Concentration fluctuations and dilution in aquifers

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 /〈 c 〉, increases with time (〈 c 〉 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 〈 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.