Page 137 - A Practical Companion to Reservoir Stimulation

PRACTICAL COMPANION TO RESERVOIR STIMULATION

EXAMPLE 1-5
If Fco = 1, then the 45" line would intersect that curve at
Comparison of Propped and tD,r = 0.02, and therefore,
Acid Fracture Performance

Using Fig. 18-19 and the definitions of dimensionless time (I- 1 9)
and cumulative production, show that a 45" straight line
drawn through any point on the curves in Fig. 18-19 will In both cases, if a more conductive fracture (for a given xf)
intersect all others at points representing equal real time and or a longer fracture (for a given FcD) can be generated, then a
equal real cumulative production. propped fracture would be more attractive than the acid
fracture,,(In Fig. 18-19, the points would be above the 45"
Solution (Ref. Section 18-6) line.) For example, if FcD = 1 and xf= 1000, then
The slope on the log-log plot of Fig. 18- 19 between any two
points is

log QDI - 1% QD~ = m(lOgfo,/i - log fg1f2). (1-15)
From Fig. 18-19, QD = 3 x
Setting m = 1 (45") and removing the log signs, Therefore, when comparing this with the acid fracture and

QDI t~ifl remembering that
- (1-16)
Q02 t~rf2 4,
QD - (1-21)
After subqtitution of the definitions, the fracture lengths x.; '
cancel out for a given reservoir,
then
(Npl) - (tl) (10002)
-~
-
-
-
(4,') (td' (1-17) NP2 - (QD)~(X?)~ (3 X = 2.5, (1-22)
&I (QD)I (x,;)I (0.12) (1002)
and if tl = t2, then Npl = NI+
The implications of the above are that a 45" line through meaning that this propped fracture would produce 2.5 times
any curve describing the performance of an acid fracture will the cumulative recovery of the acid fracture within the same
intercept a number of curves of various FcD values. Points time.
above this 45" line would mean higher N,, (for the same
time), whereas points below would mean lower N,,.
For example, suppose that tnrf = 0.1 and 0' = 7000 psi.
Then Qn = 0.12. If FcD = 5, the corresponding tnlf = 0.15
and QD = 0.22. If xf,, = 100 ft, then
x,,~ = / (0.1) (100)' = 82ft (I- 18)
, , ,

would be the required propped length to produce the same
cumulative production (if Fcn = 5 were possible).

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