Page 165 - Air and Gas Drilling Manual

.
d
d
p
=
D p p = 2 375 inches Chapter 5: Shallow Well Drilling Applications 5-7
12
D p = 0 198 ft
.
The Fanning friction factor, f, for flow in the annulus is determined from the
von Karman empirical relationship for turbulent flow conditions [2]. This empirical
relationship is
  2
 
 1 
f =   (5-5)
  D − D  
p
h

+1 14

 2 log. 


e
 av 
where e av is the average absolute surface roughness of the annulus (ft).
The openhole outer wall absolute surface roughness, e oh, of the limestone
sequence borehole annulus is assumed to be 0.005 ft (see Table 8-1) [2]. The inner
surface of the borehole annulus is the outer surface of the drill pipe. The absolute
surface roughness of commercial pipe, e p, is given as 0.00015 ft [2]. The average
absolute surface roughness of the annulus is approximated by using a surface area
weight average relationship between the openhole surface area and its roughness and
the outside surface of the drill string and its roughness. Thus, the value for e av is
π
π
 
eDH + e   DH
2
2
oh   h p   p
4
4
e =
π
π
av
  DH +   2
2
  h   DH
p
4
4
The above reduces to
π
π
   
e D 2 + e D 2
oh   h p   p
4
4
e = (5-6)
π
π
  2 +   2
av
  D h   D p
4
4
Thus, e av, is