Identification of Aquifer Stochastic Properties by Oscillatory Pumping Tests with Application to Boise Aquifer Test.

Characterization of spatially variable aquifer properties is a necessary first step towardsmodeling flow and transport. A recent technique, known as oscillatory pumping tests, consistsof injecting periodic discharge into an aquifer and measuring head response along verticalpiezometers surrounding the well. The aim is to identify the specific storativity s andconductivity K of the aquifer by an inversion procedure. Recently, an analytical solution foroscillating head in a homogeneous formation was derived and applied to the Boise aquifertest site. Equivalent properties (seq,Keq) were identified by best fit of the computed andmeasured heads. Here, this approach is generalized for heterogeneous aquifers of spatiallyvariable log-conductivity (Y=lnK), which is modeled as a stationary space random functioncharacterized by KG (geometric mean), σY 2 (variance), I and Iv (horizontal and verticalintegral scales). The aim is to identify these parameters by solving first the forwardproblem for the head H and subsequently fitting the measured heads. Semi-analyticalsolutions are obtained for the mean head amplitude (⟨|H|⟩) and phase by a first orderapproximation in σY 2. Application to a given realization requires a large ratio betweenthe well length and Iv, as well as availability of a large number of measurements(ergodicity). We define a correction term, ψ, representing the impact of heterogeneity on⟨|H|⟩. Investigating the dependence of ψ upon the distance from the pumping wellreveals the existence of a few regimes, namely a near well region in which it isindependent of period and far away region, where the solution pertains to a homogeneousaquifer of effective properties. The solution is applied to the Boise aquifer testby a best fit of ⟨|H|⟩ with the measured head in 3 piezometers, for a given valueof σY 2 = 0.5. In spite of the departure from ergodicity, the identification of KG is quiterobust and in agreement with previous tests while that of I is subject to uncertainty.