Page 279 - Air and Gas Drilling Manual

6-24 Air and Gas Drilling Manual
pipe and drill collars, and inside surface of the casing. The openhole surfaces of
boreholes will be approximated with an absolute roughness, e oh = 0.01 ft (i.e., this
example value is the same as concrete pipe which approximates borehole surfaces in
limestone and dolomite sedimentary rocks, or in similar competent igneous and
metamorphic rocks, see Table 8-1).
Equation 6-74 together with Equations 6-75 through 6-78 can be used in
sequential trial and error integration steps starting at the top of the annulus (with the
known exit pressure) and continuing for each subsequent change in annulus cross-
sectional area until the bottomhole pressure is determined.
The mixture of incompressible fluid and the gas passing through the orifices has
a high incompressible fluid volume fraction and can, therefore, be assumed to act
physically as an incompressible mixture. Thus, borrowing from mud drilling
technology, the pressure change through the drill bit, ∆P b, can be approximated by
g ( m) 2
w ˙ + w ˙
∆ P = 2 (6-79)
b
π
2 g γ C 2   D 4
mixbh   e
4
The value of C represents the aerated fluid flow loss coefficient of the drill bit
orifices (or nozzles). Experiments have shown that aerated fluid flow is very
complex. The gas and incompressible fluid components in the aerated mixture
appear to alternate their passage through the nozzles. This means the aerated flow
through the nozzles is inefficient. The value of C for aerated fluid flow should be
taken as 0.70 to 0.85. For drill bits with n equal diameter orifices (or nozzles), D e
becomes
D = n D 2 (6-80)
e n
The pressure change obtained from Equation 6-79 is added to the bottomhole
pressure P bh obtained from Equation 6-74. The pressure above the drill bit inside the
drill string, P ai, is
P = P + ∆ P (6-81)
ai bh b
The flow condition in the inside of the drill string is two phase (gas and
incompressible fluid) flow. Equation 6-44 becomes
∫ P ai dP = ∫ H dh (6-82)
()
i
P in BP 0
where