Page 235 - Air and gas Drilling Field Guide 3rd Edition

226 CHAPTER 9 Aerated Fluids Drilling

The value of f p in the aforementioned equation is determined by trial and
error using the result of the aforementioned equation, Equation (9-5) (for
), and Figure 9-4. The value of f p must be on the c ¼ 1.0 curve. These ana-
N R c
¼ 158. This clearly establishes
lyses yield a value of f p ¼ 0.80 and a N R c
that the fluid flow around the particle is transitional. The transitional terminal
velocity of the average cuttings particle from the aforementioned equation for
f p ¼ 0.80 is
V tt ¼ 1:417 ft=sec:
Equation (9-1) for the average total fluid velocity in annulus becomes
V f ¼ 1:417 þ 0:417
V f ¼ 1:834 ft=sec:

The total velocity of the fluid must be the minimum average velocity of the
incompressible fluid in the borehole annulus section where the cross-sectional
area is the largest. In this illustrative example, the largest cross-sectional area of
the annulus is in the cased section of the well where the inside diameter of the
casing is 7.921 in and the outside of the diameter of the drill pipe is 4.50 in. Thus,
this annulus cross-sectional area, A a ,is
" #
2 2
7:921 4:50

p
A a ¼
4 12 12
2
A a ¼ 0:232 ft :
The volumetric flow rate in the aforementioned annulus section is
ð
Q a ¼ 0:232Þ 1:834Þ
ð
3
Q a ¼ 0:426 ft =sec:
In field units, this is
3
ð
ð
ð 0:426Þ 60Þ 12Þ
q a ¼
231
q a ¼ 191:0 gpm:

Minimum Incompressible Fluid Volumetric Flow Rate (SI Units)
The incompressible fluid used in this illustrative example is a water-based
drilling mud with plastic properties. Therefore, the minimum volumetric flow
rate of the incompressible drilling fluid is determined using Equations (9-1)
through (9-5).
The anticipated drilling rate is 18.3 m/hr. The critical concentration velocity is
18:3
V c ¼
ð
3; 600 0:04Þ
V c ¼ 0:127 m=sec: