Borehole dilution tests in the vicinity of an extraction well

Abstract A mathematical solution is derived for a borehole dilution test conducted in the proximity of an extraction well under conditions where the Theis assumptions are applicable. The solution is similar to the steady-state velocity case except for a factor that accounts for the transient response of the aquifer to pumping. Curves calculated from the derived solution show a delay in response that increases with the specific storage of the aquifer and with the radius from the extraction well. The delay decreases with increasing values of hydraulic conductivity and aquifer thickness. Deviations of the response curves from the straight-line steady-state velocity case can be used to calculate the hydraulic diffusivity, while the limiting slope at late time can be used to calculate groundwater flux. When borehole dilution tests are conducted at several intervals over the thickness of the aquifer under steady-state velocity conditions, K ( z ) can, in principle, be calculated using several equations depending on the type of information available. Two existing methods to account for the distortion of the flow lines near the open test interval are related to well construction and development. Reasonable estimates of borehole factors can only be obtained for minimally developed wells.