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

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 similar to 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).