Some properties of a channeling model of fracture flow

The Gamma distribution and the log-normal distribution were used to describe the density distribution of the apertures within a channel. For every set of parameter values (correlation length, and the parameters of the distributions) 95 different statistically equivalent channels were generated. The aperture distribution along the channels are then used to determine the total channel volume, the hydraulic conductivity and the flow rate and residence time for a given gradient. The volumes of the channels were found to vary little whereas the hydraulic conductivity, which is primarily determined by the smallest aperture along the channels, varies considerably. For a wide density distribution the hydraulic conductivity easily spans several orders of magnitude. The flow rate and the velocity variations are primarily influenced by the conductivity variations and are only to a small extent influenced by the volume variations in the channel. The average specific area of the whole channel exhibits small variations. The hydraulic and transport properties of hypothetical fractures containing several channels are investigated by randomly picking several of the generated channels, coupling them in parallel and subjecting them to the same hydraulic head difference. The flow rate and residence time distribution of the coupled channels is used to investigate the dispersion properties of the fracture. It was found that the dispersion expressed as Peclet numbers was on the order of 1 to 4 for most of the distributions used but could attain very large Peclet numbers for (unrealistically) narrow aperture distributions. Simulations of breakthrough curves for tracers in single fracture flow experiments indicate that when few channels participate and the dispersion in the individual channels is small, the breakthrough curve is expected not to be entirely smooth but to contain distinct plateaus. This property has been noted in several experiments. (orig./HP)