Effect of water distribution on methane-carbon dioxide-water transportation in shale nanopores with Knudsen number correction

•A new transport model is derived for the CH4-CO2-H2O flow system.•Possible diffusion mechanisms and interactions are discussed.•The Knudsen number correction effect in shale nanopores is introduced.•The effect of water phase distribution on the gas–water flow is considered and discussed. The flow mechanism of a CO2-CH4-H2O system plays a key role in methane recovery and CO2 sequestration. In this paper, Knudsen number correction and water phase distribution are taken into account to establish a new transport model for the CO2-CH4-H2O flow in shale nanopores. The model is validated using data from three flow experiments, namely, methane-carbon dioxide flow experiments under dry conditions, methane with irreducible water flow characterization experiments in the nanofluidic chip, and air–water two-phase flow experiments in quartz sand. The effect of irreducible water on gas flow and methane-carbon dioxide-water relative permeability is discussed. The results in our paper show that: (1) The existence of irreducible water increases the difference caused by Knudsen number correction. (2) The existence of irreducible water has a negative effect on the gas flow in most cases. The reduction of methane and carbon dioxide permeability with irreducible water can be up to 28.53% and 21.88%, respectively. (3) The change of permeability curve is affected by gas composition fraction, water saturation, and irreducible water coverage. The study provides theoretical guidance for carbon dioxide enhancing shale gas recovery under the actual water saturation condition.