5.4 Aquifer Tests
An aquifer test is an experiment conducted at a well or piezometer to determine hydraulic properties of the aquifer. The hydraulic properties most frequently determined are transmissivity and storativity. As described by Darcy’s law, hydraulic conductivity (K in Equation 1) is the constant of proportionality related to discharge and head gradient. Thus, K is related to the ease with which water of a constant density and temperature can move through the aquifer. Table 2 has common ranges of K for all rock types. For relatively horizontal beds of uniform K and thickness, transmissivity (T) is the horizontal hydraulic conductivity multiplied by the thickness of the bed. There is an extreme variation in range of hydraulic conductivity, with transmissivity for karst aquifers often spanning more than six orders of magnitude from 1 to 1×106 m2 per day. The variations in K can occur within a single geologic formation or within sub-layers.
Storativity (S) is a measure of the volume of water an aquifer releases or takes into storage per unit surface area per unit change in water level. For confined aquifers, the storage coefficient is a function of the density and compressibility of water, the porosity and compressibility of the aquifer skeleton, and the thickness of the aquifer. Specific storage (Ss) is the storativity divided by the thickness of the aquifer. Specific storage is defined by the expression shown as Equation 6.
| Ss = ρwg(α + nβ) | (6) |
where:
| Ss | = | specific storage (L−1) |
| ρw | = | density of water (ML−3) |
| α | = | compressibility of the aquifer skeleton (T2LM−1) |
| n | = | porosity (dimensionless) |
| β | = | compressibility of water (T2LM−1) |
In general, karst aquifers are composed of hard sound rock, so compressibility of the aquifer skeleton is small (Table 7). Thus, specific storage is generally small, on the order of 1×10–6 m–1. The storativity for an unconfined (that is, water-table) aquifer is approximately equal to the specific yield (Sy), which is related to the amount of water that can be released by gravity drainage. Often in unconfined zones of karst systems the competent carbonate rock may not have many large drainable fractures. Thus, Sy is often smaller than typical clastic aquifers; however, the specific yield is generally greater than 10–3 and so the specific storage part of total storage remains negligible in unconfined karst aquifers.
Table 7 – Range in values of bulk modulus of compressibility, typical porosity, and specific storage in
m−1 and ft−1 (Modified from Jumikis, 1962).
| Material | β (m2/N) | Porosity | Ss (m−1) | Ss (ft−1) |
| Plastic clay | 2.6 × 10−7 to 2 × 10−6 | 50.0% | 2 × 10−2 to 3 × 10−3 | 8 × 10−4 to 6 × 10−3 |
| Stiff clay | 1.3 × 10−7 to 2.6 × 10−7 | 40.0% | 3 × 10−3 to 1 × 10−3 | 4 × 10−4 to 8 × 10−4 |
| Medium-hard clay | 6.9 × 10−8 to 1.3 × 10−7 | 25.0% | 7 × 10−4 to 1 × 10−3 | 2 × 10−4 to 4 × 10−4 |
| Loose sand | 5.2 × 10−8 to 1 × 10−7 | 25.0% | 5 × 10−4 to 1 × 10−3 | 2 × 10−4 to 3 × 10−4 |
| Dense sand | 1.3 × 10−8 to 2 × 10−8 | 20.0% | 1 × 10−4 to 2 × 10−4 | 4 × 10−5 to 6 × 10−5 |
| Dense, sandy gravel | 5.2 × 10−9 to 1 × 10−8 | 20.0% | 5 × 10−3 to 1 × 10−4 | 2 × 10−5 to 3 × 10−5 |
| Rock, fissured | 3.3 × 10−10 to 6.9 × 10−10 | 0.1% | 3 × 10−6 to 7 × 10−6 | 1 × 10−6 to 2 × 10−6 |
| Rock, sound | < 3.3 × 10-10 | 0.1% | < 3 × 10−6 | < 1 × 10−6 |
| Water at 25°C | 4.6 × 10−10 | – | – | – |
The most common tests are aquifer pumping tests and slug tests. Packers can be used for either aquifer pumping tests or slug tests to test short open intervals of a well bore. These tests stress the aquifer either by pumping a well (pumping test) or by suddenly changing the water level in a well (slug test), followed by measurement of the change in water level in and around the well through time. A slug test involves the sudden removal or insertion of an object into the well water which instantaneously raises or lowers the water level in the well. Single well tests, such as slug tests are inexpensive to conduct on existing wells. A multi-well aquifer test involves continuous pumping or injecting of water from/to a well which creates a cone of depression/impression respectively in the aquifer around the well, while water levels are measured in one or more observation wells at different distances from the pumping or injection well. Multiple-day aquifer pumping tests with multiple observation wells are much more expensive to conduct. Storage properties should not be estimated for single-well tests because single-well tests are not sensitive to aquifer-storage properties. Estimation of storage properties from single-well tests is also discouraged because single-well tests are affected by wellbore storage and well construction. These non-ideal effects frequently cause estimates of storage to be erroneous by orders of magnitude.
