Page 49 - A Practical Companion to Reservoir Stimulation

PRACTICAL COMPANION TO RESERVOIR STIMULATION

EXAMPLE C-7
With a 2000-psi drawdown ( p,,f = 4500 psi) experienced
Calculation of Stress-Induced Proppant-Pack near the wellbore, the instantaneous effective stress will
Permeability Impairment: Long-Term Stresses
increase by (0.7) (2000) = 1400 (o’= 3700 psi); with a 4000-
psi drawdown (pH., = 2500 psi), the effective stress will in-
Use the data in Fig. 5-27 for 20140 sand to calculate the stress- crease by (0.7) (4000) = 2800 (0 5100 psi) and result in
=
induced permeability reduction for 2000 and 4000 psi draw- permeability values equal to 200,000 and 150,000 md,
down. Will the stress on the proppant pack increase or de- respectively.
crease with time? Assume that the reservoir is 10,000 ft In the long term, the reservoir pressure will decline. As a
deep with an average density equal to 165 lb/ft3, the result, the absolute minimum horizontal stress will decrease
Poisson’s ratio is 0.25, the initial reservoir pressure is 6500 (e.g., fdr p = 5000 psi) as given by
psi, and the poroelastic constant is 0.7.
- 4
Solution (Ref. Section 5-9) 0 k Ill I ?I - 0.25 (165) (l0,OOO) - (0.7) (~ooo)]
The effective minimum horizontal stress can be‘estimated 0.75 144
from Eq. 2-4 1 : + (0.7) (5000) = 6152 psi. (C-3 1)

0.25 ( 165) ( 10,000) With the 4500-psi bottomhole pressure,
CT’H,mitr = ~ [ - (0.7) (6500)]
0.75 144 c ~ H , ~ ~ ~ ; ~ ~(0.7) (4500) = 3000 psi; (C-32)
6152
=
-
= 2303 psi. (C-30) and with the 2500-psi bottomhole pressure,
This is the stress that the proppant will experience without = 6152 - (0.7) (2500) = 4400 psi. (c-33)
drawdown. Thus, the proppant-pack permeability will be IT’H~~,~;~~
about 300,000 md (from Fig. 5-27). Thus, the effective stress on the proppant decreases with
time.

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