Assistant Professor University of Arizona - Department of Hydrology & Atmospheric Sciences
Shale gas production has grown rapidly in the past decade and now accounts for more than half of the gas production in the US. However, the physical mechanisms that control the flow dynamics in organic-rich shale are not well understood. The challenges include nanometer-scale pores and multiscale heterogeneity in the spatial distribution of the material constituents. Recently, digital rock physics (DRP), which uses high-resolution images of rock samples as input for flow simulations, has been used to understand the fluid dynamics in shale. One important issue with images of natural rock is sub-resolution porosity (pores below the instrument resolution). Sub-resolution porosity is critical for shale because a large fraction of the pores is in the nanometer range; this poses serious challenges for instruments and computational models.
In this talk, we present a micro-continuum model based on the Darcy-Brinkman-Stokes framework that couples resolved pores and sub-resolution micro-porous regions. The Stokes equation is used for resolved pores. The unresolved micro-porous regions are treated as a continuum, and a permeability model that accounts for slip-flow and Knudsen diffusion is employed. Adsorption/desorption and surface diffusion in organic matter are also accounted for. We apply our model to simulate gas flow in a 3D segmented image of a shale sample and elucidate the first-order physics that govern gas production from the shale formations.
The micro-continuum framework is useful, but it is computationally demanding which prevents simulations on statistically representative (i.e., large) high-resolution images. In the second part, we develop an efficient multiscale method to speed up the micro-continuum approach. The method decomposes the resolved pores and micro-porous region into subdomains, and solves Stokes or Darcy problems locally, only once, to build basis functions. The local bases are coupled through a global interface problem yielding an approximate global fine-scale solution, which is in excellent agreement with the reference fine-scale single-domain solution (within a few percent difference). The approximate multiscale solution can be improved through an iterative scheme to converge to the fine-scale single-domain solution. The multiscale method is much more computationally efficient and well suited for parallelization to model of fluid dynamics in large high-resolution digital images of porous materials.