Fluid mechanics of natural gas in organic-rich shale involves nanoscale phenomena that could lead to potential non-Darcy effects during gas production. In general, these are low-Reynolds-number and noncontinuum effects and, more importantly, pore-wall-dominated multiscale effects. In this study, we introduce a new lattice Boltzmann method (LBM) to investigate these effects numerically in simple pore geometries. The standard method was developed in the 1980s to overcome the weaknesses of lattice gas cellular automata and has emerged recently as a powerful tool to solve fluid dynamics problems, in particular in the areas of micro- and nanofluidics. The new approach takes into account molecular-level interactions by use of adsorptive/cohesive forces among the fluid particles and defining a Langmuir-slip boundary condition at the organic pore walls. The model allows us to partition mass transport by the walls into two components: slippage of free gas molecules and hopping (or surface transport) of the adsorbed gas molecules. By use of the standard 2D D2Q9 lattice, low-Reynolds-number gas dynamics is simulated in a 100-nm model organic capillary and later in a bundle of smaller-sized organic nanotubes. The results point to the existence of a critical Knudsen-number value for the onset of laminar gas flow under typical shale-gas-reservoir pressure conditions. Beyond this number, the predicted velocity profile shows that the mechanisms of slippage and surface transport could lead to molecular streaming by the pore walls, which enhances the gas transport in the organic nanopores. The work is important for development of new-generation shale-gas-reservoir flow simulators, and it can be used in the laboratory for organic-rich-shale characterization.