Page 406 - Air and Gas Drilling Manual

9-10 Air and Gas Drilling Manual
Empirical data indicates that turbulent flow conditions exist when the non-
dimensional Reynolds number for the flow is greater than 4,000. The empirical
relationship for the terminal velocity of a rock cutting particle in an annulus with
turbulent flow, V t3, is
1
2
s f
V t3 535 D c (9-5a)
.
f
where V t3 is the terminal velocity of the particle in turbulent flow (ft/sec).
Terminal Velocities (SI Units)
Empirical data indicates that laminar flow conditions exist when the non-
dimensional Reynolds number for the flow is between 0 and 2,000. The empirical
relationship for the terminal velocity of a rock cutting particle in an annulus with
laminar flow, V t1, is
.
V t1 0 0333 D c 2 s f (9-3b)
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),
3
s is the specific weight of the solid rock cutting (N/m ),
3
f is the specific weight of the incompressible drilling fluid (N/m ),
2
e is the effective absolute viscosity (N-sec/m ).
Empirical data indicates that transition flow conditions exist when the non-
dimensional Reynolds number for the flow is between 2,000 and 4,000. The
empirical relationship for the terminal velocity of a rock cutting particle in an
annulus with transition flow, V t2, is
2
3
s f
V t2 0 331 D c 1 (9-4b)
.
3
f e
where V t2 is the terminal velocity of the particle in transition flow (m/sec).
Empirical data indicates that turbulent flow conditions exist when the non-
dimensional Reynolds number for the flow is greater than 4,000. The empirical
relationship for the terminal velocity of a rock cutting particle in an annulus with
turbulent flow, V t3, is
1
2
s f
V t3 295 D c (9-5b)
.
f