Coupling of Darcy's equation with molecular transport and its application to upscaling kerogen permeability

Quantification of gas transport in organic rich shale is important in determining natural gas production rates. However, laboratory measurements are challenging due to very tight nature of the rock, and have large uncertainties due to presence of multiple mechanisms of gas transport at multiple pore scales. In this paper, the emphasis is on the understanding of transport inside organic material known as kerogen and prediction of its permeability. We performed nonequilibrium molecular dynamics simulations of steady-state methane flow in single-wall carbon nanotube based on a moving piston model (Riewchotisakul and Akkutlu, 2015). The piston model allows us to observe transition from convection to molecular (pore) diffusion under the reservoir conditions and to understand the effects of adsorbed methane molecules on the overall transport in the tube. The results show that the adsorbed molecules are not only mobile but also contribute a significant portion to the total mass flux. Simulations with different sizes of capillaries show that the contribution is profound in capillaries with diameter less than 10nm. The adsorbed-phase transport velocity is independent of capillary size, but strongly dependent on pressure drop across the capillary. This allowed us to formulate the transport as an additional diffusion mechanism by the capillary walls using a modified Hagen-Poiseuille equation and predict the transport enhancement. In the second part of the paper, we considered steady-state transport across a pore-network of inter-connected nano-capillaries. The preliminary simulation results show that the modified Hagen- Poiseuille equation leads to representative elementary volume of a model kerogen. The estimated permeability of the volume is sensitive to surface properties of the nanocapillary walls indicating that fluid-wall interactions driven by molecular forces could be significant during the large-scale transport within kerogen. A modified Kozeny-Carmen correlation is proposed.