16 Slug tests In a slug test, a small volume (or slug) of water is suddenly removed from a well, after which the rate of rise of the water level in the well is measured. Alternatively, a small slug of water is poured into the well and the rise and subsequent fall of the water level are measured. From these measurements, the aquifer’s transmissivity or hydraulic conductivity can be determined. If the water level is shallow, the slug of water can be removed with a bailer or a bucket. If not, a closed cylinder or other solid body is submerged in the well and then, after the water level has stabilized, the cylinder is pulled out. Enough water must be removed or displaced to raise or lower the water level by about IO to 50 cm . If the aquifer’s transmissivity is higher than, say, 250 m2/d,the water level will recov- er too quickly for accurate manual measurements and an automatic recording device will be needed. No pumping is required in a slug test, no piezometers are needed, and the test can be completed within a few minutes, or at the most a few hours. No wonder that slug tests are so popular! They are invaluable in studies to evaluate regional groundwater resources; conducted on newly-constructed wells, they permit a preliminary estimate of aquifer conditions, and are also useful in areas where other wells are operating and where well interference can be expected. But slug tests cannot be regarded as a substitute for conventional pumping tests. From a slug test, for instance, it is only possible to determine the characteristics of a small volume of aquifer material surrounding the well, and this volume may have been disturbed during well drilling and construction. Nevertheless, some authors (Ramey et al. 1975; Moench and Hsieh 1985) state that fairly accurate transmissivity values can be obtained from slug tests. The simple slug-test technique has been further developed in recent years and has consequently become more complex and requires more equipment. In this chapter, we shall present one of these more advanced techniques: the oscillation test. An oscillation test requires an air compressor to lower the water level in the well. After some time, when the head in the aquifer has resumed its initial value, the pressure is suddenly released. The water level in the well then resumes its initial level by a damped oscillation that can be measured, preferably with an automatic recorder. For conventional slug tests performed in confined aquifers with fully penetrating wells, curve-fitting methods have been developed (Cooper et al. 1967; Papadopulos et al. 1973; Ramey et al. 1975). Cooper’s method is presented in Section 16.1.1. For wells partially or fully penetrating unconfined aquifers, Bouwer and Rice (1976) devel- oped the method outlined in Section 16.2. I. All of the above methods are based on theories that neglect the forces of inertia in both the aquifer and the well: the water level in the well is assumed to return to the equilibrium level exponentially. When slug tests are performed in highly permeable aquifers or in deep wells, however, inertia effects come into play, and the water level in the well may oscillate after an instantaneous change in water level. Various methods 237
Transcript
16 Slug tests
In a slug test, a small volume (or slug) of water is suddenly removed from a well, after which the rate of rise of the water level in the well is measured. Alternatively, a small slug of water is poured into the well and the rise and subsequent fall of the water level are measured. From these measurements, the aquifer’s transmissivity or hydraulic conductivity can be determined.
If the water level is shallow, the slug of water can be removed with a bailer or a bucket. If not, a closed cylinder or other solid body is submerged in the well and then, after the water level has stabilized, the cylinder is pulled out. Enough water must be removed or displaced to raise or lower the water level by about I O to 50 cm .
If the aquifer’s transmissivity is higher than, say, 250 m2/d, the water level will recov- er too quickly for accurate manual measurements and an automatic recording device will be needed.
No pumping is required in a slug test, no piezometers are needed, and the test can be completed within a few minutes, or at the most a few hours. No wonder that slug tests are so popular! They are invaluable in studies to evaluate regional groundwater resources; conducted on newly-constructed wells, they permit a preliminary estimate of aquifer conditions, and are also useful in areas where other wells are operating and where well interference can be expected.
But slug tests cannot be regarded as a substitute for conventional pumping tests. From a slug test, for instance, it is only possible to determine the characteristics of a small volume of aquifer material surrounding the well, and this volume may have been disturbed during well drilling and construction. Nevertheless, some authors (Ramey et al. 1975; Moench and Hsieh 1985) state that fairly accurate transmissivity values can be obtained from slug tests.
The simple slug-test technique has been further developed in recent years and has consequently become more complex and requires more equipment. In this chapter, we shall present one of these more advanced techniques: the oscillation test.
An oscillation test requires an air compressor to lower the water level in the well. After some time, when the head in the aquifer has resumed its initial value, the pressure is suddenly released. The water level in the well then resumes its initial level by a damped oscillation that can be measured, preferably with an automatic recorder.
For conventional slug tests performed in confined aquifers with fully penetrating wells, curve-fitting methods have been developed (Cooper et al. 1967; Papadopulos et al. 1973; Ramey et al. 1975). Cooper’s method is presented in Section 16.1.1. For wells partially or fully penetrating unconfined aquifers, Bouwer and Rice (1 976) devel- oped the method outlined in Section 16.2. I .
