Page 249 - Air and gas Drilling Field Guide 3rd Edition

240 CHAPTER 9 Aerated Fluids Drilling

where
N vG N 0:38
X 3 ¼ L : (9-19)
N D 2:14
Equations (9-18) and (9-19) are only valid for
N vG N L 0:38 > 0:01:
N D 2:14
N GV N 0:380
Note that for L 0:01, c ¼ 1.0 [19].
N 2:14
D
The liquid holdup y L can be calculated using

y L
y L ¼ c : (9-20)
c
The interfacial tension is a function of pressure and temperature. Interfacial
tension is determined using the following empirical correlation:

ð s 74 s 280 Þ t 74Þ
ð
s ¼ s 74 ; (9-21)
206
where the temperature t is in F.

For temperatures in C, the correlation is the following:
ð s 74 s 280 Þ 1:8t C 42Þ
ð
s ¼ s 74 ; (9-22)
206

where temperature t C is in C, and
s 74 ¼ 75 1:108 p 0:349 (9-23)
and
s 280 ¼ 53 0:1048 p 0:637 ; (9-24)
where pressure p is in psia, or

s 74 ¼ 75 6:323 P 0:349 (9-25)
MPa
and
0:637
s 280 ¼ 53 2:517 P MPa (9-26)
where pressure P MPa is in MPa abs.
Illustrative Example 9.4 In this illustrative example, data in Illustrative Exam-
ple 9.3 will be resolved, but in this example, liquid holdup empirical correlations
will be considered for the flow up the annulus.
The detailed Mathcad solution for this example is given in Appendix D. Figure
9-10 shows multiphase flow pressures throughout the circulation system in the
project well while drilling at 10,000 ft (3048 m). In Figure 9-10, the bottom hole
2
annulus pressure is 3373 psia (2326 N/cm abs) in the annulus and the surface
2
injection pressure at the standpipe is 62.4 psia (43.0 N/cm abs).