Fluid flow in nanoscale organic pores is known to be affected by fluid transport mechanisms and properties within confined pore space. The flow of gas and water shows notably different characteristics compared with conventional continuum modeling approach. A pore network flow model is developed and implemented in this work. A 3‐D organic pore network model is constructed from 3‐D image that is reconstructed from 2‐D shale SEM image of organic‐rich sample. The 3‐D pore network model is assumed to be gas‐wet and to contain initially gas‐filled pores only, and the flow model is concerned with drainage process. Gas flow considers a full range of gas transport mechanisms, including viscous flow, Knudsen diffusion, surface diffusion, ad/desorption, and gas PVT and viscosity using a modified van der Waals' EoS and a correlation for natural gas, respectively. The influences of slip length, contact angle, and gas adsorption layer on water flow are considered. Surface tension considers the pore size and temperature effects. Invasion percolation is applied to calculate gas‐water relative permeability. The results indicate that the influences of pore pressure and temperature on water phase relative permeabilities are negligible while gas phase relative permeabilities are relatively larger in higher temperatures and lower pore pressures. Gas phase relative permeability increases while water phase relative permeability decreases with the shrinkage of pore size. This can be attributed to the fact that gas adsorption layer decreases the effective flow area of the water phase and surface diffusion capacity for adsorbed gas is enhanced in small pore size. Key Points A multiphase pore network flow model is proposed to study gas‐water flow pattern in nanoporous organic matter Effects of slip length, contact angle, flow area on water flow are considered and gas flow accounts for full range of transport mechanisms Water relative permeabilities decrease and gas relative permeabilities increase with the decrease of pore size