All of the above methods are based on theories that neglect the forces of inertia in both the aquifer and the well: the water level in the well is assumed to return to the equilibrium level exponentially. When slug tests are performed in highly permeable aquifers or in deep wells, however, inertia effects come into play, and the water level in the well may oscillate after an instantaneous change in water level. Various methods
237
of analyzing this response by the water level have been developed (Van der Kamp 1976; Krauss 1974; Uffink 1979, 1980; Ross 1985), but they all have the disadvantage that the aquifer transmissivity cannot be determined without a prior knowledge of the storativity. In addition, Uffink states that the skin effects also have to be taken into account and that these, too, should be known beforehand. Uffink's method is described in Section 16.1.2.
A volume of water (V) instantaneously withdrawn from or injected into a well of finite diameter (2rJ will cause an instantaneous change of the hydraulic head in the well
V ho = - nr: (16.1)
After this change, the head will gradually return to its initial head. The following solution for the rise or fall in the well's head with time was derived by Cooper et al. (1967) for a fully penetrating large-diameter well tapping a confined aquifer (Figure 16.1)
(16.2) h ho
h, = ho F(a,P), or 2 = F(a,P)
Figure 16.1 A confined aquifer, fully penetrated by a well o f finite diameter into which a slug of water has been injected
238
I
I where
1 a =
P =
1 ho = h, = rc =
Tew =
KDt - rf
( 1 6.3)
( 1 6.4)
instantaneous change of head in the well at time to = O head in the well at time t > to radius of the unscreened part of the well where the head is changing effective radius of the screened (or otherwise open) part of the well
( 1 6.5)
where f(u,ci) = [uJo(u) - 2d,(u)]* + [uY,(u) - 2aYI(u)]* and J,(u), J,(u), Yo(u), and Yl(u) are the zero and first-order Bessel functions of the first and second kind.
Annex 16.1 lists values of the function F(a,P) for different values of a and p as given by Cooper et al. (1967) and Papadopulos et al. (1973). Figure 16.2 presents these values as a family of type curves.
The Cooper curve-fitting method can be used if the following assumptions and condi- tions are satisfied: - The aquifer is confined and has an apparently infinite areal extent; - The aquifer is homogeneous, isotropic, and of uniform thickness over the area
- Prior to the test, the piezometric surface is (nearly) horizontal over the area that
- The head in the well is changed instantaneously at time to = O; - The flow to (or from) the well is in an unsteady state; - The rate a t which the water flows from the well into the aquifer (or vice versa)
is equal to the rate at which the volume of water stored in the well changes as the head in the well falls (or rises);
- The inertia of the water column in the well and the non-linear well losses are neglig- ible;
- The well penetrates the entire aquifer; - The well diameter is finite; hence storage in the well cannot be neglected.
influenced by the slug test;
will be influenced by the test;
Procedure 16.1 - Using Tables 1 and 2 in Annex 16. I , draw a family of type curves on semi-log paper
by plotting F(a,P) versus P for a range of values of ci (P on the logarithmic scale) (Figure 16.2);
- Knowing the volume of water injected into or removed from the well, calculate ho from Equation 16. I ;
- Calculate the ratio h,/ho for different values oft; - On another sheet of semi-log paper of the same scale, prepare the data curve by
plotting the values of the ratio h,/ho against the corresponding time t (t on the logar- ithmic scale);
239
0.3L 0.2
I
0.0 O . ’ L 1 0-3
Figure 16.2 Family of Cooper’s type curves F(a,B) versus p for different values of c( (after Papadopulos e t al. 1973)
- Superimpose the data plot on the family of type curves and, keeping the p and t axes of the two plots coinciding and moving the plots horizontally, find a position where most of the plotted points of the data curve fall on one of the type curves. Note the value of a for that type curve;
- For p = 1 .O, read the corresponding value o f t from the time axis of the data curve; - Substitute this value o f t together with the known value of rc into p = KDt/r: =
- Knowing rc and a = r:wS/r:, and provided that re, is also known or can be estimated, 1 and calculate KD;
calculate S.
