Scale dependence of tortuosity and diffusion: Finite-size scaling analysis

Physical and hydraulic properties of porous media are routinely measured/simulated at smaller scales e.g., pore and core. However, their determination at larger scales e.g., field and reservoir has still been a great challenge. Although understanding the scale dependence of transport modes in rocks and soils is essential, the porous media community still lacks in a solid theoretic framework. In this short communication, we propose finite-size scaling analysis from physics to investigate the scale dependence of tortuosity and diffusion coefficient. By comparing with two- and three-dimensional simulations, we demonstrate that the finite-size scaling analysis is a powerful approach. More specifically, we show that the plot of simulated tortuosity or diffusion coefficient versus scale looks scattered. However, after applying the finite-size scaling analysis, the data collapse together showing a quasi-universal trend.