Analysis of most aquifer tests involve evaluating the time series of water level changes following a change in pumping or head. This is accomplished with the direct solution of the partial differential equation describing groundwater flow in simplified geometry with specified boundary conditions. This form of mathematical solution is called an analytical solution to a boundary value problem. Many different analytical solutions have been derived for both simple and complex geometries. Most are based on axisymmetric geometry such that the solution is defined in two-dimensional space on a radial plane extending from the well and is the same for every radial plane. The simplest transient solution for flow to a well is the Theis (1935) solution. It describes the head decline with time at any radial distance from a pumping a well. It is best to have several observation wells at varying radial distance from the pumping well. This simplest case assumes:
- a single homogeneous, isotropic, infinitely large, horizontal, confined aquifer of uniform thickness;
- discharge from the well is constant;
- the well fully penetrates the confined aquifer resulting in horizontal flow;
- the well has an infinitesimal diameter;
- the well fully penetrates the confined aquifer resulting in horizontal flow;
- flow to the well is constant and laminar;
- the initial potentiometric surface is horizontal; and,
- discharge is derived exclusively from storage in the aquifer and water removed from storage is discharged instantaneously with the associated instantaneous decline in head.
For multiple observation well tests, complex methods of analysis, such as, calibrating radial numerical models can provide better results than the analytical solutions in most cases. Figure 55 shows the schematic for radial axisymmetric model for a multi-observation well test in a carbonate aquifer and the results of fitting the model for one test are shown in Figure 56.
Figure 55 – Radial axisymmetric models for simulation of aquifer tests: a) general schematic diagram for a radial axisymmetric model; and, b) specific diagram of the hydrogeologic units and radial model layering for aquifer tests conducted in west-central Florida, USA, within the Intermediate Aquifer System (IAS) and Upper Florida Aquifer (USA). Modified from Reilly and Harbaugh (1993) and Halford and Yobbi (2005).
Figure 56 – Simulated and measured drawdown for three, multi-observation-well aquifer pumping tests conducted at a karst aquifer system site in west-central Florida, USA. Drawdown is the difference between static water-level elevation before pumping and water level at the time shown on the x-axis. Circles indicate field measurements. The solid line represents calculated drawdown calculated in a simplified model of the system with the transmissivity and storativity adjusted to obtain a reasonably good fit to the field measurements. The relative positions of the aquifers and zones are illustrated in Figure 55. From Halford and Yobbi (2005).
For almost every type of hydrogeologic investigation, compilation of well locations and aquifer tests conducted in the study area is part of the literature review. Often these data are maintained by governmental agencies that regulate water-well drilling and water extraction. The types of data collected and stored varies by country and local governmental regulation. In the United States of America well drilling is regulated by state, and sometimes local, government. In some areas with no regulations, well-drilling organizations or companies may collect and store data as well logs that include basic lithology, well construction information, and aquifer tests conducted for the purpose of selecting the size of the pump. These are usually a step-drawdown test or specific capacity test, which are both single-well pumping tests and may provide estimates of transmissivity.
