TY - JOUR

T1 - Phase-field modeling of two phase fluid filled fractures in a poroelastic medium

AU - Lee, Sanghyun

AU - Mikeli, Andro

AU - Wheeler, Mary F.

AU - Wick, Thomas

N1 - Funding Information: Funding: The research of the first and third authors was partially supported by Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences, DOE Project DESC0001114, and a DOE grant DE FG02-04ER25617. The third author was also partially supported by Moncrief Grand Challenge Faculty Awards from The Institute for Computational Engineering and Sciences (ICES), the University of Texas at Austin. The second and fourth authors were supported by The J. Tinsley Oden Faculty Fellowship Research Program and Center for Subsurface Modeling at Institute for Computational Engineering and Science (ICES), the University of Texas at Austin.

PY - 2018

Y1 - 2018

N2 - We propose an immiscible two phase flow fracture model, based on a phase-field for treating crack propagation in porous media. This multifluid model is an extension of classical flow models and we take into account nonzero capillary pressure. Using lubrication theory, we provide details of the determination of effective parameters: Absolute and relative permeabilities. The phasefield formulation is a generalization of previous works by the authors and extends the single phase model to the two phase case. Here the resulting flow system has four unknowns: Resident and injected pressures and saturations, respectively. The solid contribution consists of displacements and a phase-field variable. Both systems are coupled employing a fixed-stress splitting. Therein, the flow problem is treated with an iterative scheme and the solid problem fully implicitly. Modeling and algorithms are substantiated with several numerical tests.

AB - We propose an immiscible two phase flow fracture model, based on a phase-field for treating crack propagation in porous media. This multifluid model is an extension of classical flow models and we take into account nonzero capillary pressure. Using lubrication theory, we provide details of the determination of effective parameters: Absolute and relative permeabilities. The phasefield formulation is a generalization of previous works by the authors and extends the single phase model to the two phase case. Here the resulting flow system has four unknowns: Resident and injected pressures and saturations, respectively. The solid contribution consists of displacements and a phase-field variable. Both systems are coupled employing a fixed-stress splitting. Therein, the flow problem is treated with an iterative scheme and the solid problem fully implicitly. Modeling and algorithms are substantiated with several numerical tests.

KW - Biot system

KW - finite elements

KW - fixed-stress iterative coupling

KW - fracture propagation

KW - multiphase flow

KW - phase-field fracture

UR - http://www.scopus.com/inward/record.url?scp=85058239112&partnerID=8YFLogxK

U2 - 10.1137/17M1145239

DO - 10.1137/17M1145239

M3 - Article

AN - SCOPUS:85058239112

VL - 16

SP - 1542

EP - 1580

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 4

ER -