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Beyond Thiem: A new method for interpreting large scale pumping tests in heterogeneous aquifers
Author(s) -
Schneider C. L.,
Attinger S.
Publication year - 2008
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2007wr005898
Subject(s) - aquifer , aquifer properties , isotropy , slug test , mathematics , scale (ratio) , geology , groundwater , geotechnical engineering , physics , optics , quantum mechanics , groundwater recharge
The heterogeneous character of aquifers prevents a consistent interpretation of pumping tests based on Thiem's formula which has been developed for homogeneous aquifers. We present a new mathematical method for interpreting an ensemble and single large scale pumping tests in heterogeneous confined isotropic aquifers. By combining a multiscale technique called Coarse Graining with Renormalization Group analysis, we derive an explicit formula for the coarse grained aquifer transmissivity. The coarse grained transmissivity is dependent on the radial distance from the well. Close to the well, it equals the local transmissivity in single pumping tests and the harmonic mean of the heterogeneous transmissivity field in ensemble pumping tests. In the far field of the well the coarse grained transmissivity approaches the geometric mean. The transition between both regimes is mainly determined by the transmissivities correlation length. This relation is used for an inversely estimate of the statistical properties of the transmissivity such as its geometric mean. In addition, this method allows for determining aquifer structures characterized by a correlation length from a single pumping test, while the variance can be estimated from pumping tests with ensemble averaged hydraulic heads.