Mathematical Model of Shale Oil Seepage at Micro-Nano Pore Scale

Abstract

Due to the unclear seepage mechanism for shale oil, it is hard to establish a reasonable mathematical model to describe the flowing law. In this study, a real shale pore structure was reconstructed with CT scanning and a numerical model of fluid flowing in the real shale pore is developed with COMSOL, based on the boundary slip at the micro-nano pore scale to study the causes of nonlinear seepage. A two-fluid model is employed to establish a simple mathematical model to describe the relationship between the flow rate and the pressure gradient using the effective slip length to account for the influence of pore structure and true slip, and the established model is verified with experimental data coming from Jiyang shale oil. The results indicated that the pore structure greatly affected the shape of the seepage curve. With the increase in displacement pressure, the percentage of fluid involved in the flow increased until it became stable, showing a changing trend from nonlinearity to linearity. The established model can fit the experimental data well and reasonably characterize the nonlinear seepage of shale oil.