Cross-borehole slug test analysis in a fractured limestone aquifer

Summary This work proposes new semi-analytical solutions for the interpretation of cross-borehole slug tests in fractured media. Our model is an extension of a previous work by Barker [Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in fractured rock. Water Resources Research 24 (10), 1796–1804; Butler Jr., J.J., Zhan X., 2004. Hydraulic tests in highly permeable aquifers. Water Resources Research 40, W12402. doi:10.1029/2003/WR002998]. It includes inertial effects at both test and observation wells and a fractional flow dimension in the aquifer. The model has five fitting parameters: flow dimension n, hydraulic conductivity K, specific storage coefficient Ss, and effective lengths of test well Le and of observation well Leo. The results of a sensitivity analysis show that the most sensitive parameter is the flow dimension n. The model sensitivity to other parameters may be ranked as follows: K > Le ∼ Leo > Ss. The sensitivity to aquifer storage remains one or two orders of magnitude lower than that to other parameters. The model has been coupled to an automatic inversion algorithm for facilitating the interpretation of real field data. This inversion algorithm is based on a Gauss–Newton optimization procedure conditioned by re-scaled sensitivities. It has been used to interpret successfully cross-borehole slug test data from the Hydrogeological Experimental Site (HES) of Poitiers, France, consisting of fractured and karstic limestones. HES data provide flow dimension values ranging between 1.6 and 2.5, and hydraulic conductivity values ranging between 4.4 × 10−5 and 7.7 × 10−4 m s−1. These values are consistent with previous interpretations of single-well slug tests. The results of the sensitivity analysis are confirmed by calculations of relative errors on parameter estimates, which show that accuracy on n and K is below 20% and that on Ss is about one order of magnitude. The K-values interpreted from cross-borehole slug tests are one order of magnitude higher than those previously interpreted from interference pumping tests. These findings suggest that cross-borehole slug tests focus on preferential flowpath networks made by fractures and karstic channels, i.e. the head perturbation induced by a slug test propagates only through those flowpaths with the lowest hydraulic resistance. As a result, cross-borehole slug tests are expected to identify the hydrodynamic properties of karstic-channels and fracture flowpaths, and may be considered as complementary to pumping tests which more likely provide bulk properties of the whole fracture/karstic-channel/matrix system.