Page 530 - Air and Gas Drilling Manual

Using Equation 1-1, the kinetic energy per unit volume at this position in the
annulus is
1 2 Chapter 10: Stable Foam drilling 10-55
KE V
sfake sfake sfake
2
1 2
.
.
KE sfake 0 773 2 90
2
ft - lb
.
KE sfake 324
ft 3
The overall trial and error process has selected the approximate value of q w that
restricts the foam quality at the bottom of the annulus to slightly above 0.60 and
restricts the minimum kinetic energy per unit volume in the annulus to slightly
3
above 3.00 ft-lb/ft . In this example the foam quality criteria appears to be the
controlling criteria for the trial and error process since interative changes in q w appear
to approach the foam quality limit more rapidly than the kinetic energy per unit
volume limit.
Drill Bit Nozzles
For this example the components of the stable foam (water and surfactant) are
injected into the top of the inside of the drill string. The foam is generated at the
bottom of the well when these components pass through the small drill bit nozzles.
Therefore, the flow of these components down the drill string and through the drill
bit nozzles is assumed to be aerated flow (as described in Chapter 9).
It is assumed that the 7 7/8 inch tri-cone roller cone drill bit is equipped with
three 9/32 inch diameter jet nozzles. Therefore, the inside diameter of each nozzle
D n, is
.
d n 0 2813 inches
d n
D n
12
D n 0 02344 ft
.
From Equation 6-94, the equivalent single diameter for this drill bit, D e, is

2
.
D 3 0 02813
e
.
D e 0 0406 ft
The approximate specific weight of the aerated fluid at the bottom of the
annulus (just as it passes through the nozzles), mixbh, is