Pumping Tests for Rookies

What is a Pumping Test?

Pumping tests remain the method of choice among hydrogeologists to deduce subsurface aquifer properties and well mechanics behavior. A pumping or aquifer test is a field-based method in which a water well is pumped at a constant or variable rate (volume/time) and the groundwater level depression (drawdown) is measured vs distance and/or vs time. Note that drawdown is often defined as the difference between the maximum dynamic water depth and the static water table depth.  

Drawdown measurements can be carried out by means of manual or electronic-based devices, such as pressure transducers. In both cases, the water level depression is registered within the pumping well itself and/or in observation points, such as monitoring wells or multi-piezometers. 

In addition, after the well pump is shut-down, the groundwater level rises and thus, recovery can (and must) be measured to complete the analysis. Drawdown and recovery stages, jointly or independently, are assessed in a graphical-mathematical way to infer key parameters that ultimately control the hydraulic behavior of the studied aquifer. These include hydraulic conductivity (k), transmissivity (T), storage coefficient (S), specific yield (Sy), well damage or skin (𝞂), among many others, depending on the test procedure and the model(s) used to analyze the output variables. 

Example of a synthetic pumping test

Imagine that we can reproduce a pumping test response without going out into the field. This is called a synthetic test. For this task, a numerical or analytical model is used to simulate the drawdown steady or transient response. In the former, drawdown can be reproduced as a function of the radial distance from the pumping well. Within the latter, it can be replicated as a function of time. For instance, we used the Theis (1935) Model to simulate drawdown in a confined aquifer, pumped in a fully penetrating well at a constant flow rate of 7,000 m³/day, considering a T = 500 m²/day and S = 0.001 (adim) during a pumping period of 1000 min. The results are shown in Fig. 1.

Fig.1. Example of a pumping test response in a confined aquifer

As noted, the first part of the log-log plot (continuous line) is represented by the drawdown stage. Here, a maximum drawdown of ~19 m was reached after a continuous pumping of 1000 min. The shape of the drawdown curve is the so-called Theis Curve, typical of confined aquifers. The second part of the test (discontinuous line) refers to the recovery period, that is, a water level rise as a consequence of not pumping. Both drawdown and recovery rates are basically controlled by the hydraulic parameters of the aquifer.

Interpretation and analysis

Even though performing a pumping test at a field level is always fun, in my point of view, the interpretation is the most interesting part. This is because pumping test analysis is a matter of characterizing unknown variables that are part of an unknown aquifer system. Test analysis is one of the biggest challenges for a hydrogeologist and thus, we can always rely on our best ally to support our evaluation: Geology. 

I recommend the following sequence for performing and assessing pumping test data: (1) establish a preliminary conceptual model of the aquifer, (2) pumping test design, (3) quality control procedures during the field test execution, (4) drawdown transient analysis using classic techniques, i.e., matching type curves, (5) drawdown transient analysis by means of derivative-diagnostic plots, and (6) establish a refined conceptual model of the aquifer. In this post, the focus will be made on (4), however, readers can be found detailed information about points (1)-(3) and (6) summarized here, in any Hydrogeology book, for instance, Fetter (2014), Kruseman and de Ridder (1994) and others. I will discuss step (5) as an independent post within this blog, later on. 

Type-curve analysis (4) has been widely used in Groundwater Hydrology and Reservoir Engineering, to infer subsurface properties, by comparing and matching (through a calibration process) field-based measurements and theoretical models (Fig. 2). The latter refers to pre-plotted solutions of the so-called groundwater flow equation and thus, represent ideal settings for specific aquifers (unconfined, confined, leaky), aquifer-related boundary conditions (no-flow; recharge; infinite) and pumping well-related boundary conditions (partial penetration; well storage; skin). The main outcomes of this procedure include qualitative and quantitative descriptions of the aquifer and/or the pumping well efficiency. Finally, the matching accuracy can be evaluated by means of statistical residuals. 

Fig. 2. Theoretical curves for unconfined, leaky and 

confined aquifers represented in semilog (upper)

and log-log plots (lower)

Overall, classic models for type-curve analysis include the Theis (1935) and Cooper and Jacob (1946) solutions for confined aquifers (the latter is also referred to as the straight line method approximation), the Hantush and Jacob (1955) solutions for leaky aquifers, or the Neuman (1974) solution for unconfined aquifers considering delayed drainage response. More recent and complex developments include solutions for partially penetrating wells in double-porosity aquifers (Dougherty and Babu, 1984) or saturated-unsaturated flow to partially penetrating wells in compressible unconfined systems (Tartakovsky and Neuman, 2007), among many others.

Example of a real pumping test

The following example is a real pumping test carried out in 2005 in northwest Mexico (Zacatecas state). The study zone is a graben-related aquifer composed by clastic sediments and volcanic rocks, such as tuffs and ignimbrites. A 12-hour pumping was performed with a constant flow rate of 345.6 m³/day from a 130 m, 10"-diameter irrigation well within the so-called Jalpa-Juchipila Aquifer System. The recovery period was measured during 1/2-hour. Fig. 3 shows the observed and modeled transient drawdowns using the Moench (1997) Model for a finite-diameter well with wellbore skin in a homogeneous, anisotropic unconfined aquifer.

Fig. 3. Example of a real pumping test analysis in Mexico

After the matching process was finished (Fig. 3), an unconfined aquifer response was confirmed, and the following hydraulic parameters were estimated as a result: T = 203.7 m²/day, k = 1.56 m/day and a well effective radius of 0.09 m, which is lower than the actual well radius.

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References

Cooper, H.H. and Jacob, C.E., 1946. A generalized graphical method for evaluating formation constants and summarizing well‐field history. Eos, Transactions American Geophysical Union, 27(4), pp.526-534.

Dougherty, D.E. and Babu, D.K., 1984. Flow to a partially penetrating well in a double‐porosity reservoir. Water Resources Research, 20(8), pp.1116-1122.

Fetter, C, W., 2014. Applied Hydrogeology, 4th Edition, Pearson, UK.

Hantush, M.S. and Jacob, C.E., 1955. Non‐steady radial flow in an infinite leaky aquifer. Eos, Transactions American Geophysical Union, 36(1), pp.95-100.

Kruseman, G.P. and de Ridder, N.A., 1994. Analysis and Evaluation of Pumping Test Data, 2nd Edition, IILRI, Holand. 

Moench, A.F., 1997. Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer. Water Resources Research, 33(6), pp.1397-1407.

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response. Water resources research, 10(2), pp.303-312.

Tartakovsky, G.D. and Neuman, S.P., 2007. Three‐dimensional saturated‐unsaturated flow with axial symmetry to a partially penetrating well in a compressible unconfined aquifer. Water Resources Research, 43(1).

Theis, C.V., 1935. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground‐water storage. Eos, Transactions American Geophysical Union, 16(2), pp.519-524.