A FRACTAL MODEL OF LOW-VELOCITY NON-DARCY FLOW CONSIDERING VISCOSITY DISTRIBUTION AND BOUNDARY LAYER EFFECT

Abstract

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.