Traditional methods for characterizing horizontally anisotropic aquifers are all based on pumping tests. In this paper, we present a new method for the identification of horizontal anisotropy using cross-hole slug tests, which is much more easily accessible comparing to pumping tests. Through scaler transform, an anisotropic medium was converted into an equivalent isotropic medium. When applying the analytical solutions derived for isotropic media to interpret cross-hole slug tests performed in anisotropic media, the estimated transmissivity is the geometrical mean of the anisotropic transmissivity tensor, regardless of sampling direction. However, the apparent storativity calculated from different observation wells, is equal to the true storativity scaled by a factor defined by the formation anisotropy. Thus, anisotropy can be resolved through apparent storativity that bears directional information. The proposed method was first validated by a numerical experiment and then applied to field data. It was found that the tensor results obtained by this new method with cross-hole slug tests are consistent with that obtained by applying the classical Papadopulos’ method with cross-hole pumping tests conducted in the same wells. When applied to heterogeneous media, tensor results produced by the new method may be subject to considerable errors. This is because the results are strongly sensitive to the connectivity between measurement boreholes and the formation medium. To reduce the error level, responses from a large number of observation wells located in various directions around the source well are needed. In addition to the adopted KGS solution for confined aquifers, the proposed methodology can be applied to incorporate other analytical methods for a variety of aquifer types, as long as the characteristic relationship between the measure scale and the aquifer storativity can be established.
A modified version of a published slug test model for unconfined aquifers is applied to cross-hole slug test data collected in field tests conducted at the Widen site in Switzerland. The model accounts for water-table effects using the linearized kinematic condition. The model also accounts for inertial effects in source and observation wells. The primary objective of this work is to demonstrate applicability of this semi-analytical model to multi-well and multi-level pneumatic slug tests. The pneumatic perturbation was applied at discrete intervals in a source well and monitored at discrete vertical intervals in observation wells. The source and observation well pairs were separated by distances of up to 4 m. The analysis yielded vertical profiles of hydraulic conductivity, specific storage, and specific yield at observation well locations. The hydraulic parameter estimates are compared to results from prior pumping and single-well slug tests conducted at the site, as well as to estimates from particle size analyses of sediment collected from boreholes during well installation. The results are in general agreement with results from prior tests and are indicative of a sand and gravel aquifer. Sensitivity analysis show that model identification of specific yield is strongest at late-time. However, the usefulness of late-time data is limited due to the low signal-to-noise ratios.
The present paper proposes a smoothing analysis of hydraulic head data sets obtained by means of different slug tests introduced in a confined aquifer. Laboratory experiments were performed through a 3D large-scale physical model built at the University of Calabria. The hydraulic head data were obtained by a pressure transducer placed in the injection well and subjected to a processing operation to smooth out the high-frequency noise occurring in the recorded signals. The adopted smoothing techniques working in time, frequency and time-frequency domain are the Savitzky-Golay filter modeled by third-order polynomial, the Fourier Transform and two types of Wavelet Transform (Mexican hat and Morlet). The performances of the filtered time series of the hydraulic heads for different slug volumes and measurement frequencies were statistically analyzed in terms of optimal fitting of the classical Cooper’s equation. For practical purposes, the hydraulic heads smoothed by the involved techniques were used to determine the hydraulic conductivity of the aquifer. The energy contents and the frequency oscillations of the hydraulic head variations in the aquifer were exploited in the time-frequency domain by means of Wavelet Transform as well as the non-linear features of the observed hydraulic head oscillations around the theoretical Cooper’s equation.
Periodic hydraulic experiments were conducted in a five-spot well cluster completed in a single bedding plane fracture. Tests were performed by using a winch-operated slug (submerged solid cylinder) to create a periodic head disturbance in one well and observing the phase shift and attenuation of the head response in the remaining wells. Transmissivity ( ) and storativity ( ) were inverted independently from head response. Inverted decreased and increased with oscillation period. Estimated was more variable among well pairs than , suggesting may be a better estimator of hydraulic connectivity among closely spaced wells. These estimates highlighted a zone of poor hydraulic connection that was not identified by a constant rate test conducted in the same wells. Periodic slug tests appear to be a practical and effective technique for establishing local scale spatial variability in hydraulic parameters.
Hydraulic tomography is increasingly recognized as a characterization approach that can image pathways or barriers to flow as well as their connectivity. In this study, we assess the performance of a transient analysis of tomographic slug test head data in estimating heterogeneity in horizontal hydraulic conductivity ( ), hydraulic conductivity anisotropy (the ratio between vertical and horizontal hydraulic conductivity – / ) and specific storage ( ) under actual field conditions. The tomographic experiment was carried out between two wells in a moderately heterogeneous and highly anisotropic silt and sand littoral aquifer. In this field proof-of-concept, the inversion of the two-dimensional (2D) head dataset was computed with a 2D radial flow algorithm that considers , / , and wellbore storage effects. This study demonstrated that a transient analysis of tomographic slug tests is able to capture the key features of the littoral environment of the test: the vertical profiles of and are indeed in agreement with those from other field and laboratory tests, and values exhibit physically plausible profiles. Furthermore, the simulation of independent inter-well hydraulic tests (slug and pumping tests screened over the entire aquifer) using resolved , / and tomograms produce responses very close to field observations. This study demonstrates that the effects of fine scale heterogeneity that induces -anisotropy at larger scales can be captured through a transient analysis of tomographic slug tests, which are very difficult to quantify otherwise with conventional hydraulic tests, thus allowing a better representation of properties controlling flow and transport in aquifer systems.
