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

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• 作者：Sanghyun Lee^a ; ^{shlee@ices.utexas.edu} ; Andro Mikelić^c ; ^d ; ^{mikelic@univ-lyon1.fr} ; Mary F. Wheeler^a ; ^{mfw@ices.utexas.edu} ; Thomas Wick^b ; ^{thomas.wick@ricam.oeaw.ac.at}
• 关键词：Phase field fracture ; Hydraulic fracturing ; Proppant transport ; Quasi-Newtonian flow model
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：312
• 期：Complete
• 页码：509-541
• 全文大小：3773 K
• 卷排序：312

文摘

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 then 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.