STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

Drilling Mud Hydraulics 837
In the above equation, the critical flow velocity is in ft/min and all other
quantities are specified above.
In turbulent flow the pressure losses, Ap (psi), can be calculated from the
Fanning equation [60].
QLV
Ap = -
25.8d
(4-112)
where f = Fanning factor
L = length of pipe, ft
The friction factor depends on the Reynolds number and the surface conditions
of the pipe. There are numerous charts and equations for determining
the relationship between the friction factor and Reynolds number. The friction
factor can be calculated by [63]
f = 0.046 Re-0.2 (4-113)
Substituting Equation 4-91 (4-92), and 4-113 into Equation 4-112 yields [63]
Pipe flow
7.7 x 10-5708q1.8,43
Ap =
d4.8
(4-114)
Annular flow
7.7 x 10-~ yo.8p;2q1.8L
Ap = (d,- d,)’(d, + d2)1.8
(4-115)
Example
The wellbore, drill string and drilling fluid data from the previous example
are used. Casing depth is 4,000 ft. Assuming a drill pipe length of 5,000 ft and
a drill collar length of 500 ft, find the friction pressure losses.
Flow inside the drill pipe
The critical flow velocity is
vc =[
1/(2-0.729)
(3.878~ 1o4)(0.433) 2.4(2)(0.7.29) + 1
10
= 343.54 ft/min = 5.73 ft/s
10.729/(2-0.729)
Since v < vc, the flow is laminar, and Equation 4-107 is chosen to calculate
the pressure loss pl.