Page 483 - Air and Gas Drilling Manual

10-8 Air and Gas Drilling Manual
10.4 Injection Pressure and Selection of Compressor Equipment
Over the past two decades, the analyses of stable foam 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 [10, 11].
The second methodology can include all the complexity of the fluid flow
friction losses [11]. The initial application of this methodology came from adapting
multi-phase oil and gas flow tubing production theory to stable foam 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.
10.4.1 Non-Friction Approximation
The simple non-friction methodology allows straight forward deterministic
approximate solutions of stable foam 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.
In what follows, the basic equations in Chapter 6 for stable foam drilling are
used to derive the non-friction governing equation. Letting f 0 in Equation 6-88
yields

dP
P bh H
dh
P s 0
w ˙
t
P g T av
Q g Q f
P T g

2
where P s is the surface pressure at the top of the annulus (lb/ft , abs). This surface
pressure is usually a back pressure at the top of the annulus created by an adjustable
valvue. The above equation can be rearranged and integrated to yield
P bh
T av Q g Q f H
P ln P P h
g
T w ˙ w ˙ 0
g t t
P s
Evaluating above equation at the limits, rearranging the result and solving for gas
volumetric flow rate, Q g, yields