retention curves, such as the hysteretic behavior, see our work in ref. [46].…”

“…For discussions regarding the effects of deformation on the retention curves, such as the hysteretic behavior, see our work in ref. [46]. models that involve cyclic drying/wetting processes, which leads for instance to inaccurate computation of both Bishop's effective stress of unsaturated porous media and the relative permeability.…”