Adaptive unstructured discretisation and fluid-flow property computations on segmented images of porous media

High-resolution 3D digital imaging has greatly advanced material science, providing the basis for the computational investigation of ensemble properties of granular porous media for continuum-scale multiphysics simulations. While such properties can be computed directly on the structured voxel grid of the digital image, alternatively, grains and pores may be represented by an unstructured adaptively refined finite-element mesh of the features of interest. To reduce computational cost in feature-poor regions, this mesh is coarsened dramatically. Such spatially adaptive refinement is especially attractive in media with large pore size variations.

Finite-element based single phase and two-phase flow simulations are performed to evaluate the computational advantages of this adaptive mesh refinement of pore types in different types of rocks. Our focus is on the computation of permeability, pore radius and capillary pressure.  Pore-velocity statistics are analysed systematically in order to assess method accuracy as a function of material type and process of interest. We also research ways of automatically adapting mesh size to reduce numerical errors to obtain more precise solutions.

Flow velocity distribution in an unstructured grid model of Berea sandstone as computed with CSMP++ based solver for the Stokes lubrication equation. In contrast to common practice, we use pore velocity spectra to assess solution quality because permeability is not a good measure since it is dominated by the largest pores and fluid pathways which are resolved by most tools.