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Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough‐walled fracture with flow imaging
Author(s) -
Lee Seung Hyun,
Lee KangKun,
Yeo In Wook
Publication year - 2014
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2014gl060481
Subject(s) - reynolds number , stokes flow , mechanics , reynolds equation , flow (mathematics) , fracture (geology) , hele shaw flow , reynolds averaged navier–stokes equations , physics , fluid dynamics , geology , mathematics , geotechnical engineering , computational fluid dynamics , turbulence
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.