Flow and tracer transport in fractured media: A variable aperture channel model and its properties

Abstract

Field evidences indicate that the bulk of water flow in fractured crystalline rock often occurs in preferred flow paths, or channels. A theoretical approach was proposed by Tsang and Tsang (1987) to interpret flow and transport through a two‐ or three‐dimensional fractured medium in terms of a system of statistically equivalent one‐dimensional channels. The apertures along the flow channels are characterized by an aperture density distribution and a spatial correlation length. In this paper, we present detailed studies on the properties of these channels: channel volume, channel residence time, and channel volumetric flow rate. We also calculated the dispersion in tracer transport through groups of statistically equivalent channels. The one‐dimensional channel model is then applied to breakthrough data from transport in a two‐dimensional single fracture (Moreno et al., this issue) in both a forward and an inverse calculation. We show from the inverse calculation that the aperture density distribution parameters of the one‐dimensional flow channels may be estimated from the dispersion and mean residence time of the tracer data. The tracer breakthrough curve should be obtained from line measurements with tracer sampled over several spatial correlation lengths of the variable apertures. This is in contrast to conventional point tracer measurements which is expected to fluctuate with statistical realization and may not yield pertinent information on the flow system. Based on the insight gained in such calculations, design, and analysis of field measurements are discussed. Both tracer breakthrough measurements and flow rate measurements are needed to obtain the aperture parameters of the flow systems. The permeability measurements alone are controlled by the small constrictions along the flow paths and therefore do not yield a good measure of the mean aperture in channel.