Page 271 - Air and Gas Drilling Manual

6-16 Air and Gas Drilling Manual
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1
37 .
f =− 2 log         D e i    + N 251 f      (6-47)
R
 
   
where e is the absolute roughness of the inside surface of the drill string (ft). In
general, Equation 6-47 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 =   (6-48)
D 

 2 log. 
i
+ 1 14
   e   
 
In general, Equation 6-48 is valid for values of Reynolds numbers greater than 4,000.
For follow-on calculations for flow in the drill string the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the inside surfaces of the drill
pipe and drill collars.
Equation 6-45 together with Equations 6-46 through 6-48 can be used in
sequential integration steps starting at the bottom of the inside of the drill string
(with the known pressure above the drill bit inside the drill string) and continuing
for each subsequent change in cross-sectional area inside the drill string until the
injection pressure is determined. These sequential calculation steps require trial and
error solutions. The trial and error process requires the selection of the upper limit
of the pressure in each integral on the right side of Equation 6-44. This upper limit
pressure selection must give a right side integral solution that is equal to the left
side integral solution.
6.3 Air and Gas Drilling Model
Air (or gas) drilling is a special case of the theory derived in Section 6.2 above.
The governing equations for air (or gas) drilling operations can be obtained by
setting Q m = 0 in the equations derived in Section 6.2.
There is two phase flow in the annulus (gas and rock cuttings). Setting Q m = 0
in Equation 6-25 yields

 
 
 w ˙ 
dP =  t 
  P   T av  
g
     Q g 
   P   T   
g