Page 157 - Air and gas Drilling Field Guide 3rd Edition

148 CHAPTER 6 Direct Circulation Models

through the circulating system is determined from the atmospheric pressure
and temperature of the air at the compressor location on the surface of the
earth, and the characteristics of the compressor(s). For air, the atmospheric
pressure and average annual temperatures for sea level and various elevations
above sea level can be approximated for most of North America by midlatitudes
data given in Tables 5-1a and 5-1b. These reference pressures are denoted as
p r and t r . For engineering calculations, the actual atmospheric pressure and tem-
perature of the air entering a primary compressor(s) are p at and t at and can be
approximated as
(6-2)
p at p r
t at t r ; (6-3)
2
where p at is the atmospheric pressure (psia, N/cm abs), p r is the reference atmo-
2
spheric pressure (psia, N/cm abs), t at is the atmospheric pressure (psia, N/cm 2

abs), and t r is the reference atmospheric temperature ( F, C). Also see Appendix
B for more detailed plots for atmospheric conditions for North America midlati-
tudes. Similar data as that given in Tables 5-1a and 5-1b and Appendix B for North
America midlatitudes can be obtained for most other continents and latitudes
around the world.
The aforementioned pressures and temperatures in field units must be con-
verted to units consistent with Equations (5-11) and (6-1). These are
(6-4)
P g ¼ P r
T g ¼ T r ; (6-5)
2
2
where P r is the reference atmospheric pressure (lb/ft abs, N/m abs), and T r is

the absolute atmospheric reference temperature ( R, K).
Substituting Equations (6-2) and (6-3) into Equation (5-11), the specific weight
of the gas (air) g g entering the compressor(s) is
P g S g P rl S g
g ¼ ¼ ; (6-6)
g
R e T g R e T rl
3 3
where g g is specific weight (lb/ft ,N/m ), R e is the engineering gas constant

(53.36 ft-lb/lb- R, 29.31 N-m/N-K), and S g is the specific gravity of the gas (S g ¼ 1.0
for air at standard conditions). The weight rate of flow of the gas _ w g through the
compressor is
_ w g ¼ g Q g ; (6-7)
g
where _ w g is the weight rate of flow of gas (lb/sec, N/sec) and Q g is the volumetric
3
3
flow rate of air into the circulation system (actual ft /sec, actual m /sec).
If the gas for the drilling operation is natural gas from a pipeline and the pres-
sure and temperature of the gas in the pipeline are p pl and t pl , then the pressure
and temperature of the gas entering either directly into the circulation system or
to the booster compressor are