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Gas Drilling Operations 159

The flow equation for subsonic flow is Eq. (6.30):

v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k + 1
2 3
u
2
u k k
k
u P dn P dn
Q g = 6:02CA o P up t 4 − 5 (7.9)
ðk − 1ÞS g T up P up P up
Substituting C =0.6, k = 1.4, and the critical pressure ratio of 0.53 into this
equation gives an expression of maximum gas flow rate without causing
sonic flow as

A o P up
(7.10)
Q gmax = 1:75 p ffiffiffiffiffiffiffiffiffiffiffi
S g T up
If the operating gas injection rate is higher than this value, larger orifice
area A o should be utilized.
The problem of wellbore washout is frequently encountered in gas
drilling. It may be attributed to three effects: High-velocity gas out of the bit
orifice can create hole enlargement in soft formations at the bottomhole;

Illustrative Example 7.3
For the well conditions given in Illustrative Example 6.4, check the design gas
injection rate of 1,615 scf/min against the maximum gas flow rate without
causing sonic flow.

Solution
The computer program GasDrill-09.xls.gives the follow data:
Total bit orifice area: 0.92 in 2
Upstream pressure of bit orifice: 15,845 lb/ft 2
True vertical depth at collar shoulder: 4,327 ft
o
Temperature at collar shoulder: 578 R
Equation (7.10) gives

= 2,345 scf/min
ð0:92Þð15,845Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Q gmax = 1:75 p
ð1Þð578Þ
Thedesigngas injectionrateof1,615scf/minislessthan2,345scf/min, so
sonic flow is not expected.