Geoscience Reference
In-Depth Information
The consolidation process in the aquitard is described in terms of the potential
head
by
2
2
c
v
(6.18a)
t
z
Here
c
v
is the consolidation coefficient of the aquitard. The porous flow in the
aquifer is described in terms of the potential head
h
by
2
h
h
(
S
q
)
/
kD
(6.18b)
0
2
x
t
Here,
S
is the storativity,
k
the permeability and
D
the height of the aquifer. The
actual leakage from the aquitard at the interface
z
= 0
is expressed by
q
0
.
Compatibility of the processes at the interface is guaranteed by
h =
and
q
k
'
at
z = 0
(6.18c)
0
z
Using Laplace Transform with the Laplace transform coordinate
s
, (6.18a)
becomes
2
2
c
v
s
and
h
at z = 0,
h
at
z = d
0
(6.19)
z
which provides
sinh((
d
z
)
s
/
c
)
v
h
,
sinh(
d
s
/
c
)
v
/
,
q
k
'
k
'
s
/
c
coth(
d
s
/
c
)
(6.20)
-
.
*
+
0
v
v
z
z
0
0
Inserting this in the Laplace transform of (6.18b) yields
2
h
2
(
sS
h
k
'
s
/
c
coth(
d
s
/
c
))
/
kD
h
/
with
(6.21)
v
v
s
2
x
0
.
/
,
sSd
s
s
d
coth(
d
)
-
.
*
+
s
k
'
c
c
-
*
v
v
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