Environmental Engineering Reference
In-Depth Information
Although flow-net analyses have been replaced
by groundwater flow models in most appli-
cations, they nonetheless deserve discus-
sion because they have been widely used in
the past. The technique was first proposed
by Forchheimer (
1930
). A brief description is
given here; details are provided in Cedergren
(
1988
). In the approach, steady flow is assumed
in a two-dimensional section (either vertical
or horizontal). A flow net for a homogeneous,
isotropic system consists of two sets of orthog-
onal lines: flow lines and equipotential lines. A
flow line represents a path over which a water
molecule travels from a recharge zone to a dis-
charge zone. The region between two adjacent
flow lines is termed a streamtube. An equi-
potential line represents a line of equal head or
water level. The two sets of lines are drawn to
form a series of rectangles. The flow through
a rectangle,
Q
, can be written according to
Darcy's law as:
the Hantush method. Hydraulic conductivity
was measured in the field at each piezometer
by using single-hole slug tests. The measured
hydraulic conductivity was assumed to be equal
to the vertical hydraulic conductivity. Sites were
located in sandy and fine-textured bedrock, as
well as below two of the many sloughs that were
present in the study area. Measured values of
K
s
ranged from 3 × 10
-9
m/s for clayey bedrock to
6 × 10
-6
m/s for sands. Vertical gradients ranged
from 0.006 in the sands to 1.2 in the fine-tex-
tured material. Estimates of recharge ranged
from 80 to 730 mm/year, rates considerably
greater than those estimated from the water-
table fluctuation method. The differences were
attributed to natural heterogeneities within
the system and inherent uncertainties in the
methods.
An areal average recharge rate for the study
area was obtained by averaging the water-table
fluctuation method estimates and the Darcy
method estimates and weighting the estimates
on the basis of areal coverage of different hydro-
geolog ic a l set t i ng s. T The average r ec h a r ge rate w a s
estimated to be between 10 and 35 mm/year.
A l o w n e t a n a l y s i s w a s c o n d u c t e d f for t h e a q u i -
fer under the assumption that water-level data
for April 1977 represented steady-state condi-
tions. The potentiometric surface was contoured
at 2 m intervals and a series of flow lines were
drawn perpendicular to the contours, thereby
forming rectangles of approximately equal area.
The flow through each rectangle is described
by Equation (
6.17
). Average calculated recharge
rates were between 10 and 33 mm/year.
Q
=
AK
∆∆
H
/
l
(6.17)
s
where
A
is the cross-sectional area of one of
the rectangles,
K
s
is hydraulic conductivity, and
Δ
H/
Δ
l
is the hydraulic gradient across the rect-
angle. In a simple case of a flow net for a verti-
cal section of aquifer, recharge is inflow to the
uppermost rectangle in a streamtube and is cal-
culated as
Q /A
.
Example: Central North Dakota
Rehm
et al
. (
1982
) conducted a study on recharge
to the Hagel Lignite Bed aquifer in central
North Dakota. Three methods were used for
estimating recharge: the water-table fluctu-
ation method, the Hantush method, and a flow-
net analysis. The 150-km
2
study area contained
175 piezometers and water-table wells. Thirty-
eight observation wells were used to estimate
recharge to the water-table aquifer by the
water-table fluctuation method.
S
y
was deter-
mined from soil cores by using Equation (
6.4
)
with
S
r
assumed to be equal to water content at
a pressure head of -30 kPa. An average value for
S
y
of 0.16 was obtained. Estimates of recharge
were in the range of 1 to 80 mm/year.
Ten groups of nested piezometers were used
to determine vertical hydraulic gradients for
6.4 Time-series analyses
Soil water-budget models have been devel-
oped to relate infiltration patterns to patterns
of recharge and fluctuations in groundwater
levels (e.g. Besbes and de Marsily,
1984
; Morel-
Seytoux,
1984
; Bierkens,
1998
; O'Reilly,
2004
;
Berendrecht
et al
.,
2006
). The approach is to con-
struct a soil-water budget; the calculated excess
drainage from the soil zone is transported to
the water table at a rate determined by a trans-
fer-function model, a Richards equation-based
