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HYDC05 12/5/05 5:35 PM Page 190

190 Chapter Five

Type 1 Type 2 Type 3 Type 4 Type 5

l k

l u

O u

O k

l k Known input l u Unknown input
O k Known output O u Unknown output

Fig. 5.38 Five topological types of conduit network in karst groundwater systems. After Brown and Ford (1971).

(,
∂Cz t) CQ z() into equation 5.58. Calculation of the hydraulic con-
=− o eq. 5.56
∂t πr 2 ductivity can then be made if the hydraulic gradient is
known using equation 2.9. An example of the applica-
which, for a fixed value of z, yields upon integration: tion of the single borehole dilution method is given in
Box 5.4.
⎡ Qt ⎤ In a convergent radial flow tracer test, tracer is
C exp − o ⎥ eq. 5.57
=
⎢
C
o r π 2 added to a soakaway, well or piezometer and the
⎣ ⎦ breakthrough monitored at a pumping well. A diver-
If it is assumed that the water flowing through the gent radial flow tracer test is also possible where
borehole is drawn from a width of aquifer equal tracer is added to an injection well and the forced
to twice the borehole diameter, then, for a one- plume of tracer observed in an array of surrounding
dimensional flow system with parallel streamlines, Q observation points. In comparison, a shortcoming of
o
= 2qd and equation 5.57 becomes (Lewis et al. 1966): the convergent radial flow test is that the converging
flow field counteracts spreading due to dispersion. An
⎡ 8
C exp − qt ⎤ ⎥ eq. 5.58 example of the convergent radial flow test is given
=
⎢
C
o π in Box 5.5.
⎣ d ⎦
where C is concentration at time t = 0, d is the
o
borehole diameter and q is the horizontal specific 5.8.4 Geophysical methods
discharge or darcy velocity (Section 2.3). Hence, the
dilution of tracer in the borehole should be exponen- Downhole (borehole) and surface geophysical tech-
tial, with a time constant related to the specific dis- niques are now routinely used in hydrogeological
charge. By plotting concentration versus time on investigations and take advantage of modern tech-
semilogarithmic paper, the specific discharge can be niques and instrumentation that have benefited from
calculated by substituting any two values of tracer advances in electronics and digital technology. Al-
concentration and the corresponding time interval though the two types of geophysics can be considered