Page 405 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-9
V c is the critical concentration velocity (ft/sec),
V t is the terminal velocity of the rock cuttings particle (ft/sec).
It is tacitly assumed that if the incompressible drilling fluid can carry the rock
cuttings on its own, then the injection of gas into the fluid will enhance the overall
carrying capacity of the aerated fluid.
The critical concentration velocity is the additional velocity needed to distribute
the rock cuttings through the incompressible drilling fluid at a predetermined
concentration factor. The usual concentration factor is 0.04. Therefore, the critical
concentration velocity, V c, is
V c (9-2)
,
3 600 C
where is the instantaneous drilling rate (ft/hr or m/hr),
C is the concentration factor (usually assumed to be 0.04).
Equations 9-1 and 9-2 equation can be used with any consistent set of units.
Terminal Velocities (English Units)
For direct circulation operations the terminal velocity of the rock cutting particle
is assessed in the annulus section of the borehole where the cross-sectional area is the
largest. The terminal velocity will depend on the actual flow conditions in the
annulus section (i.e., whether the flow is laminar, transitional, or turbulent).
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 0 0333 D 2 s f (9-3a)
t1 c
e
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),
3
s is the specific weight of the solid rock cutting (lb/ft ),
3
f is the specific weight of the incompressible drilling fluid (lb/ft ),
2
e is the effective absolute viscosity (lb-sec/ft ).
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 0 492 D c 1 (9-4a)
3
f e
where V t2 is the terminal velocity of the particle in transition flow (ft/sec).