**Application of WTAQ to Pumping Test Data**

By Darrel Dunn Ph.D., PG (Consulting hydrogeologist. Professional Synopsis)

This is a technical page on water table aquifer testing (aka unconfined aquifer testing). To see a non-technical page, press here.

The purpose of this web page is to describe the results of an application of WTAQ water table pumping test analysis software (129) to actual data. The pumping test selected for this study is described by Green and others (130). The test includes data from the pumped well and two observation wells.

**Description of Water Table Aquifer Tested**

The water table aquifer that was tested is composed of fine to medium grained silty sand with lenses of fine-grained calcareous sandstone. Its saturated thickness was 98 feet. The aquifer is underlain by nearly impermeable sandstone interbedded with clay.

**Pumped Well Description**

The pumped well was a 28-inch diameter bore-hole. The screened interval extended from 18 feet below the initial water table to the base of the aquifer. The screened interval was complicated. It consisted of a 12-inch diameter wire-wrapped steel screen inside 16-inch diameter slotted casing. The annulus between the screen and the casing contained a sand pack with a mean diameter of 1/16 inches, and the annulus between the slotted casing and the wall of the hole was packed with 1/4 to 3/8 inch pea gravel.

**Observation Well Description**

Two observation wells were used. They were cased with slotted 2-inch PVC pipe. The hole diameters of the observation wells are not given. The nearest observation well was 88 feet from the pumped well and was screened in the upper 58 percent of the saturated aquifer. The other observation well was 111 feet from the pumped well and was screened through the entire thickness of the saturated aquifer.

**Description of Original Pumping Tests and Analysis**

In the original investigation, a step test was performed, and graphical analysis that assumed a value of 2 for the well loss exponent yielded a well loss coefficient of 2.1E-3 ft min^{2}/gal^{2}.

Two constant rate pumping tests were performed. The first constant rate pumping test was conducted at 90 gpm for 42 hours with less than 5 percent discharge variation. Boulton analysis was applied to time-drawdown data from the two monitoring wells. The result was as follows:

Transmissivity: 9,351 gpd/ft

Storativity: 7E-3 (dimensionless)

Specific yield: 0.03 (dimensionless)

The second constant rate pumping test was conducted at 150 gpm, and the results were the same.

**Present Step Test Analysis**

In the present study, the step test data was analyzed to obtain an estimate of well loss that could be used to calculate an initial estimate the hydraulic conductivity of wellbore skin for WTAQ input. In this step test analysis “adjusted time” was plotted against “adjusted drawdown” in the manner described on the step test web page. The resulting plot (Figure 1) was subjectively fitted by parallel straight lines for each step. Such straight lines on a semi-logarithmic graph imply that, for the period of the test, the drawdown can be described by an equation of the form s=C_{1}Qlog(C_{2}t), where s is drawdown, t is time since the test began, and C_{1} and C_{2} are constants. Consequently, values for the well loss coefficient can be obtained from the vertical separation of the lines. The determination of well loss from such plots is described on the step test web page. The three values obtained from the plot in Figure 1 are 1.3E-3, 1.5E-3, and 1.1E-3 ft min^{2}/gal^{2} (average 1.3E-3). This well loss is the same order of magnitude is the one obtained in the original graphical analysis cited above ( 2.1E-3 ft min^{2}/gal^{2}). The well loss exponent was assumed to be 2 in the original analysis and in the present analysis.

A reliable value for transmissivity could not be calculated from this plot, because the drawdown in a water table aquifer composed of medium grained silty sand is likely to be affected by delayed drainage. The application of step test analysis to water table aquifers is discussed in the aforementioned web page.

Figure 1. Step Test Plot

**WTAQ Constant Rate Pumping Test Analysis**

The present analysis of the data used WTAQ. The constant pumping rate (Q) was 90 gpm and the duration of the constant pumping was 42 hours. The WTAQ analysis was conducted in two stages. First, only the pumped well data were included in the analysis. Second, the observation well data were added.

**WTAQ Type-Curve Analysis of Pumped Well Data**

Figure 2 shows the type-curve match with the observed drawdown data from the pumped well. In this figure, “TYPE CURVE DIMENSIONLESS TIME” is the expression t_{Dy}/r_{D}^{2} defined by Barlow and Moench (1999). “TYPE CURVE DIMENSIONLESS DRAWDOWN” is h_{D}, and “ADJUSTED TIME” is t/r^{2} (t is time since pumping started, and r is distance to an observation well or the well radius (r_{w}) for the pumped well. Putting the observed data on the secondary axes and putting dimensionless time multiplied by Sy/T, and dimensionless drawdown multiplied by Q/(4πT) on the primary axes allows type curve matching by successive trial values of transmissivity (T) and specific yield (Sy). This technique allows the matching to be performed on a spreadsheet rather than manually or electronically superimposing graphs and picking a match point.

Figure 2. Type curve match for pumped well with T=12,926 gpd/ft and Sy=0.35.

The type curve for the pumped well assumes (1) instantaneous drainage at the water table, (2) ratio of vertical to horizontal hydraulic conductivity equal to 0.1, and (3) skin hydraulic conductivity equal to 27 gpd/ft^{2} (calculated from well loss). The value of 0.1 for the hydraulic conductivity ratio was found by successive trial runs. The diameter of the well and partial penetration was included in the model. Sensitivity runs showed that the type curve for the pumped well was not sensitive to delayed drainage at the water table. The ratio of storativity to specific yield input to the model was 0.0245, which resulted in a storativity of 8.6E-3. The storativity of 8.6E-3 implies a specific storage of 8.75E-5, which is within the expected range for silty sand (see the storativity web page).

**WTAQ Type-Curve Analysis of Data from the Pumped Well Plus Two Observation Wells**

Figure 3 shows the type curve matches when data from two observation wells are added to the analysis. Observation Well 1 was a partially penetrating well located 88 feet from the pumped well, and Observation Well 2 was a fully penetrating well located 111 feet from the pumped well. The only change made to produce this match was adding delayed drainage and using one drainage constant (α) with a value of 0.01. It seems noteworthy that this value is the same as the reciprocal of the delay index for medium sand in a chart published by T. A. Prickett (117), and the aquifer in the present study is dominantly medium grained silty sand. The type curve for Observation Well 1 includes the effects of partial penetration

Figure 3. Type curve match for pumped well and two observation wells with T=12,926 gpd/ft, Sy=0.35, and α (drainage constant)=0.01.

Figure 3 shows that the pumped well data does not fit the type curve as well as the observation well data. Consequently, the observation well data was beneficial because it supported the interpretation based only on the pumped well. However, in this case, the second observation well does not add significant information. Also, the fully penetrating observation well (number 2) did not provide data that is any more useful than the partially penetrating well.

**Conclusions**

WTAQ worked well for analysis of this time-drawdown data from a water table aquifer.

The extra cost associated with more than one observation well and constructing fully penetrating observation wells may not always be warranted.

**Addendum**

For questions or comments (especially regarding errors and omissions, send an email to ddunn@dunnhydrogeo.com.

If you need a consulting hydrogeologist to analyze aquifer test data, send an email to the above address.