Page 414 - Air and Gas Drilling Manual

9-18 Air and Gas Drilling Manual
Therefore, the minimum volumetric flow rate of the incompressible drilling fluid
(the drilling mud) is assumed to be approximately 191 gal/min.
The results obtained for the illustrative example above require that additional
explanation be given for the utility and applicability of Equations 9-1, 9-2, 9-3a (and
9-3b), 9-4a (and 9-4b), and 9-5a (and 9-5b).
Equation 9-1 and the 0.04 concentration factor allows an estimate of the rock
particle cuttings concentration velocity, V c, in the incompressible fluid (usually
drilling mud). In Equation 9-2 this concentration velocity is added to the particle
terminal velocity (in the fluid), V t, to obtain the minimum fluid velocity, V f, in the
largest annulus cross-section of the borehole. This minimum fluid velocity gives an
allowable distribution of particles in the fluid flow that has been shown by field
operations to yield trouble free drilling operations. The concentration factor of 0.04
can be adjusted to a smaller value if drilling conditions require a more conservative
engineering planning approach.
Equations 9-3a to 9-5a (and 9-3b to 9-5b) give the terminal velocities for the
three well known flow conditions, laminar, transition, and turbulent. The terminal
velocity for laminar flow is V t1, for transition flow , V t2, and for turbulent, V t3.
These terminal velocity equations were obtained from laboratory experiments. Thus,
these are empirically derived separate equations and do not represent a single
continuous theory (of equations). Therefore, one expression will not match up with
the next expression as the Reynolds number is increased through the three flow
conditions. Thus, these expressions should be applied with prudence and
engineering judgment.
The rock cutting particle average diameter term, D c, used in all of the three
terminal velocity equations can be estimated via several methods. Two of these
methods are described below.
In vertical rotary air drilling operations where the drill string is rotated, it is
known that the mechanical interactions of the particles with the rotating drill string
will reduce the size of the particles as they are transported to the surface in the
annulus [13]. Thus, the higher the rotary speed of the drill string, the smaller the
particle diameter. The particle average diameter can be estimated as

D c (9-8)
60 N

where N is the drill string (drill bit) speed (rpm).
An alternate method can be used to approximate average diameter of particles
generated by a downhole motor using a tri-cone drill bit (no drill string rotation).
This method assumes that the average diameter of the particles is approximately half
the base diameter of the mill or insert tooth root diameter on a cone face. This is a
reasonable estimate considering that these drill bits destroy rock with a crushing
action and there is no rotation of the drill string. Figure 3.5 shows a schematic of
this crushing action and illustrates the cutting sizes generated.

9.4 Injection Pressure and Selection of Compressor Equipment
Over the past two decades, the analyses of aerated fluid vertical drilling
problems have been carried out by two distinct analytic methodologies.