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Modification of the L ocal C ubic L aw of fracture flow for weak inertia, tortuosity, and roughness
Author(s) -
Wang Lichun,
Cardenas M. Bayani,
Slottke Donald T.,
Ketcham Richard A.,
Sharp John M.
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2014wr015815
Subject(s) - tortuosity , mechanics , flow (mathematics) , inertia , reynolds number , surface finish , physics , materials science , optics , classical mechanics , porosity , composite material , turbulence
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.