Estimating the scale dependence of permeability at pore and core scales: Incorporating effects of porosity and finite size

Understanding the effect of sample size on hydraulic characteristics of porous media and estimating their scale dependent properties have been challenging in subsurface hydrology. An empirical power-law relationship has been widely applied to link permeability, k, to sample volume. However, due to its empiricism, accurately estimating the scale dependence of permeability, k(L), in soils and rocks has remained unanswered. In this paper, we combine concepts of percolation theory and finite-size effect, develop a theoretical relationship to model k(L), and evaluate the proposed model using various types of porous media. To estimate k(L), one requires porosity, critical porosity, critical scaling exponent, a fundamental length scale, system length, and permeability determined at the smallest scale. Comparison with numerical simulations shows that incorporating effects of porosity and finite size results in accurate estimates of k(L). We find reasonable agreement between the theory and the simulations with average relative error ranged between-27.5% and 10.2%.

Automated summary

This paper investigates the effect of sample size on the hydraulic characteristics of porous media and proposes a theoretical model to estimate their scale dependent properties. By incorporating porosity and finite size effects, accurate estimates of permeability's scale dependence can be achieved.