Structure, flow, and generalized conductivity scaling in fracture networks

Abstract

Abstract. We present a three-dimensional (3-D) model of fractures that within the same framework, allows a systematic study of the interplay and relative importance of the two key factors determining the character of flow in the system. The two factors of complexity are (1) the geometry of fracture plane structure and interconnections and (2) the aperture variability within these planes. Previous models have concentrated on each separately. We introduce anisotropic percolation to model a wide range of fracture structures and networks. The conclusion is that either of these elements, fracture geometry and aperture variability, can give rise to channeled flow and that the interplay between them is especially important for this type of flow. Significant outcomes of our study are (1) a functional relationship that quantifies the dependence of the effective hydraulic conductivity, on aperture variability. and on the network structure and fracture element density, (2) a relation between aperture variability and the Peclet number, and (3) a basis for a new explanation for the field-length dependence of permeability observed in fractured and heterogeneous porous formations. IntroductionThe investigation of flow and contaminant movement through fractured aquifers is currently one of the most important fields of groundwater research. It is also of critical impor- In this report, we examine the interplay and relative impor-2103

Groundwater flow into underground openings in fractured crystalline rocks: an interpretation based on long channels

“…HyperConv simulations show how, close to the percolation threshold, flow within a sparse long channel network converges to pass through a few key conductors that can be regarded as 'chokes'. The same choke effect is reported in previous variable conductance lattice network studies (Margolin et al 1998) and in a fracture network study by Robinson (1984). Within such a flow system containing chokes, the bulk of head loss within the system will occur within the chokes, leaving the network between the chokes with little head loss as a consequence.…”

“…Apart from porous medium and discrete fracture network models, lattice network models have sometimes been used to understand flow and solute transport behaviour in three dimensions. Moreno and Neretnieks (1993) and Margolin et al (1998) both used a cubic lattice model characterized by the simple probability of any single bond being present. This approach, here termed the 'classical lattice model', has the characteristic that long channels (continuous lines of bonds) are associated with short gaps and vice versa.…”

“…Margolin et al (1998) have previously shown that sparse flow systems can be produced by classical lattice networks based on variable bond conductance. In order to avoid confusion with effects caused by variable bond conductance, all the results reported here (except for some ensembles investigating variable conductance) concern systems comprising sub-channels that have the same value of conductance.…”

“…The model of Margolin et al (1998) was quite similar to HyperConv, though being of the classical lattice network type (see Fig. 6) it lacked the independent spatial correlation of bonds and gaps that HyperConv is able to simulate.…”

Scaling of fracture connectivity in geological formations

“…The connectivity of fractures, embedded in impermeable or low permeability geological formations, is thus a critical feature controlling fluid and chemical movement in these systems [e.g., Long and Billaux, 1987;Tsang and Tsang, 1987;Margolin et al, 1998]. …”