Page 413 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-17
127 5 gal/min
q
.
a3
It is again necessary to check and see if the above volumetric flow rate did
indeed give turbulent flow conditions in the largest annulus cross-sectional area.
This is accomplished by calculating the non-dimensional Reynolds number for this
annulus cross-section and the above volumetric flow rate (with the average annulus
velocity of 1.184 ft/sec).
For turbulent flow conditions, the effective absolute viscosity of a drilling mud
with a plastic viscosity must to be modified before it is used in the Reynolds
number equation [10]. Therefore, assuming turbulent flow conditions, the effective
absolute viscosity is
p
e3
32
.
0 0006267
.
e3
32
.
lb sec
0 000196
.
e3 2
ft
The effective kinematic viscosity for the drilling mud with plastic properties is
0 000196
.
e3
.
2 369
2
.
0 000083 ft /sec
e3
Substituting the values for, D h, V m3, e3 into Equation 9-6 yields the Reynolds
number for the volumetric flow rate derived from the laminar flow terminal velocity
equation. Equation 9-6 gives
0
(.293 ) ( .184 )
1
N R3
. 0 000083
N R3 4 196
,
The Reynolds number above is greater than 2,000. This indicates that the
volumetric flow rate of 127.5 gal/min produces turbulent flow conditions in the
largest cross-section of the annulus.
The turbulent flow analysis result is inconsistent with the result of the laminar
flow analysis. Also, since the turbulent flow analysis indicates turbulent flow
conditions exist at a lower volumetric flow rate than the laminar flow analysis, then
the laminar flow analysis is considered valid and the turbulent flow analysis invalid.