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

Abstract

Understanding fluid flow through a rough-walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO 2, 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 ∂ 2 u x /∂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. Key Points Velocity is first directly measured in a rough-walled fracture for Re < 0.1 The Stokes equations are valid for Re < 0.1 regardless of the fracture roughness The Reynolds equation overestimates flow rate even for Re < 0.1 ©2014. American Geophysical Union. All Rights Reserved.