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Journal Articles Journal of Hydrology Year : 2018

A generic analytical solution for modelling pumping tests in wells


The behaviour of transient flow due to pumping in fractured rocks has been studied for at 11 least the past 80 years. Analytical solutions were proposed for solving the issue of a well 12 intersecting and pumping from one vertical, horizontal or inclined fracture in homogeneous 13 aquifers, but their domain of application—even if covering various fracture geometries—was 14 restricted to isotropic or anisotropic aquifers, whose potential boundaries had to be parallel or 15 orthogonal to the fracture direction. The issue thus remains unsolved for many field cases. For 16 example, a well intersecting and pumping a fracture in a multilayer or a dual-porosity aquifer, 17 where intersected fractures are not necessarily parallel or orthogonal to aquifer boundaries, 18 where several fractures with various orientations intersect the well, or the effect of pumping 19 not only in fractures, but also in the aquifer through the screened interval of the well. 20 Using a mathematical demonstration, we show that integrating the well-known Theis 21 analytical solution (Theis, 1935) along the fracture axis is identical to the equally well-known 22 analytical solution of Gringarten et al. (1974) for a uniform-flux fracture fully penetrating a 23 homogeneous aquifer. This result implies that any existing line-or point-source solution can 24 be used for implementing one or more discrete fractures that are intersected by the well. 25 Several theoretical examples are presented and discussed: a single vertical fracture in a dual-26 porosity aquifer or in a multi-layer system (with a partially intersecting fracture); one and two 27 inclined fractures in a leaky-aquifer system with pumping either only from the fracture(s), or 28 also from the aquifer between fracture(s) in the screened interval of the well. For the cases 29 Journal of Hydrology 559 (2018) 89–99 2 with several pumping sources, analytical solutions of flowrate contribution from each 30 individual source (fractures and well) are presented, and the drawdown behaviour according 31 to the length of the pumped screened interval of the well is discussed. Other advantages of 32 this proposed generic analytical solution are also given. 33 The application of this solution to field data should provide additional field information on 34 fracture geometry, as well as identifying the connectivity between the pumped fractures and 35 other aquifers. 36 To protect this original concept of a generic solution for modelling pumping tests in fractured
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hal-01814503 , version 1 (13-06-2018)



Benoît Dewandel, Sandra Lanini, Patrick Lachassagne, Jean-Christophe Maréchal. A generic analytical solution for modelling pumping tests in wells. Journal of Hydrology, 2018, 559, pp.89 - 99. ⟨10.1016/j.jhydrol.2018.02.013⟩. ⟨hal-01814503⟩
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