Physics of fluid flow in shale reservoirs cannot be predicted from standard flow or mass-transfer models because of the presence of nanopores, ranging in size from 1 to hundreds of nanometers, in shales. Conventional continuum flow equations, such as Darcy's law, greatly underestimate the fluid flow rate when applied to nanopore-bearing shale reservoirs. As a result of the existence of nanopores in shales, the molecular mean free path becomes comparable to the characteristic geometric scale, and we hypothesize that under this condition, Knudsen diffusion, in addition to correction for the slip boundary condition, becomes the dominant mechanism. Recently a few models have been developed that use various empirical parameters to account for these modifications (Javadpour, 2009; Civan, 2010; Darabi et al., 2012). This paper aims to provide a different approach to modeling apparent permeability in shale reservoirs. The proposed model is analytical, free of any empirical coefficients, and has been derived without invoking the assumption of slip flow at the pore wall. Our model of apparent permeability represented by a single analytical equation depends only on pore size, pore geometry, temperature, gas properties, and average reservoir pressure. The proposed model is valid for Knudsen numbers less than 1 and it stands up under the complete operating conditions of a reservoir. Our model accurately predicts results as reported by other empirical models. Finally, the model shows that pore-surface roughness and mineralogy have a negligible influence on gas flow rate, whereas pore geometry and pore size play a significant role in the proportion of diffusion in total flow rate.

URTeC 1578037

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