A FRACTAL MODEL FOR LOW-VELOCITY NON-DARCY FLOW IN TIGHT OIL RESERVOIRS CONSIDERING BOUNDARY-LAYER EFFECT

Abstract

Flow in nanoscale pore-throats of tight oil reservoirs is strongly affected by boundary-layers, and exhibits low-velocity non-Darcy flow phenomena. The relationship between flow velocity and pressure gradient is highly nonlinear and difficult to be modeled mathematically. This paper proposed a low-velocity non-Darcy flow model which can account for boundary-layer effect in tight oil reservoirs. First, a modified Hagen–Poiseuille equation coupled with boundary-layer effect in a single capillary tube was derived. Then, assuming pores in tight formations following fractal distribution, an analytical expression of nonlinear correlation between flow velocity and pressure gradient in fractal porous media was developed. Finally, the proposed model was validated with experiment data, and parameters influencing low-velocity non-Darcy flow were quantitatively evaluated. The research results show that the decreasing boundary-layer thickness with the increase pressure gradient is the main reason of low-velocity non-Darcy flow in tight oil reservoirs. Our model can effectively describe the nonlinear relationship between flow velocity and pressure gradient. The relationship between threshold pressure gradient (TPG) and pseudo threshold pressure gradient (PTPG) can also be predicted using our model. Fluid viscosity has great impact on nonlinear flow behavior, and with fluid viscosity increasing TPG and PTPG increase significantly. TPG is the function of fluid type, fluid viscosity and maximum pore diameter, and decreases exponentially with the increasing maximum pore size.