Page 415 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-19
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 multiphase flow of
oil and natural gas in production tubing [16, 17].
The second methodology can include all the complexity of the fluid flow
friction losses. The initial application of this methodology also came from adapting
multi-phase oil and gas flow tubing production theory to aerated drilling annulus
problems. This production theory application includes only major friction losses
and was not applicable to complicated borehole geometry. New additions to this
methodology, which do not come from production literature, have included major
and minor losses and can be applied to complicated borehole geometry.
In Chapter 6 the basic aerated fluid drilling governing equations have been
derived and their auxiliary friction factor, and nozzle flow equations presented.
These equations form the foundation for both methodologies as they are discussed in
this treatise.
9.4.1 Non-Friction Approximation
The simple non-friction methodology allows straight forward deterministic
approximate solutions of aerated drilling problems. However, the practical
applicability of these non-friction solutions is limited to shallow (generally less than
3,000 ft of depth) wells with simple geometric profiles. The non-friction solution
will be applied to a deep well example only as a demonstration and ultimate
comparison of the results to those obtained from the friction solution.
In what follows, the basic equations in Chapter 6 for aerated drilling are used to
derive the non-friction governing equation. Letting f 0 in Equation 6-74 yields

dP
P bh H
dh
P e 0
w ˙
t
P g T av
Q g Q m
P T g

2
where P bh is the pressure at the bottom of the annulus (lb/ft , abs),
2
P e is the pressure at the exit from the annulus (lb/ft , abs).
The above equation can be rearranged and integrated to yield
P bh
T av Q g Q m H
P ln P P h
g
T g w ˙ t w ˙ t 0
P e
Evaluating above equation at the limits, rearranging the result and solving for gas
volumetric flow rate, Q g, yields