Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough‐walled fracture with flow imaging
Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough‐walled fracture with flow imaging
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DOI：
10.1002/2014gl060481
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发表时间：
2014-07
影响因子：
5.2
通讯作者：
Seung Hyun Lee;K. Lee;I. Yeo
中科院分区：
文献类型：
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作者：
Seung Hyun Lee;K. Lee;I. Yeo
了解流体在粗壁裂缝中的流动在许多问题中都很重要，例如石油和地热储层的开采、二氧化碳的地质储存和放射性废物储存库的安置。为了加深对裂缝流动的理解，我们在雷诺数（Re）为0.014至0.086的情况下，首次直接测量了粗糙壁裂缝的流速。这些结果被用于数量级分析，以评估Stokes方程和Reynolds方程背后的假设，它们是通过简化Navier-Stokes方程推导出来的。即使在非常粗糙的子区域，粘性力也比惯性力至少大2个数量级，这表明Stokes方程在Re < 0.1时是有效的。然而，即使在Re < 0.1的中等粗糙度下，推导Reynolds方程时所做的∂2ux/∂z2优于其他粘性项的假设也不满足。雷诺方程高估了流速。
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 ∂2ux/∂z2 is dominant over other viscous terms was not satisfied even at moderate roughness for Re < 0.1. The Reynolds equation overestimated flow rate.