Page 278 - Air and Gas Drilling Manual

Chapter 6: Direct Circulation Models 6-23
The Fanning friction factor f given in the above equation is determined by the
standard fluid mechanics empirical expressions relating the friction factor to the
Reynolds number, diameter (or hydraulic diameter), and absolute pipe roughness. In
general, the values for Reynolds number, diameter, and absolute pipe roughness are
known. The classic expression for the Reynolds number is
( D h − ) V
D
p
N = (6-75)
R
ν
Three flow conditions that can exist in the annulus. These are laminar,
transitional, and turbulent flow conditions.
The empirical expression for the Fanning friction factor for laminar flow
conditions is
f = 64 (6-76)
N R
This equation can be solved directly once the Reynolds number is known. In
general, Equation 6-76 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. This equation cannot be solved
directly and must be solved by trial and error. This empirical expression is
   
  e  
.
1   D − D p  251 
h
=− 2 log  +  (6-77)
f  37 . N R f 
 
   
In general, Equation 6-77 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 =   (6-78)
  D − D  
h
p


+ 1 14
 2 log. 


e
 
In general, Equation 6-78 is valid for values of Reynolds numbers greater than 4,000.
For follow-on calculations for 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