Abstract
The advection-dispersion equation, ADE, has commonly been used to describe solute transport in fractured rock. However, there is one key question that must be addressed before the mathematical form of the so-called Fickian dispersion that underlies the ADE takes on physical meaning in fractures. What is the required travel distance, or travel time, before the Fickian condition is met and the ADE becomes physically reasonable? A simple theory is presented to address this question in tapered channels. It is shown that spreading of solute under forced-gradient flow conditions is mostly dominated by advective mechanisms. Nevertheless, the ADE might be valid under natural flow conditions. Furthermore, several concerns are raised in this paper with regard to using the concept of a field-scale matrix diffusion coefficient in fractured rocks. The concerns are mainly directed toward uncertainties and potential bias involved in finding the continuum model parameters. It is illustrated that good curve fitting does not ensure the physical reasonability of the model parameters. It is suggested that it is feasible and adequate to describe flow and transport in fractured rocks as taking place in three-dimensional networks of channels, as embodied in the channel network concept. It is argued that this conceptualization provides a convenient framework to capture the impacts of spatial heterogeneities in fractured rocks and can accommodate the physical mechanisms underlying the behavior of solute transport in fractures. All these issues are discussed in relation to analyzing and predicting actual tracer tests in fractured crystalline rocks.
Highlights
In the radioactive-waste-management community, particular effort has been directed toward studying the hydrodynamic dispersion and residence-time distribution of solutes in fractured systems
Even though the classical ADE has been shown to be applicable in some homogeneous porous media such as a carefully designed packed bed reactor (Delgado 2006), there are numerous studies suggesting that the continuum model does not adequately represent the real nature of solute transport in geological formations, which often exhibit non-Fickian behavior. (Matheron and de Marsily 1980; Long et al 1982; Pankow et al 1986; Berkowitz et al 1988; McKay et al 1993; Guerin and Billaux 1994)
They noted that the field-scale matrix diffusion coefficients generally exhibited enhanced values in comparison to laboratory measurements and that the coefficients increased with observation distance
Summary
In the radioactive-waste-management community, particular effort has been directed toward studying the hydrodynamic dispersion and residence-time distribution of solutes in fractured systems. In a survey study, Zhou et al (2007) reviewed 40 field tracer tests conducted at different fractured sites and analyzed the tracer BTCs by the continuum model They noted that the field-scale matrix diffusion coefficients generally exhibited enhanced values in comparison to laboratory measurements and that the coefficients increased with observation distance. It is worth emphasizing that the dispersion caused by flow channeling in a rock volume is shown to increase in proportion to the observation distance, due primarily to the effect of velocity dispersion (Liu et al 2017) This is embodied in the CNM; in more general scenarios, where essential spatial heterogeneities in fractured rocks, i.e., deterministic and stochastic fractures, fracture zones and tunnels, are introduced into the system, the CNM can explain the apparent scale dependency of dispersion, provided conductive channels connect to form effective transport paths with different flow rates. The only difference was that the tube radius in Eq (4) was replaced by half-width of the channel to give
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