Page 24 - A Practical Companion to Reservoir Stimulation

RESERVOIR AND WELL CONSIDERATIONS

EXAMPLE A-6 EX AMPLE A-7
Stimulation Treatment Choice: Productivity Index Ratios for
Fracturing vs. Acidizing Damaged and Undamaged Wells

Using the data given in Example A-5 for a 40-acre-spacing Calculate the PI ratios (compared to zero skin) at steady state
well, predict production rates at steady state for a range of for a well where the penetration of damage ranges up to 10 ft
permeabilities and for skin effects equal to 0 and 10. Comment and the permeability impairment ranges up to 95% (Wk, = 20).
on whether the well for these cases is a candidate for fracturing Assume that r, = 745 ft (40 acres) and r,, = 0.328-ft (7%-in.)
or acidizing. well radius [ln(re/r,,) = 7.731.

Solution (Ref. Section 1-3) Solution (Ref. Sections 1-3,1-3.1)
Equation A- 16 can be reduced to The productivity index ratio between the ideal case (s = 0) and
a real case (s # 0) can be obtained from Eq. 1-69:
920 k
= 7.73s. (A- 17)
(A-18)
If permeabilities range between 10 md and 0.01 md, then
the rates given in Table A-9 can be expected at steady state. Furthermore, the skin effect, s, is given in terms of k, and r, by
If the permeability were 10 md, then elimination of the Eq. 1-77.
skin effect (if it were possible) from 10 to 0 would result in a As an example, if rr = 3 ft (the damaged ring is then
production rate increase from 519 STB/d to 1190 STB/d, a 3 ft - rM = 2.672 ft) and Wk, = 10, then from Eq. 1-77,
substantial benefit. Thus, matrix stimulation would be indi-
cated, whereas hydraulic fracturing would be subjected to net 2
J
present value considerations (Ref. Chapter 8). s = (10 - 1)ln- 0.328 G 20, (A-19)
If the permeability were 0.01 md, then elimination of the
skin effect from 10 to 0 would result in an increase in the and
production rate from 0.5 STB/d to 1.2 STB/d, an unattractive
prospect. In general, reservoirs with permeabilities of 1 md or
less are usually candidates for hydraulic fracturing, while
those with permeabilities of 10 md and above are candidates At Wk, = 50, the skin effect is 108 and the PI ratio is 15.
for matrix stimulation. Reservoirs with permeabilities be- Figure A-9 is a graph summarizing the solution to this
tween 1 and 10 md require intensive study and sound design example.
practices for the appropriate choice of stimulation treatments.
The logarithmic relationship of the damage radius is evi-
dent. Increasing the damage radius from l ft to 3 ft (with
wk,= 10) results in a ratio of PIS equal to 1.32, whereas
s= 10 S=O increasing the damage from 1 ft to 10 ft results in a ratio equal
k (md) q (STBld) q (STBld)
to only 2.18.
10 51 9 1190 On the other hand, given a damage radius, the ratio of the
1 52 119 PI is almost directly proportional to the permeability impair-
ment.
0.1 5 12
0.01 0.5 1.2

A-13