Page 320 - Air and Gas Drilling Manual

Chapter 8: Air, Gas, and Unstable Foam Drilling 8-3
In Chapter 6 the basic direct circulation drilling planning governing equations
have been derived and summarized. In Chapter 7 the basic reverse circulation
drilling planning governing equations have been derived and summarized. In this
chapter only direct circulation illustrative examples are discussed. Reverse
circulation examples are discussed in Chapter 5.
8.2 Minimum Volumetric Flow Rate
There are various research groups that over the past three decades have developed
several mathematical and empirical models for use in attempting to describe the gas
flow mechanics of air and gas drilling operations. Each of the models developed
over the decades have made a variety of assumptions concerning the specific weight
of the gas and rock cuttings mixture created at the bottom of the hole as the drill bit
advances.
8.2.1 Discussion of Theories
In 1957, R. R. Angel developed the first field useful mathematical and
empirical model for air and gas drilling operations [3, 4]. This initial work by
Angel was supported by industry (i.e., Phillips Petroleum Company) and continues
to be useful to drilling supervisors and drilling engineers even today. This modeling
effort drew heavily from the large body of engineering knowledge related to industrial
pneumatic conveying (the transport of solids by flowing air). Thus, this model was
developed from the outset to be an engineering tool. The major air and rock cuttings
mixture assumption made in this model was that the rock cutting particles move
together from the bottom of the borehole to the surface with the velocity of the local air
flow. Through the decades other researchers have improved on this model [5].
In 1981, interest in air and gas drilling technology found its way into academic
research [6, 7]. This research was carried out at University of Tulsa and
Pennsylvania State University and was supported by U. S. Department of Energy.
In this effort experimental work was carried out to ascertain the relationship between
the motion of the air and the rock cuttings particles. This experimental work found
that the vertical drilling annulus geometry with an upward flow of air and rock
cuttings chokes in much the same way as industrial pneumatic conveying. This
experimental work also showed that under simulated practical drilling conditions
small rock particles flow with a velocity that was near that of the air. This research
effort resulted in a model that was a variation on the original Angel work. The slip
of the rock cutting particles relative to the air flow was ignored. The model resulted
in a air and rock mixture value that was nearly the same as that given by the original
Angel model.
In 1983, the first model was proposed that took into account a rock cutting
particle velocity that was different from that of the air flow [8]. This model can
yield an improved air and rock mixture value which can improve the accuracy of the
predictions from the model. The problem with this model is that the individual
average velocities of the particles are difficult to determine analytically for inclusion
in this model.
In 1992, additional theoretical work was carried out to further refine the
inclusion of the effect of rock cuttings particle velocities [9]. This model also
suffered from the difficulty involved in determining average particle velocities.