A Stochastic Study of Flow Anisotropy and Channelling in Open Rough Fractures

Abstract

The quantification of fluid flow in rough fractures is of high interest for reservoir engineering, especially for deep geothermal applications. Herein, rough self-affine fractures are stochastically generated with incremental shear displacement and geometrically described by two aperture definitions, the vertical aperture a vert and the effective aperture a eff. In order to compare their effect on fracture flow, such as anisotropy and channelling, Local Cubic Law (LCL) model-based 2D fluid flow is simulated. The particularity of this approach is the combination of a stochastic generation of self-affine fractures with a statistical analysis (560 individual realizations) of the impact of the LCL's aperture constraint on fracture flow. The results show that aperture definition affects the quantitative interpretation of flow anisotropy and channeling as well as the aperture distribution of the fractures with shearing. Higher values of mean aperture for a given fracture are found using a vert , whereas the aperture standard deviation is larger with a eff. In addition, flow anisotropy is significantly sensitive to aperture definition for small shear displacements and shows a relative higher dispersion with a eff. Thus, LCL prediction models based on a vert are expected to lead to higher dispersion of anisotropy results with a higher uncertainty (factor ~ 2). Realizations based on a vert lead to an enhanced clustering of high flow rates for higher shearing displacements. This channeling development results in higher total flow rates for these simulations. These findings support the direct calibration of pre-existing LCL anisotropy simulations based on a vert towards more representative results using a eff .

Creation of a Mixed‐Mode Fracture Network at Mesoscale Through Hydraulic Fracturing and Shear Stimulation

“…The first nucleation point of substantial fracture growth appears to determine the trajectory a propagating fracture may take. This interpretation is in line with the concept of channelized fluid flow and heterogeneous pore fluid pressure fields in rough-walled fractures (Auradou et al, 2006;Marchand et al, 2019).…”

Stochastic 3D Navier‐Stokes Flow in Self‐Affine Fracture Geometries Controlled by Anisotropy and Channeling

“…For flow perpendicular to the shearing, the mean overestimation is around 1%–9%. The significant differences between the NS simulations are the consequence of the extended travel distance between inlet and outlet (of more than 10%), which leads to reduced local pressure gradients and enhances the anisotropy compared to pure LCL investigations (Marchand et al., 2020).…”

“…The ratio of the flow between the two extreme cases, where the flow is oriented perpendicular or parallel to the shearing, is called flow anisotropy (FA) (Auradou et al., 2006). Besides laboratory experiments (Gentier et al., 1997; Rasmuson & Neretnieks, 1986), FA was also investigated numerically (Koyama et al., 2006; Mallikamas & Rajaram, 2005; Marchand et al., 2020). Investigations were mostly limited to linear flow conditions, while nonlinear effects were only briefly addressed (Liu et al., 2020).…”

“…Other authors proposed further modifications to account for different geometrical effects (Konzuk & Kueper, 2004; Wang et al., 2015). However, all LCL‐based approaches still have two major limitations: (a) the fracture is simplified to a 2D geometry (Marchand et al., 2020), and (b) the Darcian‐type LCL is assumed to be valid only for sub‐laminar flow (Zimmerman et al., 2004). A critical Re () for considering nonlinear effects is under discussion and spans from <1 to >10 (Cunningham et al., 2020).…”

Effect of anisotropy of fracture surface on fluid flow

“…Koyama et al [1] performed numerical studies on the effect of anisotropy on flow at different scales, which shows during the direct shear test, the aperture was not identical, which causes anisotropy in the flow. Marchand et al [9] demonstrated that flow anisotropy is dependent on changes in fracture aperture. Deng et al [10] showed that anisotropy in hydraulic behavior depends on the anisotropy of the fracture geometry.…”