pumping test

10. Pumping tests and applications

Pumping tests are carried out to determine:

how much groundwater can be taken from a well
what effects pumping will have on the aquifer
what effects pumping will have on neighbouring well supplies.

While collecting data during a pumping test is relatively straightforward, the interpretation of pumping test data requires specialist skills. There are several things you should consider before starting a pumping test:

Pumping tests should be carried out at or near the proposed rate of water take.
Avoid influences such as the pumping of neighbouring wells shortly before or during the test and for a period of recovery afterward.
Monitor neighbouring wells during the test if it’s likely they will be affected.
Make sure water discharged during the test does not interfere with shallow aquifer tests or cause unfavourable effects such as erosion.

In water-related science and engineering there are two similar but distinct definitions in use for drawdown

In subsurface hydrogeology, drawdown is the change in hydraulic head observed at a well in an aquifer, typically due to pumping a well as part of an aquifer test or well test.

In surface water hydrology and civil engineering, drawdown refers to the lowering of the water level in a man-made reservoir or tank.

In either case, drawdown is the change in head or water level relative to background condition, indicating the difference in head which has occurred at a given location relative an initial time at the same location.

Time duration:

There is no set time for how long a pumping test should take. A pumping test should continue long enough to determine the effects of the proposed pumping.

As a guide, a minimum 24 hour constant rate test is generally required. Tests taking longer than 24 hours may be required for large takes, such as community supplies, or situations where it may take longer to determine effects.

General Parameters:

How an aquifer responds to pumping can be estimated by measuring:

transmissivity - the thickness and permeability of an aquifer (how easily water can enter)
storativity – how much water is stored in an aquifer.

While a consultant will be able to work out transmissivity from data collected from the pumped well, you will also need data on lowering water levels (drawdown) from a neighbouring well to measure storativity.

Carrying out the test

Before starting the test, measure groundwater levels in both the pumping test well and neighbouring wells to ensure what are the conditions. This may take from a few hours to a day of observation, without the wells being pumped.

Start pumping the test well. Monitor the rate of pumping and keep it constant throughout the test. Measure the rate of discharge using an orifice meter or an accurately calibrated flow meter. Keep the rate of discharge constant to an accuracy of five percent.

Monitor groundwater levels often enough to accurately show how levels change. For example, you could take measurements in the pumping well at the following time intervals (in minutes) after you start:

1, 2, 3, 4, 5, 7, 9, 12, 15, 20, 25, 30, 40, 50, 60, 90, 120, 150, 180, 240, 300, 360, 480, 600 and then every three hours.

Measure groundwater levels accurately - noting the exact time you made the measurement. Battery powered groundwater probes can be used that have a light or alarm which goes off when it’s dipped into water.

After pumping stops, keep monitoring groundwater for a period similar to the pumping test, or until water levels have recovered to the pre-test level.

Test reports

Pumping test reports should include the following:

Date, location and site diagram.
Contact details for the well owner and consultant.
Drawdown measurements, time of measurement and flow rate (including soft copy).
Well logs and construction details for all wells monitored.
Estimated characteristics of the aquifer (including transmissivity and storativity) and assessment of effects.

.

Pumping Test Analyses

Pumping Test Analyses

Thiem, 1906 (Distance-Drawdown Method)

Distance-Drawdown method with Jacob, 1963 unconfined correction

Cooper and Jacob, 1946

A generalized graphical method for evaluating formation constants and summarizing well field history (Cooper Jacob Straight Line Method)

Theis, 1935

Constant discharge from a fully penetrating well in a nonleaky aquifer

Theis, 1935 (Unconfined)

Constant discharge from a fully penetrating well in a nonleaky aquifer

Theis, 1946 (Recovery)

Recovery test after constant discharge from a fully penetrating well in a nonleaky aquifer

Analysis methods

An appropriate model or solution to the groundwater flow equation must be chosen to fit to the observed data. There are many different choices of models, depending on what factors are deemed important including:

leaky aquitards,

unconfined flow (delayed yield),

partial penetration of the pumping and monitoring wells,

finite wellbore radius — which can lead to wellbore storage,

dual porosity (typically in fractured rock),

anisotropic aquifers,

heterogeneous aquifers,

finite aquifers (the effects of physical boundaries are seen in the test), and

combinations of the above situations.

Nearly all aquifer test solution methods are based on the Theis solution; it is built upon the most simplifying assumptions. Other methods relax one or more of the assumptions the Theis solution is built on, and therefore they get a more flexible (and more complex) result.

