Page 161 - Air and Gas Drilling Manual
P. 161
Chapter 5: Shallow Well Drilling Applications 5-3
3
bottomhole kinetic energy per unit volume of no less than 3.0 ft-lb/ft (see Chapter 8
for details). The basic equations used to determine the minimum volumetric flow
rate are derived in Chapter 6.
The minimum volumetric flow rates are calculated assuming that the boreholes
(surface to bottom) are openholes (not cased). The calculations for determining a
minimum volumetric flow rate is a trial and error process. The equations needed to
determine the minimum volumetric flow rate are outlined below. The critical
equation for determining the minimum volumetric flow rate is derived in Chapter 6.
This is the equation for the bottomhole pressure, P bh, in the annulus. This equation
is
2 aH 05 .
a
−
2
P bh = P ( at 2 + bT av) ebT av 2 (5-1)
T av
a
a
2
where P bh is the bottomhole pressure in the annulus (lb/ft , abs),
2
P at is the atmospheric pressure at the exit from the annulus (lb/ft , abs),
H is the depth of the borehole (ft),
T av is the average temperature of the borehole over the depth interval (˚R).
The constants a a and b a are
S w
˙
g
a = 1 + s (5-2)
a
R w ˙ g
and
b = f R 2 w ˙ g 2 (5-3)
a gD − 2
π
2 ( D ) S 2
h p g D ( 2 − p)
2
h D
4
where S g is the specific gravity of the gas (i.e., S g = 1.0 for air at standard
conditions),
R is the gas constant for API standard dry air (53.36 ft-lb/lb-˚R),
˙ w is the weight rate of flow of rock cuttings solids (lb/sec),
s
˙ w is the weight rate of flow of the gas (usually air) (lb/sec),
g
P g is the pressure of the gas entering the circulation system (in these
2
calculations the API standard atmospheric pressure) (lb/ft , abs),
f is the Fanning friction factor,
2
g is the acceleration of gravity (32.2 ft/sec ),
D h is the diameter of the borehole (ft),
D p is the outside diameter of the drill pipe (in these calculations the pipe body
outside diameter) (ft).
It should be noted that the above equations are for any set of consistent units.
