Narrow Results

The apparent liquid permeability (ALP) of shale is challenging to be characterized due to complex wettability and nanopore size distribution. The nanopores in organic matter of shale are usually hydrophobic and the nanopores in inorganic matter are hydrophilic. The flow behaviors in these two different nanopores are quite different, and accurately predicting the ALP of shale is difficult. This paper proposes a fractal model for predicting the ALP of shale with dual wettability. The nonflowing boundary layer effect of water in inorganic pores and the slip effect in organic pores are considered, and the equations for describing the flow rate in single organic pore and inorganic pore are derived, respectively. With the assumption of the fractal distributions of organic pores and inorganic pores in shale, the analytical expression for predicting the ALP of shale is derived, and the key parameters influencing shale ALP are analyzed with sensitivity study. The research results show that the nonflowing boundary layer can reduce the ALP of inorganic pores, but slip effect will increase the ALP of organic pores. ALP of inorganic pores is affected by the thickness of nonflowing boundary layer, which is determined by the displacement pressure gradient, fluid viscosity, and pore size distribution. ALP of inorganic pores is more affected by contact angle and pore size distribution.

Seepage flow in low permeability reservoirs is strongly influenced by the boundary layer, which is characterized by a low-velocity non-Darcy flow phenomenon, and a nonlinear relationship between velocity and pressure gradient. The viscosity is not uniformly distributed in the pore throat and has a great effect on the nonlinear flow behavior. In this paper, a low-velocity non-Darcy flow model is proposed. By quantitatively characterizing the boundary layer thickness and considering the non-uniform distribution of viscosity for the first time, a modified Hagen–Poiseuille equation combining the boundary layer effect and viscosity distribution in a single capillary is derived. Then, the analytical expression of the nonlinear relationship between the flow rate and pressure gradient in the fractal porous media is established, assuming that the pores in the tight formation are fractal distribution. Finally, the validity of the model is verified by experimental data. The relative error between the model and experimental data, with a permeability smaller than 3mD, is 3.27%. And the parameters affecting low-velocity non-Darcy flow are also analyzed. The results showed that the influence of boundary layer is one of the causes of low-velocity non-Darcy flow in tight reservoir. The study has also revealed that the non-uniform distribution of viscosity in the pore throat has a great influence on the nonlinear flow, which is often neglected in previous works.

The paper presents a new strategy for improving the accuracy of solutions near the boundary in the integral identity associated with the parametric integral equation system (PIES) for two-dimensional (2D) potential problems. A significant reduction in accuracy in the zone close to the boundary, also known as the boundary layer effect, is directly associated with the nearly singular properties of kernels present in the integral identity. The paper shows that these singularities can be efficiently eliminated by regularizing the integral identity with the help of the so-called regularizing function with appropriate coefficients. The analyzed examples demonstrate a significant improvement in accuracy, where all integrals of the regularized integral identity are accurately calculated using low-order standard Gauss–Legendre quadrature. The proposed regularization algorithm is independent of the actual boundary shape, its representation and assumed boundary conditions.