The Impact of Sub-Resolution Porosity of X-ray Microtomography Images on the Permeability

Abstract

There is growing interest in using advanced imaging techniques to describe the complex pore-space of natural rocks at resolutions that allow for quantitative assessment of the flow and transport behaviors in these complex media. Here, we focus on representations of the complex pore-space obtained from X-ray microtomography and the subsequent use of such 'pore-scale' representations to characterize the overall porosity and permeability of the rock sample. Specifically, we analyze the impact of sub-resolution porosity on the macroscopic (Darcy scale) flow properties of the rock. The pore structure of a rock sample is obtained using high-resolution X-ray microtomography (3.16 3 µm 3 /voxel). Image analysis of the Berea sandstone sample indicates that about 2 % of the connected porosity lies below the resolution of the instrument. We employ a Darcy-Brinkman approach, in which a Darcy model is used for the sub-resolution porosity, and the Stokes equation is used to describe the flow in the fully resolved pore-space. We compare the Darcy-Brinkman numerical simulations with core flooding experiments, and we show that proper interpretation of the sub-resolution porosity can be essential in characterizing the overall permeability of natural porous media.

Stokes‐Brinkman Flow Simulation Based on 3‐D μ‐CT Images of Porous Rock Using Grayscale Pore Voxel Permeability

“…To use BF‐LBM, which equivalently solves the Stokes‐Brinkman equation macroscopically, it is assumed that Stokes flow in a fully permeable region (i.e., apparent pore) and Darcy‐like flow in a partially permeable region (i.e., gray zone) coexist. For the consistency of the variable, the volume‐averaged (or Darcy) velocity u , which is discharge per unit area, is used; thus, the continuity equation and governing equation are expressed as (Brinkman, ; Soulaine et al, ) where p is fluid pressure; μ and μ e are dynamic viscosity and effective dynamic viscosity, respectively; and k v is voxel permeability. These equations indicate that the voxel permeability k v of a “gray voxel” must be known, so a procedure is proposed for classifying each voxel into three types (i.e., apparent pore, apparent solid, and gray voxel) based on the gray‐level histogram of μ‐CT images and the experimentally measured PSD.…”

“…To resolve the limitations of the binary approach for porous rock, the multiscale approach based on the incorporation of macroresolution and subresolution pores has the focus of attention (Baveye et al, ; Knackstedt et al, ; Lin et al, , ; Scheibe et al, ; Sok et al, ; Soulaine et al, ). Subresolution pores, which are too small to be represented by a unit pixel, are represented as intermediate gray voxels that must be statistically estimated to be either “solid” or “pore.” Because each voxel has a statistically acceptable probability of being either phase, it seems reasonable to state that a 16‐bit gray‐level voxel can be one of three types: an apparent pore voxel with a low CT number, an apparent solid voxel with a high CT number, and a gray zone voxel with an intermediate CT number.…”

Micro-continuum Approach for Pore-Scale Simulation of Subsurface Processes

“…This example deals with a relatively large domain; however, the same idea can be used to simulate flow using high-resolution images of natural porous media (e.g., scanned with micro-tomography technique), in which some structures are much smaller than the image resolution and cannot be fully resolved. In that context, the subresolution porosity, can be modeled as a porous medium, and the DBS formulation can used to assess its importance on the macroscopic flow (Apourvari and Arns 2014; Soulaine et al 2016). …”

“…In some settings, e.g., single-phase fluid flow, DRP may ultimately become a complementary tool to laboratory flow experiments. For example, it is now somewhat routine to estimate the absolute permeability by solving the Navier-Stokes equations using high-resolution images of rock samples (Arns et al 2005;Kainourgiakis et al 2005;Zhan et al 2009;Khan et al 2011;Mostaghimi et al 2013;Andrä et al 2013a, b;Guibert et al 2015;Soulaine et al 2016). Even though the 'pore-scale' flow simulators can now handle up to billion-cell representations (Trebotich and Graves 2015), the actual physical scale of the rock sample is a few cubic millimeters.…”

Downscaling‐Based Segmentation for Unresolved Images of Highly Heterogeneous Granular Porous Samples

“…Scheibe et al () show how breakthrough curves of passive transport in a reconstructed geologic porous medium are greatly affected by the type of segmentation and threshold values employed. Once the three phases have been identified, the porous‐solid phase is generally assumed spatially homogenous and its conductivity estimated through empirical relationships, such as the Carman‐Kozeny equation, that are not universal and may not work for a highly heterogeneous sample (Iassonov et al, ; Scheibe et al, ; Soulaine et al, ; Wildenschild & Sheppard, ). Yet, an accurate knowledge of the pore geometry is essential to calculate hydraulic conductivity, hydrodynamic dispersion, or effective surface reaction rates (Mehmani & Tchelepi, ; Yang et al, ; Yoon et al, ) in at‐scale and multiscale models (Battiato, ; Battiato et al, ; Sun et al, ; Yousefzadeh & Battiato, ).…”