Modification of the Local Cubic Law of fracture flow for weak inertia, tortuosity, and roughness. Issue 4 (8th April 2015)

• Record Type: Journal Article
• Authors: Wang, Lichun; Cardenas, M. Bayani; Slottke, Donald T.; Ketcham, Richard A.; Sharp, John M.
• Is Part Of: Water resources research. Volume 51:Issue 4(2015:Apr.)
• Page Start: 2064
• Page End: 2080
• Publication Date: 2015-04-08
• Subjects: modified Local Cubic Law -- Local Cubic Law -- roughness -- Navier‐Stokes equations -- fluid flow -- fracture; Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2014WR015815
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: The classical Local Cubic Law (LCL) generally overestimates flow through real fractures. We thus developed and tested a modified LCL (MLCL) which takes into account local tortuosity and roughness, and works across a low range of local Reynolds Numbers. The MLCL is based on (1) modifying the aperture field by orienting it with the flow direction and (2) correcting for local roughness changes associated with local flow expansion/contraction. In order to test the MLCL, we compared it with direct numerical simulations with the Navier‐Stokes equations using real and synthetic three‐dimensional rough‐walled fractures, previous corrected forms of the LCL, and experimental flow tests. The MLCL performed well and the effective errors ( δ ) in volumetric flow rate range from −6.7% to 13.4% with an arithmetic mean of | δ | (<| δ |>) equal to 3.7%. The MLCL is more accurate than previous modifications of the LCL. We also investigated the error associated with applying the Cubic Law (CL) while utilizing modified aperture field. The δ from the CL ranges from −14.2% to 11.2%, with a slightly higher <| δ |> = 6.1% than the MLCL. The CL with the modified aperture field considering local tortuosity and roughness may also be sufficient for predicting the hydraulic properties of rough fractures. Key Points: We present a modified Local Cubic Law for hydraulic properties of fractures The MLCL takes into account tortuosity, roughness, and weak inertial effects The MLCL improves estimating effective and local volumetric flow rate