Apparent permeability model for shale oil transport through elliptic nanopores considering wall-oil interaction

Abstract

The shale oil transport mechanisms in inorganic matrix (iOM) and organic matrix (OM) nanopores are still not well understood, and the shape of nanopores is complex and diverse. Therefore, it is of critical importance to clarify the oil transport mechanisms in nanopores with different cross-sectional shapes. In this study, a model for oil transport is proposed to analyze the apparent permeability and flow enhancement based on the Hagen–Poiseuille equation. The proposed model takes into account the near-wall oil flow in iOM nanopores and the adsorbed oil flow in OM nanopores. In addition, the effects of different circular and elliptical cross-sections of nanopores and size of nanopores are considered. The proposed model is validated with the simulation data of non-equilibrium molecular dynamics and the Lattice Boltzmann method. The results indicate that: (1) the flow enhancement in iOM and OM nanopores first decreases rapidly and then stabilizes with an increasing length of semi-major axis a and semi-minor axis b because of the decreasing wall-oil interaction, and the apparent permeability of iOM increases as the axis a and axis b increase. When axis b is 2 nm, the permeability of OM increases with an increase in length of axis a, as length of axis b becomes larger, the permeability first decreases and then increases; (2) in iOM and OM nanopores, with a constant cross-sectional area, compared to nanopores with circle cross-sections, the flow enhancement becomes greater in nanopores with elliptical cross-sections, and the higher the ratio ω of the length of axis a to that of axis b, the greater the flow enhancement. The permeability of iOM nanopores decreases with an increasing ratio ω, while the permeability of OM nanopores first decreases and then increases. When the cross-sectional area is small, the permeability of OM nanopores increases with an increase in ratio ω, and as the cross-sectional area becomes greater, the permeability decreases with an increasing ratio ω. The proposed model demonstrates that elliptical cross-sections of nanopores can provide theoretical support for the development of shale oil reservoirs.