Page 283 - Air and Gas Drilling Manual

6-28 Air and Gas Drilling Manual
64
f =
(6-90)
N
R
This equation can be solved directly once the Reynolds number is known. In
general, Equation 6-90 is valid for values for Reynolds numbers from 0 to 2,000.
The empirical expression for the Fanning friction factor for transitional flow
conditions is known as the Colebrook equation. The Fanning friction factor cannot
be determined directly and must be solved by trial and error. This empirical
expression is
   
  e  
1   D − D p  251 
.
h
=− 2 log  +  (6-91)
f  37 . N R f 
 
   
where e is the absolute roughness of the annulus surface (ft). In general, Equation 6-
94 is valid for values of Reynolds numbers from 2,000 to 4,000.
The empirical expression for the Fanning friction factor for turbulent flow
conditions is known as the von Karman equation. This empirical expression is
  2
 
f =   1   (6-92)
  D − D  
h
p


+ 1 14
 2 log. 


e
 
In general, Equation 6-92 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. The openhole surfaces of
boreholes will 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 6-88 together with Equations 6-89 through 6-92 can be used in
sequential trial and error 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.
If the stable foam is not preformed at injection, the flow down the inside of the
drill string is that of an aerated fluid mixture. Such an aerated mixture can be
assumed to pass through the nozzles in much the same manner as an incompressible
fluid. Thus, borrowing from mud drilling technology, the pressure change through
the drill bit, ∆P b, can be approximated by