Curve Matching With Multiple Observation Wells

When you analyze a pumping test with more than one observation well, AQTESOLV matches one set of aquifer properties to the drawdown data from all of the wells in your data set.

One set of aquifer properties matched to two observation wells from a constant-rate pumping test in an unconfined aquifer with delayed yield.

In the figure shown above, the curve-fitting analysis determines the properties of an unconfined aquifer with delayed yield from the two observation wells displayed on the graph.

Of course, if your data set has multiple observation wells, you may match wells individually or in groups with AQTESOLV as well. To perform visual curve matching on selected wells, choose Wells from the Edit menu to see all of the wells in your data set. Right click over a well in the list and choose Hide Observations to turn off the display of the well; to turn on the display a previously hidden well, choose Show Observations when you right click over a well.

Choose Edit>Wells to add, modify or delete wells from an AQTESOLV data set.

To select more than one well at a time, hold down the Ctrl key when clicking on wells in the list shown above.

AQTESOLV allows you to select which wells to use for automatic curve matching, too. Choose Automatic from the Match menu and click the Active Wells tab. Remove the check next to any well that you wish to ignore during automatic matching.

Choose Match>Automatic>Active Wells to select wells to match with automatic curve matching.

Selections in the Active Wells list shown above only affect the wells used for automatic matching, not the display of well data.

Visit the Support Center and the Knowledge Base at the AQTESOLV website for additional tips and examples.

Analyzing Pumping Tests With Multiple Observation Wells

AQTESOLV allows you to analyze pumping tests with more than one observation well. For example, Figure 1 shows the interpretation of drawdown data recorded in the pumped well and three observations wells during a constant-rate pumping test conducted in a nonleaky confined channel aquifer (near Estevan, Saskatchewan, Canada).

Figure 1. Constant-rate pumping test in nonleaky confined channel aquifer (Walton 1970).

Prior to late-time boundary effects, one observes infinite-acting aquifer conditions in the drawdown response at all wells (Figure 1).

Analysis of multiple observation wells is not limited to nonleaky confined aquifers. In the following figure, we see the analysis of drawdown data from a constant-rate pumping test in a leaky confined aquifer with three observation wells.

Figure 2. Constant-rate pumping test in leaky confined aquifer (USBR 1995).

Interpretation of this test uses the Hantush and Jacob (1955) method for a leaky confined aquifer with incompressible aquitard(s). Prior to the onset of leakage, the aquifer behaves like a nonleaky confined aquifer of infinite extent as shown in Figure 2 by the superimposed Theis (1935) solution (red curve).

We can use AQTESOLV to analyze multi-well tests in phreatic aquifers, too. For example, two  fully penetrating observation wells are used for the interpretation of a constant-rate pumping test in an unconfined aquifer with delayed yield near Gironde, France (Figure 3).

Figure 3. Constant-rate pumping test in unconfined aquifer with delayed yield (Neuman 1975).

Analysis in the example above is performed with the Neuman (1974) method for an anisotropic water-table aquifer with delayed gravity response; one can see from the composite plot how the shape of the drawdown response is affected by radial distance from the pumping well (Figure 3).

Figure 4 shows the interpretation of a multi-well constant-rate pumping test in a double-porosity fractured aquifer using a solution by Moench (1984).

Figure 4. Constant-rate pumping test in double-porosity fractured aquifer (Moench 1984).

In the example above, the blue curve on the composite plot shows the fit to drawdown data from the pumped well while the red curve is matched to observation well data.

In each of the preceding examples, one set of aquifer properties was used to match drawdown data from all observation wells in a data set. At times, however, you may wish to match only a few wells by themselves. You may accomplish this task using either visual or automatic curve matching in AQTESOLV.

Sometimes you start out with only one or two observation wells in a data set and wish to add more wells later. Adding observation wells is easy with AQTESOLV. Choose Wells from the Edit menu and click New to enter data for a new well.

To find worked examples of pumping tests with multiple observation wells, check out the AQTESOLV Help file/manual or visit the Application Gallery at the AQTESOLV web site.

Entering Pumping Rates Into AQTESOLV

Entering pumping rates from an aquifer test into AQTESOLV requires little effort. The first thing to remember is that all pumping rates are entered as a sequence of constant-rate steps. For each step, enter the time when the step begins (as elapsed time since the start of the test) with the corresponding pumping rate. For your convenience, AQTESOLV provides options to type the rates into a spreadsheet, import them from a file or copy/paste them from another spreadsheet.

Constant-Rate Test

For a constant-rate pumping test, you only need to enter one rate into AQTESOLV. For example, if the pumping rate during a constant-rate test is 100 gpm (gallons-per-minute), enter the rate as shown below.

Pumping rate entry for a constant-rate test.

Note that there's no need to duplicate the rate in the spreadsheet after the first entry. AQTESOLV assumes that the rate doesn't change until you add a new one. Duplicating rates in successive rows of the spreadsheet only serves to slow down calculations.

The following figure shows an interpretation of drawdown data from a constant-rate pumping test with the Theis (1935) type-curve method.

Analysis of drawdown data from constant-rate pumping test.

Constant-Rate Test With Recovery

Now consider a constant-rate pumping test with recovery. For this case, enter the constant-rate portion of the test as above and add a row to the rates spreadsheet to indicate the start of recovery. For example, if pumping at 100 gpm ceases after 24 hours (1440 minutes), enter the constant rate and recovery periods as follows.

Pumping rate entry for a constant-rate test with recovery.

The next graph shows the rate history for the example above. The rate during the pumping test is a constant 100 gpm. After one day (1440 minutes), the test ends and the rate is zero during recovery.

Rate history for constant-rate test with recovery.