Remarks - Because the type curves in Figure 16.2 are very similar in shape, it may be difficult
to obtain a unique match of the data plot and one of the type curves. As the horizon- tal shift from one curve to the next is small and becomes smaller as a becomes
240
smaller, the error in S will be as large as the error in a, but the error in KD will still be small. Papadopulos et al. (1973) showed that, if a < an error of two orders of magnitude in c1 will result in an error of less than 30 per cent in the calcu- lated transmissivity. In addition, the effective radius of the well rew (i.e. the skin factor as rew = rwe-skin) will often not be known;
- The well radius r, influences the duration of a slug test: a smaller rc will shorten the test; this is an advantage in aquifers of low permeability;
- To analyze slug tests, Ramey et al. (1975) introduced type curves based on a function F, which has the form of an inversion integral and is expressed in terms of three independent dimensionless parameters: KDt/r;S, rf/2r;S, and the skin factor. To reduce these three parameters to two, Ramey et al. showed that the concept of effec- tive well radius (Tew = rwe-skin) also works for slug tests. If rew is used in the function F, the two remaining independent parameters relate to Cooper's dimensionless para- meters c1 and p. The set of type curves given by Ramey et al. (see also Earlougher 1977) are identical in appearance to Cooper's, and either set will produce approxi- mately the same results for the aquifer transmissivity.
16.1.2 Uffink's method for oscillation tests
In an oscillation test, the well is sealed off with an inflatable packer, through which an air hose is inserted. Air is forced through the hose under high pressure, thereby forcing the water in the well through the well screen into the aquifer and lowering the head in the well. After a certain time, when the head has been lowered to, say, 50 cm and is held there by the over-pressure, the pressure is suddenly released. The response of the head in the well to this sudden change can be described as an exponen- tially damped harmonic oscillation (Figure 16.3), which can be measured, preferably with an automatic recorder.
This oscillation response is given by Van der Kamp (1976) and Uffink (1 984) as
h, = ho e-%os o t (16.6)
Figure 16.3 Damped harmonic oscillation
24 1
where ho = instantaneous change in the head at time to (= O) h, = head in the well at time t (t > to) y = damping constant of head oscillation (Time-’) o = angular frequency of head oscillation (Time-’)
The damping constant, y, and the angular frequency of oscillation, o, can be expressed as
y = o,B (1 6.7)
and
O = o,J1-B2 (16.8)
where o, = ‘damping free’ frequency of head oscillation (Time-’) B = parameter defined by Equation 16.13 (dimensionless)
The values of y and o, and consequently of o, and B, can be derived directly from the oscillation time T, and the ratio between two subsequent minima or maxima, ln(h,/ hn+ = 6, of the observed oscillation
6 y = - - Ln
2-7C ‘L
o = -
6
o, = ‘5,
(1 6.9)
(16.
(16.
(16.
The relation between the frequency and damping of the head’s oscillation and the aquifer’s hydraulic characteristics can be approximated by the following equation (Uffink 1984)
where
skin = skin factor, and
J1-B2 O = tan( )
( 16.1 3)
(1 6.14)
( 1 6.1 5)
The nomogram in Figure 16.4 gives the relation between the parameters B and (r:o0)/4KD for different values of CL, as calculated by Uffink.
242
I 0.9 1
10-3 2 4 6 8 1 0 2 2 4 6 8 10-l 2 4 6 8_10°
'f0 4KD
Figure 16.4 Uffink's nomogram giving the relation between Band (rfwo/4KD) for different values of CI
Oscillation tests in confined aquifers can be analyzed by Uffink's method if the follow- ing assumptions and conditions are satisfied: - The assumptions and conditions underlying Cooper's method (Section 16.1. I ) , with
the exception of the seventh assumption, which is replaced by: The inertia of the water column in the well is not negligible; the head change in the well at time t > to can be described as an exponentially damped cyclic fluctua- tion.
The following condition is added: - The storativity S and the skin factor are already known or can be estimated with
fair accuracy.
Procedure 16.2 - On arithmetic paper, plot the observed head in the well, h,, against the corresponding
- From the h, versus t plot, determine the head's oscillation time rn; - Read the values of two subsequent maxima (or minima) of the oscillation, h, and
- Knowing 6, calculate the parameter B from Equation 16.1 1 ; - Knowing 6 and B, calculate o, from Equation 16.12; - Knowing B, and provided that CL is also known, find the corresponding value of
- Knowing rfo0/4KD, ro and o,, calculate KD; - Repeat this procedure for different sets of rn and ln(hn/hn+l).
