Environmental Engineering Reference
In-Depth Information
When water is injected into a well, the opposite phenomenon (mound of
injection) occurs, also as a result of the finite hydraulic conductivity of the
aquifer material. The left half of Figure 4.4 illustrates the mound of injection.
The injection flow rate depends on hydraulic head and transmissivities of
the aquifer. The turbine or pump location affects the injection flow rate inso-
far as it drops some of the hydraulic head that could function to “push” more
water into the aquifer at a higher rate. That is, there is a trade-off between
the amount of head allocated to the turbine for electricity generation and
the amount of head pressure functioning to inject water flow back into the
aquifer.
The governing equation describing hydraulic and water flow parameter
interactions is the corollary in groundwater hydraulics to the thermal con-
duction problem. The general form of the groundwater equation for water
flow in an aquifer
8
is
S
T
∂
∂
h
t
1
∂
∂
∂
∂
h
r
⋅
= ⋅
r
⋅
(4.3)
r
r
where S = storage coefficient, T = transmissivity [ft
2
/min] (m
2
/s), h = hydrau-
lic head [ft] ([m]), drawdown = h
initial
- h [ft] ([m]), and r = radius from well
[ft] ([m]).
This equation applies to confined aquifers. However, the drawdown or
head calculated for a confined aquifer using this equation can be correlated
to the height of an injection mound operating in an unconfined aquifer. If
the assumption that the pumping occurs over a long time is adopted, the
Cooper-Jacob approximation to the Theis equation, expressed in terms of
drawdown over time, can be used:
2 3
4
.
⋅
Q
T
2 25
2
.
T t
r S
⋅
⋅
drawdown
=
⋅
log
(4.4)
⋅
π
⋅
⋅
where Q = water flow [ft
3
/min] [m
3
/s]. With the goal of estimating the height
of the mound of injection (negative drawdown), the following assumptions
are made:
Q = -133.7 ft
3
/min (-0.0631 m
3
/s)
S = 0.1 (unconfined aquifer) or 0.0001 (confined aquifer)
T = 2 ft
2
/min (0.00308 m
2
/s)
r = 1 ft (0.305 m)
t = 6 hours = 360 min
k
T
= T ÷ aquifer thickness (ft/min or cm/s)
