Environmental Engineering Reference
In-Depth Information
The volume of groundwater released from or taken into
storage per unit surface area of aquifer per unit head
decrease or increase is
or contour of measuring points that have equal head, or
potential. These lines depict equal head or groundwater pres-
sure and are called equipotential lines, similar to the contour
lines on topographic maps to depict elevation or the lines that
depict atmospheric pressures on weather maps.
L
2
1-ft head change
S
¼
volume of water
=
ð
Þ
(4.11)
To estimate the amount of groundwater potentially
removed from storage, the storage coefficient,
S
c
,is
multiplied by the thickness of the aquifer, or
4.6.1 Equipotential Lines
The groundwater levels in a minimum of three wells
should be measured in order to depict a three-dimensional
groundwater-level surface. In general, the well locations are
marked on a map, and the groundwater-level measurement
of each well is listed with respect to a common datum for all
wells. Lines can then be drawn, manually or by software, to
connect the wells of equal groundwater potential and create
an equipotential map.
A useful property of equipotential line maps is that they
not only depict the contour of equal pressures in an aquifer
but can indicate the direction of groundwater flow. This is
because the groundwater-flow direction will cross equipo-
tential lines at a right angle because groundwater follows the
steepest hydraulic gradient along a path of least resistance.
The direction of groundwater flow is not always constant
over time, because groundwater potentials change in
response to changes in recharge and discharge.
S
¼
S
c
b
(4.12)
The storage coefficient in confined aquifers ranges from
10
5
to 10
3
and for unconfined aquifers is the specific yield
and ranges from 0.1 to 0.3.
4.5.3 Heterogeneity
Hydraulic conductivity can vary in an aquifer in the vertical
and horizontal directions and gives rise to the conditions of
aquifer heterogeneity. These differences in hydraulic con-
ductivity reflect the absolute differences in consolidated or
unconsolidated rock or sediments through which groundwa-
ter moves. Also, heterogeneity is a reflection of the deposi-
tional characteristic of the sediments, for example the
depositional trend of a meandering river where coarse
gravels and sands fine upward to silts and clays.
Aquifer heterogeneity is an important condition that can
be evaluated by using several approaches. One approach is
called hydraulic tomography (Yeh and Liu 2000). Whereas
conventional aquifer tests produce a non-unique average of
aquifer properties over space and time, hydraulic tomogra-
phy tests use multiple wells that are discretized vertically by
packers, such that screened intervals remain flowing and are
considerably smaller than the entire well-screen interval.
One of the multiple wells is pumped at the packed depth
interval, and groundwater-level changes are measured over
time. Subsequent pumping tests are done by lowering the
pump to different levels in the well. The data are then
evaluated by a mathematical model.
4.6.2 Flow Net Analysis
The use of equipotential lines to create maps of groundwater-
flow direction is referred to as flow net analysis. Only a few
equipotential lines are necessary to perform such analysis.
By convention, a common contour interval between lines of
equipotential is used, similar to the constant contour interval
used for topographic maps. In practice, the number of wells
usually is limited. Groundwater-flow lines of a similar inter-
val are then drawn at right angles to the equipotential lines.
The volume of groundwater can now be estimated from such
a map, because two adjacent lines of groundwater flow form
a flow tube and this prescribes a cross-sectional area. This is
yet another extension of Darcy's Law: the product of aquifer
thickness,
b
, and width,
w
, between adjacent equipotential
lines can be substituted into the
A
of
Q
¼
KiA
to estimate
4.6
Groundwater Flow
the discharge of groundwater.
So far we have looked at the flow of groundwater through
porous media from the perspective of one or two measuring
points only. In a laboratory experiment like Darcy's original
column tests, two measuring points were needed to determine
the head gradient that caused water to flow. If we place a
number of such measuring points in Darcy's column, it
becomes possible to generate a three-dimensional surface
4.7
Groundwater Recharge and Discharge
Areas
The strength of flow net analysis is that a few measurements
of head in an unconfined or confined aquifer can reveal
much information about groundwater-flow direction and
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