THE FRACTAL MATHEMATICAL MODELS FOR SPONTANEOUS AND FORCED IMBIBITION WITH DIFFERENT CROSS-SECTION SHAPES IN SHALE OIL RESERVOIR

Large-scale hydraulic fracturing is the critical technology for effective shale oil production. However, the imbibition flow mechanisms of fracturing fluid in shale micropores and the influence of shale microstructure and physical properties are still indistinct, which makes the optimization goal of fracturing flowback unclear and restricts the enhancement of shale oil recovery. Therefore, based on SEM and XRD experiments, it is analyzed that shale has the characteristics of multiple pores, which are divided into organic pores, brittle mineral pores, and clay pores. Nonetheless, how the tube cross-section controls the interface displacement is not well discussed in the available literature, especially in irregular triangles, rectangles and other non-circular shapes. This paper studies the influence of cross-section shapes on the capillary force by considering the corner flow of the wetting phase, and it analyzes the imbibition dynamics of different types of pores. Using the shale multi-pores physical model and fractal theory, the shale semi-analytical solution models of SI and FI are established. Theoretical analysis of the water imbibition mechanisms shows that the key factors controlling SI and FI volume include imbibition time, fluid properties, pore cross-section shapes, tortuosity, and forced pressure.