On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space

Abstract

This article describes how much the computed absolute permeability is impacted by the slip effect at the fluid/solid interface, in the context of single-phase pore-scale flow. While this effect is well quantified in microchannels or simple geometries, the present study focuses on its average effect in real rock matrix geometries, obtained by means of high-resolution X-ray microtomography. Due to the inherently finite resolution of the technique, an uncertainty exists on the true position of the fluid/solid interface and its morphological features below the image resolution (unseen roughness). We demonstrate that both these uncertainties can be interpreted as a slip condition, and consequently we focus on how a slip length can impact the computed absolute permeability, after having provided an estimation of a meaningful bound on the slip coefficient. To that extent, two strategies are employed: the global deviation of permeability and the theoretically established linear deviation. Three high-definition 3D geometries are used as practical examples of our methodology. Results are discussed in terms of relative deviation versus specific surface area and lead to quantities of interest involving the linear deviation of permeability. Article Highlights Uncertainty on the permeability is quantified by means of a slip length based on micro-CT voxel size. The linear deviation from a permeability value is established asymptotically and involves only a prescribed slip. A ratio involving the relative linear deviation, the specific area and the permeability is a non-dimensional quantity of interest.