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Guidelines on remediation of contaminated sites

Appendix 4.9
Pumping tests

There are two normal strategies for pumping tests; step-by-step pumping test using varied yield and using constant yield. These strategies can be combined by extending the final stage as long as desired.

Before, during, and after the period of pumping, observations of the water level in a number of wells are carried out. During pumping, the discharge rate of the pump is observed. In connection with pumping tests of a duration longer than approximately one day, the barometric pressure is also measured, as are the water levels of nearby recipients, if any.

The observations will normally be conducted according to a logarithmic time scale, i.e. with short intervals in connection with start-up and after pumping is finished. Automatic data collection using pressure transducers is often seen. As a main rule, the following observation frequency should be observed for pump well and observation wells after pumping start/stop:

This section concerns interpretation of pumping test data. The drawdown and recovery observed are processed as functions of time and distance and are interpreted by comparing theoretical type models, which yields values for the aquifer’s hydraulic properties; transmissivity (pump well), aquifer coefficient (observation well) and leak conditions (observation well). Other information yielded concerns the boundary conditions of the aquifer (positive boundaries (such as water courses) or negative boundaries (such as low-permeable clay barriers)). In addition to this, information on the anisotropy of the aquifer is available.

The following methods are used:

	Linear mapping with a view to assessment of water-level variations not caused by pumping (such as barometric effect).
	Single logarithmic mapping with a view to interpretation of aquifer transmissivity and aquifer coefficient.
	Double logarithmic mapping with a view to interpretation of aquifer transmissivity, aquifer coefficient and leakage.

First, the water level observations from all wells are plotted linearly using the same time scale. These plots provide information on the correlation between aquifer pressure level and e.g. variations in barometric pressure, variations in neighbouring coastal waters and/or variations in neighbouring water abstraction areas. On the basis of the linear plots, these influencing factors can be taken account of. However, it is rarely possible to carry out ideal quantitative corrections, and in reality the corrections will be semi-quantitative. In addition to this, the observation wells can be divided into three groups:

	Wells which are clearly affected by pumping
	Wells which are partly affected
	Wells which are unaffected

The theoretical method assumptions can be briefly outline as follows:

	The aquifer is homogenous and isotropic.
	The aquifer is of infinite extent.
	The radius of the pumping well is infinitesimal.
	The well is led through the entire vertical extent of the aquifer.
	Water infiltration occurs throughout the entire thickness of the aquifer.
	Water discharge from the aquifer occurs instantaneously and corresponding to drawdown.
	The hydraulic parameters are identical throughout the entire aquifer and do not vary over time.

And specifically for aquifers with leakage:

	Leakage occurs between less permeable overlying and underlying strata.
	Leakage is proportional to the drawdown in the aquifer in question.
	The hydraulic gradient in overlying and underlying strata changes instantaneously and corresponds to the drawdown in the aquifer in question.

Interpretation of pumping tests in artesian/confined aquifers with no leakage and aquifers with free water level (given the assumption that there is a small drawdown relative to the thickness of the aquifer) is based on Theis' formula:

	(1)
	(2)

1

Theis’ formula here assumes that formations above and below the aquifer are impermeable.

In connection with tensioned/artesian aquifers with leakage the following analytical equation is used:

(3)

where

r/B = leakage factor

W(u,r/B) = well function for tensioned/artesian leakage
                  aquifers (Walton function).

In connection with prolonged pumping in unconfined aquifers with delayed water discharge, interpretation must be carried out when the effect of the delayed water discharge subsides, whereupon drawdown will once again follow a Theis curve.

Two different methods are used to interpret test-pumping data. One is a single-logarithmic rectilinear adaptation method, whereas the other method is line of best fit in a double-logarithmic plot.

