Page 237 - Air and gas Drilling Field Guide 3rd Edition

228 CHAPTER 9 Aerated Fluids Drilling

The value of f p in the aforementioned equation is determined by trial and error
), and
using the result of the aforementioned equation, Equation (9-5) (for N R c
Figure 9-4. The value of f p must be on the c ¼ 1.0 curve. These analyses yield
¼ 158. This clearly establishes that the fluid flow
a value of f p ¼ 0.80 and a N R c
around the particle is transitional. The transitional terminal velocity of the average
cuttings particle from the above equation for f p ¼ 0.80 is
V tt ¼ 0:432m=sec:
Equation (9-1) for the average total fluid velocity in annulus becomes
V f ¼ 0:432 þ 0:127
V f ¼ 0:559 m=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 201.2 mm and the outside of the diameter of the drill pipe is 114.3
mm. Thus, this annulus cross-sectional area, A a ,is

p 2 2
A a ¼ ð 0:2012Þ 0:1143ð Þ
4
2
A a ¼ 0:02153 m :
The volumetric flow rate in the aforementioned annulus section is
ð
ð
Q a ¼ 0:0215Þ 0:559Þ
3
Q a ¼ 0:0121 m =sec:
In field units, the aforementioned is
q a ¼ 12:04 liters=sec
q a ¼ 722:7 lpm:

9.4 NONFRICTION AND FRICTION ILLUSTRATIVE EXAMPLES
Over the past two decades, the analyses of aerated fluid vertical drilling problems
have been carried out by two distinct analytic methodologies.
The first methodology ignores the major and minor friction losses due to fluid
flow inside the drill string and in the annulus. This methodology includes only
the fluid column weight [14, 15]. This methodology was originally derived and
adapted for aerated drilling from the large body of literature pertaining to multi-
phase flow of oil and natural gas in production tubing [16, 17].
The second methodology can include all the complexity of fluid flow friction
losses. The initial application of this methodology also came from adapting