Proppant Settlement and Long-Term Conductivity Calculation in Complex Fractures

The current research on fracture conductivity ignores the placement of the proppant in fractures and relies on single-fracture conductivity testing and calculation, which cannot represent the overall conductivity of complex fracture systems. This research proposes a calculation method for the long-term conductivity of complex fractures based on proppant placement. This method considers fracture morphology, proppant placement, proppant embedment, and deformation under high closing pressure. The research results show that fracture conductivity decreases with increasing time, which can be divided into three stages: the embedding stage, the creep stage, and the stabilization stage. The long-term conductivity of the main fracture is higher than that of the branching fracture. With increasing closing pressure, the conductivities of both the main fracture and the branching fracture decrease. This is because increasing closure stress accelerates proppant embedment and creep, compressing the fluid flow space and further reducing fracture conductivity. Fracture conductivity is related to the placement of the proppant and sand concentration. Increasing the sand ratio can significantly increase the placement of the proppant in the main fracture and branching fractures, thereby improving fracture conductivity. Increasing the fracturing fluid viscosity can increase its proppant migration capacity. The proppant does not easily settle prematurely in high-viscosity fracturing fluid and can enter more into branching fractures, thereby improving their conductivity.