Page 263 - Air and gas Drilling Field Guide 3rd Edition

254 CHAPTER 10 Stable Foam Drilling

where V t1 is the terminal velocity of the particle in laminar flow (ft/sec), D c is the
approximate diameter of the rock cutting particle (ft), g s is the specific weight of
3
the solid rock cutting (lb/ft ), g f is the specific weight of the incompressible dril-
2
3
ling fluid (lb/ft ), and m e is the effective absolute viscosity (lb-sec/ft ).
Empirical data indicate that transition flow conditions exist when the nondi-
mensional Reynolds number for the flow around the particle is between 1 and
2000. The empirical relationship for the terminal velocity of a rock cutting parti-
cle in an annulus with transition flow V t2 is
" 2 #
ðg g Þ 3
f
s
V t2 ¼ 0:492 D c 1 ; (10-8a)
e
ðg f m Þ 3
where V t2 is the terminal velocity of the particle in transition flow (ft/sec).
Empirical data indicate that turbulent flow conditions exist when the nondi-
mensional Reynolds number for the flow around the particle is greater than
2000. The empirical relationship for the terminal velocity of a rock cutting parti-
cle in an annulus with turbulent flow V t3 is
!#1
"
2
s
g g f
V t3 ¼ 5:35 D c ; (10-9a)
g f
where V t3 is the terminal velocity of the particle in turbulent flow (ft/sec).
Terminal Velocities (SI Units)
Empirical data indicate that laminar flow conditions exist when the nondimen-
sional Reynolds number for the flow around the particle is between 0 and 1.
The empirical relationship for the terminal velocity of a rock cutting particle in
an annulus with laminar flow, V t1 ,is

s
V t1 ¼ 0:0333 D 2 g g f ; (10-7b)
c
m e
where V t1 is the terminal velocity of the particle in laminar flow (m/sec), D c is the
approximate diameter of the rock cutting particle (m), g s is the specific weight of
3
the solid rock cutting (N/m ), g f is the specific weight of the incompressible dril-
3
2
ling fluid (N/m ), and m e is the effective absolute viscosity (N-sec/m ).
Empirical data indicate that transition flow conditions exist when the nondi-
mensional Reynolds number for the flow around the particle is between 1 and
2000. The empirical relationship for the terminal velocity of a rock cutting parti-
cle in an annulus with transition flow V t2 is
2 #
"
3
ðg g Þ
s
f
V t2 ¼ 0:331 D c 1 ; (10-8b)
e
ðg f m Þ 3
where V t2 is the terminal velocity of the particle in transition flow (m/sec).