Page 307 - Air and Gas Drilling Manual

7-16 Air and Gas Drilling Manual


2



 


 
  T


1 + f     P P g   T av g    Q g      dh (7-45)

π
 2gD i  D 2  
  4 i  
     


where
˙ w = ˙ w + ˙ w
t g s
The exit pressure in reverse circulation air (or gas) drilling operations is atmospheric
pressure, P at, at the top of the inside of the drill string. Separating variables in
Equation 7-45 yields
∫ P ai dP = ∫ H dh (7-46)
()
P at BP 0
i
where
     P   T   2 
g
       av  Q  
 w ˙     P   T  g   

g
BP() =  t   1 + f   
i π
  P   T av    2 gD  D 2  
g
i
     Q g    4 i  
   P   T          
g

Using Equations 7-5, 7-6 or 7-10, 7-7 and 7-12, Equation 7-46 can be rearranged to
give
∫ P ai P ( PdP = a i ∫ H dh (7-47)
2
P at 2 + b T av) T av 0
i
where
w  
 S    ˙ s
a = 1 +    (7-48)
i
˙
 R     w  
g