Aquifer tests

The hydraulic properties of aquifers are determined using (a) pumping or recharge tests and (b) water-level changes reflecting long-term effects of conditions at the aquifer boundaries: both approaches representing hydrodynamic analysis of the aquifer. The first method is widely applied because it permits evaluation of the aquifer parameters in a relatively short period of time. The second method is the cheapest and in some aquifer systems provides an opportunity to observe such processes as seepage, recharge and evaporation. Therefore, both methods are useful to varying degrees depending on the objectives of the field studies. Test observations and analysis are briefly discussed below. The problems mentioned are described in detail in many papers, among which are those by the following researchers: Hantush (1956), Schelkachov (19591, Bochever and Verigin (1961), and Ferris et al. (1962).

6.1.1

Aquifer response to changing discharge or head

Ground-water levels (heads) change in response to pumping or recharge and in response to fluctuations of water stage in contiguous bodies of surface water. The magnitude

4

B P

Extrapolated trend.

1

Time

FIG. 6.1.1. Hydrograph from hypothetical observation well showing definition of drawdown.

6.1 p a w I

Ground-water studies

and the timing of the head changes are related to (a) the magnitude and location of the change in flow or water stage, (b) the hydraulic properties of the aquifer such as trans- missivity and coefficient of storage, and (c) the shape and size of the aquifer, or more generally the three-dimensional distribution of the hydraulic properties in the subsurface.

A n example of changes in head due to near-by pumping is shown schematically in Figure 6.1.1. Head in most aquifers changes continuously in response to fluctuations in climate. In Figure 6.1.1, such variation is indicated as the antecedent trend line, before t = O. If pumping had not started at t = O, the graph would have continued along the dashed line marked ‘Extrapolated trend’, After pumping starts the effect on head due only to pumping is the difference between observed head and extrapolated trend, identified as the ‘drawdown’, and measured at time t. Drawdown is the response due only to the change in boundary conditions imposed by a test: pumping that started at t = O. Analysis of the relation between observed drawdown, s, rate of discharge from the pumping well, Qw, distance from the pumping well at which drawdown is observed, Y, and time, t, can produce estimates of the hydraulic properties of the aquifer.

6.1.1.1

Figure 6.1.1.1 illustrates the differences in paths of ground-water flow caused basically by the nature of changes in storage. In the confined aquifer, water is released from storage throughout the entire thickness of the aquifer due to compression of the rock and decompressior, of the water. Thus flow lines tend to be horizontal or parallel to the impermeable confining beds. However, in the unconfined aquifer, flow lines terminate on the water table where storage changes result mostly from dewatering of the pore spaces. Thus, the flow to wells in unconfined aquifers is likely to contain significant vertical flow components. Also, pore space does not drain instantaneously as heads are lowered in the unconfined aquifer. Therefore the generally applied assumption that water storage is related linearly to head may not accurately represent conditions in the un- confined aquifer.

Many equations used for analysing aquifer tests are based on assumptions that most nearly describe confined aquifers. W h e n these equations are applied also to analyse tests made in unconfined aquifers, they may yield less accurate results.

None of the equations commonly used for analysing aquifer tests can provide exact measures of the aquifer properties. Variations of aquifer properties in space and time and of control conditions during the test, errors in measurement, inaccurate extra- polation of trend lines (see Fig. 6.1,1), and uncontrolled extraneous effects on head all combine to produce uncertainty in test results. Nevertheless, experience has shown that careful tests do produce estimates of hydraulic properties which are sufficiently accurate for engineering purposes.

Profiles of flow in confined and unconfined aquifers

6.1.1.2

If in the vicinity of a pumping well heads change relatively slowly with time, the aquifer contains no boundaries over a large area around the well and the well is pumped at a constant rate Qw, the transmissivity can be determined from the well-known Dupuit formula for steady flow. In non-dimensional form this formula can be written as

Steady flow to a completely penetrating well

Q w loge (rzIr1)

2;n (s1

-

T = 6.1(1)

where SI is the drawdown observed at distance r1 from the pumping well, sz is the draw- down at distance YZ, and T is transmissivity of the aquifer. Equation 6.1 (1) is a valid approximation if the pumping well accepts flow from the full thickness of the aquifer, and if the ratio ii = r2S/4Tt is less than about 0.05, where S refers to the storage CO-

6.1 puxc 2

Determining hydrodynamic parameters of ground-water flow

Aquifer

'Radi&, r

I. Confined aquifer

II. Unconfined aquifer

FIG. 6.1.1.1. Schema of unsteady flow to a well.

efficient. If S is unknown, but its value is desired for some preliminary purpose, commonly it is estimated to equal 0.1 to 0.2 in unconfined aquifers, and to equal 10-6 multiplied by the aquifer thickness expressed in feet for confined aquifers. If the thickness were expressed in metres (m) the foregoing rule-of-thumb would require the multiplier to be 3.28 m .

If drawdown and discharge data are available only at a pumped well the following approximate relations are useful in obtaining a rough preliminary estimate of the trans- missivity.

If r 2 in Equation 6.1 (1) is taken at large distance, re, from the pumping well where sz is about equal to zero, and YI is taken at the radius of the pumping well, rW, Equation 6.1 (1) may be written as

6.1(2)

6.1 pugc 3

Ground- water stiidîes

where sw is the drawdown observed in the pumping well. For conditions commonly encountered in unconfined aquifers it might be assumed that re is about 1,000 feet (300 m) and if rw is taken as 1 foot (30 cm) then Equation 6.1 (2) reduces to the follow- ing non-dimensional approximation:

6.1(3)