Page 246 - Air and gas Drilling Field Guide 3rd Edition

9.4 Nonfriction and Friction Illustrative Examples 237

Liquid velocity number N vL :
r ffiffiffiffiffi
4 g L
N vL ¼ F vL u SL : (9-11)
s
Gas velocity number N vG :
r ffiffiffiffiffi
4 g L
N vG ¼ F vG u SG : (9-12)
s

Pipe diameter number N D :
r ffiffiffiffiffi
N D ¼ F D D g L : (9-13)
s

Liquid viscosity number N L :

s ffiffiffiffiffiffiffiffiffi
1
4
N L ¼ F L m L 3 : (9-14)
L
g s
where u SL is the superficial velocity of the liquid phase (ft/sec, m/sec), u SG is the
superficial velocity of the gas phase (ft/sec, m/sec), s is the liquid–gas interfacial
tension (dyne/cm, dyne/cm), D is the hydraulic diameter of the flow cross section
(ft, m), and m L is the liquid viscosity (cp, cp).
USCS unit conversion constants are

F vL ¼ 1:938
F vG ¼ 1:938
F D ¼ 120:872
F L ¼ 0:15726

SI unit conversion constants are

F vL ¼ 1:7964
F vG ¼ 1:7964
F D ¼ 31:664
F L ¼ 0:55646

Figure 9-7 is the first chart and is an empirical graphic representation of
the relationship between parameter CN L versus N L [5]. Guo and colleagues [19]
found that Figure 9-7 can be replaced by the following correlation equation:
Y
CN L ¼ 10 ; (9-15)