Theoretical Analysis of Capillary Rise in Porous Media

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• 作者：Shahram Farhadi Nia ; Kristian Jessen
• 关键词：Capillarity ; Imbibition ; Homogeneous porous media ; Fractured porous media ; Analytical Solution
• 刊名：Transport in Porous Media
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：110
• 期：1
• 页码：141-155
• 全文大小：1,040 KB
• 参考文献：Bear, J.: Dynamics of Fluids in Porous Media. Courier Dover Publications, New York (2013)
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• 作者单位：Shahram Farhadi Nia (1)
  Kristian Jessen (1)
  
  1. University of Southern California, 925 Bloom Walk, HED311, Los Angeles, CA, 90089-1211, USA
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geotechnical Engineering
  Industrial Chemistry and Chemical Engineering
  Civil Engineering
  Hydrogeology
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Netherlands
• ISSN：1573-1634

文摘

In this work, we study the dynamics of capillary-driven fluid invasion in three different settings including: (1) a single capillary tube, (2) a homogeneous porous medium, and (3) a fractured porous medium. A Lambert W functional form is proposed to describe the invasion dynamics in a single capillary tube, that predicts both early-time Washburn-type behavior (\(\sqrt{t}\)) and late-time behavior. We extend the formulation to describe homogenous porous media and to include viscosity, pressure, and gravity effects in both advancing and defending fluids. Solutions for closed systems, where the advancing fluid compresses the defending fluid, are then developed. Finally, we extend the theory to describe fractured systems and propose a convolution integral formulation and a new explicit solution for fluid invasion into a fractured porous medium. Keywords Capillarity Imbibition Homogeneous porous media Fractured porous media Analytical Solution