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The scale dependence of permeability: Effects of pore-throat size distribution and pore connectivity
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  • Behzad Ghanbarian,
  • Misagh Esmaeilpour,
  • Robert Ziff,
  • Muhammad Sahimi
Behzad Ghanbarian
Kansas State University

Corresponding Author:[email protected]

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Misagh Esmaeilpour
Kansas State University
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Robert Ziff
University of Michigan
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Muhammad Sahimi
University of Southern California
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Scaling has been a long-standing challenge in subsurface hydrology, soil physics, and many other research disciplines. The effect of length scale (or sample dimension) has been known in the literature, and inconsistent results have been reported. For example, experimental measurements typically show that permeability k should increase with increasing scale. However, numerical simulations and some theoretical estimations appear to imply the opposite. In this study, we simulated permeability in twelve synthetic and four Fontainebleau pore networks with different pore-throat size distributions. For each pore network, simulations were carried out for ten pore coordination numbers Z = 1.5, 1.65, 1.75, 2, 3, 3.25, 3.5, 4, 5, and 6. We found a transition in the scale dependence of the permeability in the synthetic pore networks. More specifically, our results showed that the permeability increased with the scale for larger pore coordination numbers, while it decreased with the scale for smaller Z. In Fontainebleau pore networks, however, the trends were decreasing permeabilities regardless of the value of Z. We invoked concept of finite-size scaling analysis, a vigorous theoretical framework from physics, to address the effect of scale on the permeability. Although the plot of the permeability versus the network size for each pore network appeared scattered, the data collapsed together by applying finite-size scaling analysis. Our results demonstrated that finite-size scaling analysis is a promising approach to address the effect of scale on permeability.