The purpose of design is to improve the chance that a test will yield acceptably accurate values of the hydraulic coefficients.
Site evaluation. Frequently the cost of testing is reduced by using combinations of production and abandoned wells rather than installing new wells for the purpose. F e w existing well configurations are suitable for test purposes, and most wells are ill-equipped for observation. Evaluation of existing facilities in the area where tests are proposed, to find those which are potentially usable, is the first step in design. Recognizing that an aquifer test involves applying a known stress to a known aquifer, and observing the response, one m a y easily establish criteria for site evaluation, as follows:
The control well
The control well must be equipped with reliable power, pump, and discharge control equipment.
The water discharged must be conducted away from the control well so it cannot return to the aquifer during the test. This point is of special importance in testing shallow unconfined aquifers.
The well head and discharge lines should be accessible for installing discharge regulating and monitoring equipment.
It should be possible to measure depth to water in the control well before, during and after pumping.
The diameter, depth and position of all openings in the control well should be known, as should total depth.
The observation wells
1. Response of all wells to changing water stages should be tested by injecting a known volume of water into each well and measuring the subsequent decline of water level. The initial rise of water should be dissipated within 3 to 4 hours (to within about 0.01 foot (3 mm) of the original level) if the observation well is to reflect satisfactorily changes of head in the aquifer during the test. Quicker response is preferable. Long-abandoned wells tend to become clogged,
6.1 puge I2
Determining hydrodynamic parumeters of ground-water flow
and consequently the response test is one of the most important pre-pumping examinations to be made where such wells are to be used for observation.
2. Total depth, diameter and screened interval should be known for each observation well.
3. Radial distance from the control well to each of the observation wells must be determined.
The aquijïer
1. Depth to and thickness of the aquifer should be known, as well as the changes in aquifer configuration in the area to be sampled by the test.
2. Near-by aquifer discontinuities caused by changes in lithology, or by incised streams and lakes, should be mapped.
3. Estimates of all pertinent hydraulic properties of the aquifer and adjacent rocks must be made by any means feasible. Estimates of transmissivity and coefficient of storage should be made. Also, if leaky confining beds are suspected leakance coefficients should be estimated.
For unconfined aquifers, conductivity to vertical flow is important. In the absence of any data, hydraulic conductivity to vertical flow = 10 gpd/ft2 = 1.4 ft/d = 0.43 m/d; assume transmissivity = 100,000 gpd/ft (U.S. gallons per day per foot) = 14,000 ft2 per day = 1,300 m2/d; artesian storage coefficient = 1 x x aquifer thickness, in feet; specific yield = 0.20 in unconfined systems.
The importance of making the pre-test site evaluation cannot be overstressed. T o ignore any one of them is to invite failure of the test. Although site evaluation of existing well configurations is emphasized, all elements apply equally where wells are to be specially installed for testing the aquifer.
Response prediction. The pre-test evaluation serves two general purposes. First, it des- scribes the aquifer and control well with sufficient detail so that the appropriate type curve to be used for data analysis is evident (provided of course that such a curve exists analogous to the aquifer and site conditions). Secondly, it provides the basis for pre- dicting the outcome of the test with available facilities and draws attention to deficiencies in observation-well locations. If site conditions deviate markedly from all type-curve formulations known, the site should be abandoned for testing purposes unless the cost of a special-purpose type-curve development is considered acceptable.
If a suitable type curve is available, estimates of the hydraulic properties are entered into the response equation, with the magnitude and type of control, to find the expected head or drawdown distribution at the available observation wells. Test data, to be most effective, must sample a variety of positions on the type curve(s). If the observation wells are not located to accomplish such a sampling, calculated results will be in doubt;.
As an example, consider the non-leaky artesian model of Theis. Figure 6.1.1.6 shows schematically the drawdown versus time expected in a particular observation well located a distance YI from a control well. It is commonly impossible to obtain meaningful drawdown measurements during the first minute of the test. Thus only the flat part of the curve at the upper right, after t = 1 minute, can be defined by measurements in the available observation well. Study of the matching process in Figure 6.1.1.4a shows that such data willproduce accurate measurement of transmissivity because the data curve can be located relatively accurately with respect to W(u), the ordinate, disregarding the misfit along the abscissa. Finding the match point with respect to u is more difficult as the data curve cannot be placed as accurately along the abscissa. For the curves shown on Figure 6.1.1.6 it is unlikely the storage coefficient could be obtained within f an order of magnitude. If the pumping test is to provide accurate values of both T and S, drawdowns must be observed over both the steep and flat parts of the type curve.
If only one observation well is to be drilled for testing, where should it be located?
