Page 114 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch03_061-117.qxd 8/17/10 7:48 PM Page 77

3.10 Nonsteady Radial Flow 77
If, on semilogarithmic paper, the values of drawdown are plotted on the arithmetic scale
and time on the logarithmic scale, the resulting graph should be a straight line for higher val-
ues of t where the approximation is valid. The graph is referred to as the time-drawdown
curve. On this straight line an arbitrary choice of times t and t can be made and the corre-
2
1
sponding values of s and s recorded. Inserting these values in Eq. 3.18, we obtain
2
1
s s 264(Q>T) log(t >t ) (3.19)
1
2 1
2
Solving for T,
T 264 Q log(t >t )>(s s ) (3.20)
1
2
2 1
Thus transmissivity is inversely proportional to the slope of the time-drawdown curve.
For convenience, t and t are usually chosen one log cycle apart. The Eq. 3.20 then reduces to:
1
2
T 264 Q> s (U.S. Customary Units) (3.21a)
where T is the transmissivity, in gpd/ft; Q is the well flow in gpm; and s is the change in
drawdown, in ft, over one log cycle of time.
An equivalent equation using the SI units is:
T 0.1833 Q> s (SI Units) (3.21b)
3
3
where T is the transmissivity, in m /d/m; Q is the well flow, in m /d; and s is the change
in drawdown, in m, over one log cycle of time.
The coefficient of storage of the aquifer can be calculated from the intercept of the
straight line on the time axis at zero drawdown, provided that time is converted to days. For
zero drawdown, Eq. 3.18 gives:
2
0 264(Q>T) log[0.3 Tt >(r S)]
0
that is,
2
0.3 Tt >(r S) 1
0
which gives
S 0.3 Tt >r 2 (U.S. Customary Units) (3.22a)
0
where S is the coefficient of storage of an aquifier, dimensionless; T is the transmissivity,
gpd/ft; t is the time at zero drawndown, d; and r is the distance between an observation
0
well and a pumping well, ft.
An equivalent equation using the SI units is:
S 2.24 Tt >r 2 (SI Units) (3.22b)
0
where S is the coefficient of storage of an aquifier, dimensionless; T is the transmissivity,
3
m /d/m; t is the time at zero drawndown, d; and r is the distance between an observation
0
well and a pumping well, m.

EXAMPLE 3.3 DETERMINATION OF THE T AND S COEFFICIENTS OF AN AQUIFER USING THE
APPROXIMATION METHOD
A time-drawdown curve for an observation well at a distance of 225 ft (68.6 m) from a pumping
3
well discharging at a constant rate of 350 gpm (1907.5 m /d) is shown in Fig. 3.5. Determine the
transmissivity and storage coefficient of the aquifer.