TY - JOUR

T1 - Simulation of solute transport through fractured rock

T2 - A higher-order accurate finite-element finite-volume method permitting large time steps

AU - Matthäi, Stephan K.

AU - Nick, Hamidreza M.

AU - Pain, Christopher

AU - Neuweiler, Insa

PY - 2009/7/10

Y1 - 2009/7/10

N2 - Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fastest flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure-(semi)-implicit transport scheme for the advection-diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2-4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a highly accurate overall solution. Numerical and fracture-related mechanical dispersions are compared in the realistic DFM models using second-order accurate runs as reference cases. With a CFL histogram, we establish target error criteria for CFL overstepping. This analysis indicates that for extreme fracture heterogeneity, only a few transport steps can be sufficient to analyse macro-dispersion. This makes our implicit method attractive for quick analysis of transport properties on multiple realisations of DFM models.

AB - Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fastest flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure-(semi)-implicit transport scheme for the advection-diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2-4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a highly accurate overall solution. Numerical and fracture-related mechanical dispersions are compared in the realistic DFM models using second-order accurate runs as reference cases. With a CFL histogram, we establish target error criteria for CFL overstepping. This analysis indicates that for extreme fracture heterogeneity, only a few transport steps can be sufficient to analyse macro-dispersion. This makes our implicit method attractive for quick analysis of transport properties on multiple realisations of DFM models.

KW - DFM

KW - DFN

KW - Discrete fracture and matrix model

KW - Dispersion

KW - FEM

KW - FVM

KW - Hybrid element

KW - Passive tracer advection

KW - Solute transport

KW - Unstructured mesh

UR - http://www.scopus.com/inward/record.url?scp=77952236984&partnerID=8YFLogxK

U2 - 10.1007/s11242-009-9440-z

DO - 10.1007/s11242-009-9440-z

M3 - Article

AN - SCOPUS:77952236984

VL - 83

SP - 289

EP - 318

JO - Transport in porous media

JF - Transport in porous media

SN - 0169-3913

IS - 2

ER -