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Gas Compressors 121

where the positive sign (+) represents upward flow and the negative sign (–)
represents downward flow. The γ m , the specific weight of the mixture at
depth H, is expressed as

_ W s + _ W g + _ W l
γ = (6.3)
m
Q s + Q g + Q l
where

_ W s = weight flow rate of solid, lb/sec or N/sec
_
W g = weight flow rate of gas, lb/sec or N/sec
_ W l = weight flow rate of liquid, lb/sec or N/sec
3
3
Q s = volumetric flow rate of solid, ft /sec or m /sec
3 3
Q g = volumetric flow rate of gas, ft /sec or m /sec
3
3
Q l = volumetric flow rate of liquid, ft /sec or m /sec
The sum of the volumetric flow rates of solid and liquid is usually less
than 5% of the total volumetric flow rate in air, gas, mist, and unstable
foam. Equation (6.3) can be simplified to
_ _ _
γ = W s + W g + W l (6.4)
m
Q g
The volumetric flow rate of gas is related to the weight flow rate of
gas through the ideal gas law:
_
Q g = 53:3W g ðT s + GHÞ (6.5)
S g P

where
T s = ambient temperature, °Ror °K
G = geothermal gradient, °F/ft or °C/m
S g = gas specific gravity, air = 1.0
The weight rate of solids depends on bit diameter (d b ), rate of penetration
(R p ), and specific gravity of solids (S s ):
2 R p
−5 2
_ W s = 62:4 π d b S s = 9:45 × 10 d S s R P (6.6)
4 12 3,600 b
where

d b = bit diameter, in or m
S s = specific gravity of solid related to freshwater
R p = rate of penetration, ft/hr or m/hr