Page 243 - Air and gas Drilling Field Guide 3rd Edition

234 CHAPTER 9 Aerated Fluids Drilling

The volumetric flow rate of drilling fluid in consistent units is
ð 0:723Þ
Q f ¼
ð 60Þ
3
Q f ¼ 0:01215 m =sec:
The weight rate of flow of the drilling mud is
ð
ð
_ w f ¼ 1:2ð Þ 9810:0Þ 0:01215Þ
_ w f ¼ 143:0N=sec:
Equation (9-7) can be solved by trial and error. The value of q g is selected and
_ w g determined from
_ w g ¼ g Q g :
g
Substituting the values of H, _ w f ; _ w g ; _ w s ; Q f ,P s ,P bh ,T g , and T av into Equation
(9-7), a value of Q g can be determined. The trial and error process is carried
out until the right side and the left side equal each other. This gives an air volumetric
flow rate of
3
Q g ¼ 0:187 actual m =sec:
The air volumetric flow rate in field units is
q g ¼ 187:0 actual liters=sec:

9.4.2 Major and Minor Losses for Homogeneous Multiphase Flow
The governing equations for the second methodology are also presented in
Chapter 6 [see Equation (6-26)]. These equations require much complicated trial
and error solutions to obtain solutions that can be used in operational applica-
tions. The basic assumption for these equations is that the flow of the incom-
pressible fluid and the gas proceed in the annulus and inside drill string as a
homogeneous multiphase flow. This means that the theory does not account
for any relative motion between the two fluids. This homogeneous flow assump-
tion extends to the exclusion of the cuttings stream relative movement with
respect to fluids in the annulus.
Illustrative Example 9.3 carries out the solution of the examples described in
Illustrative Examples 9.1 and 9.2. This solution assumes a homogeneous flow of
fluids and cuttings in the annulus and a homogeneous flow of fluids inside the drill
string.
Illustrative Example 9.3 In this illustrative example, data given in Illustrative
Examples 9.1 and 9.2 are used for solutions using the friction solution method
given in Chapter 6. The objective of this example is to determine the approxi-
mate volumetric flow rate of the air required to be injected with the incompress-
ible drilling fluid volumetric flow rate of 191 gpm (723 lpm) in the top of the