Relationship between the critical Reynolds number and aperture for flow through single fractures: Evidence from published laboratory studies

Abstract

An evaluation of published laboratory studies of flow through single rough fractures was conducted to establish a relationship between aperture (2b) and critical Reynolds number (Rec) under controlled conditions for physically measured fractures. Of the relevant 47 published laboratory studies, only six reported physically measured apertures along with adequate hydraulic testing information to determine the corresponding Rec value and show that the fractures follow the cubic law reasonably well. Our analysis indicates a logarithmic relationship between 2b and Rec for cubic-law fractures in the reported aperture range (100–500 µm), consistent with theoretical and modeling studies. Discrete fracture network models used for simulating flow and transport in fractured rock aquifers require reliable values for 2b, usually obtained from the cubic law, using T values from straddle-packer hydraulic tests. The cubic law requires specification of the number of permeable fractures (N) in each test interval, but, distinguishing the permeable from the impermeable fractures is problematic. The relationship between 2b and Rec determined from the laboratory tests provides a fluid-mechanics basis for estimating the number of permeable fractures in straddle-packer tests. Constant-head step-tests carefully done with many steps provide precise identification of the flow rate at the onset of nonlinear flow, and numerous tests have shown that flow deviates from linearity at larger flow rates for larger values of transmissivity (T). A procedure was previously developed to relate N, 2b, and Rec using hydraulic test data, but this approach requires knowledge of the relation between 2b and Rec, thereby motivating this work.