Numerical investigation of steady liquid water flow in a variably saturated fracture network

Abstract

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 4092 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 ...

Effective transmissivity of two-dimensional fracture networks

“…The results, shown in Fig. 5, agree fairly well with the conductivities that were computed by Kwicklis and Healy [14]. They used the numerical simulator TOUGH [13], and associated each computed permeability with the mean value of the two potentials at the top and bottom edges of the block.…”

“…However, in contrast to methods that solve for the detailed flow field through the entire network, the proposed upscaling procedure requires solution of only a single nonlinear equation. The method has been tested against numerical simulations conducted by Priest [12] on saturated flow through a fracture network, and also against the unsaturated flow simulations of Kwicklis and Healy [14]. In both cases the proposed upscaling method gave accurate predictions of the macroscopic hydraulic conductivity.…”

“…2) can be removed because they are clearly not part of the network that will actually conduct fluid. As there are four nodes at which four segments meet (nodes 4,6,10,13), and six nodes at which three segments meet (nodes 5,7,9,12,14), the mean coordination number of the conducting network is z = (4-4 + 6-3)/(4 + 6) = 3.40.…”

“…3) that was studied by Kwicklis and Healy [14]. They constructed a fracture network consisting of 9 fractures trmsecting a 5 m x 5 m square region, which resulted in 51 fracture segments.…”

“…They used the numerical simulator TOUGH [13], and associated each computed permeability with the mean value of the two potentials at the top and bottom edges of the block. Our method has the advantage, however, of requiring the solution of only a single equation for each value of the pressure head, as opposed to the 51 simultaneous equations that were solved [14] when computing the actual flow field (the nine fracture segments were each discretized into more than one computational elements; see Fig. 3).…”