The single-logarithmic method is based on the fact that the integral W(u) can be represented by an infinite series. For low values of u, (1) can be approximated by:

(4)

Test data with drawdown/recovery are plotted on the y-axis and time is plotted on a logarithmic x-axis. A straight line is placed through data and D s (drawdown/recovery) is read for an interval corresponding to a factor of 10 (e.g. 10 minutes and 100 minutes). T and S are calculated in the following way:

	(5)
	(6)

where to is time (seconds) corresponding to the point of intersection between the line of best fit through the data and the line of zero drawdown/recovery.

For aquifers with no leakage, test date are plotted double logarithmically with drawdown/recovery on the y-axis and time on the x-axis. After this, a likewise double-logarithmic plot of W(u) is superimposed on u until the best possible convergence is obtained, given parallel axes. The values in pairs from drawdown/recovery data and time (s,t) and (W(u), 1/u) are called the match point; readings are taken of these. Transmissivity T and permeability k can then be calculated:

	(7)
k = T/m	(8)
	(9)

where

s = drawdown/recovery (m)
m = aquifer thickness (m)

Double logarithmic mapping and line of best fit are also used correspondingly in connection with aquifers with leakage. In this case, drawdown/recovery time is interpreted against Walton’s leak-type curves. In this interpretation, the permeability p' (m/second) of the overlying and underlying strata can also be described by:

(10)

where m' is the thickness of the overlying and underlying strata (m).

Interpreting pumping tests requires an assessment of the extent to which actual conditions correspond to the theoretical assumptions that were described earlier. The greatest differences between actual conditions and theory are:

1. The radius of the pump well is not infinitesimal.
2. The pump well is rarely led through the entire vertical extent of the aquifer.
3. The aquifer is of finite extent.
4. The aquifer is rarely homogenous and isotropic.
5. Fissured aquifers may display double porosity and permeability may vary with pressure.
6. Leak flow is not instantaneous corresponding to decrease in water level in the aquifer.

In pre-quaternary sediments, d) and e) in particular can prevent correct determination of permeability. With a view to the outlined limitations, either corrections, a) - c), can be carried out if this is deemed relevant; or the limitations can be taken account of in connection with interpretation. In addition to this, visual assessment of bore samples compared against the geology of the site is a basic part of assessment of the hydraulic parameters of the aquifer. In this way, an acceptable estimate of transmissivity and permeability can be obtained.

In connection with interpretation, it is important to note that account often needs to be taken of corrections to the data in order to obtain useful results. In connection with tensioned/artesian aquifers it is normally necessary to correct the data to account for changes in barometric pressure (barometric effect), as this influences the water levels of wells. In addition to this, other phenomena may cause groundwater fluctuation (tidal effect, other pumping, borehole effect, partial screen installation in the aquifer, decreasing thickness, delayed water discharge, etc.). Because of this, pumping tests are open to misinterpretations, which necessitates a critical approach to using the models.

Pumping test data can be interpreted using semi-logarithmic and double-logarithmic mapping of data. Interpretations which have been carried out using double-logarithmic mapping should be considered the most accurate estimates of transmissivity, and greatest emphasis is normally given to data from the recovery. Interpretations based on single-logarithmic mapping should be considered as acceptable estimates of transmissivity.

In connection with step-by-step pumping tests, the drawdown is considered as being made up according to the following:

s = BQ + CQ²

where B is traditionally formation loss and C is screen loss. Through analogy to pipe hydraulics it can be inferred that high C values are to be expected when the velocity (particle velocity) of the water is high, i.e. where large quantities of water pass through small cross sections. This might indicate that the well has been poorly executed. Methods of determining B and C are found in /1/. In principle, when interpretation has been carried out it is possible to calculate future drawdown in connection with any given pumping, which may assist dimensioning of any remedial equipment.

Reporting should include:

	The execution of the pumping test
	The results of the pumping test

if desired with the following supplements:

	The results of the pumping test, linear mapping
	The results of the pumping test, single-logarithmic mapping
	The results of the pumping test, t/r2 mapping

Reference

Large amounts of useful literature concerning pumping tests are available, including guidelines from the Environmental Protection Agency /1/, which contain further references.

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