•A nanoscale multiphase pore network transport model is proposed.•Multiphase transport in dual wettability nanoporous shale is studied.•Effects of slip length, contact angle, flow area on water flow are considered.•Gas flow accounts for multiple transport mechanisms. Fluid transport in nanoporous shale is known to be affected by the nanoscale fluid transport mechanisms, surface wettability and heterogeneous pore structure. The pores of shale are believed to be dual surface wettability with gas-wet organic pores and water-wet inorganic pores. Investigation on the nanoscale multiphase transport behavior in dual surface wettability nanoporous shale has practical implication in understanding inject water distribution during injected water flow in and flow back process. In this study, we propose a nanoscale gas and water multiphase pore network transport model to study nanoscale confined gas and water transport behavior in dual wettability nanoporous shale. A 3-D shale pore network model is constructed from 3-D image that is reconstructed from 2-D shale SEM image of organic-rich sample. Water transport considers the boundary slip length determined by the contact angle. Bulk gas transport in inorganic pores considers slip effect while bulk gas transport and surface diffusion for adsorbed gas are both considered in organic pores. Injected water flow in process is modeled by water displacing gas process while injected water flow back process is modeled by gas displacing water process. Gas and water relative permeabilities during injected water flow in and flow back process at different TOC volumes and inorganic pore contact angle are analyzed in detail and are compared with relative permeabilities without nanoscale transport mechanisms. Study results reveal that nanoscale gas and water relative permeabilities are influenced by the total organic carbon (TOC) in volumes and inorganic pore water contact angle while nanoscale transport mechanisms influence on the relative permeabilities can be neglected.