Practical Considerations for Selection of Representative Elementary Volumes for Fluid Permeability in Fibrous Porous Media

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• 作者：A. G. Hendrick (1) agh@email.arizona.edu
  R. G. Erdmann (12) erdmann@arizona.edu
  M. R. Goodman (1) mgoodman@email.arizona.edu
• 关键词：Stokes flow &#8211 ; Tensor permeability &#8211 ; Representative elementary volume &#8211 ; REV &#8211 ; Porous media
• 刊名：Transport in Porous Media
• 出版年：2012
• 出版时间：November 2012
• 年：2012
• 卷：95
• 期：2
• 页码：389-405
• 全文大小：749.4 KB
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• 作者单位：1. Department of Materials Science and Engineering, The University of Arizona, 1235 E James E Rogers Way, Tucson, AZ 85721, USA2. Program in Applied Mathematics, The University of Arizona, Tucson, AZ, USA
• ISSN：1573-1634

文摘

We investigate the lower bound of the area of a square-shaped representative elementary volume (REV) for the permeability tensor for transverse Stokes flow through randomly packed, parallel, and monodisperse cylinders. The investigation is significant to flow models using small calculation regions for fibrous porous media, such as modeling defect formation during directional solidification in the mushy zone of dendritic alloys. Using 90 ensembles of 1,000 domains, where each ensemble comprises domains with the same number and size of cylinders, we develop correlations between the permeability tensor invariants and macroscopic features of the domain. We find that for ensembles of domains with fewer than 200 cylinders, the eigenvectors of the permeability tensors exhibit preferential alignment with the domain axes, demonstrating that the estimated permeability is significantly affected by the periodic boundary conditions for these cases. Our results also suggest that the anisotropy of the permeability tensor may not be insignificant even for large sampling volumes. These results provide a practical lower bound for the calculation volumes used in permeability simulations in fibrous porous media, and also suggest that modelers should consider using an anisotropic tensor for small calculation volumes if phenomena such as channeling are important.