  Accurate modeling of gas relative permeability 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 gas relative
permeability 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, gas relative permeability at higher
gas saturations, and the universal scaling from percolation theory at lower gas
saturation 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 gas relative permeability
reasonably well in shales and tight porous rocks. More specifically, we found
that the crossover point, gas saturation at which transport crosses from
percolation theory to the EMA, is non-universal. The value of crossover gas
saturation is a function of pore space characteristics such as pore size
distribution broadness and critical gas saturation. This means that one should
expect the crossover gas saturation to vary from one rock sample to another.
