Page 36 - A Practical Companion to Reservoir Stimulation

ROCK MECHANICS

EXAMPLE B-6
implies downward migration from the bottom of the reser-
Estimation of Fracture Height Migration
voir.
From Fig. B-3 at 300 psi net pressure, the upward and the
Calculate the fracture height for 300 psi and 500 psi net downward fracture migrations would be 24 ft and 12 ft,
pressure for a formation with the confining stresses and data respectively. For 500 psi net pressure, the upward and the
shown in Table B-2. downward fracture height migrations would be 162 ft and
Solution (Ref. Section 10-2) 48 ft, respectively.
This exercise demonstrates the means to calculate the
Equations 10-3 and 10-4 have the following forms if stresses allowable net pressure for a tolerable fracture height migration.
are in psi, height in ft, density in Ib/ft3 and the critical stress
intensity factor in psi 6 The relevant illustration is Fig.
10-2. I 0, = 4500psi I
0.02 17 I h = 60ft I
Ap = [.. [I - C] I ob = 5100psi I
I K,~ = 1000 psi VK I

I 0, = 5900psi I
p = 55 1m3
+ 0.0069 p (h I, - 0.5h). (B-22)
Table B-2-Confining stresses and data for formation for
0.02 17 Example B-6.
AP = [.[I -

-I ( ) I :

+ 0.515(0, - era) Jhd cos I 20 80 277 370

- 0.0069p(hd - 0.5h). (B-23) I 30 I 90 I 323 I 430

In both Eqs. B-22 and B-23, the inverse cosine must be
entered in degrees.
Table B-3 is a summary of fracture height migration, both 140 433 578
upward (from the base of the reservoir) and downward (from 120 180 473 630
the top of the reservoir), and the corresponding net pressures.
Finally, Fig. B-3 is a graph of net pressure, Ap, for both 150 21 0 492 656
upward and downward fracture height migration. The quan- 200 260 51 4 685
tity Ahu implies migration above the top of the reservoir; Ahd
Table B-3-Net pressure required for upward and
downward fracture height migration for Example B-6.

%-I