Page 162 - Water and wastewater engineering

WELLS 4-17

In either instance, the degree of interference and its impact on capacity must be evaluated. This
can be accomplished by an investigation of the well interference hydraulics.
The degree of interference, that is, the additional drawdown in a well that is caused by the
operation of another well, is a function of the duration of pumping as well as the aquifer prop-
erties. When multiple wells are used, it is generally more efficient to operate the well for time
periods substantially less than those required to achieve steady state. Thus, the selection of a time
period for investigation of interference effects is a critical part of the analysis.
The Michigan Safe Drinking Water Act (MSDWA, 1976) requires that the design drawdown
be that which results from 100 days of continuous drawdown at the design yield. If the maximum
day demand can be met with only one well in service, then the drawdown may be calculated for
only one well. Otherwise, the calculation must be made with all the wells required to meet the
maximum day demand.

Unsteady Flow in a Confined Aquifer. Pumping times that are too short to achieve steady
state drawdown result in unsteady flow in the aquifer. A solution for estimating drawdown result-
ing from unsteady flow in a confined aquifer (transient-flow) was developed by Theis (1935).
Using heat-flow theory as an analogy, he found the following for an infinitesimally small diam-
eter well with radial flow:
Q ⎛ e u ⎞
s ∫ u ⎜ ⎟ du (4-1)
T ⎝ u ⎠
4p
where s drawdown ( H h ), m
2
rS
u
4 Tt
r distance between pumping well and observation well, or radius of pumping well, m
S storage coefficient
2
T transmissivity, m /s
t time since pumping began, s
Note that u is dimensionless. Some explanations of the other terms may be of use. The lower
case s refers to the drawdown at some time, t, after the start of pumping. Time does not appear
explicitly in Equation 4-1 but is used to compute the value of u to be used in the integration.
The transmissivity and storage coefficient also are used to calculate u. You should note that
the r term used to calculate the value of u may take on values ranging upward from the radius
of the well. Thus, you could, if you wished, calculate every point on the cone of depression
(i.e., value of s ) by iterating the calculation with values of r from the well radius to infinity.
The integral in Equation 4-1 is called the “well function of u ” and is evaluated by the following
series expansion:
2 3
u u
u
Wu() 0 577216 ln u (4-2)
.

22!
33!
A table of values of W ( u ) was prepared by Ferris et al. (1962). Values of W( u ) are reproduced in
Table 4-3. The following example demonstrates the evaluation of the integral and calculation of
drawdown.