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 μm average aperture fractures and a subhorizontal set containing four 25 μm average aperture fractures. The other two networks had identical fracture orientation and contained either all 125 μm or all 25 μm 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.