Scale Dependency of Petrophysical Properties in Homogeneous Porous Rocks

Petrophysical properties e.g., porosity and permeability are known to vary with scale of measurement for a variety of rock types. Accordingly, the scale dependency of permeability has been the subject of active research over the past several decades in the field of porous media and fluid transport. Due to various types and levels of heterogeneities in earth materials, addressing the scale dependency of petrophysical characteristics using either laboratory experiments or numerical simulations is necessary. In this study, via the OpenPNM package, we created homogeneous cubic pore networks of different sizes (e.g., 3, 10, 40, 60, 80, 100, 150, 200 nodes along each direction) to study the scale dependence of permeability. Networks were composed of cylindrical pore throats of the same size (e.g., 10, 20 and 30 microns) and the same length (100 microns). We found that as the network size increases permeability decreases, while porosity increases in homogeneous pore networks, in contrast to theoretical/observational direct proportionality between porosity and permeability. We argued that such a behavior is due to the scale dependency of tortuosity; tortuosity increases as the network size increases. Our results showed that the scale-dependent effect of tortuosity on permeability is greater than that of porosity.