From the Theis-type curve, w e find the time'scale is proportional to r2. To produce a detectable drawdown of 0.01 foot (3 mm) 2 minutes after pumping starts, the time scale should be shifted about 2 orders of magnitude to the right on Figure 6.1.1.6. Thus, an observation well at a distance of about 10n from the control well would provide
6.1 page 13
Ground-water stirdies
I
0.001
0.01 o. 1
Time (t), in minutes
FIG. 6.1.1.6. Pumping response as predicted in observation wells.
definitive data for both Tand S, assuming that our assay of the test site is correct. Further- more, test observations made over a 24-hour period will obviously afford all the curve definition needed to determine T and S accurately.
Where several wells are available, predicted response should be plotted as t/v2 or r2/f for all wells on one sheet of graph paper. The total of all information from the test site should afford complete definition of curve shape. It is not required that each well provide data fitting both the steep and flat parts of the type curve. Data from one or more of the wells having small Y may plot only in the flat, others in the steep part. The objective of design is to assure adequate response measurements over the whole of the test facility- not piecemeal.
Where site conditions are more complicated, such as those including partial pene- tration or unconfined flow, the prediction of observation-well response is of course less certain. However, for all proposed test sites such a prediction must be made so that one can guard against major deficiencies in the well configuration. M a n y test configu- rations are rescued from failure by the simple expedient of drilling only one observation well at a key point in the system.
Artesian or confined systems are generally more amenable to testing than unconfined systems. Artesian flow to wells is described by the simpler set of boundary conditions.
In unconfined systems, mobility of the upper boundary, vertical flow components, and non-linear release of water from storage are difficult to treat, but have been successfully attacked recently. However, all these complicating features of unconfined flow affect the early response simultaneously. Present state of knowledge does not provide a means for recognizing quantitatively the magnitude of response due to each factor individually.
The most significant theoretical advances in testing unconfined systems have been made by N. S. Boulton, of the University of Sheffield, Sheffield, England. Boulton (1 954a) presented type curves for non-steady flow assuming negligible de-watering of the aquifer, linear release from storage and termination of flow lines on the water table.
Extensive values of the type curves for water-table response from the latter study were published by Stallman (1962), and curves applicable to response at depth were developed from Boulton's (1954ct) model by electric analogue (Stallman, 1965). Delayed yield from storage, expressed as an exponential function of time, was analysed by Boulton (19546, 1963).
Before analytical work described the effects of vertical flow and delayed yield in un- confined flow to wells, it was c o m m o n practice to 'pump long enough' so such effects become negligible and response approached that of the simple artesian model. However, no criteria existed for judging h o w long is 'long enough'. With the analytical solutions
G.l page 14
Determining hydrodynamic parameters of ground- water flow
n o w available some criteria are available for judging the length of time required for attaining effectively an artesian response in an unconfined system.
According to Boulton (1954~) and Hantush (1964, p. 366) vertical flow components in unconfined aquifers significantly affect response when
t < 5mS/Kz in the region O < r/m < 0.2 6.1(3 1) where t is time, m is the aquifer thickness, S is specific yield, and K, is vertical hydraulic conductivity. Equation 6.1 (31) was derived analytically assuming that non-steady radial and vertical flow components exist in the vicinity of a fully penetrating well, specific yield is constant in time and space and drawdown is negligible compared with aquifer thickness. Equation 6.1 (31) produces a startling revelation of the pumping time required for approaching artesian-type flow. For m = 100 feet, S = 0.2, and K, = 10 feet per day, we find response is affected by vertical flow for as long as t = 10 days, near the pumped well. If the aquifer thickness is 1,000 feet, equations of artesian flow should not be applied to the first 100 days of observation.
Electric analogue studies (Stallman, 1965) showed vertical flow components to be significant in the region
Tt/r2S < 1 ; (r/m) (K,/K,)* < 3 6.1(32) where Kr is horizontal hydraulic conductivity and the other terms are as previously defined.
Criteria such as Equations 6.1 (31) and 6.1 (32) are not n o w available from type curves for delayed yield. However, a dimensionless plot of column drainage (Stallman, 1967) has shown that about 70 per cent of the ultimate drainage due to lowering the water table will be attained at
t = 10S~/Kz 6.1(33)
Thus, for K, = 10 feet per day (3.04 m/d), s = 10 feet (3.04 m), and S = 0.2, delayed yield willbe pronounced for at least t = 2 days.
If the pumping time in a test can be extended long enough to surpass the time re- quirements evident from Equations 6.1 (31) to 6.1 (33) equations of radial artesian flow can be employed for data analysis, provided the control well fully penetrates the aquifer.
If the control well partially penetrates the aquifer, equations accounting for partial penetration (Hantush, 1964, p. 355; Stallman, 1965) must be employed, or one is re- stricted further to using data in the region
r < 1.5 m (Kr/K,)* 6.1(34) Use of type curves for predicting response at a test site and the liberal use of criteria like Equations 6.1 (31) to 6.1 (34) for design purposes is necessary to the extent that one ,nay reduce the prospect of failure to achieve the test objective, i.e. to measure accurately the hydraulic properties of the aquifer,