Page 311 - Air and Gas Drilling Manual

7-20 Air and Gas Drilling Manual
2
aH
−
2
2
a
b T
P
a
av
bh
=
e
T av
2
2
−
P
b T
a
in
av
Equation 7-64 can be rearranged and a solution obtained for P in. This yields (7-64)
  2 aH   05 .
a
 2 + 2 e  T av 
 P bh b T av  −  1  
a
   
P in =  2 aH  (7-65)
 a 
 e T av 
 
 
The empirical von Karman relationship for determining the approximate
Fanning friction factor for the annulus is
  2
 
 1 
f =   (7-66)
  D − D  
h
p


+ 1 14
 2 log. 


e
 
For follow-on calculations for flow in the annulus the absolute roughness for
commercial pipe, e p = 0.00015 ft, will be used for the outside surfaces of the drill
pipe and drill collars, and inside surface of the casing. For a dual pipe drill string,
the inside surfaces of the annulus in the drill string will also have the absolute
roughness of commercial pipe. For conventional drill strings, the openhole surfaces
of boreholes can be approximated with an absolute roughness, e oh = 0.01 ft (i.e., this
example value is the same as concrete pipe which approximates borehole surfaces in
limestone and dolomite sedimentary rocks, or in similar competent igneous and
metamorphic rocks, see Table 8-1).
Equation 7-65 together with Equations 7-60, 7-61 and 7-66 can be used in
sequential calculation steps starting at the bottom of the annulus and continuing for
each subsequent change in cross-sectional area in the annulus until the surface
injection pressure is determined.
7.4 Aerated Fluid Drilling Model
The aerated fluid drilling governing equations are very little changed from the
reverse circulation general derivation given in Section 7.2. The flow condition
inside of the drill string is three phase flow (gas, fluid, and solids). The exit
pressure in aerated fluid drilling operations is the atmospheric pressure, P at.
Therefore, Equation 7-26 becomes