In a fractured aquifer, how to distinguish the following?
(1) Longitudinal and Transverse Dispersion
(2) Transverse Dispersion and Matrix Diffusion
(3) Matrix Diffusion and Macro-Dispersion
Whether the above distinctions remain the same - irrespective of - the scale at which - we look at the problem?
Thanks for your time.
Suresh Kumar.
http://www.doe.iitm.ac.in/gskumar/
First, we need to be clear on definitions. Diffusion is the (thermodynamic) process by which particles or solute enter the pore space under a concentration gradient. Dispersion is the spreading outward of particles or solute in collisions with the rock matrix being invaded. In a fractured aquifer despersion will occur as the particles/solute follow bifurcating fracture networks. Matrix diffusion is diffusion from the fracture into the pore space of the tructured medium and can be recognized as a decrease in particle/solute concentration as as the particles/solute travel along a fracture pathway.
So suppose we have an injection well and a pumping withdrawal well in a fractured aquifer. Let the water level stabilize in the injection well due to pumping from the withdrawal well. Add the solute to the injection well and observe the arrival of the solute at the pumping well. The concentration of solute in water from the pumping will rise over a span of time to a more-or-less steady state value. That is longitudinal dispersion. The concentration in the pumping well will be less than that introduced into the injection well. That is transverse dispersion. For a fixed rate of injection the concentration in the pumping well will decline. That is matrix diffusion.
This is an idealized schematic picture and assumes that matrix diffusion is a slow process with respect to solute transport through the fractures, which more or less is the definition of a fractured aquifer.
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