Page 306 - Air and Gas Drilling Manual

2



f =

(7-44)

      D − 1 D  Chapter 7: Reverse Circulation Models 7-15
h
p


+ 1 14
 2 log. 


e
 
In general, Equation 7-44 is valid for values of Reynolds numbers greater than 4,000.
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 7-40 together with Equations 7-41 through 7-44 can be used in
sequential integration steps starting at the top of the annulus (with the known exit
pressure) and continuing for each subsequent change in annulus cross-sectional area
until the bottomhole pressure is determined. These sequential calculation steps
usually require trial and error solutions. The trial and error process requires the
selection of the upper limit of the pressure in each integral on the right side of
Equation 7-40. This upper limit pressure selection must give a right side integral
solution that is equal to the left side integral solution.
7.3 Air and Gas Drilling Model
Air drilling techniques are used extensively in reverse circulation drilling
operations. This is particularly the case for reverse circulation drilling operations
that utilize dual wall pipe. Dual wall pipe reverse circulation operations use either
special skirted tri-cone drill bits (see Chapter 3) or air hammers with air hammer bits
(see Chapter 11). In general, reverse circulation air drilling operations utilize either
compressed air or compressed inert atmospheric air (stripped of most of its oxygen)
as drilling gases.
Air (or gas) drilling is a special case of the theory derived in Section 7.2 above.
The governing equations for air (or gas) drilling operations can be obtained by
setting Q m = 0 in the equations derived in Section 7.2.
Two phase flow conditions occur inside of the drill string (gas and solids).
Setting Q m = 0 in Equation 7-25 yields
 
 
 w ˙ 
dP =  t 
  P   T av  
g
     Q g 
   P   T   
g