Modeling gas relative permeability in shales and tight porous rocks

Accurate modeling of gas relative permeability (k(rg)) has practical applications in oil and gas exploration, production and recovery of unconventional reservoirs. In this study, we apply concepts from the effective-medium approximation (EMA) and universal power-law scaling from percolation theory. Although the EMA has been successfully used to estimate relative permeability in conventional porous media, to the best of our knowledge, its applications to unconventional reservoir rocks have not been addressed yet. The main objective of this study, therefore, is to evaluate the efficiency of EMA, in combination with universal power-law scaling from percolation theory, in estimating k(rg) from pore size distribution and pore connectivity. We presume that gas flow is mainly controlled by two main mechanisms contributing in parallel: (1) hydraulic flow and (2) molecular flow. We then apply the EMA to determine effective conductances and, consequently, k(rg) at higher gas saturations (S-g), and the universal scaling from percolation theory at lower S-g values. Comparisons with two pore-network simulations and six experimental measurements from the literature show that, in the absence of microfractures, the proposed model estimates k(rg) reasonably well in shales and tight porous rocks. More specifically, we found that the crossover point - gas saturation (S-gx) at which transport crosses from percolation theory to the EMA - is non-universal. The value of S-gx is a function of pore space characteristics such as pore size distribution broadness and critical gas saturation. This means that one should expect S-gx to vary from one rock sample to another.