Page 228 - Introduction to Petroleum Engineering

SINGLE‐PHASE FLOW IN PIPE 215
a kinetic energy term

p v
v , (11.21)
L KE L

and a friction term
p v 2
f (11.22)
L fric 2 D
that depends on a dimensionless friction factor f. If the flow velocity of the fluid
does not change appreciably in the pipe, the kinetic energy term can be neglected
and the pressure gradient equation reduces to the simpler form

p v 2
gsin f (11.23)
L 2 D
Equation 11.23 is valid for single‐phase incompressible fluid flow. If we assume the
right‐hand side is constant over the length L of the pipe, the pressure change from
one end of the pipe to the other is

v 2
p gLsin f L (11.24)
2 D
The friction factor f depends on flow regime. For laminar flow with Reynolds
number N Re 2000, the friction factor is inversely proportional to Reynolds
number:

64
f (11.25)
N Re
For turbulent flow, the friction factor depends on Reynolds number and pipe rough-
ness. Pipe roughness can be quantified in terms of relative roughness ξ which is a
fraction defined relative to the inner diameter of the pipe as

/
dD 1 (11.26)
p
in which d is the distance of a protrusion from the pipe wall. Typical values of pipe
p
relative roughness ξ range from 0.0001 (smooth) to 0.05 (rough). The length of pro-
trusions inside the pipe may change during the period that the pipe is in service. For
example, buildup of scale or pipe wall corrosion can change the relative roughness
of the pipe. One correlation for friction factor for turbulent flow is (Beggs, 1991,
page 61)

1 21 25
.
.
1142log 09 . (11.27)
f N Re