An analysis of hydrodispersive transfer in aquifers

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Abstract
This work is concerned with the nonreactive transport of solute materials in groundwater, or hydro‐dispersive transfer. Several types of flow fields are considered: linear (or uniform) flow with one‐ and two‐dimensional dispersion and radial flow under diverging and converging conditions. The analysis includes the two main possibilities for introduction of solutes into an aquifer: continuous and instantaneous (or slug) injection. Different solutions from the literature plus some original solutions for dispersion in a linear flow field have been unified by transposing the solutions into dimensionless variables of concentration (CR), time (tR), and the Peclet number (P). This permits an analysis of the errors committed in some commonly used approximations for dispersion as a function of P. In the case of radial flow, a numerical method using finite differences has been developed that can be applied to either diverging or converging flow problems. Results in dimensionless form when compared to the only analytical approximations that could be found (for continuous injection in a diverging flow field) indicate that the approximate solutions are in error when P ≤ 10. The radial flow results are also compared to those for linear flow fields to demonstrate that in most cases either approach can be used as long as P > 3. A series of dimensionless type curves has been developed showing CR versus tR for practical ranges of P. A simple method of interpreting tracer tests is proposed using these type curves. One is able to directly determine dispersivity and kinematic porosity using curve matching techniques. Results from some recent field tests in France are analyzed using this approach. There is definite confirmation from these investigations that the apparent (macroscopic) dispersivity can vary depending on the distances used in the field.

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