Jing Li

A Fractal Model for Gas–Water Relative Permeability in Inorganic Shale with Nanoscale Pores

A reliable gas–water relative permeability model in shale is extremely important for the accurate numerical simulation of gas–water two-phase flow (e.g., fracturing fluid flowback) in gas-shale reservoirs, which has important implication for the economic development of gas-shale reservoir. A gas–water relative permeability model in inorganic shale with nanoscale pores at laboratory condition and reservoir condition was proposed based on the fractal scaling theory and modified non-slip boundary of continuity equation in the nanotube. The model not only considers the gas slippage in the entire Knudsen regime, multilayer sticking (near-wall high-viscosity water) and the quantified thickness of water film, but also combines the real gas effect and stress dependence effect. The presented model has been validated by various experiments data of sandstone with microscale pores and bulk shale with nanoscale pores. The results show that: (1) The Knudsen diffusion and slippage effects enhance the gas relative permeability dramatically; however, it is not obviously affected at high pressure. (2) The multilayer sticking effect and water film should not be neglected: the multilayer sticking would reduce the water relative permeability as well as slightly decrease gas relative permeability, and the film flow has a negative impact on both of the gas and water relative permeability. (3) The increased fractal dimension for pore size distribution or tortuosity would increase gas relative permeability but decrease the water relative permeability for a given saturation; however, the effect on relative permeability is not that notable. (4) The real gas effect is beneficial for the gas relative permeability, and the influence is considerable when the pressure is high enough and when the nanopores of bulk shale are mostly with smaller size. For the stress dependence, not like the intrinsic permeability, none of the gas or water relative permeability is sensitive to the net pressure and it can be ignored completely.

Anomalous Capillary Rise under Nanoconfinement: A View of Molecular Kinetic Theory

Understanding the capillary filling behaviors in nanopores is crucial for many science and engineering problems. Compared with the classical Bell-Cameron-Lucas-Washburn (BCLW) theory, anomalous coefficient is always observed because of the increasing role of surfaces. Here, a molecular kinetics approach is adopted to explain the mechanism of anomalous behaviors at the molecular level; a unified model taking account of the confined liquid properties (viscosity and density) and slip boundary condition is proposed to demonstrate the macroscopic consequences, and the model results are successfully validated against the published literature. The results show that (1) the effective viscosity induced by the interaction from the pore wall, as a function of wettability and the pore dimension (nanoslit height or nanotube diameter), may remarkably slow down the capillary filling process more than theoretically predicted. (2) The true slip, where water molecules directly slide on the walls, strongly depends on the wettability and will increase as the contact angle increases. In the hydrophilic nanopores, though, the magnitude may be comparable with the pore dimensions and promote the capillary filling compared with the classical BCLW model. (3) Compared with the other model, the proposed model can successfully predict the capillary filling for both faster or slower capillary filling process; meanwhile, it can capture the underlying physics behind these behaviors at the molecular level based on the effective viscosity and slippage. (4) The surface effects have different influence on the capillary filling in nanoslits and nanotubes, and the relative magnitude will change with the variation of wettability as well as the pore dimension.