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Gas Drilling Operations 157

Assuming an isentropic process for an ideal gas flowing through bit
orifices, the temperature at the orifice downstream may be predicted
using the following equation (Guo and Ghalambor, 2005):

k−1

k
P dn
T dn = T up (7.6)
P up
where
o
o
T dn = downstream temperature, Ror K
o o
T up = upstream temperature, Ror K
2
P dn = downstream pressure, lb/ft or N/m 2
2 2
P up = upstream pressure, lb/ft or N/m
The upstream temperature may be lower than the geothermal tempera-
ture at the bit depth because the downstream gas cools the bit body, and
the bit body, in turn, cools the upstream gas. The process can continue
until a dynamic equilibrium with geothermal and gas temperatures is
reached at the bottom of the hole.
The downstream temperature predicted by Eq. (7.6) should be compared
with the ice point (the hydrate point for gas drilling with natural gas) and the
dew point of the water at in situ pressure to identify possible ice/hydrate and
condensation problems. The ice point of water at bottomhole pressure may
o
be assumed to be 32 F. The hydrate point of water can be found in many
sources, including Guo and Ghalambor (2005). The dew point of water
vapor at bottomhole pressure can be estimated based on the humidity of
the gas, the water removal efficiency of the compressor, the in situ water
saturation pressure, and the pressure above the bit orifice.
Two solutions to the ice/hydrate balling problem are reducing the gas
injection rate to avoid a sonic flow (see the next section) and using bits
with large orifices without installing bit nozzles. Both of these methods
can reduce the pressure drop at the bit so the downstream to upstream
pressure ratio will not become too low.

7.3.5 Problems Associated with Sonic Flow at the Bit
Two flow conditions required for fluid to flow through restrictions such
as orifices and nozzles are sonic flow and subsonic flow, also referred to
as critical flow and subcritical flow. Pressure waves, being mechanical
waves, obey the same principle as sound waves. When the fluid flow
velocity in an orifice is equal to or greater than the traveling velocity of