Ground Penetrating Radar Imaging of an Aquifer During a Pumping Test

We have imaged the temporal and spatial response of an unconfined aquifer during a pumping test using ground penetrating radar (GPR) profiling. In particular, we have observed the transient behavior of the reflection generated by the water content variation occurring in the transition zone between the overlying residually saturated material and the water saturated capillary fringe below. The progressive arrival time delay of this reflection was measured and used to infer its drawdown that occurred during the pumping test. We also observed several other phenomena on the GPR profiles that are related to drainage: (1) the development of a series of diffractions indicating localized irregularities in water saturation and (2) the velocity pull-up of stratigraphic reflections due to increased electromagnetic (EM) wave velocity in the overlying section. Comparing the GPR profiling data and piezometer measurements, we have observed that the drawdown of the transition zone reflection is smaller and delayed relative to the measured hydraulic head drawdown. From the combined GPR and piezometer data, we have inferred that a 0.20 m increase in the combined thickness of the transition zone and capillary fringe occurred before the drawdown of the GPR transition zone reflection commenced. Once achieved, this 0.20 m increased thickness remained for the duration of the pumping test. Using the distance-drawdown relationship obtained from GPR profiling, we have estimated the drained water volume due to the downward movement of the transition zone. The results of our analysis account for only a fraction of the pumping well production, approximately 45% on the first day and about 25% on the second day. Of the various reasons examined to explain this result, we have concluded that it is likely that the behavior of the GPR reflection originating from the transition zone is representative of the shallower, less saturated portion of the transition zone and undetected drainage is occurring in the deeper, more saturated portion of the transition zone

Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity

A specific form of the Fokker–Planck equation with a time- and scale-dependent dispersivity is presented for modelling solute transport in saturated heterogeneous porous media. By taking a dispersivity in the form of separable power-law dependence on both time and scale, we are able to show the existence of similarity solutions. Explicit closed-form solutions are then derived for an instantaneous point-source (Dirac delta function) input, and for constant concentration and constant flux boundary conditions on a semi-infinite domain. The solutions have realistic behaviour when compared to tracer breakthrough curves observedunder both field and laboratory conditions. Direct comparison with the experimental laboratory data of Pang and Hunt [J. Contam. Hydrol. 53 (2001) 21] shows good agreement between the source solutions and the measured breakthrough curves