On Laminar Flow of Non-Newtonian Fluids in Porous Media

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• 作者：Hassan E. Fayed ; Nadeem A. Sheikh ; Oleg Iliev
• 关键词：Laminar flow ; Non ; Newtonian ; Power law ; Carreau model ; Friction factor
• 刊名：Transport in Porous Media
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：111
• 期：1
• 页码：253-264
• 全文大小：1,347 KB
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• 作者单位：Hassan E. Fayed (1)
  Nadeem A. Sheikh (1)
  Oleg Iliev (1) (2)
  
  1. Numerical Porous Media SRI Center, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
  2. Department of Flows and Materials Simulation, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany
  
• 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

Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.