Analysis of slug-tests with high-frequency oscillations

Extensive slug-test experiments have been performed at the Hydrogeological Experimental Site (HES) of Poitiers in France, made up of moderately fractured limestones. All data are publicly available through the "H+" database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr). Slug-test responses with high-frequency (> 0.12 Hz) oscillations have been consistently observed in wells equipped with multiple concentric casing. These oscillations are interpreted as the result of inertia-induced fluctuations of the water level in the annular space between the inner and outer casing. In certain cases, these high-frequency oscillations overlap with lower frequency (< 0.05 Hz) oscillations, which leads to complex responses that cannot be interpreted using conventional models. Slug-test data have been processed in the Fourier-frequency domain, in order to remove the high-frequency component by a signal-filtering method. The corrected signals have been interpreted with the model of (McElwee and Zenner, 1998), which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Hydraulic conductivity values interpreted from dual-frequency slug-tests compare well to those interpreted from "standard" overdamped or underdamped slug-test responses. Introduction Slug testing is a common field method for estimating aquifer permeability. It consists in inducing an abrupt change in water level in a well and monitoring the subsequent water level recovery. In highly permeable aquifers and/or deep wells, the abrupt pressure change in the test well may result in ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 Author manuscript, published in "Journal of Hydrology 334 (2007) 282-289" DOI : 10.1016/j.jhydrol.2006.10.009 ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 oscillations of the water level about the equilibrium level. Such slug-tests are generally said to be underdamped and the oscillations are interpreted as caused by the inertia of the water column above the well screen (or open borehole), see e.g. (Butler, 1997). Since the work by (Van Der Kamp, 1976), a number of theoretical models accounting for inertial effects have been developed for the analysis of underdamped slug-tests, see e.g. refs. in (Butler, 1997; McElwee, 2002). In the Hydrogeological Experimental Site (HES) of Poitiers in France, two types of slug-test oscillations have been consistently observed: (1) low-frequency (< 0.05 Hz) oscillations that rapidly vanish, and (2) high-frequency (> 0.12 Hz) oscillations with a slow damping. The two types of oscillations overlap in certain wells, which leads to complex responses that cannot be interpreted using conventional models. In this paper, we introduce a signal processing method that enables to filter the oscillations according to their frequency signature. It will be shown that the removal of high-frequency (HF) oscillations yields a signal that can be interpreted with the model of (McElwee and Zenner, 1998), which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Slug test experiments The Hydrogeological Experimental Site (HES) is located 2-km southeast from Poitiers, France. The studied aquifer is made up of moderately fractured limestones 100 m thick, overlain by a 5-20 m thick clay unit. Twenty-five fully penetrating wells of large diameter (0.23 m at 120-m depth) were drilled between 2002 and 2004. The wells are located according to a geometric pattern of symmetry 4, inspired from the classic "five-spot" well configuration used in oilfield production. This geometric well array occupies a square area of 210 m x 210 m. The wells were cased with 0.24-m-diameter steel pipe to depths ranging from 15 m to 80 m. Below the steel casing, certain wells were left uncased while others were partly or fully screened with 0.17-m-diameter machine-slotted PVC to prevent a risk of collapse (Fig. 1). The PVC pipes are either suspended to the steel casing or rest on the borehole bottom. They have not been sealed to the outer steel casing so that they can be removed for further optical investigations such as borehole-camera logging. In natural undisturbed groundwater conditions, the water table in wells ranges between 18 m and 25 m below the ground surface. The ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 overall research objective related to this site is to improve the understanding of flow and solute transport in calcareous aquifers, down to depths planned for drinking and/or agricultural water supply. Preliminary studies have shown that flow is mainly located in a few horizontal features interpreted as bedding planes, which are hydraulically connected by subvertical fractures. One of the specific research topics explored in the HES is the investigation of spatial variability of hydrodynamic parameters by multiple hydraulic-tests in the geometric well array (Delay et al., 2004). As a part of this study, a large number of slug tests (about 100) were performed in order to estimate the hydraulic conductivity of the