Page 189 - Air and gas Drilling Field Guide 3rd Edition

180 CHAPTER 7 Reverse Circulation Models

2 3 2
1
6 7
f ¼ 6 7 : (7-52)
D i
4 5
2 log þ 1:14
e
For follow-on calculations for flow in the drill string, the absolute roughness for
commercial steel drill pipe, e p ¼ 0.0005 ft or e p ¼ 0.0002 m, will be used for
the inside surfaces of the drill pipe and drill collars.
Equations (7-46), (7-47), (7-51), and (7-52) 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
k þ 1
2 3
2
2
k P ai k P ai _ w g
2g P bh g 4 k 7 : (7-53)
6
5 ¼
bh
k 1 P bh P bh A bi
These equations will generally yield results that show that the annulus bottom
hole pressure P bh differs very little from the pressure above the drill bit inside the
drill string P ai for most practical parameters. Therefore, it can usually be assumed
that
P bh P ai : (7-54)
The flow in the annulus is single-phase flow (air or gas). Setting Q m ¼ 0in
Equation (7-37) yields
2 3
6 _ w g 7
6 7
dP ¼
4 5
P g T av
Q g
P T g
8 9
32
2
P g T av
> >
> >
Q g
> >
f 6 P T g 7
< =
1 6 7 dh: (7-55)
4 p 2 2 5
> 2gD h D p D D >
> >
4
> h p >
: ;
Separating variables in Equation (7-59) yields
P bh
dP
ð ð H
¼ dh; (7-56)
B a PðÞ
P in 0