LAUSR

Abstract The residual opening of fluid-driven fractures is conditioned by proppant distribution and has a significant impact on fracture conductivity - a key parameter to determine fluid production rate and well performance. A 2D model follows the evolution of the residual aperture profile and conductivity of fractures partially/fully filled with proppant packs. The model accommodates the mechanical response of proppant packs in response to closure of arbitrarily rough fractures and the evolution of proppant embedment. The numerical model is validated against existing models and an analytic solution. Proppant may accumulate in a bank at the fracture base during slick water fracturing, and as hydraulic pressure is released, an arched zone forms at the top of the proppant bank as a result of partial closure of the overlaying unpropped fracture. The width and height of the arched zone decreases as the fluid pressure declines, and is further reduced where low concentrations of proppant fill the fracture or where the formation is highly compressible. This high-conductivity arch represents a preferential flow channel and significantly influences the distribution of fluid transport and overall fracture transmissivity. However, elevated compacting stresses and evolving proppant embedment at the top of the settled proppant bed reduce the aperture and diminish the effectiveness of this highly-conductive zone, with time. Two-dimensional analyses are performed on the fractures created by channel fracturing, showing that the open channels formed between proppant pillars dramatically improve fracture transmissivity if they are maintained throughout the lifetime of the fracture. However, for a fixed proppant pillar height, a large proppant pillar spacing results in the premature closure of the flow channels, while a small spacing narrows the existing channels. Such a model provides a rational means to design optimal distribution of the proppant pillars using deformation moduli of the host to control pillar deformation and flexural spans of the fracture wall.