Ground-water development in East St. Louis area, Illinois. Urbana, IL ...

is intercepted and the cone is deep enough so that the
induced infiltration balances discharge.
The area of the river bed over which recharge takes
place is replaced by a line source. According to the
image well theory (Ferris, 1959), the effect of a line
source on the drawdown in an aquifer, as a result of
pumping from a well near the line source, is the same
as though the aquifer were infinite and a like recharging
well were located across the line source, and on
right angles thereto, and at the same distance from the
line source as the real pumping well. Based on the image
well theory and the nonequilibrium formula, the drawndown
distribution in an aquifer bounded by a line source
under equilibrium conditions is given by the following
equation:
where:
(1)
bed (Walton, 1960a), or effects of induced infiltration if
the effects of partial penetration are excluded. Walton
(1963) gave methods for proving whether or not water
levels stabilize because of the effects of induced infiltration.
According to Walton (1963) the coefficient of transmissibility
can often be determined from distancedrawndown
data for observation wells on a line parallel
to the recharge boundary. Provided the wells are not
too distant from the pumped well and not too
close to the recharge boundary, the effects of induced
infiltration on drawdowns in the wells is approximately
equal because the wells are for practical purposes
equidistant from the image well associated with the
recharge boundary. A plot of maximum drawdowns in
the observation wells versus the logarithm of distance
from the pumped well will yield a straight-line graph.
The slope of the straight line is substituted in the following
equation (Cooper and Jacob, 1946) to compute
the coefficient of transmissibility:
where:
(5)
In terms of the distance between the pumped well
and the line source or recharge boundary, equation 1 was
expressed by Rorabaugh (1956) as
where:
If T is known, the distance from the pumped well to
the recharge boundary, a, can be computed with maximum
drawdowns in each observation well on a line
parallel to the stream and the following equation:
where:
(6)
For the particular case where the observation well is
on a line parallel to the recharge boundary, equation 2
may be written as follows:
Equations 1 through 3 assume that the cone of depression
has stabilized, water is no longer taken from
storage within the aquifer, and equilibrium conditions
prevail. The pumping period required to stabilize water
levels can be computed by using the following equation
(see Foley, Walton, and Drescher, 1953):
where:
In many cases the stabilization of the cone of depression
can be attributed either to the effects of slow
gravity drainage, effects of leakage through a confining
(3)
(4)
The maximum drawdowns in the observation wells
are much less because of the effects of recharge than
they would be if the aquifer were infinite; thus, the coefficient
of storage cannot be determined from the distance-drawdown
graph.
The nonequilibrium formula (Theis, 1935) and computed
values of T and a can be used to determine
the coefficient of storage. Several values of the coefficient
of storage are assumed, and maximum drawdowns
in each observation well are computed taking
into consideration the effects of the image well associated
with the recharge boundary and the pumped well.
The computed drawdowns in each observation well are
then compared with actual drawdowns, and the coefficient
of storage that provided computed drawdowns
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