Numerical Study of Bromide as a Tracer for Aquifer Macrodispersivity Tests: Comparing Conservative Behavior to Mildly Nonlinear Adsorption

Using a Freundlich adsorption isotherm for bromide $\left({\text{Br}}^{-}\right)$ published earlier, we used two-dimensional groundwater simulations to compare the dispersion of a conservative tracer to ${\text{Br}}^{-}$ undergoing mildly nonlinear adsorption ( $\text{exponent}=0.893$ ; $\text{coefficient}=0.0412$ ). Variances of the natural logarithm of hydraulic conductivity fields were varied over an order of magnitude to simulate mildly and strongly heterogeneous flow fields. To estimate the apparent accuracies of longitudinal $\left(A_L\right)$ and horizontal transverse $\left(A_T\right)$ dispersivities measured using conservative tracers in field experiments, we considered two operationally defined decisions: the amount of ${\text{Br}}^{-}$ injected (1.0 and 0.1 kg) and the lowest tracer concentration value used in dispersivity computations as a result of analytical quantification limits or background concentrations (0.1 ppm). Results from both operational criteria were compared using hypothesis testing. $A_L$ values for the conservative simulations in mild heterogeneity were within a factor of 2, as were $A_T$ values at confidence levels $>95\%$ . $A_L$ values for the conservative simulations in strong heterogeneity were within a factor of 2 at confidence levels $>90\%$ ; similarly for $A_T$ values the confidence levels were $>80\%$ . These results support the convention that the most reliable macrodispersivity values are accurate within a factor of 2. Comparisons of dispersivities calculated from the reactive runs to those of the conservative simulations for the same travel distance, all other parameters being the same and only using concentrations $>0.1\text{ppm}$ , yielded identical confidence levels for the respective dispersivities as the conservative runs reported above. This conclusion was true for both masses of the tracer considered. A practical result of this research is that we cannot exclude the use of a mildly sorbed tracer, as modeled herein, in making dispersivity measurements as accurate as those of a conservative tracer.