Page 92 - A Practical Companion to Reservoir Stimulation

F. Evaluation of lkeatments and Postfracture Performance

EXAMPLE F-1 EXAMPLE F-2

Calculation of Folds of Productivity Index Increase Calculation of Effective Wellbore Radius
from a Fractured Well and Fracture (Equivalent) Skin Effect

Assume a well with the variables shown in Table F- 1. Calcu- Assuming that a 1000-ft-long fracture in a reservoir with 1
late the folds of productivity index increase for three fracture md permeability has a dimensioned conductivity, k,w, equal
lengths: 500, 1000 and 1500 ft. to 2000 md-ft, calculate the effective wellbore radius and the
skin effect. The actual wellbore radius is 0.328 ft.
Solution (Ref. Section 11-2)
From the McGuire and Sikora solution (Fig. 11 -I), the group Solution (Ref. Section 11-2)
of variables in the abscissa must be calculated. Note that w The relative capacity parameter, a, can be calculated from
must be in inches and A in acres. Thus, Eq. 11-1:

- wkJe = (0.2)( 180,000) a= (3.14)( 1)( 1000) = 0.785. (F-4)
k 0.1 (2) (2000)
Then, from Fig. 1 1-4, the dimensionless effective wellbore
radius is 0.3.
From Eq. 11-3,
Since A = I60 acres, then
[ (160)(43,560)]2 I ri. = (0.3)( 1000) = 300. (F-5)

r, = = 1490ft. Since r:. = r,,,e-’, then
3.14
r,+, 0.328
For the three fracture lengths, the penetration ratios Ur, are s = In; = In- = -6.8.
equal to 0.33,0.67 and I, respectively. Therefore, the ordinate rw 300
values are 6, 10 and 12, respectively. This skin effect is the equivalent skin effect as a result of
The folds of increase J/J<, can then be obtained (for ex- the presence of the fracture of the given length and conductiv-
ample, for the 500-ft fracture) from ity. Essentially, at pseudoradial flow, this is the skin effect
(and effective wellbore radius) that the reservoir will “see.”

For the 1000-ft and 1500-ft lengths, the folds of increase
are then 10.8 and 13, respectively.

w = 0.2 in.
I A = 160acres I
I kf = 180,000 md I
I r, = 0.328 ft I

~~ ~~~
k = 0.1 md
Table F-1-Well and reservoir variables for Example F-1.

F- 1