Estimating the scale dependence of permeability and formation factor in heterogeneous porous media

Abstract:

The scale dependency of petrophysical properties, such as porosity and permeability has been well documented in the literature. It has been known that small- and large-scale heterogeneities can cause the scale-dependent behavior in soils and rocks. Some studies based on numerical simulations showed that as sample volume increases, permeability should decrease. However, most experimental measurements of permeability demonstrated the opposite. In this study, we applied concepts from percolation theory and compared theoretical estimations of scale-dependent permeability and formation factor with pore-scale simulations. We generated pore networks with 12 distinctive pore-throat size distributions and simulated formation factor and permeability for several lattice sizes (i.e., 10, 20, 30, 40, and 60). Based on percolation theory, three and two scale-dependent models respectively for the permeability formation factor were proposed. Comparing theoretical estimations with pore-scale numerical simulations showed promising results. We found relative errors ranged between -3 and 4.4 % for the permeability and between -0.3 and 3.7% for the formation factor.