Page 265 - Air and Gas Drilling Manual

6-10 Air and Gas Drilling Manual
D
− ) V
( D
h
p
=
N
ν
R
where D h D p is the hydraulic diameter for the annulus (ft), (6-27)
V is the velocity (ft/sec),
2
ν is the kinematic viscosity of the drilling fluid (ft /sec).
There are three flow conditions that can exist in the annulus. These are laminar,
transitional, and turbulent flow conditions [1].
The empirical expression for the Fanning friction factor for laminar flow
conditions is
f = 64 (6-28)
N R
This equation can be solved directly once the Reynolds number is known. In
general, Equation 6-28 is valid for values for Reynolds numbers from 0 to 2,000.
The empirical expression for the Fanning friction factor for transitional flow
conditions is known as the Colebrook equation. The Fanning friction factor cannot
be determined directly and must be solved by trial and error. This empirical
expression is
   
  e  
1 =− 2 log    D − D p  + 251   (6-29)
.
h
f  37 . N R f 
 
   
where e is the absolute roughness of the annulus surface (ft). Note the logarithm in
the above equation is to the base ten. In general, Equation 6-29 is valid for values
of Reynolds numbers from 2,000 to 4,000.
The empirical expression for the Fanning friction factor for turbulent flow
conditions is known as the von Karman equation. This empirical expression is
  2
 
 1 
f =   (6-30)
  D − D  
p
h

+ 1 14

 2 log. 


e
 
Note the logarithm in the above equation is to the base ten. In general, Equation 6-
30 is valid for values of Reynolds numbers greater than 4,000.
For follow-on calculations for the flow in the annulus the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the outside surfaces of the drill