Stochastic modeling of oscillatory pumping in heterogeneous aquifers with application to Boise aquifer test

Oscillatory pumping tests consist of injecting periodic discharge into an aquifer and measuring head response along vertical piezometers surrounding the well. The aim is to identify the specific storativity s and conductivity K of the aquifer, which are generally spatially variable. Recently, an analytical solution for oscillating head in a homogeneous formation was derived and applied to the Boise aquifer test site (Rabinovich et al., 2015). Equivalent properties S-eq, K-eq were identified by best fit of the computed and measured heads. Here, this approach is generalized for heterogeneous aquifers of spatially variable logconductivity (Y = InK), which is modeled as a stationary space random function characterized by K-G (geometric mean), sigma(2)(Y) (variance), I and I-nu (horizontal and vertical integral scales). Semi-analytical solutions are obtained for the mean head amplitude (<vertical bar H vertical bar >) and phase by a first order approximation in sigma(2)(Y). Application to a given realization requires a large ratio between the well length and I-nu, as well as availability of a large number of measurements (ergodicity). We define a correction term, psi representing the impact of heterogeneity on < H >. Investigating the dependence of psi upon the distance from the pumping well reveals the existence of a few regimes, namely a near well region in which it is independent of period and far away, where the solution pertains to a homogeneous aquifer of effective properties. The solution is applied to the Boise aquifer test by a best fit of <vertical bar H vertical bar > with the measured head in 3 piezometers, for a given value of sigma(2)(Y) = 0.5. In spite of the departure from ergodicity, the identification of K-G is quite robust and in agreement with previous tests while that of I is subject to uncertainty. An additional method for improving the identification of K by conditioning on measured point-wise head (co-kriging) is also outlined.