Environmental Engineering Reference
In-Depth Information
Several factors can complicate the use of
temperature-depth profiles to estimate drain-
age rates. Horizontal water movement within
the saturated zone can affect measured pro-
files; Lu and Ge (
1996
) extended the Bredehoeft
and Papadopulos (
1965
) analytical solution to
account for horizontal groundwater flow. Heat-
transport processes other than conduction and
advection may be important within the unsat-
urated zone. Heat flow due to evaporation, con-
densation, vapor-phase transport, and advective
soil-gas movement are commonly assumed to
be negligible in unsaturated zones of humid
and semihumid settings. However, these proc-
esses can account for a substantial portion of
total heat flow within unsaturated zones of arid
regions (Scanlon and Milly,
1994
; Thorstenson
et al
.,
1998
; Walvoord
et al
.,
2002a
,
b
; Constantz
et al
.,
2003
). Analyses of temperature-depth pro-
files in arid regions generally employ sophisti-
cated numerical models that can account for
these additional processes.
0
(a)
50
100
150
200
250
16
18
20
22
Temperature (°C)
D
= 50 mm/yr
D
= 10 mm/yr
D
= 1 mm/yr
Measured temperature
Example: Frenchman Flat, Nevada
Frenchman Flat is a sediment-filled basin within
the Basin and Range Province in southern
Nevada. Temperature sensors were emplaced
at depths of 30.5, 61, 91.5, 152.5, and 213.5 m
in borehole PW-1 that extended from land sur-
face down to the water table at a depth of about
240 m (Constantz
et al
.,
2003
). The borehole was
then sealed with grout, and temperatures were
recorded over time. Measured temperatures
increased in a fairly linear fashion with depth
(
Figure 8.4a
) at a rate of about 0.012°C/m.
The Bredehoeft and Papadopulos (
1965
) solu-
tion was used to calculate temperature at any
depth,
T
(
z
):
0
(b)
0.2
0.4
0.6
1.2
0.6
0.8
1
0
0.05
0.1
0.15
0.2
z
/
L
-(
T
(
z
)-
T
0
)/(
T
L
-
T
0
)
Tz
( )
=+−
0
T
(
T
T f B z L
) ( , / )
(8.3)
Figure 8.4
(a) Measured temperatures and those predicted
from Equation (
8.3
) for a steady vertical drainage rate (
D
)
of 1, 10, and 50 mm/yr for the unsaturated zone underlying
Frenchman Flat, NV (Constantz
et al
.,
2003
). (b) The same
measured temperatures (triangles) and those predicted from
Equation (
8.3
) for values of
B
of 0.6 and 1.2 plotted in the
dimensionless form suggested by Stallman (
1967
).
L
0
f Bz L
( ,
/
)
=−
(1
e
Bz/L
) / (1
−
e )
B
(8.4)
B vC L K
=
zw
/
(8.5)
T
where
z
, depth, is equal to 0 at the top of the
measurement interval and increases down-
ward,
T
0
is temperature at the top of the inter-
val,
L
is the thickness of the interval (183 m for
this example),
T
L
is temperature at the bottom
of the interval, and
v
z
is vertical velocity. To
apply the method, type-curve matching is used.
Data are plotted in dimensionless form with
z/L
on the y axis and (
T
(
z
) -
T
0
)/(
T
L
-
T
0
) on the x axis.
Type curves given in Figure 2 of Bredehoeft and
