Fluid flow in isotropic porous media with one porosity scale is a well understood process and a common scenario in numerous simulations published in the literature. However, there exists a class of porous materials that exhibit two porosity scales with strong permeability contrast between the two scales. Examples of such materials are aggregated soils and fractured sedimentary rocks such as shale. In sedimentary rocks, fluid could flow through the micro-fractures at the larger scale as well as through the nanometer-size pores of the rock matrix at the smaller scale. In this paper, we shall refer to the larger and smaller pores of sedimentary rocks as the micro-fractures and nanopores, respectively. Due to preferentially oriented micro-fractures in the rock, fluid could flow predominantly in the direction of the discontinuities, resulting in an anisotropic flow pattern at the larger scale. We idealize such material as a transversely isotropic medium with respect to fluid flow. In addition, the nanopores of sedimentary rocks such as shale are so small that Darcy's law may not hold at this scale. To better understand the impact of non-Darcy flow on the overall flow pattern, we present a hydromechanical model for materials with two porosity scales that accommodates both transverse isotropy at the larger scale and non-Darcy flow at the smaller scale. Even though this study is motivated by shale properties, the discussion revolves around a generic material with two porosity scales whose fluid flow characteristics are similar to those of shale. The overarching goal of this paper is to better understand the impacts of transverse isotropy and non-Darcy flow on the fluid flow pattern in this material.
Zhang, Q., Choo, J., & Borja, R. I. (2019). On the preferential flow patterns induced by transverse isotropy and non-Darcy flow in double porosity media. Computer Methods in Applied Mechanics and Engineering, 353, 570–592. https://doi.org/10.1016/j.cma.2019.04.037