Effect of fluid slippage on eddy growth and non-Darcian flow in rock fractures

Effects of Slip Length and Inertia on the Permeability of Fracture with Slippery Boundary Condition

“…Inertial effects can lead to permeability reduction, which is directly related to development and growth of RZs inside the pores and fractures [16,21]. We resorted to the open source of MATLAB code to be able to capture and quantify the growth of RZs In terms of slippery boundary condition (BC), we followed previous study [21] by specifying a slip length (L s ) along the fracture walls.…”

“…Inertial effects can lead to permeability reduction, which is directly related to development and growth of RZs inside the pores and fractures [16,21]. We resorted to the open source of MATLAB code to be able to capture and quantify the growth of RZs In terms of slippery boundary condition (BC), we followed previous study [21] by specifying a slip length (L s ) along the fracture walls. Different from previous study, we considered six cases with different L s : (1) Case 1: No slip case with L s equal to 0 m; (2) Case 2: L s was homogeneous and set to be the minimum value in the case 3; (3) Case 3: L s varies along the fracture length that depends on the fracture aperture field following the equation proposed by [21]; (4) Case 4: L s was homogeneous and set to be the arithmetic mean value in the case 3; (5) Case 5: L s was homogeneous and set to be the median value in the case 3; and, (6) Case 6: L s was homogeneous and set to be the maximum value in the case 3.…”

“…Inertial effects can lead to permeability reduction, which is directly related to development and growth of RZs inside the pores and fractures [16,21]. We resorted to the open source of MATLAB code to be able to capture and quantify the growth of RZs (https://figshare.com/articles/Automatic_ detection_of_2D_recirculation_zone_volume_/5811399).…”

“…For instance, many studies reported that the rock surface can be switched from hydrophilic to hydrophobic after its exposure to a non-wetting fluid [20]. The slippery BC, in fact, has been tested to enhance fracture flow (i.e., permeability) via both laboratory and numerical experiments [20,21]. Note that the enhanced fracture flow might not increase the longitudinal dispersion coefficient within the simplified parallel plate model [21,22] for the first time investigated the competition between the inertial force and slippery BC effects in changing fracture permeability, where inertial force on the one hand reduces permeability, while slippery BC, on the other hand, enhances permeability.…”

“…The slippery BC, in fact, has been tested to enhance fracture flow (i.e., permeability) via both laboratory and numerical experiments [20,21]. Note that the enhanced fracture flow might not increase the longitudinal dispersion coefficient within the simplified parallel plate model [21,22] for the first time investigated the competition between the inertial force and slippery BC effects in changing fracture permeability, where inertial force on the one hand reduces permeability, while slippery BC, on the other hand, enhances permeability. By employing a homogeneous slip length along fracture boundary, they found out that slippery effects dominated over inertial effects when the pressure gradient was small, and the inertial effects gradually caught up with that caused by the slippery BC with a further increase in pressure gradient [21].…”