Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging

Understanding fluid flow through a rough-walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first direct measurement of flow velocity across rough-walled fractures at Reynolds number (Re) of 0.014 to 0.086. The results were used for an order of magnitude analysis to evaluate assumptions underlying the Stokes and the Reynolds equations, which are derived from simplifying the Navier-Stokes equations. Even at very rough subregions, viscous forces were at least 2 orders of magnitude greater than inertial forces, indicating that the Stokes equations are valid for Re < 0.1. However, the assumption made in the derivation of the Reynolds equation that partial derivative(2)u(x)/partial derivative z(2) is dominant over other viscous terms was not satisfied even at moderate roughness for Re < 0.1. The Reynolds equation overestimated flow rate.