Page 285 - Air and Gas Drilling Manual

6-30 Air and Gas Drilling Manual
P
≥
for air
P
ai
0 528
P . bh (6-98)
bh
for natural gas P ai ≥ (6-99)
.
0 549
the flow through the orifice or nozzle throat is sonic. Under these sonic flow
conditions, the upstream pressure, P ai, does not depend on downstream pressure, P bh.
For these sonic flow conditions the upstream pressure P ai is
˙
wT bh . 05
g
P = (6-100)
ai . 05
  k+  1 
  gk S   2   k−  1 
A n      
  R   k + 1  
 
If the upstream pressure is less than the right hand side of either Equations 6-98
or 6-99, the flow through the orifices or nozzles is subsonic and the upstream
pressure will be dependent on the pressure and temperature at the bottom of the
borehole annulus. Under these subsonic conditions the upstream pressure is
k
 w  2 k  −1
  ˙ g 
   A n   
P = P  + 1  (6-101)
ai bh    
2 g  k  P γ bh 
bh
  k − 1  
 
Note that Equations 6-100 and 6-101 do not account for friction flow loss through
the orifices and nozzles.
The flow condition in the inside of the drill string is two phase (gas and fluid)
flow. Equation 6-44 becomes
∫ P ai dP = ∫ H dh (6-102)
()
i
P in BP 0
where