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122 Part II Gas Drilling Systems

The weight rate of liquid depends on the misting water rate and the
formation fluid influx rate:

_ 5:616Q x 5:615Q f
W l = 62:4S x + 62:4S l
3,600 3,600 (6.7)
−2
_ W l = 9:74 × 10 ðS x Q x + S l Q f Þ

where
S x = specific gravity of misting liquid related to freshwater
3
Q x = misting liquid flow rate, bbl/hr or m /hr
S l = specific gravity of formation fluid related to freshwater
3
Q f = formation fluid influx flow rate, bbl/hr or m /hr
The weight rate of gas depends on the volumetric gas flow rate Q g (scf/min)
and the specific gravity of gas S g :

Q g
−3
_ W g = 0:0765S g = 1:275 × 10 S g Q g (6.8)
60
Substituting Eqs. (6.5) through (6.8) into Eq. (6.4) gives

S g P
γ = 1 + 0:074d b S s R p + 76:3ðS x Q x + S l Q f Þ (6.9)
m
S g Q go
53:3ðT s + GHÞ
The flow velocity of gas can be formulated based on the volumetric
gas flow rate, the flow path cross-sectional area, and the ideal gas law:

Q g ðT s + GHÞ
v g = 9:77 (6.10)
AP
Substituting Eqs. (6.9) and (6.10) into Eq. (6.2) yields
" 2 #
S g P
dP = 1 + 0:074d S s R p + 76:3ðS x Q x + S l Q f Þ
b
S g Q g
53:3ðT s + GHÞ
8 2 9

(6.11)
> Q go ðT s + GHÞ >
> f 9:77 >
> >
< AP =
× 1± dH
2g c D H
> >
> >
> >
: ;