Equivalent mean flow models for fractured aquifers: Insights from a pumping tests scaling interpretation

Abstract

[1] We investigate if a mean equivalent flow model can be defined to describe hydraulic head variations in a crystalline aquifer characterized by multiscale heterogeneity. We analyzed in particular the hydraulic response of a crystalline aquifer to pumping tests covering a large range of spatial and temporal scales. Pumping tests appear to be well designed to test the medium hydraulic properties and to track scaling effects, since the perturbation induced by pumping grows with time and samples increasingly large volumes. We tested well-test interpretation frameworks underpinned by equivalent media models that basically contain scaling information. Interpretations of drawdown time series, recorded in piezometers located at distances ranging from 2 to 400 m from the pumping well and of durations ranging from 5 to 90 days, show that the temporal evolutions of drawdown are well modeled by fractional flow models [Barker, 1988;Acuna and Yortsos, 1995]. Estimates of flow dimensions are consistent across the whole site and lie in the range [1.4-1.7]. To investigate the nature of diffusion, we defined a methodology based on the evolution of the characteristic time or amplitude of hydraulic head variations with the distance from the pumping well. For most of the piezometers, those aligned along the main fault, it is possible to define a scaling law for all piezometers with a unique set of parameters. The derived exponents imply that hydraulic head diffusion is anomalously slow, a characteristic that is taken into account only in the model of Acuna and Yortsos [1995], based on diffusion in fractals.

Pressure Transients in a Fractal-Cluster Model of Porous Media

“…Figures 7 and 8 show results matched to punctual data selected from Le Borgne et al (2004), from tests in a highly heterogeneous fractured aquifer. The names of the wells include their distance to the pumping well.…”

Fractional flow in fractured chalk; a flow and tracer test revisited

“…A survey of some 12 studies (see Table 1) indicates flow dimensions mostly less than 2 (between linear and radial) linked to flow dominated by single fractures or fracture zones which intersect the pumped well (e.g. Bangoy 1999, Leveinen et al 1998, Le Borgne et al 2004). Flow dimensions larger than 2 are reported from pumping tests in partially penetrating wells (Verbovsek 2009) and packer tests (Kuusela-Lahtinel et al 2003) in fractured rocks and where a pervasive 3D fracture network is accessed through a single fracture intersecting a pumped well ( Marechal et al 2003, Marechal et al 2004).…”

“…The drawdown curves up to 19 hours for boreholes M1, M2, M3 and M4 were fitted to the fractional flow GRF model of Barker (1988) using a Fortran program which employs the method described in Le Borgne et al (2004) and calculates best fit curves using the Levenberg-Marquardt method (Press et al 1992). The program gives the best fit estimates for apparent transmissivity, T a , apparent storativity S a , flow dimension, n, and RMSE (root mean square error) for the fit.…”

Timescales of regional circulation of saline fluids in continental crystalline rock aquifers (Armorican Massif, western France)

“…Hydrodynamic properties of crystalline rock aquifers of the Armorican basement have been intensively investigated at several research sites (Ploemeur and St-Brice-enCogles sites, Fig. 2) (Le Borgne et al, 2004Borgne et al, , 2006Dorn et al, 2012;Leray et al, 2013;Roques et al, 2014;Touchard, 1999) (Fig. 2).…”