Applications and Examples

Abstract

Leap and Kaplan (1988) and Hall et al. (1991) presented a type of push-pull test for determining regional groundwater velocity and effective porosity if the hydraulic conductivity of the aquifer and local the hydraulic gradient are known. The hydraulic conductivity could be determined by a pumping test conducted in the same well at the same time as the push-pull tracer test described here; the hydraulic gradient could be determined from water level measurements in a set of nearby wells surrounding and including the push-pull test well. The procedure involves injecting a constant-concentration test solution containing a nonreactive tracer into the aquifer using a single well, allowing the test solution to drift downgradient with the regional groundwater flow, and then extracting the tracer solution/groundwater mixture from the same well by continuous pumping to determine the temporal displacement of the tracer center of mass. The basic equations (using the notation of Hall et al. 1991) are:

$$ {\hbox{q}} = \frac{\text{Qt}}{{{{\pi b}}{{\hbox{d}}^{{2}}}{\hbox{KI}}}} $$

$$ {\hbox{n}} = \frac{{\pi {\text{b}}{{\text{K}}^{{2}}}{{\text{I}}^{{2}}}{{\text{d}}^{{2}}}}}{\hbox{Qt}} $$

where q is the apparent groundwater (Darcy) velocity, n is effective porosity, Q is the extraction pumping rate, t is the time elapsed from the start of extraction pumping until the centroid of the tracer mass has been extracted, b is the aquifer saturated thickness, d is the elapsed time from the end of tracer injection until the centroid of the tracer mass is extracted (drift time + t), K is the saturated hydraulic conductivity, and I is the local hydraulic gradient. Obviously, uncertainties in computed values of q and n will reflect uncertainties in values of K and I.