Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture

This study provides an evaluation of various modifications of the cubic law, expanding upon previous work as follows: (1) Experimentally measured flow rates and apertures are the basis for the evaluation; (2) a rock fracture is used rather than an analog or numerically simulated fracture; (3) the fracture is not disturbed at any point during the testing; and (4) detailed measurements of the apertures and the top and bottom fracture surface profiles (931,988 measurements in total) are obtained, enabling assessment of the impact of fracture surface undulation and model discretization on the simulated flow rates. The cubic law calculated with either the geometric mean aperture or incorporating surface roughness factors provided reasonable (+/-10%) estimates of the observed flow rates for Re < 1. The cubic law applied locally (LCL) over-predicted the observed flow rates by at least 1.9 times. Modifying the LCL to incorporate a solution for tapered plates and correcting for surface undulation reduced the over-prediction to at least 1.75 times the measured flow rates. The primary conclusions that we can draw from this work are as follows: (1) There appears to be merit to conducting further studies of the cubic law applied at the single-fracture scale to determine whether similar results are achievable in all fracture types; and (2) the current understanding of when the LCL will provide an adequate representation of the true flow behavior is not entirely correct; more investigation into the effect of fracture surface undulation and other causes of abrupt aperture change (e.g., rock debris trapped within the fracture plane) is required.