Diffusion‐to‐Imbibition Transition in Water Sorption in Nanoporous Media: Theoretical Studies

The ability to predict multiphase fluid transport in nanoporous rocks such as shales is critical for many geoscience applications, for example unconventional hydrocarbon production, geologic carbon sequestration, and nuclear waste disposal. When the pore sizes approach nanoscales, the impact of the molecular interaction forces between fluids and solids becomes increasingly important. These forces can alter macroscopic fluid phase behavior and control transport. Recent experimental studies have shown that capillary condensation and subsequent imbibition of liquid water can occur in hydrophilic nanoporous media even if the vapor phase is at a critical relative humidity (rhcrit) well below vapor saturation. This study presents a theoretical investigation of the processes controlling adsorption, capillary condensation and imbibition in nanoporous media, using the square‐gradient classical density functional theory. The proposed theoretical model explicitly includes the relevant interaction forces among fluids and solids in macroscopic porous media. Application of the model to a relative‐humidity‐controlled water adsorption experiment is presented to demonstrate the impact of water‐pore wall attractive forces on multiphase water behavior in a hydrophilic silicon nanoporous medium. The model represents well the measured time‐dependent evolution of the water imbibition front inside the nanoporous medium and also explains the diffusion‐like water transport regimes observed at rh rhcrit. The study furthermore gives an insight on hysteresis phenomenon in adsorption and desorption isotherms. Key Points The square gradient theory‐based model explains diffusion‐to‐imbibition transition at a critical relative humidity in nanoporous media The model presented has an inherent feature to represent hysteresis in adsorption and desorption isotherms Hysteresis in the predicted isotherms is explained by the existence of the different energy barriers for adsorption and desorption