A modeling framework is developed to describe proppant transport (including gravitational settling and tip-screen out) in a hydraulic fracturing simulator that can function as either fully-3D or pseudo-3D. The simulator locally enforces mass balance of fluid and proppant and applies appropriate boundary conditions for mechanical calculations. The simulator uses recently developed constitutive equations that smoothly capture the transition from Poiseuille flow to Darcy flow as the proppant concentration transitions from a dilute mixture to a packed bed. We develop new constitutive relations that enable the model to describe fracture closure against proppant (at either low or high concentration) after the end of injection. We also develop a framework for modeling proppant settling in a pseudo-3D model. The method ensures a continuous solution, which guarantees convergence and accuracy with refinement of the temporal and spatial discretization. The framework allows proppant to settle into a proppant bank at the bottom of the fracture. The proppant bank can grow, remain stationary, or erode, depending on flow conditions. The simulator can describe tip-screen out (TSO) and the tendency for the volumetric flowing fraction of proppant to exceed the volumetric fraction of proppant due to the tendency of proppant to flow at the center of the fracture aperture. Pseudo-3D simulations are compared to the fully-3D simulations for both hydraulic fracturing and long-term production. For hydraulic fracturing, the pseudo-3D simulations are able to substantially reproduce the results from the fully-3D simulations and are far more computationally efficient. The simulation methods are compared using a variety of values for proppant size, fluid viscosity, and proppant density. An optimized proppant schedule is tested in order to improve horizontal proppant placement and prevent excessive tip screen-out. The simulations indicate that because fracture closure can be slow in very low permeability formations, substantial settling occurs after the end of injection, significantly worsening vertical proppant placement. For simulation of long-term production, the pseudo-3D results deviate strongly from the fully-3D simulations, indicating that the pseudo-3D model is not suitable for simulating the production phase, as currently formulated.

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