Is the permeability of naturally fractured rocks scale dependent?

Abstract

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 outcrop‐data‐based Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finite‐element analysis and flow‐based upscaling have been used to determine keq eigenvalues and anisotropy. While our results indicate a convergence toward a scale‐invariant keq REV with increasing sample size, keq magnitude can have multi‐modal 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 late‐ as opposed to early (through‐going) 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.

Stress Influence on Fracture Aperture and Permeability of Fragmented Rocks

“…Here using deformable rock blocks and analyzing the entire rock layer under the in situ stresses, the influence of block deformations on the fracture apertures were considered. However, in some other research works, the in situ stresses are directly projected on the fracture surfaces without considering the rock deformation (Azizmohammadi & Matthäi, ). To quantify the effect of ignoring the block deformations, a comparative study is conducted here for the α = 22.5° case, named α = 22.5°‐Solid Blocks.…”

“…Historically, the flow simulations in fractured and fragmented rocks have been conducted by making simplifications on mechanical modeling or by ignoring the mechanics‐flow interaction altogether. Some of the common simplifications that their effect is investigated in this paper are as follows: Two‐dimensional modeling while ignoring the actual triaxial stress states, for example, Zhang and Sanderson (), Zhang et al (), Latham et al (), and Min et al (). Considering the stress influence on fracture apertures by projecting in situ stresses on fractures and using stiffness relationships in shear, normal, and dilation behaviors (e.g., Barton et al, ), without conducting mechanical analysis of the solid phase, for example, Azizmohammadi and Matthäi (); and Not considering the influence of the neighboring layers with different mechanical properties, which is inevitable in 2‐D studies. …”

“…To obtain the full permeability tensor of the ensemble, two steady state flow problems were solved in two perpendicular directions. The ensemble absolute permeability tensor, k E , was computed by solving Darcy's law , modified for the volume‐averaged fluid velocity ( u ), pressure gradient ( ∇p ), and viscosity ( μ ), where 〈 〉 is the volume averaging operator (Azizmohammadi & Matthäi, ; Durlofsky, ). …”

“…The variation of stress within the rock layer is simulated in a newly constructed mechanical model of the fragmented rock and analyzing it under realistic boundary stresses. This is ignored in models which simply project far‐field stresses on the fractures (e.g., Azizmohammadi and Matthäi, ). Frictional interfaces are defined between the rock blocks, also permitting opening and closing of the fractures in addition to frictional sliding.…”

Permeability of Three‐Dimensional Numerically Grown Geomechanical Discrete Fracture Networks With Evolving Geometry and Mechanical Apertures

“…Upscaling requires the definition of a representative elementary volume which is sufficiently large and intensely fractured. This poses a challenge in sparsely fractured rocks where properties are highly scale‐dependent (Azizmohammadi & Matthäi, ).…”