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10
4
10
2
10
0
10
−2
10
−4
10
−6
10
−8
10
−10
10
−2
10
−1
10
0
10
1
10
2
10
3
FIGURE H.1
Injection of fluid at a constant rate at the center of a disk-shaped reservoir. Plot of the
dimensionless pore pressure
Δρ
/
ρ
*
with respect to the dimensionless time t =
t/t
*
(equal to
V/V
*
) for three
values of the dimensionless radius
Q = r/R
. This plot indicates that the pressure response is similar to the
response of an unbounded reservoir as long as
t
≤
0.2 and that the pressure is approximately uniform
and proportional to the volume of fluid injected when
t
≥
10
. The dashed-line curves correspond to the
solution
F
for an unbounded reservoir.
ρ
*
= μ
Q
o
/kL, t
*
= L
2
/c
with
L
denoting a relevant length scale of the reservoir. Also
x
refers to the position of the
field point, and
x
i
to the position of the source
i
. At large time, the induced pore pressure
is approximately given by
ρ
≅
V/(SV
reservoir
)
where
V
is the total volume of fluid injected (
V = nQ
o
t)
and
V
reservoir
is the volume of the
reservoir.
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