Characterizing Aquifers - Hydrogeology: Objectives, Methods, Applications - page 134

Figure 71 Example of a step-wise pumping test (La Trinité, Alpes-Maritimes).
The drawdown, s, at a given time, t, is given by Jacob's equation:
s = B⋅Q + C⋅Q 2 .
It is the sum of two head losses, characterizing the aquifer/pumping well
assemblage (Forkasiewicz, 1972):
￿ B⋅Q corresponds to a linear loss of head, caused by laminar fl ow in
the aquifer around the well. It is infl uenced by the aquifer and by the
catchment portion of the well;
￿ C⋅Q 2 corresponds to a quadratic, not linear, loss of head, caused
by turbulent fl ow in the well (perforation and tubing) and in the
surrounding rock (fractures and conduits). It essentially depends on
the pumped discharge, and characterizes the pumping equipment.
The specifi c discharge/drawdown relationship s/Q = f(Q) is linear,
and allows for the direct graphic measurement of the losses of head by the
coeffi cients B and C (Figure 72a).
B is, indeed, given by the intersection of the line with the axis of specifi c
drawdowns, and C is equal to the slope of the line.
The relationship in the preceding example therefore becomes, s/Q =
2⋅10 -3 + 1.04⋅10 -4 ⋅Q.
The well's characteristic curve (Figure 72b) is represented by the
function: s = f(Q). It can be plotted with the help of intermediary and
extreme points, calculated with Jacob's equation. It allows the defi nition of
a critical exploitation discharge, as a function of the maximum acceptable
drawdown (55 m 3 ·hr -1 in the preceding example).