Page 129 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

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3.13 Aquifer Boundaries 91
3.13.1 Recharge Boundaries

The conditions along a recharge boundary can be reproduced by assuming that the aquifer is
infinite and by introducing a negative image well (for example, a recharge image well for a
discharging real well) an equal distance on the opposite side of the boundary from the real
well, the line joining the two being at right angles to the boundary (Fig. 3.10). The draw-
down, s, at any distance, r, from the pumping well and r i from the image well is the alge-
braic sum of the drawdowns due to the real well, s r , and buildup due to the image well, s i
s = s + s = (528 Q>T) log(r >r) (U.S. Customary Units) (3.36a)
i
r
i
s = (528 Q>T) log(2a>r ) (U.S. Customary Units) (3.37a)
w
w
where s the drawdown at any distance, r, from a pumping well, ft; s r the drawdown due
to real well, ft; s i the drawdown due to image well, ft; s w the drawdown at the well, ft;
r any distance between the drawdown location and the pumping well, ft; r i the distance
between the drawdown location and the image well, ft; r w the radius of the pumping well,
ft; Q pumping discharge rate, gpm; T transmissivity, gpd/ft; a the distance between
the stream and the pumping well ft.
The following are two equivalent equations using the SI or metric units of: s (m), s r (m),
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s i (m), s w (m), r (m), r i (m), r w (m), Q (m /d), T (m /d/m), and a (m):
s = s + s = (0.366 Q>T) log(r >r) (SI Units) (3.36b)
i
r
i
= (0.366 Q>T) log(2a>r ) (SI Units) (3.37b)
s w w
EXAMPLE 3.8 DETERMINATION OF A WELL DRAWDOWN AND CONE OF DEPRESSION PROFILE

A gravel-packed well with an effective diameter of 24 in. (610 mm) pumps water from an artesian
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aquifer having T 3.2 l0 gpd/ft (397.4 m /d/m) and S 3.4 l0 . The well lies at a distance
of 1,000 ft (304.8 m) from a stream that can supply water fast enough to maintain a constant head.
3
Find the drawdown in the well after 10 days of pumping at 700 gpm (3,815 m /d). Determine the
profile of the cone of depression with a vertical plane through the well normal to the stream.
Solution 1 (U.S. Customary System):
In the region of interest, the use of a semilogarithmic approximation is valid:
s w (528 Q>T) log(2a>r w )
s (528 Q>T) log(r i >r)
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528 Q>T (528 700)>(3.2 l0 ) 11.55 ft
Drawdown at the well:
a 1,000 ft
r w 24 in.>2 1 ft
s w (528 Q>T) log(2a>r w )
s w 11.55 log 2,000 38.0 ft
Drawdown at 500 ft from the stream:
r 500 ft
r i a r 1,000 500 1,500 ft
s 11.55 log(1,500>500) 5.5 ft