Comparison between “Poissonian” and “mechanically-oriented” DFN models for predicting flow structure and permeability.

Abstract:

A major use of Discrete Fracture Network models (DFN) is to evaluate permeability and flow structure in hardrock aquifers from geological observations of fracture networks. Although extensively studied, there has been little interest in the spatial structure of DFN models, generally assumed to be Poissonian, i.e. spatially random. In this paper, we compare the results of Poissonian DFN to new DFN models where fractures result from a growth process defined by simplified rules for nucleation, growth and fracture arrest. This ‘mechanical’ model is characterized by a large proportion of T-intersections, and a distribution of the number of intersections per fracture models from Poissonian DFN. Flow distributions and permeability were calculated for 3D networks with up to 1,200 fractures and power-law fracture length distributions. For the same statistical properties in orientation and density, the permeability is significantly smaller in mechanical models than in their Poissonian equivalent, with ratios between 3 and >10. We estimate flow channeling by calculating the participation ratio of the distribution of flow per fracture (Pf), which gives the number of fractures that carry a significant part of the flow. Pf is much larger for Poissonian model than for mechanical ones. Moreover we find that permeability scales linearly with Pf, illustrating the close relationship between the geological structure, flow structure, and permeability. In most of hardrock aquifers (illustrated with examples from Sweden), the density of fracture is about a few fractures per meter, while the flow localizes in a few channels at the kilometric scale. There are several reasons why channeling is so extreme, including a large distribution of fracture transmissivities, but this observation also questions the use of Poissonian models in describing the actual fracture network structure.