Numerical Investigation of Liquid Flow Behaviors through Closed Rough Fractures in the Self-Propped Shale Formation

The surface morphology of fractures formed by hydraulic fracturing is usually rough. The roughness of the fracture surface is the main reason the actual fracture conductivity deviates from the ideal flat plate model result. In this paper, based on the three-dimensional reconfiguration of actual rough hydraulic fractures, a randomly generated geometric model of a micro-convex body with a rough fracture surface is used as an example of a hydraulic fracture in a shale reservoir. Assuming that the flow in the fracture conforms to the laminar flow pattern, the velocity and pressure fields of the fluid flow on the fracture surface are solved by the finite element method. The effects of micro-convex body size, uniformity, density, and shape on the non-uniform flow of the rough fracture surface are analyzed. The three-dimensional model shows that the average velocity is minimum in the near fully closed fracture. The fluid bypasses the micro-convex body during the flow, forming multiple nonlinear flow regions. The streamlined tortuosity increases with the density and size of the micro-convex bodies and depends on the distribution of the micro-convex areas. The bypassing accelerates the pressure drop and slows down the flow rate. The greater the degree of micro-convex body aggregation, the more significant the decrease in flow velocity. The more locations where the curvature of the micro-convex edge is not zero, the more nonlinear flow zones can significantly reduce the flow rate and thus affect oil and gas production. Targeted optimization of the proppant placement pattern to make the trailing part of the micro-convex body as close to streamlined as possible can reduce the nonlinear flow area and slow down the flow rate reduction.