Wells and Words

By David W. Abbott, P.G., C.Hg.
Todd Engineers

How long should a pumping test be conducted to obtain aquifer properties?

Discussions in the groundwater hydrology literature about the recommended elapsed time (ET) of a pumping test has been relegated to a generalized footnote in many texts (Walton, 1970; Kruseman and de Ridder, 1970; Fetter, 1980; Driscoll, 1986; Roscoe Moss, 1990; and USBR, 1995) providing ranges from 8-hours for a confined aquifer to 72-hours or more for an unconfined aquifer. In general, the duration of time that a test must be conducted should be determined by the time needed to identify aquifer properties. Lohman (1965, USGS PP 451, page 99) notes that: “the duration of the test, therefore, need simply be long enough to obtain a straight-line plot” of the modified non-equilibrium (Cooper-Jacob) formula.

The ET of a test depends on project goals, accuracy and precision of data projections beyond the testing period, and institutional statutes. However, the recommended ET of a test is connected distinctly to (1) aquifer properties, (2) data analysis methods, and (3) the purpose of the test.

Aquifer properties (transmissivity and storativity) describe and predict the shape and rate at which the cone-of-depression expands and deepens during a test, notwithstanding any heterogeneous or anisotropic aquifer properties or overlying drainage. Given these two aquifer properties, the behavior of the cone at any distance from the pumping well can be predicted for any length of ET and discharge, except for deviations due to (a) long-term water level trends/fluctuations, and (b) hidden aquifer boundaries, including influences from other pumping wells.

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The magnitude of long-term water level trends cannot be predicted from tests alone, but are related to the regional distribution of aquifer recharge and discharge. Non-pumping water levels must be collected systematically to understand the magnitude of these fluctuations, trends, and their subsequent impact to well yields. In general, low-permeability aquifers (i.e., fractured bedrock) will have greater fluctuations than high-permeability aquifers (i.e., unconsolidated alluvium), given the same amount of recharge and/or discharge.

The rate of expansion of the cone in confined aquifers is rapid, while in unconfined aquifers it is slower. In addition, leakage (aka delayed yield) slows the expansion of the cone in unconfined aquifers. Therefore, duration of a test for an unconfined aquifer is usually longer than for a confined aquifer.

When the edge of the cone encounters a recharge boundary, the drawdown per unit time slows or is zero -- indicating that the amount of water pumped is equivalent to the amount of water recharged to the aquifer – steady state. This recharge is either from vertical leakage of overlying materials or from direct recharge from surface water. In contrast, when the cone meets an impermeable boundary, the drawdown accelerates per unit time -- deepening the cone. Once reached, data collected post-boundary cannot be used for analysis to describe the cone and predict long-term aquifer responses to pumping.

In low-yield aquifers or large diameter wells, aquifer properties cannot be determined unless the ET of the test exceeds the critical time (see Driscoll , Groundwater and Wells , 1986) to account for casing storage. The critical time may range from minutes in high-yield aquifers to days in low-yield aquifers.

Data analysis methods can determine the duration of the test. Observation (obs) wells are a critical component to any test; without them the storativity cannot be determined. However, the spatial position of the obs well compared to the pumping well is crucial to determining the recommended ET. Some of the physical constraints that can limit the usefulness of an obs well include the following: (a) Is the open interval opposite equivalent aquifers in both wells? and (b) Is the horizontal distance between the wells too far -- or too close? Obs wells (or boundaries) located at large distances from the pumping well will require tests of longer duration to observe significant aquifer responses; especially in low-yield aquifers.

Field data analysis, interpretation, and observations are usually the key to successful tests. Initially, all tests should be planned for at least 24 hours; while field analysis and interpretation of the early-time data can be used to adjustment the ET (shorter or longer) to provide an accurate and cost effective test. For example, if a test encounters a surface water recharge boundary at 6-hours, there is no reason to continue the test to 24-hours.

Usually, long-term (>12 hours) tests pose significant logistical and analytical challenges, particularly on single well tests. Logistical problems include maintaining a constant discharge (or head) with uninterrupted operation of the pump and associated equipment including motors, pumps, fuels, and discharge lines for extended periods of time. Analytical problems include correction of the drawdown from atmospheric barometric changes, regional water level fluctuations, and hidden pumping from nearby wells. In summary, the shorter the pumping test -- the more likely that logistical problems can be easily resolved, while drawdown data will not require analytical corrections.

ET is a logarithmic (log) function of the analytical solutions to pumping tests. The log function squeezes or compresses the distribution of time. Figure 1 shows a Cooper-Jacob plot. Note that the arithmetic length on the time axis from 1 to 3 days is the same length between 8 hours and 24 hours. Table 1 compares the test data based on a log cycle and arithmetic approach. A 72-hour test is equivalent to 3.5 log cycles (starting from one minute) or 3,320 minutes. Note that in less than one day (1,000 minutes), 85.7% of the 3.5 log cycles have been measured; while arithmetically only 23.1% of the 3,320 minutes have been collected. This implies that drawdown measurements during a test are weighted in favor of early-time data rather than late-time data, unless the test is operated to extraordinary lengths. In other words, extending the test to reach 72-hours would require a three-fold increase of the length of time (and consequently expenses) to gain an additional 76.9% of arithmetic drawdown data that will only provide an additional 14.3% of log distribution.

The purpose of the pumping test can determine the duration of the test. Tests are conducted to (a) estimate well efficiency and performance, (b) ascertain long-term well yields, (c) determine effective dewatering plans, (d) locate unknown groundwater barriers, (e) resolve influences to nearby wells, streams, and wetlands, (f) determine responses from over- and under-lying aquifers and confining units, and (f) measure water quality.

If the purpose of the test is to identify the areal extent of the aquifer; then, rest assured, aquifer boundaries will be identified during long-duration tests, since all aquifers are bounded either by an impermeable or more permeable formation. Most aquifer boundaries can be identified reasonably well from an understanding of the hydrogeologic framework.

Conducting a reliable, analyzable, and cost effective test with either primary or secondary porosity (i.e., fractures) requires the aquifer be pumped at a realistic, constant, and measurable discharge for an appropriate ET, extending beyond casing storage. Obs wells that respond clearly during a test are highly desirable for a complete description of the aquifer parameters. The flexibility in determining the ET of a pumping test allows for better use of capital investments in collecting data that is hydraulically coherent and defensible. In my opinion, instead of multiple-day, -week, or -month pumping tests, a strategically located and designed obs well is a technically superior solution to understanding long-term aquifer responses.

David W. Abbott is with Todd Engineers in Emeryville and may be reached at dabbott@toddengineers.com.