Cross-well slug interference tests: An effective characterization method for resolving aquifer heterogeneity

Summary

In this study the potential of cross-well slug interference tests for high resolution aquifer characterization of hydraulic heterogeneity was assessed. The cross-well slug interference tests were performed at the research site “Stegemühle”, located in the Leine River valley near Göttingen, Germany. The geological composition of the subsurface, consisting mainly of 3.5 m silt and clay overlying 2.5 m sand and gravel, was determined by geophysical well logging and bore core data. To account for lateral changes a refraction seismic survey was conducted. Based on these data an area, characterized by an aquifer thickness of approximately 2 m and an average hydraulic conductivity of 5.0 × 10⁻⁴ m/s (determined by pumping tests), most appropriate for cross-well slug interference tests, was chosen. Altogether 196 cross-well slug interference tests were performed using a tomographic measurement array. The cross-well slug interference tests were evaluated using type curve analysis, which provided detailed information concerning the vertical changes of hydraulic conductivity and specific storage. To assess hydraulic strata connectivity a travel time based tomographic inversion approach was utilized. The potential of the inversion approach to determine lateral changes could be successfully demonstrated by the reconstruction of the pinch out of a high diffusivity layer close to the bottom of the aquifer. The results demonstrate that the combined evaluation of cross-well slug interference tests based on type curve analysis and travel time inversion allows for the development of a detailed model about subsurface hydraulic heterogeneity.

Introduction

Slug tests have traditionally been utilized as a technique to determine the hydraulic conductivity (K) of an aquifer over a relatively small scale. A slug test essentially consists of measuring the recovery of head in a well after a near instantaneous change in head at the well. The most important advantageous of slug tests are the low costs, its simplicity, the short duration (at least in high permeability media) and that no water needs to be handled, which is a very important advantage at sites of suspected groundwater contamination. When a slug test is performed in a cross-well mode, however, it can provide considerably more information. Despite the common perception that a slug test only affects a small volume of the aquifer in the vicinity of the test well (e.g. Ferris and Knowles, 1963, Rovey and Cherkauer, 1995), response data with a reasonable signal to noise ratio can be collected at distances of over several hundred times the radius of the screen of the test well (e.g. Barker and Black, 1983, Sageev, 1986). The area affected by a slug test is strongly dependent on the dimensionless storage parameter. The smaller the dimensionless storage parameter the larger the response amplitude in the observation well and the larger the radius of influence. Barker and Black (1983), have shown that the aquifer parameters derived from the analysis of a slug test are spatially weighted averages of the continuously varying parameters over the whole aquifer, whereby the weights will clearly decline with increasing distance from the well.

A number of analytical and semi-analytical methods for the evaluation of cross-well slug interference tests based on type curve analysis for different types of aquifers and geologic media have been reported in the literature (e.g. Karasaki et al., 1988, Novakowski, 1989, Chu and Grader, 1991, Hyder et al., 1994, Butler, 1995, Spane, 1996, Butler and Zhan, 2004, Audouin and Bodin, 2007).

However, there are only a small number of field studies that have intensively applied the different methods for detailed site characterization. Field studies that have used cross-well test characterization of sedimentary unconfined aquifers are reported by Spane et al., 1996, Belitz and Dripps, 1999. Spane (1996) proposed an analytical approach which is based on the transformation of type curves developed for constant-rate pumping tests to type curves for cross-well slug interference tests. In Spane et al. (1996) the method is applied to an aquifer composed of clayey sands and gravels. These investigations demonstrate a high correspondence between pumping test responses and slug interference responses which suggests that the test conditions imposed by the performed cross-well slug interference tests are comparable to those existing during the early stages of pumping tests. Belitz and Dripps (1999) applied the semi-analytical solution developed by Hyder et al., 1994, Butler, 1995, to the evaluation of cross-well slug interference tests performed in unconsolidated silts and clays. These investigations showed that the additional evaluation of the pressure response in an observation well next to the pressure response in the test well yields information about wellbore skin and aquifer anisotropy and improves the calculation accuracy of specific storage.

Field studies in fractured rocks are reported in Novakowski, 1989, Audouin and Bodin, 2007. Novakowski (1989) derived a semi-analytical solution for cross-well slug test accounting for wellbore storage effects at the observation well. This analytical method was applied in the investigation of hydraulic properties of a horizontally arranged fracture zone within an Ordovician-aged shale. A semi-analytical solution for the interpretation of cross-well slug interference tests in fractured media was developed by Audouin and Bodin (2007) and is based on the previous work of Barker (1988). This solution approach account for inertial effects at both the test and the observation wells as well as for the fractional flow dimension in the aquifer. The developed solution has been used successfully for the evaluation of cross-well slug interference tests performed in fractured and karstic limestones. Based on the comparison of hydraulic conductivity values estimated from cross-well slug interference tests with those interpreted from pumping tests, Audouin and Bodin (2007) concluded that cross-well slug interference tests are an important characterization method for identifying the hydrodynamic properties of karstic channels and fracture flow paths.

In this study the potential of cross-well slug test to characterize the hydraulic heterogeneity in highly permeable porous granular aquifers is assessed. The pressure disturbances recorded in the observation wells are evaluated by two methods: (a) type curve analysis and (b) the application of a travel time based tomographic inversion approach, which is based on the analysis method presented in Brauchler et al. (2007). The data base comprises a suite of tomographic cross-well slug interference tests recorded between five wells which are arranged in a five-point star configuration. The center well of the five-point star configuration served as a test well, and the four surrounding wells served as observation wells. Fig. 1 shows the tomographic configuration and map plan deployment of the five-well test system. Each of the four vertical profiles comprises seven slugged intervals and seven observation points isolated with double packer systems. Thus, each profile consists of 49 transient pressure curves. For the design and evaluation of the cross-well slug interference tests detailed data were collected about the structural composition and the hydraulic properties of the aquifer by means of surface and wireline geophysics, bore core data, pumping tests and multi-level slug tests.

• As a first step in the analysis, the cross-well slug interference tests were analyzed using the (semi) analytical solution developed by Hyder et al., 1994, Butler and Zhan, 2004. This initial evaluation provided detailed information concerning the subsurface hydraulic properties. The usage of a double packer system allowed to determine hydraulic conductivity and specific storage for different depth intervals of the aquifer which provided first insight into aquifer heterogeneity in vertical direction. However lateral changes, e.g. the pinching out of a high permeable zone, cannot be identified by using existing analytical solutions.

• For the assessment of hydraulic strata connectivity a hydraulic travel time based tomographic approach was applied. This inversion scheme follows the procedure of seismic ray tomography and is based on the transformation of the transient ground water flow equation into the eikonal equation using an asymptotic approach (Virieux et al., 1994). The eikonal equation can be solved with ray tracing techniques or particle tracking methods, which allow the calculation of pressure propagation along trajectories (Vasco and Datta-Gupta, 1999, Vasco et al., 1999, Vasco et al., 2000, Vasco and Karasaki, 2006, Kulkarni et al., 2000, Datta-Gupta et al., 2001, Brauchler et al., 2003, Brauchler et al., 2007, He et al., 2006). The applied inversion approach is an extension of the analysis method presented by Brauchler et al. (2007). The main feature of this procedure is a travel time integral relating the square root of the peak travel time, assuming a Dirac point source at the origin, to the inverse square root of diffusivity. Although, the travel time of a pressure signal between two wells is primarily a function of the hydraulic diffusivity (D), the ratio of hydraulic conductivity (K) and specific storage (S_s), the inversion results improve strongly the significance of the K and S_s estimates based on type curve analysis with regard to hydraulic strata connectivity.