Estimating Permeability and Its Scale Dependence at Pore Scale Using Renormalization Group Theory

Investigating hydraulic and petrophysical properties of porous media has been an active area of research. Despite numerous progress in modeling flow and transport over the past decades, we are still far from accurately estimating the scale dependence of soil and rock properties. In this study, we propose applying renormalization group theory (RGT) at the pore scale. Using the RGT, we determine the scale dependence of effective pore-throat radius (r(teff)) and develop two theoretical models to estimate permeability (k) in pore networks of various sizes. The first theoretical model estimates k(L) from the r(teff)(L) and simulated formation factor F(L), while the second model uses information at the smallest scale (L = L-min) in addition to r(teff)(L) and F(L). By comparing with 25 pore-network simulations, we show that the RGT estimates the scale-dependent k reasonably well. The first model estimates k(L) with average relative errors ranged between -53.1% and -3.0%, while the second model between -1.0% and 14.33%. We also conduct fluid flow simulations in 40 other pore networks above the representative elementary volume and compare the results of the RGT with those of the effective-medium approximation (EMA). Results showed that both RGT and EMA accurately estimate k from pore-throat radius distribution and formation factor with root mean square log-transformed error = 0.119 and 0.096, respectively.

Automated summary

Investigating hydraulic and petrophysical properties of porous media has been an active area of research. In this study, we propose applying renormalization group theory (RGT) at the pore scale to determine the scale dependence of effective pore-throat radius and develop two theoretical models to estimate permeability in different pore networks. The results show that the RGT estimates the scale-dependent permeability reasonably well.