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178 Part III Underbalanced Drilling Systems

2
where P is pressure in lbf/ft at conduit length L in ft; P s is pressure in
2
lbf/ft at conduit length L =0;and
2
a = 0:0014d b S s R p + 0:25W m Q m + 1:44S l Q f + 0:019S g Q go cos ðθÞ (9.4)
TQ go

b = 0:033Q m + 0:023Q f (9.5)
TQ go

c = 9:77TQ go (9.6)
A

d = 0:33Q m + 0:22Q f (9.7)
A

f
e =± (9.8)
2gD H cos ðθÞ
m = cde (9.9)
2
1 + d e
2
n = c e (9.10)
2 2
ð1 + d eÞ
where
2
g = 32.2 ft/sec ; d b = bit diameter, in
S s = solid specific gravity, water = 1
R p = rate of penetration (ROP), ft/hr
W m = liquid weight, lbm/gal
Q m = liquid flow rate delivered by pump, gal/min
S l = formation fluid specific gravity, water = 1
Q f = formation fluid influx rate, bbl/hr
3
Q go = volumetric gas flow rate, ft /min
S g = specific gravity of gas, air = 1
T = absolute temperature, °R
θ = inclination angle, degrees
A = cross-sectional area of flow path, in 2
D H = hydraulic diameter of the flow path, ft
f = friction factor