Abstract
Size and shape of individual flow-features, and not their ‘organization’ in sets of predominant orientation, are the major influences on the ability of groundwater to percolate through sparse channel networks. Measurements in background fractured crystalline rocks proposed for nuclear waste repositories provide useful insight. Flow-features are observed as locations of increased transmissivity during packer or flow testing in boreholes. They are conceived here as channels on fracture surfaces. Findings are based on numerical modelling and a general formula by Barker (2018) for the percolation of two-dimensional (2D) objects in 3D space. Equidimensional shapes are found to be the least efficient at forming percolating networks. As discs are evolved into highly eccentric ellipses, percolation thresholds for number, area and intersection density decrease. At the same time, the percentage of features forming the active flow path declines from about 10% for discs to a few per cent for 50:1 ellipses. Compiling recent field measurements of area density of flow-features reveals low values within a limited range (0.01–0.8 m−1). When this range is combined with practical values of likely channel width, long narrow flow-features are the only reasonable components of a sparse percolating network. Conventional equidimensional discrete fracture networks are considered unlikely. Innovative field investigation and modelling methods based only on hydrogeological measurements are suggested. It is concluded that this consideration of shape supports the approach, broadly termed the ‘long channel’ concept. Barker J.A. (2018) Intersection statistics and percolation criteria for fractures of mixed shapes and sizes. Comput Geosci 112:47–53.
Highlights
Channel networks and sparsenessGroundwater flow in sparse networks of channels defies easy characterization largely because of the difficulty of meaningful sampling of such sparse systems
In channel network models such as that of Margolin et al (1998), sparseness is possibly best indicated by the creation of ‘chokes’, which are links within a network
The ‘long-channel concept’, introduced by Black et al (2017) is at odds with recent applications of discrete fracture network’ (DFN) models to background crystalline rock (BCR) that are based on equidimensional flow-features
Summary
Groundwater flow in sparse networks of channels defies easy characterization (i.e. derivation of parameters such as average channel length and width, frequency of intersections, etc.) largely because of the difficulty of meaningful sampling of such sparse systems. In channel network models such as that of Margolin et al (1998), sparseness is possibly best indicated by the creation of ‘chokes’, which are links within a network. Intersection density and its associated parameter channel density are probable indicators of sparseness. In fractured rocks, it is widely accepted that only a small proportion of all observable fractures (containing channels) facilitate flow. The question arises: ‘What is the minimum channel density required to ensure a continuous network of interconnected (flowing) channels across a region under consideration?’
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