Concentration fluctuations and dilution in aquifers

The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity held is analyzed to quantify its variability and dilution. Detailed numerical evaluations of the concentration variance sigma(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 df solute are (1) initially, the concentration fields become more irregular with time, i.e., coefficient of variation, CV = sigma(c)/[c], increases with time ([c] being the mean concentration); (2) owing to the action of local dispersion, at large times (t > VRT), sigma(c)(2) is a linear combination of [c](2) and (partial derivative[c]/partial derivative x(i))(2), and the CV decreases with time (at the center, CV congruent to (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 proportional to 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.