timet (t > to) (see Figure 16.3);
h,+l, and calculate 6 from 6 = In(hn/hn+J;
rfoJ4KD from Figure 16.4;
243
16.2 Unconfined aquifers, steady-state flow
16.2.1 Bouwer-Rice’s method
To determine the hydraulic conductivity of an unconfined aquifer from a slug test, Bouwer and Rice (1976) presented a method that is based on Thiem’s equation (Equa- tion 3.1). For flow into a well after the sudden removal of a slug of water, this equation is written as
The head’s subsequent rate of rise, dh/dt, can be expressed as
dh Q - - -- dt - nrf
( 1 6.1 6)
( 1 6.1 7)
Combining Equations 16.16 and 16.17, integrating the result, and solving for K, yields
rf ln(Re/rw) I h - In 2 2d t h,
K = ( 1 6.1 8)
where rc = radius of the unscreened part of the well where the head is rising rw = horizontal distance from well centre to undisturbed aquifer Re = radial distance over which the difference in head, ho, is dissipated in the
d = length of the well screen or open section of the well ho = head in the well at time to = O h, = head in the well at timet > to
flow system of the aquifer
The geometrical parameters rc, rw, and d are shown in Figure 16.5. Bouwer and Rice determined the values of Re experimentally, using a resistance
network analog for different values of rw, d, b, and D (Figure 16.6). They derived the following empirical equations, which relate Re to the geometry and boundary con- ditions of the system: - For partially penetrating wells
A + B ln[(D-b)/rw] - I
dlrw 1 where A and B are dimensionless parameters, which are functions of d/rw;
- For fully penetrating wells
where C is a dimensionless parameter, which is a function of d/rw.
(1 6.1 9)
(16.20)
Since K, rc, rw, Re, and d in Equation 16.18 are constants, (l/t)ln(ho/h,) is also a constant. Hence, when values of h, are plotted against t on semi-log paper (h, on the logarithmic scale), the plotted points will fall on a straight line. With Procedure 16.3, below, this straight-line plot is used to evaluate (l/t)ln(ho/h,).
Figure 16.5 An unconfined aquifer, partially water has been removed
penetrated by a large-diameter well from which a slug of
-Io 2 4 6 alo3 2 4 6 8 1 0 4
d/rw
Figure 16.6 The Bouwer and Rice curves showing the relation between the parameters A, B, C, and d/r,
245
The Bouwer-Rice method can be applied to determine the hydraulic conductivity of an unconfined aquifer if the following assumptions and conditions are satisfied:
- The aquifer is homogeneous, isotropic, and of uniform thickness over the area
- Prior to the test, the watertable is (nearly) horizontal over the area that will be
- The head in the well is lowered instantaneously at to = O; the drawdown in the
- The inertia of the water column in the well and the linear and non-linear well losses
- The well either partially or fully penetrates the saturated thickness of the aquifer; - The well diameter is finite; hence storage in the well cannot be neglected; - The flow to the well is in a steady state.
The aquifer is unconfined and has an apparently infinite areal extent;
influenced by the slug test;
influenced by the test;
watertable around the well is negligible; there is no flow above the watertable;
are negligible;
Procedure 16.3 - On semi-log paper, plot the observed head h, against the corresponding time t (h,
- Fit a straight line through the plotted points; - Using this straight-line plot, calculate (l/t)ln(ho/hI) for an arbitrarily selected value
of t and its corresponding h,; - Knowing d/rw, determine A and B from Figure 16.6 if the well is partially penetrat-
ing, or determine C from Figure 16.6 if the well is fully penetrating; - If the well is partially penetrating, substitute the values of A, B, D, b, d, and rw
into Equation 16.19 and calculate ln(Re/rw). If the well is fully penetrating, substitute the values of C, D, b, d, and rw into Equation 16.20 and calculate ln(R,/r,);
on logarithmic scale);
- Knowing ln(R,/rw), (l/t)ln(h,,/hJ, r,, and d , calculate K from Equation 16.18.
Remarks - Bouwer and Rice showed that if D >> b, an increase in D has little effect on the
flow system and, hence, no effect on Re. The effective upper limit of ln[(D-b)/rw] in Equation 16.19 was found to be 6 . Thus, if D is considered infinite, or D - b is so large that ln[(D-b)/rw] > 6, a value of 6 should still be used for this term in Equation 16.19;
- If the head is rising in the screened part of the well instead of in its unscreened part, allowance should be made for the fact that the hydraulic conductivity of the zone around the well (gravel pack) may be much higher than that of the aquifer. The value of rc in Equations 16.17 and 16.18 should then be taken as r, = [rf + n(r$-rf)]0.5, where ra = actual well radius and n = the porosity of the gravel envelope or zone around the well;
- It should not be forgotten that a slug test only permits the estimation of K of a small part of the aquifer: a cylinder of small radius, Re, and a height somewhat larger than d;
- The values of ln(Re/rw) calculated by Equations 16.19 and 16.20 are accurate to within 10 to 25 per cent, depending on the ratio d/b;
- In a highly permeable aquifer, the head in the well will rise rapidly during a slug
246
test. The rate of rise can be reduced by placing packers inside the well over the upper part of the screen so that groundwater can only enter through the lower part. Equations 16.19 and 16.20 can then be used to calculate ln(Re/rw);
- Because the watertable in the aquifer is kept constant and is taken as a plane source of water in the analog evaluations of Re, the Bouwer and Rice method can also be used for a leaky aquifer, provided that its lower boundary is an aquiclude and its upper boundary an aquitard.
