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 a proppant pack. 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 only 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 this aperture and partially diminish the effectiveness of this highly-conductive zone, with time. Contrary to conventional wisdom, simulations suggest that, for a given mass of proppant, uniform distribution throughout the full height of the fracture may not be as effective as a wedge at the fracture base with an open-arch formed above. This arched zone results in a higher overall fracture transmissivity than a uniform proppant distribution. However, this may require further demonstration by production simulations since part of the pay-zone might be disconnected from, or poorly-connected to, the preferential pathway for fluid flow, and this may increase the hydrocarbon diffusion length.
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