On the use of continuum approximations for regional modeling of groundwater flow through crystalline rocks

Two main issues associated with the application of the stochastic continuum approach to numerical modeling of regional groundwater flow and mass transport through crystalline rocks is addressed. First, the problem of conductivity upscaling from a highly heterogeneous subgrid (measurement) conductivity field to a less heterogeneous supragrid (model) one is studied. Secondly, the question of whether the intervening rock masses between major fracture zones can allow for a sufficient spatial homogenization of a dispersion phenomenon as required by invoking the ergodic hypothesis is studied. For the sake of this paper, it is assumed that the observed spatial variability of apparent conductivity data, determined by 3m double-packer tests, obeys a statistically isotropic and stationary lognormal random function in two dimensions with a logconductivity variance σ 2 ln K of 16. The result of the numerical simulations undertaken suggests that the upscaling of a highly heterogeneous subgrid conductivity field may benefit from considering the anisotropy characteristics caused by an insufficient homogenization of the subgrid heterogeneity on the scale of a supragrid model block. Concerning the spreading of a conservative solute the treatment was restricted to a single realization with a characteristic field dimension of 32 λ ln K , where λ ln K is the logconductivity integral scale. The solute dispersion was studied in two orthogonal directions by particle tracking. Despite an isotropic logconductivity field, the particle tracking produces different dispersivities, which demonstrates that the particular realization studied was not large enough to provide ergodicity.