The reliable prediction of the permeability of subsurface formations is of paramount importance to geophysicists, petroleum engineers and groundwater scientists. Permeability is commonly derived by empirical cross-property correlations based on logging measurements. Use of these relationships introduces considerable uncertainty in reservoir characterisation studies. A major source of the uncertainty is related to the present inability to effectively characterize complex rock microstructure at the pore scale. A significant reduction in the level of uncertainty requires the development of techniques to accurately characterize rock microstructure and to relate this information to measured flow properties. Research has been undertaken to develop realistic reconstructions of three-dimensional (3D) porous materials (Joshi, 1974; Adler et al., 1990, 1992; Hazlett, 1997; Yeong and Torquato, 1998). These methods have been very instructive in understanding general properties of complex media; however, direct prediction of permeability by Adler et al (1990, 1992) and Hazlett (1997) from reconstructed samples have been only in fair agreement with experimental data. More recent reconstruction methods (Thovert et al., 2001; Arns et al., 2003) have led to good agreement for conductive transport properties. These methods have yet to be tested for permeability.
Direct measurement of a 3D structure is now readily available from synchotron and X-ray-computed microtomography (X-raY−JµCT) (Dunsmuir et al., 1991; Spanne et al., 1994) and laser confocal microscopy (Fredrich et al., 1995). These techniques provide the opportunity to experimentally measure the complex morphology of the pore space of sedimentary rock in three dimensions, at resolutions down to a few micrometers. One can then replace synthetic images derived from statistical models with experimental data and base transport calculations directly on the measured three-dimensional microstructure. This has been done previously for fluid permeability of Fontainebleau sandstone by a number of groups (Spanne et al., 1994; Schwartz et al., 1994; Auzerias et al., 1996; Martys et al., 1999; Manwart et al., 2002). Due to limitations in computing resources and experimental constraints, the results of these studies have been limited in scope and inconclusive. First, the number of samples studied was limited by computational requirements. Second, due to limitations on µCT detector size and the natural heterogeneity of rock at small scales, it is difficult to make direct comparison with experiment; in all cases, the imaged microplugs exhibited a different porosity to the original core material on which experiments were performed. In the work of Spanne et al. (1994), the numerical calculation of permeability on five images of sizes 443 to 843 at 10−µm resolution exhibited broad variability and consistently underestimated the experimental data. Schwartz et al. (1994) and Auzerias et al. (1996) considered a 2803 image of Fontainebleau sandstone at 7.5−µm resolution. Predictions of permeability were within ≈ 15% of experimental values. Martys et al. (1999) considered four large subsets of Fontainebleau (5103, 5.7 µm per voxel) across a range of porosity and predictions were in agreement (≈15% to 40%) with the experiment. In the work of Manwart et al. (2002), calculations on a single 3003, 7.5 µm per voxel data set was, after rescaling the permeability prediction to account for porosity variation, in reasonable agreement (≈ 30%) with the experiment. However, calculations on a single smaller subset 1003 led to significant (> 100%) errors.
Previously (Arns et al., 2001, 2002), we reported large-scale computational studies of the electrical conductivity and the elastic properties directly on microtomographic images. We showed that an extensive study incorporating careful simulation and minimization of several sources of numerical error allows one to derive accurate predictions of properties. The calculation of electrical conductivity Arns et al., 2001) and elasticity (Arns. et al., 2002) on digitized images of Fontainebleau sandstone at sample sizes down to (700 µm)3 was in excellent agreement with experimental measurements over the full range of porosity. In this paper, we extend the computational study to the calculation of permeability. We find that although the fluctuations in the permeability are greater than that observed for the electrical conductivity and elasticity, one can still perform accurate numerical micropermeametry on 3D digitized images of sedimentary rock at these small scales. The results highlight the exciting potential to predict properties from core material not suited for laboratory testing including drill cuttings, sidewall core or damaged core.