Concentration fluctuations and dilution in aquifers

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(c)/2 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)/, increases with time ( being the mean concentration); (2) owing to the action of local dispersion, at large times (t > VRT), σ(c)/2 is a linear combination of 2 and (a /ax(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 α 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.