As with borehole geophysics, having more wells available and some wells with longer intervals of the well open to the formation is better for regional water supply studies. The dual or triple porosity nature of karst aquifers is so variable, that one well may not intersect any dissolution features while another well only a meter away may intersect a major conduit. Compilation of all the water-well data available in a study area can be enlightening and is often critical to assessing characteristics such as the heterogeneity present in the aquifer. For example, water-level or potentiometric contour maps of highly heterogenous karst aquifers often display sudden changes in gradient (that is, the contour interval divided by the distance between contours) over short distances, broad “U” shaped troughs in the contours that indicate the presence of highly transmissive areas, often dominated by major conduit flow. Wells in karst areas are often constructed like fractured rock aquifer wells which typically have a surface casing through the surficial material with the annular space between the casing and earth cemented down to the top of rock and below that, the borehole is uncased within the carbonate sequence. Borehole flowmeter logging and packer testing data will often indicate that only small zone of the borehole is contributing most of the flow to the well. Thus, it is best to use the transmissivity obtained from aquifer tests as qualitative data for understanding the location of the most transmissive parts of the aquifer. Traditional methods of aquifer test analysis, based on simplistic radial axisymmetric geometry using type-curve analysis may be successfully employed for some types of karst aquifers, however, the appropriate application of these methods must be carefully evaluated in light of the karst conceptual model and with an awareness of the potential effects of extreme heterogeneity and conduit-dominated hydraulic properties. Otherwise, misleading or erroneous interpretations may be obtained from the analysis of pump or slug test data. Curves showing drawdown or recovery of water level versus time obtained from well tests in karst aquifers may be difficult to analyze by traditional “curve-matching” techniques because of irregularities in the shape of the curves produced by dewatering of fractures, delayed release from storage in conduits and fractures, or other aquifer heterogeneities (Figure 57).
Figure 57 – Illustrations of potential effects of pumping an open-borehole well in a fractured karst aquifer on resultant time-drawdown curves: a) irregular drawdown resulting from successive dewatering of multiple fractures and conduits; and, b) initial sharp drawdown caused by rapid dewatering of shallower-depth fractures and conduits, followed by stabilizing of drawdown due to groundwater held in storage in highly-transmissive conduits and fractures, at which time the system reaches steady-state. Modified from Hartmann and others (2014).
When a slug test is conducted in a high yielding karst well, the system is generally underdamped (that is, the water level will oscillate rapidly with sudden removal or insertion of the slug). This occurs because the transmissivity is large and storage is small for most karst systems, thus the diffusivity (transmissivity divided by storage) is large and slug tests are underdamped in all systems with large diffusivity (Butler, 1997). For underdamped slug tests, a data logger needs to record water level values more frequently than overdamped tests (that is, at least 5 measurements per second).
Many excellent textbooks and US Geological Survey reports provide more thorough discussions of aquifer and slug tests and include additional solutions for evaluating aquifer tests. Textbook discussions of analyzing hydraulic tests of formations and aquifers have been developed by: Lee, 1982; Driscoll, 1986; Dawson and Istok, 1991; Kruseman and de Ridder, 1994; Walton, 1996; Hall and Chen, 1996; Kasenow, 1997; and Butler, 1997. Some of the US Geological Survey reports related to hydraulic testing include: Ferris and others, 1962; Benthall, 1963; Stallman, 1971; Lohman, 1979; and Reed, 1980. The book by Lee (1982) discusses well testing from the perspective of petroleum engineering applications and is not commonly used by hydrogeologists. The book by Driscoll (1986) “Groundwater and Wells” is an excellent reference covering all aspects of well design, drilling, and hydraulic testing. The Kruseman and de Ridder (1994) book is popular as a textbook and covers most types of hydraulic tests in detail. The book by Butler (1997) is a good textbook for conducting and analyzing slug tests. Reports that provide examples of fitting aquifer test data to models of pumped aquifers include Garcia and others, 2016; Sepúlveda and Kuniansky, 2009; and Halford and Yobbi, 2005, 2006. The only reports specific to karst are those by Halford and Yobbi (2005, 2006). Many karst aquifers dominated by complex non-symmetric conduit networks defy the geometry of axisymmetric type-curve fitting analysis methods and may require more complex analysis for multi-well aquifer test data with either using analytical solutions with anisotropic capability or fully three-dimensional model fitting with the capability to incorporate laminar and turbulent flow (non-Darcian flow).