The equivalent permeability,
keq of stratified fractured porous rocks and its anisotropy is important for hydrocarbon reservoir engineering, groundwater hydrology, and subsurface contaminant transport. However, it is difficult to constrain this tensor property as it is strongly influenced by infrequent large fractures. Boreholes miss them and their directional sampling bias affects the collected geostatistical data. Samples taken at any scale smaller than that of interest truncate distributions and this bias leads to an incorrect characterization and property upscaling. To better understand this sampling problem, we have investigated a collection of outcropâdataâbased Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finiteâelement analysis and flowâbased upscaling have been used to determine
keq eigenvalues and anisotropy. While our results indicate a convergence toward a scaleâinvariant
keq REV with increasing sample size,
keq magnitude can have multiâmodal distributions. REV size relates to the length of dilated fracture segments as opposed to overall fracture length. Tensor orientation and degree of anisotropy also converge with sample size. However, the REV for
keq anisotropy is larger than that for
keq magnitude. Across scales, tensor orientation varies spatially, reflecting inhomogeneity of the fracture patterns. Inhomogeneity is particularly pronounced where the ambient stress selectively activates lateâ as opposed to early (throughâgoing) fractures. While we cannot detect any increase of
keq with sample size as postulated in some earlier studies, our results highlight a strong
keq anisotropy that influences scale dependence.