TY - JOUR
T1 - Flow in porous media with low dimensional fractures by employing enriched Galerkin method
AU - Kadeethum, T.
AU - Nick, H. M.
AU - Lee, S.
AU - Ballarin, F.
PY - 2020
Y1 - 2020
N2 - This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.
AB - This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.
KW - Enriched Galerkin
KW - Finite element method
KW - Fractured porous media
KW - Heterogeneity
KW - Local mass conservative
KW - Mixed-dimensional
UR - http://www.scopus.com/inward/record.url?scp=85086137954&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2020.103620
DO - 10.1016/j.advwatres.2020.103620
M3 - Article
AN - SCOPUS:85086137954
SN - 0309-1708
VL - 142
JO - Advances in Water Resources
JF - Advances in Water Resources
M1 - 103620
ER -