The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

Abstract

Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length‐aperture scaling), and experiments (Barton‐Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture‐matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real‐world large‐scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton‐Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton‐Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low‐permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

Is the permeability of naturally fractured rocks scale dependent?

“…This is touched on by Bisdom et al . [], but was not the primary focus of their analysis. There also is a debate whether aperture‐fracture length correlations seen on the 0.1–10 meter scale apply at scales above.…”

“…Where it is varied with fracture length, this pre‐imposes a scale variance. There are several studies that address the impact of geo‐mechanical aperture on equivalent permeability [ Paluszny and Matthai , ; Nick et al ., ; Bisdom et al ., , , ]. Yet they do not consider the full tensor of equivalent permeability and its potential variation with direction and scale.…”

“…[] also introduced a workflow for integrating geo‐mechanics and full‐tensor permeability calculations into outcrop modeling studies. Arguably, these studies may not have investigated sufficiently large samples of the fracture population to reproduce the statistics seen in the field [ Paluszny and Matthai , ; Nick et al ., ; Bisdom et al ., , , ]. While studies like Bogdanov et al .…”

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

“…Within an isolated fracture, the nonuniform resistance offered by uneven fracture walls leads to irregularities in the flow, the magnitude of which depends on the roughness in the fracture's aperture (Cardenas et al, 2007;de Dreuzy et al, 2012;Fiori & Becker, 2015;Johnson et al, 2006;Kang et al, 2016;Keller et al, 1999Keller et al, , 1995 and the Reynolds number of the flow (Cardenas et al, 2009;Zou et al, 2017). In a fracture network, larger features can play a more dominant role than in-fracture aperture variability in determining the structure of the fluid velocity field (Bisdom et al, 2016;de Dreuzy et al, 2012;Karra et al, 2015;Makedonska et al, 2016). While it is understood that macroscale network traits influence the arrangement of the fluid flow field within a fracture network (Edery et al, 2016;Hyman & Jiménez-Martínez, 2018), a direct link between geometric and topological properties of the fracture network and upscaled transport observables is still lacking.…”

Size Effect on the Permeability and Shear Induced Flow Anisotropy of Fractal Rock Fractures

“…Thus, various analytical equations, experimental tests and numerical methods have been proposed to quantify the aperture distribution and flow behavior in the fracture under normal and shear stresses. [8][9][10][11] Single fracture has been approximately modeled by using two smooth parallel plates that are separated by a constant distance, with the fluid flowing through it that follows the cubic law. 12,13 However, in the nature, the surfaces of most rock fractures are rough, which results in nonuniformly distributed aperture fields in fractures.…”