Page 185 - Air and gas Drilling Field Guide 3rd Edition

176 CHAPTER 7 Reverse Circulation Models

where
2 3
6 _ w g þ _ w m 7
6 7
B a PðÞ ¼
4 5
P g T av
Q g þ Q m
P T g
8 9

2 32
P g T av
> >
Q g þ Q m
> >
> >
f 6 T g 7
< P =
1 6 7 ;
2
> 2gD h D p 4 p D D 2 5 >
> h p >
4
> >
: ;
2
where P in is the injection pressure into the top of the annulus space (lb/ft abs,
2
N/m abs).
The friction factor f given in the equation just shown is determined by the
standard fluid mechanics empirical correlations relating the friction factor to
the Reynolds number, diameter (or hydraulic diameter), and absolute pipe rough-
ness. In general, the values for Reynolds number, diameter, and absolute pipe
roughness are known. The classic correlation for the Reynolds number is

D h D p V
N R ¼ ; (7-39)
n
where D h –D p is the hydraulic diameter for the annulus (ft, m).
Three flow conditions can exist in the annulus. These are laminar, transitional,
and turbulent.
The empirical correlation for the friction factor for laminar flow conditions is
64
f ¼ N R : (7-40)
This equation can be solved directly once the Reynolds number is known. Equa-
tion (7-40) is valid for values for Reynolds numbers from 0 to 2000.
The empirical correlation for the friction factor for both transitional flow con-
ditions and wholly turbulent flow conditions (for Reynolds numbers greater than
2000) can be determined from the Haaland correlation [6]. This empirical expres-
sion is
2 3 2
6 7
6 7
6 7
6 7
6 7
1
6 7
f ¼ 6 7 ; (7-41)
2
1 1:11 3
0
6 7
e av
6 7
6 7 7
6
B D h D p C
6 6:9 7 7
6
B C
6 þ 7 7
1:8 log6
4 @ 3:7 A
4 N R 5 5