Numerical simulation was used to study steady liquid water movement in a 5-m by 5-m vertical section containing a hypothetical fracture network under conditions of variable saturation. The fracture network was assumed to be embedded within an impermeable rock matrix. Three variations of a network were considered. The "mixed" network consisted of two fracture sets, a subvertical set containing five 125 /am average aperture fractures and a subhorizontal set containing four 25 /am average aperture fractures. The other two networks had identical fracture orientation and contained either all 125 •m or all 25/am average aperture fractures. The TOUGH simulator was used to calculate the total steady liquid water flux through the network, the flux through individual fracture segments, and the pressure head at each fracture segment. A unit hydraulic gradient was imposed on the network by applying fixed pressure head boundaries (ranging from -0.25 to 0.0 m of water) of equal value to the top and bottom. Saturation and permeability versus pressure head relations for the two sets of fractures were determined with the VSFRAC model, which assumed that aperture was variable within an individual fracture. Results showed that the spatial distributions of pressure head and flux within the network, as well as the location of the dominant pathways, depended strongly on the prescribed boundary pressure head. For the mixed network, both pressure head and flux tended to become more spatially uniform when the boundary pressure head approached the pressure head at which the permeability thickness products of the large-and small-aperture fractures are equal (the crossover pressure head). These results imply that for systems similar to the one considered here, interpretation of actual measurements of pressure head and flux may be quite complex, and that representation of variably saturated fracture networks as an equivalent continuum may be more valid for some ranges in pressure head than for others. Equivalent permeability as a function of pressure head was calculated for the fracture network, illustrating how information collected on individual fractures may be used to estimate the flow properties of rock at larger scales. 4091
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KWICKLIS AND HEALY: NUMERICAL iNVESTIGATION OF STEADY LIQUID WATER F• Ow
From these studies it is clear that heterogeneity within fractured rock exists over a variety of scales. Within single fractures, spatial variations inaperture will control the locations of the principal pathways for liquid flow within the fracture. At larger scales, individual fracture transmissivities and network interconnectedness dictate the locations of the dominant pathways for flow. The scale-dependent nature of heterogeneities within saturated fracture systems was reflected in the work of Smith et al. [1987], who demonstrated with a three-dimensional fracture network model that estimates of hydraulic or tracer aperture based on borehole measurements were sensitive to a number of geometric factors, including aperture variation ...
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