Gas transport in shale matrix coupling multilayer adsorption and pore confinement effect

Accurate prediction of gas transport in shale formations mainly consisting of micro- and nano-scale pores is a great challenge since most existing models only consider monolayer adsorption and the underlying multi-physics are either partially or completely overlooked. In this work, we have proposed a comprehensive single-component gas transport model integrating multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The new analytical model is developed based on Bravo layer-sequence-model and then upscaled using an Effective Medium Approximation (EMA) method, where the generalized Brunauer-Emmett-Teller (BET) model, the modified Peng-Robinson equation of state (EoS) model, and the Sutton's viscosity model are innovatively incorporated. The newly developed model has been successfully validated against simulation and experimental results with the assistance of an efficient iterative ensemble smoother (ES) algorithm. It is observed that the pore confinement effect is of importance when the pore size is smaller than 50 nm. The increase of gas viscosity due to the real gas effect is significant under reservoir conditions. The apparent permeability is found to increase greatly as the adsorption layer number increases, implying that the application of Langmuir model in existing gas transport models may substantially underestimate it. Given inorganic nanopores, the viscous flow is important at any pore sizes and the Knudsen diffusion plays a role in the pores that are less than 5 nm under reservoir conditions. As for organic nanopores, the contribution of surface diffusion is tangible when the pore size is below 150 nm and the Knudsen diffusion is negligible under high pressures.