Stochastic continuum modeling of flow and transport in a crystalline rock mass: Fanay-Augeres, France, revisited

A stochastic discrete-fracture model was used by Cacas et al.(a,b) to interpret flow measurements and transport experiments in a fractured crystalline rock mass at Fanay-Augeres. They considered continuum models to be incapable of properly interpreting small-scale measurements or tracer tests in fractured systems, which, in their view, require three-dimensional modeling of numerous discrete channels; in their opinion, continuum modeling applies only to average flow on a relatively large scale. Cacas et al. considered their discrete fracture model to have been validated by its demonstrated ability to reproduce selected experimental results. In this paper, flow and transport at Fanay-Augeres are modeled by viewing the fractured rock as a stochastic continuum in a manner originally proposed by Neuman(c,d). The stochastic continuum approach obviates the need for detailed information about fracture geometry or assumptions about how individual fractures control flow and transport. All it requires is the delineation of a few dominant features, which can be embedded into the stochastic continuum model as heterogeneous porous slabs. Though a fault zone has been identified at the Fanay-Augeres experimental site, it has been modeled neither by Cacas et al. nor in this paper. In fact, in this paper, a larger selection of experimental results than those considered by Cacas et al. are reproduced merely by modeling the rock as a statistically homogeneous continuum in two dimensions. These results demonstrate that a continuum approach may be well suited for the analysis of flow and transport in fractured rock. This does not constitute a validation of the continuum approach, just as the results of Cacas et al. fall short of validating the discrete fracture approach. Instead, the two sets of results illustrate jointly the well-established principle that an open system, especially one as complex as fractured hydrogeologic environments tend to be, cannot be described uniquely on the basis of sparse data and need not be described in great detail to capture its salient behavior by a model.