Constant-Rate Pumping Tests

by Glenn M. Duffield, President, HydroSOLVE, Inc.

What Is A
Constant-Rate Pumping Test?

Typical well configuration for pumping test in nonleaky confined aquifer
Figure 1. Typical well configuration for pumping test in nonleaky confined aquifer.

The most common form of pumping test is the constant-rate pumping test in which a control well is pumped at a constant rate and water-level response (drawdown) is measured in one or more surrounding observation wells and optionally in the control well itself.

The goal of a constant-rate pumping test is to estimate hydraulic properties of an aquifer system such as transmissivity, hydraulic conductivity and storativity (storage coefficient).

Methods
Of Analysis

Common methods of interpreting constant-rate pumping tests include the following:

Time-Drawdown Analysis

Pumping test, Theis 1935 method, Gridley, IL
Figure 2. Estimation of aquifer properties by matching Theis (1935) type-curve solution to time-drawdown data collected in an observation well during a constant-rate pumping test in a nonleaky confined aquifer (data from Walton 1962).

Typically, aquifer properties are estimated from a constant-rate pumping test by fitting mathematical models to drawdown data through a procedure known as curve matching. Curve matching may be performed using type-curve methods on log-log plots (Figure 2) or straight-line methods on semi-log plots (Figure 3).

Pumping test, Cooper and Jacob (1946), Gridley, IL
Figure 3. Estimation of aquifer properties by matching Cooper and Jacob (1946) straight-line solution to time-drawdown data (squares) collected in an observation well during a constant-rate pumping test in a nonleaky confined aquifer. The derivative shown on the plot (crosses) guides the fit of the straight line to drawdown data from the infinite-acting radial flow period (data from Walton 1962).

Distance-Drawdown Analysis

Distance-drawdown plots (drawdown versus radial distance) are used to estimate aquifer properties from pumping tests with more than one observation well. A single drawdown measurement per well, each recorded at the same time, is plotted on a distance-drawdown graph.

Figure 4 shows the estimation of aquifer properties from distance-drawdown data collected at the end of a constant-rate pumping test in an unconfined aquifer using the Cooper and Jacob (1946) straight-line solution.

Distance-drawdown analysis, Cooper and Jacob (1956)
Figure 4. Estimation of aquifer properties by matching Cooper and Jacob (1946) solution to distance-drawdown data collected in three fully penetrating observation wells after 2045 minutes of constant-rate pumping in an unconfined aquifer (data from USBR 1995).

Composite Plot

The composite plot, another tool for analyzing data from multiwell pumping tests, displays drawdown as a function of t/r² where t is time since pumping began [T], and r is radial distance from pumping well [L].

By normalizing the distance between observation and pumping wells (t/r²), composite plots show data from fully penetrating observation wells matching the same Theis (1935) type curve or the same Cooper and Jacob (1946) straight line when the aquifer conforms to the Theissian model (Figure 5).

Composite plot analysis for multiple observation wells in nonleaky confined aquifer
Figure 5. Use of composite plot to estimate aquifer properties by matching Cooper and Jacob (1946) straight-line solution to drawdown data collected in three fully penetrating observation wells during a constant-rate pumping test in an unconfined aquifer (data from USBR 1995).

The composite plot is valuable for the analysis of pumping tests that depart from the Theis model, too. Figure 6 shows a composite plot on semi-log axes for a constant-rate pumping test conducted in a leaky confined aquifer (USBR 1995). At early time, the drawdown data from all three observation wells follow the Theis type curve for a nonleaky confined aquifer (shown in red); subsequent deviation from the Theis curve marks the onset of vertical leakage into the pumped aquifer.

Composite plot analysis for multiple obesrvation wells in leaky confined aquifer
Figure 6. Use of composite plot to estimate aquifer properties by matching Hantush and Jacob (1955) type-curve solution to drawdown data collected in three fully penetrating observation wells during a constant-rate pumping test in a leaky confined aquifer. Theis (1935) solution for a nonleaky confined aquifer shown by red curve (data from USBR 1995).