Consistent prediction of absolute permeability in carbonates without upscaling

Abstract

<jats:p>We describe a study focused on the absolute permeability of reservoir carbonate rocks from the Middle East and involving comparison of experimental data and numerical estimates obtained by combining digital-rock and Lattice-Boltzmann Methods (LBM). The question of the “representativeness” of the site at which the simulation is performed is addressed as follows. First, a low-resolution, CT X-ray scan of the core plug is performed to identify regions of large porosity (millimeter-sized vugs, etc.). These regions are then avoided to postselect smaller sites (site volume ~ 1 mm<jats:sup>3</jats:sup>) which are to be scanned at higher resolutions (voxel size &lt; dominant pore-throat size of the core plug). A “representativeness” criterion based on an empirically-inspired “representativeness” measure (<jats:italic>R</jats:italic>-measure) is used to eliminate those sites for which <jats:italic>R</jats:italic> &gt; <jats:italic>b</jats:italic>, where <jats:italic>b</jats:italic> is an upper bound (typically, <jats:italic>b</jats:italic> = 1). Essentially, the measure estimates how well the postselected sites capture the experimental porosity and the dominant pore-throat size of the core plug. This leads to a small set of sites for which the simulations are both computationally manageable and yield a reasonable estimate of the permeability: the experimental and predicted values differ by a factor of about 3 on average, which is a particularly significant result given the challenging heterogeneous pore space of carbonate samples. We believe the suggested methodology to be an adequate and practical way to circumvent upscaling.</jats:p>

Estimating Permeability of Porous Media from 2D Digital Images

“…Based on KC equation, Chen et al [17] developed a bridge function connecting capillary radius in 2D space to that in 3D space. As stated by Chen et al [17], for a given capillary with pore radius r (a) Bulk porosity of 3D parent samples versus areal porosity of 2D crosssections [17,26,31,36,46,53]; (b) porosity of 3D samples versus average porosity of 2D slices.…”

“…In addition, areal porosity of 2D cross-section can be obtained by thin section analysis or digital image processing techniques. Moreover, by using digital image processing techniques, various pore structure parameters (pore size distribution, the maximum pore size, minimum pore size, average pore radius, pore perimeter, and specific surface area) of 2D cross-sectional images can be easily determined [27,36,46,52,53]. For example, for a given 2D digital image, parameters (r max , r min , and ϕ 2D ) can be determined by using the Avizo software, which can effectively determine pore space morphology and extract pore networks [25].…”

“…In addition, to estimate permeability in 3D from 2D images, Saxena et al [26] also assumed that ϕ 2D was similar to ϕ 3D . Figure 2a compares bulk porosity of 3D parent samples versus areal porosity of 2D cross-sections [17,26,31,36,46,53]. Taking the data from Saxena et al [26], for example, Saxena et al conducted modeling on 4 samples (i.e., a Fontainebleau sandstone, a Berea sandstone, a Bituminous sand sample, and a Grosmont carbonate).…”

“…Recently, as a promising technique for modeling the fluid flow in porous media at the pore scale, the lattice Boltzmann Method (LBM) has been widely applied by scholars to predict properties (e.g., permeability and relative permeability) of porous media [45][46][47][48][49]. For example, Khodja et al [46] stated that compared to the traditional methods of computational fluid dynamics, the LBM was ideally suited for massively parallel computation, and it had the advantages of simplicity and flexibility in dealing with complicated geometry. Thus, in this paper, the D3Q19 LBM model was applied to validate our derived model.…”

“…Figure 2. (a) Bulk porosity of 3D parent samples versus areal porosity of 2D cross-sections[17,26,31,36,46,53]; (b) porosity of 3D samples versus average porosity of 2D slices.…”