Page 77 - Handbook Of Multiphase Flow Assurance

72 4. Hydraulic and thermal analysis

If the Reynolds number is below 2100, the laminar Moody friction factor as a function of
Reynolds number is
f Moody = 64/Re
f Fanning = f Moody / 4
Many different friction factor correlations are available for turbulent flow but the simplest
of these is the Blasius (1913) correlation.

.
f = 0 3164Re −025
.
Moody
For turbulent flow it is convenient to determine friction factor f from a non-recursive for-
mula (Swamee and Jain, 1976)
−2
f Fanning = f Moody /4 = ( 4 ×log ( /.37ε ( D) + .574 /Re . 09 )) .
−6
ε = pipe wall roughness [m]; typical aged carbon steel roughness is 45 μm or 45 × 10 m. Re
is Reynolds number.
For hydraulically smooth pipes f Fanning = 0.0791/Re 0.25 .
For flow analysis it is helpful to estimate shear of fluid acting either on a solid or on pipe
wall. We summarize several shear correlations.

[
(
Pa /
Shear_rateγ 1/ s] = shear_stressτ [ ] dynamic_viscosity µ[ Pas] ffor Newtonian fluids).
Shear rate for laminar flow γ Laminar = 8 v Ave /D.
Average flow velocity v Ave = Q/A.
Shear stress exerted by flowing fluid on pipe wall τ wall = D ΔP/(4L)

τ = 8µ V / D
Laminaratwall Ave
__
τ = ρ Vf /2
2
__
Turbulentatwall Fanning
τ = DP ( L)
∆ /4
w wall
For single-phase flow we can illustrate that laminar pressure drop is inversely propor-
tional to pipe diameter to the power 4, whereas turbulent flow is inversely proportional to
diameter to the power 5.
4
2
/
∆P Laminar = 32µ Lv Ave / D ( ) = 128 µ LQ (π D )
2
5
L v
/ 2
∆P Turbulent = 4 ρ Ave 2 f Faanning ( D) = 32ρ LQf /(π 2 D )
Other equations such as Weymouth or Panhandle may also be used to calculate pressure
drop in gas flow. Panhandle B formula (1956) is for gas flow with medium Reynolds number
values.
P − )
[
/
. 253
Q MMscf d] = 0 .028 ED ( ( 1 2 P 2 2 /( S . 0 961 ZTL)) . 051