Analysis of solute transport in a divergent flow tracer test with scale-dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale-dependent dispersion. In this study, Laplace-transformed analytical solutions to advection-dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale-dependent dispersivity. Breakthrough curves obtained using the scale-dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale-dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale-dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale-dependent dispersivity model is 1.3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale-dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1.3 for the scale-dependent dispersion model if the dispersion process is more accurately characterized by scale-dependent dispersion. Copyright (c) 2007 John Wiley & Sons, Ltd.