Macrodispersivity and large-scale hydrogeologic variability

Although groundwater velocities vary over a wide range of spatial scales it is generally only feasible to model the largest variations explicitly. Sma ller-scale velocity variability must be accounted for indirectly, usually b y increasing the magnitude of the dispersivity tensor (i.e. by introducing a so-called macrodispersivity). Most macrodispersion theories tacitly assum e that a macrodispersivity tensor which works well when there is only small -scale velocity variability will also work well when there is larger-scale variability. We analyze this assumption in a high resolution numerical expe riment which simulates solute transport through a two-scale velocity field. Our results confirm that a transport model which uses an appropriately adj usted macrodispersivity can reproduce the large-scale features of a solute plume when the velocity varies only over small scales. However, if the velo city field includes both small and large-scale components, the macrodispers ivity term does not appear to be able to capture all of the effects of smal l-scale variability. In this case the predicted plume is more well mixed an d consistently underestimates peak solute concentrations at all times. We b elieve that this result can be best explained by scale interactions resulti ng from the nonlinear transformation from velocity to concentration. Howeve r, additional analysis will be required to test this hypothesis.