Transient pumping well flow in weakly heterogeneous formations

Abstract

The solution of pumping well flow serves for identifying aquifer's properties. Most results available in the literature assume homogeneous aquifers or at most stratified structures. This study investigates the unsteady well flow in heterogeneous aquifers by modeling the hydraulic conductivity as a three-dimensional stationary random function of axisymmetric anisotropy and Gaussian correlations. The main result of the investigation is the mean drawdown in a transient flow toward a fully penetrating well pumping at a constant rate. The solution is obtained in terms of one quadrature over time and is easily calculated. Closed form approximations of the mean head are developed for moderate and large times. The mean drawdowns derived in the study generalize the Theis and Copper and Jacob distributions for aquifers of constant transmissivity. It is shown that the transmissivity, which is identified by using the Cooper and Jacob asymptotic, is precisely the effective conductivity for uniform horizontal flow Khefu. This is compared with the finding that the equivalent conductivity for the steady state flow approaches Khefu with distance from the well [Indelman et al., 1996].