Page 272 - Air and Gas Drilling Manual



2


  T


av


Q
 



g


 
  T


g
1 + f     P P g Chapter 6: Direct Circulation Models 6-17

  dh
(6-49)
π
 2 ( h − )  ( D 2 − )  
D
gD
2
D
p
  4 h p  
     


where (see Equation 6-13)
˙ w = ˙ w + ˙ w
t g s
The exit pressure in direct circulation air (or gas) drilling operations is atmospheric
pressure, P at, at the top of the annulus. Separating variables in Equation 6-49 yields
∫ P bh dP = ∫ H dh (6-50)
P
a
P at B () 0
where
     P   T   2 
g
       av  Q  
 w ˙      P   T  g   
g
B () =  t   1 + f  π   
h (
P
a
  P   T av    2 gD − D p)  D ( 2 − D p)  
2
g
     Q g    4 h  
   P   T           
g
Using Equations 6-5, 6-6 or 6-10, 6-7 and 6-12, Equation 6-50 can be rearranged to
give
∫ P bh P ( PdP = a a ∫ H dh (6-51)
2
P at 2 + b T av) T av 0
a
where
w  
 S    ˙ s
a = 1 +    (6-52)
a
˙
 R     w  
g