Theis solution

The Theis equation was adopted by Charles Vernon Theis (working for the US Geological Survey) in 1935 (see references), from heat transfer literature (with the mathematical help of C.I. Lubin), for two-dimensional radial flow to a point source in an infinite, homogeneous aquifer. It is simply

$s=\frac{Q}{4\pi T}W(u)$

$u=\frac{r^2 S}{4Tt}$

where s is the drawdown (change in hydraulic head at a point since the beginning of the test), u is a dimensionless time parameter, Q is the discharge (pumping) rate of the well (volume divided by time, or m³/s), T and S are the transmissivity and storativity of the aquifer around the well (m²/s and unitless), r is the distance from the pumping well to the point where the drawdown was observed (m or ft), t is the time since pumping began (minutes or seconds), and W(u) is the "Well function" (called the exponential integral, E1, in non-hydrogeology literature).

Typically this equation is used to find the average T and S values near a pumping well, from drawdown_(hydrology) data collected during an aquifer test. This is a simple form of inverse modeling, since the result (s) is measured in the well, r, t, and Q are observed, and values of T and S which best reproduce the measured data are put into the equation until a best fit between the observed data and the analytic solution is found. As long as none of the additional simplifications which the Theis solution requires (in addition to those required by the groundwater flow equation) are violated, the solution should be very good.

The assumptions required by the Theis solution are:

homogeneous, isotropic, confined aquifer,

well is fully penetrating (open to the entire thickness (b) of aquifer),

the well has zero radius (it is approximated as a vertical line) — therefore no water can be stored in the well,
aquifer is infinite in radial extent,

horizontal (not sloping), flat, impermeable (non-leaky) top and bottom boundaries of aquifer,

Even though these assumptions are rarely all met, depending on the degree to which they are violated (e.g., if the boundaries of the aquifer are well beyond the part of the aquifer which will be tested by the pumping test) the solution may still be useful.

Thiem solution

Steady-state radial flow to a pumping well is commonly called the Thiem solution, it comes about from application of Darcy's law to cylindrical shell control volumes (i.e., a cylinder with a larger radius which has a smaller radius cylinder cut out of it) about the pumping well; it is commonly written as:

$h - h_0 = \frac{Q}{2\pi T} ln\left( \frac{r}{R} \right)$

In this expression h0 is the background hydraulic head, h-h0 is the drawdown at the radial distance r from the pumping well, Q is the discharge rate of the pumping well (at the origin), T is the transmissivity, and R is the radius of influence, or the distance at which the head is still h0. These conditions (steady-state flow to a pumping well with no nearby boundaries) never truly occur in nature, but it can often be used as an approximation to actual conditions; the solution is derived by assuming there is a circular constant head boundary (e.g., a lake or river in full contact with the aquifer) surrounding the pumping well at a distance R.

Jacob Straight-Line Distance-Drawdown Method

At another approach to drawdown analysis of a confined aquifer.If several observation wells are available and simultaneous measurements of head are made in all the wells at a particular time, a straight line method of analysis called the Jacob Straight-Line Distance-Drawdown Method can be used to analyze the data.

Overhead: Jacob Straight-Line Distance-Drawdown

Drawdown values for each well are plotted on a linear scale, with the well distances (from the pumping well) plotted on a log scale.

Drawdown will vary from well to well based on the Theis function, and the wells nearest to the pumping well will fall along a straight line.

By extending the line up to the zero drawdown axis, we can get a value of r0 - the distance at which drawdown is zero.We can also get D(h0?h), which is the change in drawdown over one log cycle of distance.

The distance drawdown formulas for this method are:

and

The methods discussed above are provided by GWB of Rajasthan.

Well test

This article discusses Water well testing; the testing of other wells, eg. water wells, is a separate field.

A Well test is conducted to evaluate the amount of water that can be pumped from particular water well. More specifically, a well test will allow prediction of the maximum rate at which water can be pumped from a well, and the distance that the water level in the well will fall for a given pumping rate and duration of pumping.

Well testing differs from Aquifer testing in that the behavior of the well is primarily of concern in the former, while the characteristics of the aquifer (the geological formation or unit that supplies water to the well) are quantified in the latter.

When water is pumped from a well the water level in the well falls. This fall is called drawdown (change in hydraulic head from the pre-test conditions). The amount of water that can be pumped is limited by the drawdown produced. Typically, drawdown also increases with the length of time that the pumping continues.

Calculations

All calculations and data analyses must accompany the final

report. All calculations should clearly show the data used for

input, the equations used and the results achieved. Any

assumptions made as part of the analysis should be noted in

the calculation section. This is especially important if the data

were corrected to account for barometric pressure changes,

off-site pumping changes, or other activities which have

affected the test. The calculations should reference the