Page 293 - Air and Gas Drilling Manual

7-2 Air and Gas Drilling Manual
are usually treated and untreated fresh water, treated and untreated salt water
(formation water), and water-based drilling muds.
It is assumed that the compressible gases can be approximated by the perfect gas
law. Further, it is assumed that the mix of compressed gas and incompressible fluid
will be uniform and homogeneous. When the solid rock cuttings are added to the
mixture of compressible gas and incompressible fluid, then the solid rock cutting
particles will be uniform in size and density and will be distributed uniformly in the
mixture of gas and fluid. Also, it is assumed that the rock particles move with the
same velocity as circulating gas and fluid and that the resulting uniform mixtures
can be approximated by known basic fluid mechanics relationships [1].
The assumption of uniformity of the two or three phases in the mixtures is an
important issue in light of the technology developed for gas lift assistance of oil
production [2, 3]. The aeration of oil (or other formation fluids) at the bottom of a
well with the flow of gas from the surface (down the annulus between the casing and
the production tubing) is similar to the aeration of circulating fluid and entraining of
rock cuttings at the bottom of a well with a flow of gas and fluid from the surface
(down the annulus). However, the gas lift published pressure gradient plots have
been extrapolated from empirical data derived from experiments carried out on small
inside diameter production tubing. New experiments with aerated drilling fluids
have shown that the present production pressure gradient plots do not correlate with
new experiments carried out on larger diameter tubulars [4].
Reverse circulation operations do not have the variety of air and gas techniques
available. In general, reverse circulation operations use compressed air or other gases
as drilling fluids, and aerated fluids as drilling fluids.
7.2 General Derivation
The term, P in, represents the pressure of the injected drilling fluid into the top of
the annulus. The U-tube representation in Figure 7-1 shows the largest annulus
space between the outside of the drill pipe and the inside of the casing. Next is the
annulus space between the outside of the drill pipe and the inside of the openhole.
Then at the bottom of the annulus is the space between the outside of the drill
collars and the inside of the openhole. At the bottom of the drill string is the single
large opening in the drill bit which allows the drilling fluids with entrained rock
cuttings to pass into the inside of the drill string. The schematic shows the smaller
inside diameter of the drill collars. Above the drill collars is the larger inside
diameter of the drill pipe. At the top of the drill pipe the drilling fluid with the
entrained cuttings exits the circulation system at a pressure, P e.
As in all compressible flow problems, the process of solution must commence
with a known pressure and temperature and in this case the pressure and temperature
at the exit. Therefore, the derivation will begin with the analysis of the inside of the
drill string. Figure 7-1 shows the pressure, P, at any position in the inside of the
drill string which is referenced from the surface to a depth h. The total depth of the
well is H. The differential pressure, dP, in the upward flowing three phase flow
occurs over an incremental distance of dh. This differential pressure can be
approximated as [1]