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- Title
Concentration fluctuations and dilution in aquifers.
- Authors
Kapoor, Vivek; Kitanidis, Peter K.
- Abstract
The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity field is analyzed to quantify its variability and dilution. Detailed numerical evaluations of the concentration variance σ c2 are compared to an approximate analytical description, which is based on a characteristic variance residence time (VRT), over which local dispersion destroys concentration fluctuations, and effective dispersion coefficients that quantify solute spreading rates. Key features of the analytical description for a finite size impulse input of solute are (1) initially, the concentration fields become more irregular with time, i.e., coefficient of variation, CV=σ c/〈 c〉, increases with time (〈 c〉 being the mean concentration); (2) owing to the action of local dispersion, at large times ( t > VRT), σ c2 is a linear combination of 〈 c〉2 and (∂〈 c〉/∂ x i)2, and the CV decreases with time (at the center, CV ≅ ( N)1/2 VRT/ t, N being the macroscopic dimensionality of the plume); (3) at early time, dilution and spreading can be severely disconnected; however, at large time the volume occupied by solute approaches that apparent from its spatial second moments; and (4) in contrast to the advection-local dispersion case, under advection alone, the CV grows unboundedly with time (at the center, CV ∝ t N/4), and spatial second moment is increasingly disconnected from dilution, as time progresses. The predicted large time evolution of dilution and concentration fluctuation measures is observed in the numerical simulations.
- Publication
Water Resources Research, 1998, Vol 34, Issue 5, p1181
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1029/97WR03608