Page 236 - Air and gas Drilling Field Guide 3rd Edition

9.3 Minimum Volumetric Flow Rates 227

The specific weight of the sedimentary rock to be drilled is approximately
ð
g ¼ 2:7Þ 1000:0Þ 9:81Þ
ð
ð
s
3
g ¼ 26487:0N=m ;
s
where the specific gravity of sedimentary rock is assumed to be approximately
2.7 (see Chapter 6).
3
The specific weight of the 1200.0-kg/m incompressible drilling fluid in con-
sistent units is
ð
g ¼ 1200:09:81Þ
f
3
g ¼ 11772:0N=m :
f
The viscosity of the incompressible drilling fluid in consistent units is
ð
m ¼ 30 0:001Þ
f
N sec
m ¼ 0:030 :
f
m 2
Assuming laminar flow conditions around the particle, Stokes’ law will be used
to determine the initial value of the particle terminal velocity. Equation (9-3) is
" #
2
ð 0:00914Þ
V tl ¼ ð 28487:0 11772:0Þ
ð
18 0:030Þ
V tt ¼ 2:28 m=sec:
The incompressible drilling fluid density r f is
2
4
r ¼ 1200:0 N sec =m :
f
The kinematic viscosity is
0:030
n ¼
1200:0
2
n ¼ 0:0000250 m =sec:
The Reynolds number of the fluid flow around the average cuttings particle
[Equation (9-6)] is
ð
2:28 0:00914Þ
¼
0:0000250
N R c
¼ 832:
N R c
This Reynolds number verifies that the flow around the particle is not laminar.
Assuming that the flow conditions around the particle is transitional, Equation
(9-4) becomes
" # 0:5

ð
4 28487:7 11772:0 ð 9:81Þ 0:00914Þ
V tt ¼ :
3 11772:0 f p