Page 234 - Air and gas Drilling Field Guide 3rd Edition

9.3 Minimum Volumetric Flow Rates 225

The viscosity of the incompressible drilling fluid in consistent units is
m ¼ 30 0:001Þ 0:02089Þ
ð
ð
f
lb sec
m ¼ 0:0006267 :
f
ft 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 3
2
0:36
12
6 7
6 7
7 168:5 75:0ð Þ
V tl ¼ 6
ð
4 18 0:0006267Þ5
V tt ¼ 7:46 ft=sec:
The incompressible drilling fluid density r f is
75:0
r ¼
f
32:2
lb sec 2
r ¼ 2:329 :
f
ft 4
The general equation for kinematic viscosity of the fluid is
n ¼ ; (9-6)
m
r
2
where n is kinematic viscosity (ft /sec). The kinematic viscosity is
0:0006267
n ¼
2:329
2
n ¼ 0:0002691 ft =sec:
The Reynolds number of the fluid flow around the average cuttings particle
[Equation (9-5)] is

0:36
7:46
12
¼
0:0002691
N R c
¼ 832:
N R c
This Reynolds number is greater than 3 and therefore the flow around the parti-
cle is not laminar.
Assuming that the flow conditions around the particle are transitional, Equa-
tion (9-4) becomes
30:5

0:36
2
32:2ð Þ
4 168:5 75:0

6 12 7
V tt ¼ 6 7 :
3 75:0 f p
4 5