Effect of Shearing on Non-Darcian Fluid Flow Characteristics through Rough-Walled Fracture

• Main Authors: Biao Li, Weiya Xu, Long Yan, Jianrong Xu, Mingjie He, Wei-Chau Xie
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Water
• Subjects: non-Darcian flow; roughness; shear displacement; Forchheimer equation
• Online Access: https://www.mdpi.com/2073-4441/12/11/3260

The heterogeneous fracture geometry induced by the presence of roughness and shearing complicates the fracture flow. This paper presents a numerical investigation of the non-Darcian flow characteristics of rough-walled fractures during shear processes. A series of fracture flow simulations were performed on four types of fractures with different joint roughness coefficients (JRCs), and the different shear displacements were imitated by degrees of mismatch on two fracture surfaces. The results show that the disorder of fracture geometries and the increase in flow rate are the main causes for the emergence of an eddy flow region, which can significantly reduce the fracture conductivity and change the fracture flow from linear to nonlinear. The Forchheimer equation provides a good model for the nonlinear relationship between the hydraulic gradient and the flow rate in the fracture flow. When the shear displacement or JRC increased, the linear permeability coefficient <inline-formula><math display="inline"><semantics><mrow><msub><mi>k</mi><mi>v</mi></msub></mrow></semantics></math></inline-formula> decreased, while the nonlinear coefficient <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> increased. A three-parameter equation of <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> was used to examine the inertial effect induced by the fracture roughness JRC and the variation coefficient of aperture distribution <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mi>s</mi></msub><mo>/</mo><msub><mi>e</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>. The critical Reynolds number was a combined effect of aperture, viscous permeability, and inertial resistance, assuming the flow becomes non-Darcian when the inertial part is greater than 10%.