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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2016

Phase-field modeling of proppant-filled fractures in a poroelastic medium

Résumé

In this paper we present a phase field model for proppant-filled fractures in a poroelastic medium. The formulation of the coupled system involves four unknowns; displacements, phase field, pressure , and proppant concentration. The two-field displacement phase-field system is solved fully-coupled and accounts for crack irreversibility. This solution is than coupled to the pressure equation via a fixed-stress iteration. The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator function that distinguishes between the fracture and the reservoir. The transport of the proppant in the fracture is modeled by using a power-law fluid system. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The concentration is solved with cell-centered finite elements. Nonlinear equations are treated with Newton's method. Our developments are substantiated with several numerical examples in two and three dimensions.
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Dates et versions

hal-01278240 , version 1 (23-02-2016)

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Sanghyun Lee, Andro Mikelic, Mary F Wheeler, Thomas Wick. Phase-field modeling of proppant-filled fractures in a poroelastic medium. Computer Methods in Applied Mechanics and Engineering, 2016, 312, pp.509-541. ⟨10.1016/j.cma.2016.02.008⟩. ⟨hal-01278240⟩
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