As before, do not duplicate pumping rates in successive rows of the rates spreadsheet. Between 0 and 1440 minutes, AQTESOLV recognizes that the constant rate is 100 gpm. AQTESOLV knows from the data entered that the rate after 1440 minutes is zero during recovery.

The plot below illustrates the analysis of drawdown and recovery data from a constant-rate pumping test with recovery.

Analysis of constant-rate pumping test with recovery.

Variable-Rate Test

Entering pumping rates for a variable-rate test is likewise straightforward. Enter a new rate into AQTESOLV when the rate changes. For example, consider a step-drawdown test consisting of three one-hour steps of 50, 100 and 150 gpm. As before, the first step starts at an elapsed time of zero. The second and third steps begin at 60 and 120 minutes, respectively.

Pumping rate entry for step-drawdown test.

The rate history for this step-drawdown test example is illustrated in the graph below.

Rate history for step-drawdown test.

Enter only one row per step in the rates spreadsheet to indicate when the step begins. During each step, the pumping rate is assumed to remain constant.

Interpretation of a step-drawdown test with recovery is shown in the following figure.

Interpretation of drawdown and recovery data from a step-drawdown test.

Visit the Knowledge Base at the AQTESOLV website for more helpful tips on using the software!

AQTESOLV Examples and Tutorials

The Help file installed with AQTESOLV is chock-full of examples with step-by-step instructions for using the software.

Accessing Examples in the AQTESOLV Help System

To access the Help system, choose Contents and Index from the Help menu in the AQTESOLV application. Go to the Quick Start chapter in the Contents tab to explore the many detailed tutorials for analyzing pumping tests, slug tests and constant-head tests.

To download a PDF version of the AQTESOLV manual, please visit the Support Center at the AQTESOLV website.

Intermittent Pumping

One of the many applications for the variable pumping rate option in AQTESOLV is to simulate drawdown resulting from intermittent pumping in one or more pumping wells. Use this feature for pumping test interpretation or drawdown modeling.

In the following figure, AQTESOLV predicts drawdown due to an irrigation well extracting water from a nonleaky confined aquifer with daily on/off cycles extending over a growing season of 245 days. During each pumping cycle, the well withdraws groundwater at 220 gallons-per-minute (gpm) for 12 hours followed by 12 hours of recovery. At the end of the growing season, all pumping stops and sustained recovery begins. Drawdown in the pumping well (blue line) clearly shows the cycles of intermittent pumping; whereas the two observation wells (red lines) located 500 and 2000 ft from the extraction well demonstrate how the cyclic drawdown response dissipates with distance.

Drawdown due to intermittent (cyclic) pumping in a nonleaky confined aquifer.

Entering a lot of pumping cycles by hand can be tedious, so AQTESOLV makes the task easy for you. One method is to prepare the cyclic rate history in Excel and copy/paste the rates from Excel into AQTESOLV. Alternatively, you may enter just one cycle into AQTESOLV and have the software repeat the cycle a specified number of times (find details in the AQTESOLV manual).

If your primary interest is the average drawdown at relatively distant observation wells over long periods of intermittent pumping, it is often sufficient to assume a constant average pumping rate. The following figure shows the predicted drawdown for a well extracting at 110 gpm over the same 245-day growing season as the previous intermittent pumping scenario.

Drawdown assuming average pumping rate in a nonleaky confined aquifer.

The two preceding examples applied the Theis (1935) nonequilibrium solution to predict drawdown under intermittent pumping conditions in a nonleaky confined aquifer of infinite extent; however, you may use virtually any of the pumping test solutions in AQTESOLV to forecast drawdown for constant- or variable-rate pumping in nonleaky confined, leaky confined, unconfined or fractured aquifers. Plus, AQTESOLV allows you to add no-flow or constant-head boundaries to model surface water boundaries and limited aquifers as required.

Distance-Drawdown Analysis

Distance-drawdown analysis is a useful technique for estimating aquifer properties when drawdown measurements are taken during a pumping test at several observation wells located at different radial distances from the control (pumped) well. To perform distance-drawdown analysis, one plots a single drawdown observation per well, each recorded at the same time since the start of pumping, on a graph of drawdown versus radial distance.

Most of us are familiar with estimating an aquifer's transmissivity and storativity from distance-drawdown data using the Cooper and Jacob (1946) method as shown in the following figure.

Distance-drawdown analysis for an unconfined aquifer.

Did you know that you may perform distance-drawdown analysis with pumping test methods in AQTESOLV other than Cooper and Jacob? For example, you may match distance-drawdown data with the Hantush and Jacob (1955) method for a leaky confined aquifer (see figure below).

Distance-drawdown plot for a leaky confined aquifer.

To display a distance-drawdown graph in AQTESOLV, choose Distance-Drawdown from the View menu. The Distance-Drawdown option is active when you have more than one observation well in your data set. If your data set includes more than one pumping well, the Distance-Drawdown option is inactive as distance-drawdown analysis assumes radially symmetric flow around a single pumping well; however, you may use AQTESOLV to prepare contour plots of drawdown (plan and cross section) when multiple pumping wells are present.

To learn more about AQTESOLV, take the guided tour or download the demo!

Plot Orientation in AQTESOLV

Many groundwater hydrologists prefer plotting drawdown data from a pumping test with the origin placed in the upper left corner of the graph. When formatted this way, a graph shows drawdown increasing downward.

Analysis of drawdown and recovery from a pumping test in a confined aquifer.

To have AQTESOLV orient your drawdown plot in this manner, choose Format from the View menu and check Origin in Upper Left.

For additional AQTESOLV tips, visit the Knowledge Base and Examples at the AQTESOLV Support Center.

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