Effect of Pore-Scale Heterogeneity on Scale-Dependent Permeability: Pore-Network Simulation and Finite-Size Scaling Analysis

A long-standing issue in subsurface hydrology and many other related disciplines has been the scaling problem. Although the effect of length scale has been known for years, inconsistent results have been reported in the literature. Experimental data mostly indicate that the permeability k should increase with increasing sample volume, whereas simulations and some theoretical predictions appear to imply the opposite. In this paper, we use the concept of finite-size scaling to propose a vigorous theoretical framework for addressing the effect of length scale on the permeability. We simulate fluid flow in 12 synthetic and 4 Fontainebleau pore networks to investigate the effect of small-scale heterogeneities, such as pore-throat size distribution and pore connectivity. Simulations were carried out for 10 pore coordination numbers, namely, Z = 1.5, 1.65, 1.75, 2, 3, 3.25, 3.5, 4, 5, and 6. For the synthetic pore networks we find a transition in the scale dependence of the permeability, with our results indicating that the permeability increases with the scale for larger pore coordination numbers, whereas the opposite is true for smaller Z. In Fontainebleau pore networks, on the other hand, the trends are decreasing permeabilities regardless of Z. Although the plot of the permeability versus the network size for each pore network appears scattered, through finite-size scaling analysis the data collapse onto a single quasi-universal curve. Our results demonstrate that finite-size scaling analysis is a powerful approach for addressing the effect of length scale on the permeability.

Automated summary

The issue of scaling in subsurface hydrology and related disciplines has been long-standing. Experimental data and simulations show inconsistent results on the effect of length scale on permeability. Finite-size scaling analysis proves to be a powerful approach to address the impact of length scale on permeability, showing different trends in permeability with scale in different pore networks.