Quantification of natural gas transport in organic-rich shale is important in predicting natural gas production. However, laboratory measurements are challenging due to tight nature of the rock and include large uncertainties. The emphasis of this work is to understand mass transport mechanisms inside the organic nanoporous material known as kerogen under subsurface conditions and describe its permeability. This requires a multi-scale theoretical approach that includes flow measurements in model nanocapillaries and within their network. Molecular dynamics simulation results of steady-state supercritical methane flow in single-wall carbon nanotube are presented in this article. A transition from convection to molecular diffusion is observed. The simulation results show that the adsorbed methane molecules are mobile and contribute a significant portion to the total mass flux in nanocapillaries with diameter 10 nm. They experience cluster diffusion that is dependent on the applied pressure drop across the capillary. A modified Hagen-Poiseuille equation is proposed considering the convective-diffusive nature of the overall transport in nanocapillary. The molecular-level study of steady-state transport is extended to a simple network of interconnected nanocapillaries representing kerogen. The modified Hagen-Poiseuille equation leads to a representative elementary volume of the model kerogen. The estimated permeability of the volume is sensitive to compressed and adsorbed fluids density ratio and 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 shale. A modified Kozeny-Carman correlation is proposed, relating kerogen porosity and tortuosity to the permeability.