Depletion modeling of liquid dominated geothermal reservoirs Page: 49 of 147
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where h is the drawdown in meters, and the subscript 2 referres to the liquid
zone deeper in the reservoir. These equations are similar to the unconfined sys-
tem with the influx term replaced by w2; the rate from the two phase zone.
Furthermore, it was assumed that the rate from the two phase zone was propor-
tional to the difference in pressure between the two zones:
wl = c (hz - hi) (55)
There are now three equations with three unknowns, Wj, ht, and h2. The draw-
down in the deep zone, h2, is of interest since this is what is monitored in the ob-
servation well. The solution to these equations is:
t
ha(t) = CiWp(t)- CzfWp(t -r)e~T/Kdr (56)
o
where:
p2i42S2
(57a)
Cz — c Cf
z- 1 (pi-4i-51)(p2i4252)
K —--
c pi^4i*^i + Pz^z^z
It is also possible to calculate the drawdown in the two phase zone:
t
hi(t) = C3f Wp(t-T)e~r/KdT
o
where:
Q — _®_
ifi i A i S i) (p 2i4 2 S 2)
The constants in Eq.56 were reported as being:20
C1=1.488xlO-0 m/kg
C2=8.716xl0-n m/kg day
(57b)
(57c)
(58)
(59)
39
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Olsen, G. Depletion modeling of liquid dominated geothermal reservoirs, report, June 1, 1984; California. (https://digital.library.unt.edu/ark:/67531/metadc1087217/m1/49/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.