TY - JOUR
T1 - A dimensionally-reduced fracture flow model for poroelastic media with fluid entry resistance and fluid slip
AU - Bergkamp, Elisa A.
AU - Verhoosel, Clemens V.
AU - Remmers, Joris J.C.
AU - Smeulders, David M.J.
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/4/15
Y1 - 2022/4/15
N2 - We develop a model which couples the flow in a discrete fracture to a deformable porous medium. To account for the discrete representation of the fracture, a dimensionally-reduced fluid flow model is proposed. The fluid flow model incorporates both a reduced permeability of the fracture walls due to the skin effect, and a slip of fluid flowing along the permeable fracture walls. Biot's model for poroelastic media is coupled to a fracture flow model based on a thin-film approximation of the compressible Navier-Stokes equations. The fracture flow model incorporates a fluid entry resistance parameter to relate the leak-off through the fracture walls to a pressure jump across the fracture walls, and the Beavers-Joseph-Saffman slip rate coefficient to represent the fluid slip along the fracture walls. The numerical model is based on a thermodynamic framework in which all energy storage and dissipative mechanisms in the problem are identified, including the mechanisms related to the interface effects. The thermodynamic framework is employed to solve the nonlinear coupled problem up to a specified energy range through a Picard iteration technique and to study the model and its results. Studies are presented for a range of fluid entry resistance parameters and Beavers-Joseph-Saffman slip rate coefficients, showing the capability of the model to simulate skin and slip effects in a dimensionally-reduced fracture setting.
AB - We develop a model which couples the flow in a discrete fracture to a deformable porous medium. To account for the discrete representation of the fracture, a dimensionally-reduced fluid flow model is proposed. The fluid flow model incorporates both a reduced permeability of the fracture walls due to the skin effect, and a slip of fluid flowing along the permeable fracture walls. Biot's model for poroelastic media is coupled to a fracture flow model based on a thin-film approximation of the compressible Navier-Stokes equations. The fracture flow model incorporates a fluid entry resistance parameter to relate the leak-off through the fracture walls to a pressure jump across the fracture walls, and the Beavers-Joseph-Saffman slip rate coefficient to represent the fluid slip along the fracture walls. The numerical model is based on a thermodynamic framework in which all energy storage and dissipative mechanisms in the problem are identified, including the mechanisms related to the interface effects. The thermodynamic framework is employed to solve the nonlinear coupled problem up to a specified energy range through a Picard iteration technique and to study the model and its results. Studies are presented for a range of fluid entry resistance parameters and Beavers-Joseph-Saffman slip rate coefficients, showing the capability of the model to simulate skin and slip effects in a dimensionally-reduced fracture setting.
KW - (Extended) finite element method
KW - Fluid entry resistance
KW - Fluid slip
KW - Fracture flow
KW - Poroelasticity
KW - Thermodynamic framework
UR - http://www.scopus.com/inward/record.url?scp=85124159216&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2022.110972
DO - 10.1016/j.jcp.2022.110972
M3 - Article
AN - SCOPUS:85124159216
SN - 0021-9991
VL - 455
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 110972
ER -