Page 45 - A Practical Companion to Reservoir Stimulation

PRACTICAL COMPANION TO RESERVOIR STIMULATION

EXAMPLE C-4
and in oilfield units,
Friction Pressure Drop Calculation
5.2 x IO-'ffpLv 2
Calculate the pressure drop per 1000 ft of vertical tubing, APf = (C- 16)
with a 3.5-in. outside diameter, for a polymer solution at d
100°F. The rheological properties, n' and K;;,,., are 0.39 and where the Ap, is the pressure in pounds per square inch.
4.5 x lo-* Ibf-sec"'/ft*, respectively. Perform this calculation If NRe is greater than 2100, the flow is turbulent and the
for a range of injection rates up to 100 BPM. The fluid density Fanning friction factor is given by
is 60 Ib/ft3. Plot the results on log-log paper.
(C-17)
Solution
(Ref. Section 5-2.3 and a fluid mechanics textbook)
To calculate the friction pressure drop for any type flow, the where
Reynold's numbers must first be calculated. For a power law log n' + 2.5
fluid this is given by c= 50 (C- 18)

and

1.4 - log n'
b= (C- 19)
7
While Eq. C-10 is for consistent units, for oilfield units it
becomes The calculation of the pressure drop is then given by
Eq. C-16.
A sample calculation is performed with q = 20 BPM.
0.249pv""'d"'
NRe = From Eq. C- 13 (and remembering that for OD = 3.5 in. the
961l'K ( ; - ' (C-11) ID z 3 in.), the velocity is
1

'
"
)
I
20
where p is in Ib/ft', v is in ft/sec, d is in in., and K' is in v = 17.17 - = 3.81 ft/~e~. (C-20)
lbf-sec"'/ft*. 3=
The velocity is given by the obvious: From Eq. C- 1 I, the Reynold's number is then calculated:
(C- 12) (0.249) (60) (38.1)1'61(3"'39)
NRe =
(96°,39) (4.5 x lo-*) ( 1.39)0.39
and in oilfield units,
= 2.6 x lo4. (C-21)
4
v = 17.17-, (C- 13) Therefore, the flow is turbulent.
d2
From Eqs. C- 17, C- 18 and C- 19, the friction factor is equal
where q is barrels per minute. to 0.003, and from Eq. C- 16,
If the NRe is less than 2100, laminar flow is in effect, and in
such case the Fanning friction factor is (5.2 x (0.003) (60) (1000) (38.1)'
APf =
16 3
(C- 14)
fr. = -> = 453 psi. (C-22)
NRe
leading to the classic pressure drop resulting from friction Figure C-3 is a plot of the expected pressure drops. Clearly,
the laminar and turbulent flow regimes are indicated by the
2fr. PLVL sharp bend in the results. These values are likely to be
Ap+ = (C- 15)
d significantly lower in an actual operation because of the
liberal use of friction reducing agents.

C- 6