Page 275 - Air and Gas Drilling Manual

6-20 Air and Gas Drilling Manual
k
w 


P = P      ˙ A g n   2 + 1    k  −1 (6-63)
ai bh   k  
2 g   P γ bh 
bh
  k − 1  
 
The flow in the inside of the drill string is single phase flow (air or other gases).
Setting Q m = 0 in Equation (6-43) yields
 
 
 w ˙ g 
dP =  
  P   T av  
g
     Q g 
   P   T   
g
   2 
    P g   T av  
    P     Q g  
  T


1 − f  π g   dh (6-64)

 2gD i  D 2  
  4 i  
     


Separating variables in Equation 6-64 yields
∫ P ai dP = ∫ H dh (6-65)
()
P in BP 0
i
where
     P   T   2 
g
       av  Q  
 w ˙     P   T  g   

g
BP() =  g   1 − f   
i π
  P   T av    2 gD  D 2  
g
i
     Q g    4 i  
   P   T          
g

Using Equations 6-5, 6-6 or 6-10, and 6-7, Equation 6-65 can be rearranged to give