Numerical simulation of transport and placement of multi-sized proppants in a hydraulic fracture in vertical wells

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The placement of proppant in hydraulic fractures, which is governed by slurry flow, proppant transport and settlement, can significantly affect the conductivity of the fracture, and this will subsequently affect the productivity of the hydraulically fractured wells. To investigate proppant transport mechanisms and placement profiles in a hydraulic fracture, computational fluid dynamics coupled with discrete element method is used to model slurry flow and micro-mechanical interactions of proppant particles in a fracture. The effect of the solid phase is introduced in terms of volumetric porosity and particle interaction forces, and a contact model is used to simulate the particle-to-particle and the particle-to-wall interactions. The particles are modelled as real spheres, and for a two-dimensional computational model, an out-of-plane length of the maximum particle diameter is assumed. The proppants are injected into the fracture through seven perforations to mimic the slurry flow in a fracture in vertical wells. When the proppants are injected into a fracture driven by thin fracturing fluids, they quickly settle out of the fluid and accumulate on the fracture bottom, forming a proppant dune. A three-layer flow pattern forms in the fracture consisting of: (1) a stationary proppant bed at the bottom, (2) a proppant-fluid mixture layer above it, and (3) a clean fluid layer at the top. During the early stages, the motion of the proppants is governed by suspension, settlement and fluidization, and the injected proppants mainly settle and accumulate near the wellbore. When the equilibrium height of the dune is reached, the dune changes to a proppant bank. Then the later injected proppants are transported to overshoot the bank and dragged deeper into the fracture. A new proppant transport mechanism, vortex, is observed, which governs the proppant motion after they leave the proppant bank.