An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin.
We present a distributed-order fractional diffusion-wave equation (dofDWE) to describe radial groundwater flow to or from a well, and three sets of solutions of the dofDWE for flow from a well for aquifer tests: one for pumping tests, and two for slug tests. The dofDWE is featured by two temporal orders of fractional derivatives, and , which characterise small and large pores, respectively. By fitting the approximate solutions of the dofDWE to data from slug tests in the field, we determined the effective saturated hydraulic conductivity, , transmissivity, , and the order of fractional derivatives, in one test and and in the second test. We found that the patterns of groundwater flow from a well during the slug tests at this site belong to the class of sub-diffusion with < 1 and < 1 using both the short-time and large-time solutions. We introduce the concept of the critical time to link as a function of and . The importance of the orders of fractional derivatives is obvious in the approximate solutions: for short time slug tests only the parameter for flow in large pores is present while for long time slug tests the parameters and are present indicating both large and small pores are functioning.
► Agreement between more than one type of hydraulic test increases the confidence in . ► Constant head step tests can be used to validate the Darcian flow assumption for slug tests. ► A method is proposed that validates the two main assumptions in the Hvorslev model. A series of rising and falling head slug tests with different initial applied head differentials (Δ ) were conducted in open fractured dolostone and sandstone boreholes using straddle packers isolating specific depth intervals (1.5 m length) to examine the influence of non-Darcian flow. The open holes were developed and inspected using video and acoustic televiewing (ATV) to ensure that evidence of skin effects due to drilling were absent. The transmissivity ( ) values obtained from both the rising and falling head slug tests were very similar at low initial applied head; however, the values were progressively smaller at larger Δ , suggesting error due to non-Darcian flow. Non-Darcian flow behavior was confirmed by constant head step tests conducted in the same test intervals where the injection rate ( ) vs. applied head (d ) relationship became non-linear at relatively low injection rates, and the non-Darcian data also resulted in lower values. For a series of slug tests conducted at different Δ , non-Darcian flow effects gradually increased as Δ increased, consistent with the trends for constant head step tests conducted in the same test intervals. To maintain Darcian flow conditions in the fractured dolostone and sandstone tested in this study, Δ must be kept small, generally less than 0.2 m. This study demonstrates that by conducting both “stepped” slug tests and constant head step tests, the Darcian flow assumption for both types of tests can be rigorously validated. However, when only slug tests are conducted, it is necessary to conduct a series of “stepped” slug tests, including tests with small applied head differentials, to avoid errors due to non-Darcian flow.
Slug tests performed using mini‐piezometers with internal diameters as small as 0.43 cm can provide a cost effective tool for hydraulic characterization. We evaluated the hydraulic properties of the apparatus in a laboratory environment and compared those results with field tests of mini‐piezometers installed into locations with varying hydraulic properties. Based on our evaluation, slug tests conducted in mini‐piezometers using the fabrication and installation approach described here are effective within formations where the hydraulic conductivity is less than 1 × 10−3 cm/s. While these constraints limit the potential application of this method, the benefits to this approach are that the installation, measurement, and analysis is cost effective, and the installation can be completed in areas where other (larger diameter) methods might not be possible. Additionally, this methodology could be applied to existing mini‐piezometers previously installed for other purposes. Such analysis of existing installations could be beneficial in interpreting previously collected data (e.g., water‐quality data or hydraulic head data).
This paper quantifies the influence of seasonal hydraulic head changes in shallow low-permeability soils on the hydraulic conductivity ( ) values obtained from slug tests. A total of 61 slug tests with durations between 3 and 6 weeks were conducted between 2007 and 2010 in 17 monitoring wells (MWs) installed in a clay deposit in Lachenaie, Canada. Beginning in 2012, vibrating wire piezometers (VWPs) were sealed in some of the MWs to record the seasonal hydraulic head cycles. To get a better understanding of the influence of seasonal head changes on the variability of measurements for the Lachenaie tests sites, a series of 936 slug tests were modelled using COMSOL. The seasonal head changes measured with the VWPs were applied as a boundary condition 2 m away from the MW intake zone. Different types of slug test (rising- or falling-head) were launched at different times of the year. The velocity graph method, a graph of the apparent hydraulic head in the MW versus its rate of change, was used to interpret both the experimental and numerical slug test data. Both the experimental and numerical results show that seasonal head changes have a systematic influence upon the middle part of the velocity graph, the part used to calculate . This influence depends on time of year, type of test (rising- or falling-head), initial hydraulic head difference and clay properties. In Lachenaie, the influence of seasonal hydraulic head changes on is shown to be at least of the same order (factor 1.1) as the influence of clay deformation.