Page 297 - Air and Gas Drilling Manual

7-6 Air and Gas Drilling Manual
determination of the volumetric flow of natural gas being supplied to the drilling
operation.
7.2.2 Three-Phase Flow in the Drill String
The weight rate of flow of incompressible drilling fluid (usually drilling mud),
˙ w , into the well is
m
˙ w m = γ m Q m (7-11)
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
g
m
annulus space and flow to the bottom of the annulus where the two-phase flow
entrains the rock cuttings. The weight rate of flow of solids, ˙ w , entrained by the
s
two-phase flow is
π
. ) ( . ) κ
˙ w = D 2 (62 4 2 7 (7-12)
s h
4
where ˙ w is the weight rate of flow of solids 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 and the average
specific gravity of sedimentary rocks is 2.7. If igneous or metamorphic rocks are to
be drilled, then an average value of 2.80 and 3.00, respectively, can be used if the
actual specific gravity of the rocks to be drilled is not known [5].
The total weight rate of flow, ˙ w , inside the drill string from the bottom of the
t
string to the surface is
˙ w = ˙ w + ˙ w + ˙ w (7-13)
t g m s
The drilling muds and the rock cutting solids do not change volume when the
pressure is changed. However, the air (or gas) does change volume when the
pressure is changed and, therefore, the gas volume is a function of depth. Thus, the
specific weight of the gas at any position inside the drill string is
PS
γ = (7-14)
R T av
where T av is the average temperature of the gas over the depth interval (˚R). This
average temperature term is determined by taking the average of the sum of the
geothermal temperature at the top and bottom of the depth interval. The geothermal
temperature at depth, t h, is determined from the approximate expression