Flow to partially penetrating wells in unconfined heterogeneous aquifers: Mean head and interpretation of pumping tests

G. Dagan, S. C. Lessoff

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A partially penetrating well of length Lw and radius R w starts to pump at constant discharge Qw at t = 0 from an unconfined aquifer of thickness D. The aquifer is of random and stationary conductivity characterized by KG (geometric mean), Y 2 (log conductivity variance), and I and Iv (the horizontal and vertical integral scales). The flow problem is solved under a few simplifying assumptions commonly adopted in the literature for homogeneous media: Rw/Lw ≪1, linearization of the free surface condition, and constant drainable porosity n. Additionally, it is assumed that Rw/I < 1 and Lw/Iv ≫ 1 (to simplify the well boundary conditions) and that a first-order approximation in Y2 (extended to finite Y2 on a conjectural basis) is adopted. The solution is obtained for the mean head field H(R, z, t) and the associated water table equation. The main result of the analysis is that the flow domain can be divided into three zones for H: (1) the neighborhood of the well R ≪I, where H = (Qw/LwK A)h0(R, z, tKefuv/nD), with h0 being the zero-order solution pertaining to a homogeneous and isotropic aquifer, KA being the conductivity arithmetic mean, and Kefuv being the effective vertical conductivity in mean uniform flow, (2) an exterior zone R I in which H = (Qw/LwKefuh)h 0(R□Kefuv/Kefuh, z, tKefuv/nD), with Kefuh being the horizontal effective conductivity, and (3) an intermediate zone in which the solution requires a few numerical quadratures, not carried out here. The application to pumping tests reveals that identification of the aquifer parameters for homogeneous and anisotropic aquifers by commonly used methods can be applied for the drawdown measured in an observation well of length Low ≫ Iv (to ensure exchange of space and ensemble head averages) in the second zone in order to identify Kefuh, Kefuv, and n. In contrast, the use of the drawdown in the well (first zone) leads to an overestimation of Kefuh by the factor KA/Kefuh.

Original languageEnglish
Article numberW06520
JournalWater Resources Research
Issue number6
StatePublished - 2011


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