Dynamic model for the simultaneous adsorption of water vapor and methane on shales

Abstract

Water is almost ubiquitous in shale gas reservoirs. To analyze simultaneous water vapor and methane adsorption in shales, a dynamic model with a time-dependent boundary and diffusivity and a noninstantaneous adsorption mechanism was proposed. The analytical solution of the model was obtained via integral transformation method. The model was applied to match the dynamic data of simultaneous CH4–H2O adsorption. The results suggest that the strength for gas adsorption to shale is characterized by adsorption rate coefficient and desorption rate coefficient, where the adsorption strength of shale to water vapor is stronger than that to methane, and the conversion rate from water vapor to adsorbed water on adsorption sites is larger. The methane and water vapor diffusion coefficients first increase to a maximum and then decrease with time. The maximum methane diffusion coefficient ranges from 5.83 × 10−13–1.08 × 10−11 m2/s; the maximum water vapor diffusion coefficient ranges from 2.06 × 10−19–4.53 × 10−13 m2/s. The methane diffusivity and its variation rate are larger than those of water vapor. The methane and water vapor diffusion coefficients first increase with the density of free gases in pores and then decrease in the late period of the adsorption process. Water vapor reduces the adsorption strength of shale to methane and free methane-to-adsorbed methane conversion rate on adsorption sites. The methane diffusion coefficient in dry shale increases with time, and its growth rate reaches zero at adsorption equilibrium, which ranges from 6.60 × 10−14–4.82 × 10−11 m2/s; the methane diffusivity increases exponentially with the methane adsorption amount and free methane density in pores.