aquifer in the vicinity of boreholes. The slug tests were performed after an important series of pumping tests, which ensured that each well was properly developed. The slug tests were initiated by a sudden release of water in the inner casing (falling-head initiation), with the help of a 3 m capacity tank equipped with a rapid flow valve. Experiments were conducted following the recommendations by (McElwee, 2002) and (Butler et al., 2003): (1) in each well, multiple slug tests involving various initial head displacements (injection of various volumes of water) were performed to test for repeatability and nonlinear effects, and (2) for each slug test, the water-level recovery was monitored over time with a pressure transducer placed within 0.5 m below the static level, which minimised the errors in measured heads caused by the acceleration of the water column. Head data were recorded with a 2 Hz frequency data logger. All slug-test data are publicly available through the "H+" database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr), see (de Dreuzy et al., 2006). Fig. 2 illustrates the 4 typical behaviours of slug-test responses obtained in the HES: standard-overdamped behaviour (no oscillation), standard-underdamped behaviour with low-frequency (< 0.05 Hz) oscillations, overdamped responses with high-frequency (> 0.12 Hz) oscillations, and underdamped responses combining both low-frequency and high-frequency oscillations. Interpretation of high-frequency oscillations For an inertial system, the oscillation damping and frequency are directly related to the effective length Le of the water column involved in the slug test (Butler, 1997): ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 ( ) ( ) 2 1 2 2 1 4 ln n n e n n g t t L W W π + + − ≈ ⎡ ⎤ + ⎣ ⎦ where g is the acceleration of gravity, tn and Wn are the time and amplitude of the nth peak in the slug response, respectively. Analysis of HES slug-test oscillations with the above formula yields Le values of the order of 10 m for high-frequency oscillations, and 130 m for low-frequency oscillations. Several authors propose theoretical definitions of the effective column length of Le, based on geometrical considerations about the well casing/screen system (see the review by (Butler, 1997)). Although the definitions of Le vary according to authors, Le values should always be larger than the length of the water column above the well screen plus one-third of the screen length. For the HES wells, Le values should thus be systematically larger than 50 m. The value Le ≈ 130 m calculated from low-frequency oscillations in slug-test data is consistent with this lower bound, but the value Le ≈ 10 m cannot be related to the inertia of the water column in the well. It must also be noted that high-frequency oscillations occur only in wells equipped with multiple concentric casing at the depth of the static piezometric level. Therefore, it is very likely that high-frequency oscillations result from inertiainduced fluctuations of the water level in the annular space between the inner-PVC casing and outersteel casing (see Fig. 3). Before the slug-test initiation, the water level in the well annulus is at equilibrium with, on the one hand, the water level in the inner PVC casing and, on the other hand, the hydraulic head in the aquifer. During a slug test, a volume of water injected in the inner casing will flow to the well annulus before flowing into the aquifer. If the momentum of the injected water column is great enough, more water flows to the well annulus than what can flow into the aquifer. This results in head differences between the inner casing and the well annulus, which progressively return to equilibrium according to damped oscillatory fluctuations. Similar perturbations where reported by (Shapiro and Hsieh, 1998) for slug tests performed between packers. As these high-frequency oscillations do not contain any information about the aquifer properties, they may be removed from the slug-test responses to make the interpretation easier. In the next section, we describe how the HES slug-test data have been filtered using a signal-processing technique. ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 ha l-0 02 60 61 4, v er si on 1 4 M ar 2 00 8 Filtering of slug-test data In order to remove the undesirable oscillations from the slug-test responses, the measured data have been processed in the Fourier-frequency domain. The first step consists in performing a discrete Fourier transform (DFT) on water level data. The resulting frequency spectrum allows determining precisely the frequency of the undesirable oscillations. For the example illustrated in Fig. 4, the highfrequency oscillations are represented by the narrow peak centred on 0.14 Hz. The other peak represents the frequency of the underdamped signal. The whole HES slug-test data set shows highfrequency components ranging between 0.13 and 0.16 Hz. In the time domain, the filtering of a discrete signal i(t) may be described by the convolution principle: