Permeability estimation on tomographic images using curved boundary schemes in the lattice Boltzmann method. (September 2020) - Rao, Parthib; Schaefer, Laura
Highlights: As opposed to the widely-used bounceback scheme, we employ curved boundary schemes within the LBM framework to numerically estimate the permeability of a porous medium based on its 3D microtomographic image. Curved boundary schemes coupled with an MRT-collision-based fluid solver lead to permeability estimates that are more accurate and show smaller numerical artifacts. Compared to the (rough) stair-step approximation, a smoother approximation of the pore-matrix interface is obtained using the classical marching cubes algorithm. Additional pre-processing steps, such as voxelization and ray-triangle intersection algorithm that is used to measure sub-grid distances, are described in detail. The overall numerical approach and its software implementation is validated on three canonical pore geometries, including a random packing of spheres; a brief discussion of the associated computational costs is also presented. Abstract: The lattice Boltzmann method (LBM) is a widely-used numerical technique for simulation of single- and two-phase flow in geometries that are obtained using tomographic imaging of natural porous media. Due to ease of implementation and numerical robustness, a vast majority of LBM-based pore-scale simulations employ the so-called bounceback scheme to enforce no-slip velocity boundary condition. Bounceback, however, requires an implicit and tight coupling between the numerical (computational) and image (voxel) grid. This coupling results in large discretization errors, since the pore-matrix interface within the 3D image is rough. This leads to overestimation of the interfacial area, and thereby inaccurate permeability predictions. The use of the bounceback scheme also causes other numerical artifacts, such as viscosity-dependent permeability results. In order to address these deficiencies, in this work, the classical marching cubes algorithm is used to reconstruct a surface mesh from the 3D voxel grid; this mesh approximates the pore-matrix surface with higher accuracy compared to the inherent stair-stepped representation. In addition, (nominally) second-order accurate curved boundary schemes are used to enforce no-slip velocity conditions at the reconstructed pore-matrix interface.The various pre-processing steps, such as surface mesh generation and voxelization, that are necessary to use curved boundary schemes are described in detail. The proposed approach of using curved surfaces and boundary schemes is tested and validated on benchmark pore geometries, including a random packing of monodisperse spheres. We conclude that compared to current methods, curved boundary schemes provide a viable option for obtaining more accurate transport properties for Digital Rock Physics-based applications.