期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 312, 期 -, 页码 509-541出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.02.008
关键词
Phase field fracture; Hydraulic fracturing; Proppant transport; Quasi-Newtonian flow model
资金
- Department of Energy National Energy Technology Laboratory [DE-FE0023314]
- Aramco [UTA 11-000320]
- Statoil [STNO-4502931834]
- Austrian Academy of Sciences
- Institute for Computational Engineering and Sciences JT Oden fellowship
- Center for Subsurface Modeling at UT Austin
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1546251, 1546145, 1546553] Funding Source: National Science Foundation
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. (C) 2016 Elsevier B.V. All rights reserved.
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