Abstract
A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.
Highlights
Introduction and scopeTo aid safety assessment of geological radioactive waste repositories, a variety of models are developed based on the advection-dispersion equation, ADE, to address the problem of water flow and solute transport in fractured crystalline rocks (Berkowitz 2002)
It has been increasingly recognized that the residence time distribution of a solute in fractured rocks cannot be described as a Fickian process (Matheron and De Marsily 1980)
When matrix diffusion is taken into consideration, the results shown in Fig. 8 suggest that matrix diffusion (Neretnieks 1980) causes strong retardation of solute transport, due to the great capacity of the porous rock in retaining the solute (Mahmoudzadeh et al 2016), and it dominates eventually over hydrodynamic dispersion in determining the spreading of a tracer pulse
Summary
This result is the solution to cf(t) obtained by multiplying the transport equation in a single flow path (or channel), i.e. Eq (1), with q and integrating over all the channels with different flow rates In other words, it gives the joint residence time distribution of a tracer pulse or the breakthrough curves at the point of observation by solving the following equation:. Fickian dispersion dominates and is increasingly overshadowed by velocity dispersion, which can, cause important differences when predicting solute transport over long distances based on the data obtained from field experiments over short distances Following this discussion, the authors go one step further to relate the q distribution of the channels to the aperture field of fractures by the generalized the cubic law of laminar flow in a slit (Bird et al 2002; Neretnieks 2002).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
