Page 261 - Air and Gas Drilling Manual

6-6 Air and Gas Drilling Manual
accurate determination of the volumetric flow rate of natural gas being supplied to
the drilling operation.
6.2.2 Three-Phase Flow in the Annulus
The weight rate of flow of incompressible drilling fluid (usually drilling mud),
˙ w , into the well is
m
˙ w m = γ m Q m (6-11)
where ˙ w is the weight rate of flow of drilling mud (lb/sec),
m
3
γ m is the specific weight of the drilling mud (lb/ft ),
3
Q m is the volumetric flow rate of drilling mud (ft /sec).
The weight rates of flow ˙ w and ˙ w enter the well through the top of the drill
g
m
string and flow to the bottom of the string and exit into the annulus through the
openings in the drill bit (open orifices or the bit nozzles). After passing through the
drill bit, the fluids entrain the rock cuttings generated by the drill bit as the bit is
advanced. The entrained weight rate of flow of the solids, ˙ w , is
s
π
. ) ( . ) κ
˙ w = D 2 (62 4 2 7 (6-12)
s h
4
where ˙ w is the weight rate of flow of solid rock cuttings (lb/sec),
s
D h is the diameter of the drilled hole (i.e., the bit diameter) (ft),
κ is the penetration rate (ft/sec).
3
In the above equation the specific weight of fresh water is 62.4 lb/ft . The average
specific gravity of sedimentary rocks is 2.7. If igneous or metamorphic rocks are to
be drilled, an average value of 2.80 and 3.00, respectively, can be used if the actual
specific gravity of the rocks to be drilled are not known [5].
The total weight rate of flow, ˙ w , in the annulus from the bottom of the well to
t
the surface is
˙ w = ˙ w + ˙ w + ˙ w (6-13)
t g m s
The drilling mud and the rock cutting solids do not change volume when the
pressure is changed. However, the air (or gas) does change volume as a function of
pressure change and, therefore, as a function of depth. Thus, the specific weight of
the gas at any position in the annulus is
PS
γ = (6-14)
R T av

where T av is the average temperature of the gas over a depth interval (˚R). This
average temperature term is determined by taking the average of the sum of the