Page 309 - Air and Gas Drilling Manual

7-18 Air and Gas Drilling Manual
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 7-53 together with Equations 7-48, 7-49 and 7-54 can be used in
sequential calculation steps starting at the top of the inside of the drill string and
continuing for each subsequent change in cross-sectional area in the inside of the
drill string until the pressure above the drill bit inside of the drill string is
determined.
There is a single water course in reverse circulation drill bits. Using Equation
7-53 the pressure at the bottom of the inside of the drill string, P ai, is obtained. The
pressure at the bottom of the annulus, P bh, can be obtained by trial and error using
the expression
 2 k+ 1  2
w 
 k    P  k  P  k   ˙ g
ai
ai
2g   P γ bh    −    =   (7-55)
bh
 k − 1     P   P     A bi 
bh
bh
Note that Equation 7-55 does not account for friction flow loss through the single
drill bit orifice.
The above equations will generally yield results that show that for most practical
parameters the annulus bottomhole pressure, P bh, differs very little from the pressure
above the drill bit inside the drill string, P ai. Therefore, it can usually be assumed
that
P bh ≈ P ai (7-56)
The flow in the annulus is single phase flow (air or gas). Setting Q m = 0 in
Equations 7-39 yields
 
 
 w ˙ 
dP =  g 
  P   T av  
g
     Q g 
   P   T   
g
   2 
    P g   T av Q  
    P     g  
  T


1 − f  π g   dh (7-57)

(
 2gD h − D )  ( D 2 − D )  
2
p
  4 h p  
     


Separating variables in Equation 7-57 yields