Page 277 - Air and Gas Drilling Manual

6-22 Air and Gas Drilling Manual
The empirical von Karman relationship for determining the approximate
Fanning friction factor for the inside of the drill string is
  2
 
f =  1  (6-73)
  D  
i
+ 1 14
 2 log. 

e 
 
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 6-72 together with Equations 6-67, 6-68 and 6-73 can be used in
sequential calculation steps starting at the bottom of the inside of the drill string and
continuing for each subsequent change in cross-sectional area in the drill string until
the surface injection pressure is determined.
6.4 Aerated Fluid Drilling Model
Aerated fluid drilling governing equations are very little changed from the direct
circulation general derivation given in Section 6.2. The gases used in aerated fluid
drilling are usually either air, or natural gas, or nitrogen (air stripped of oxygen).
The fluids used are usually drilling mud, or diesel oil, or formation oil.
The flow condition in the annulus is three phase flow (gas, fluid, and solids).
The exit pressure in aerated fluid drilling operations is the atmospheric pressure, P at,
at the exit at the top of the annulus. Equation 6-26 becomes
∫ P bh dP = ∫ H dh (6-74)
P
a
P at B () 0
where
 
 
 w ˙ 
B () =  t 
P
a
  P   T av  
g
     Q + Q m 
g
   P   T   
g
   2 
    P g   T av Q + Q  
    P     g m  
  T

1 + f  π g   

 2 ( h − )  ( D 2 − )  
2
gD
D
D
p
  4 h p  
      
