Page 216 - Air and Gas Drilling Manual

5-58 Air and Gas Drilling Manual
The constants a i and b i are
˙
g
s
a =   S   + w   (5-13)
 1
i
 R    w ˙ g  
and
b = f  R   2 w ˙ g 2 (5-14)

π
i
2 gD  S    2 4
g
i
  D i
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 (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
f is the Fanning friction factor,
2
g is the acceleration of gravity (32.2 ft/sec ),
D i is the inside diameter of the drill pipe (in these calculations the inside
diameter of the drill pipe or innertube of dual wall pipe) (ft).
It should be noted that the above equations are for any set of consistent units.
Unless field test data are available that give the actual rock specific gravity, the
approximate average specific gravity for sedimentary rock is assumed to be 2.7, the
average specific gravity for igneous rock is assumed to be 2.8, and the average
specific gravity for metamorphic rock is assumed to be 3.0 [1].
Illustrative Examples 5.4, 5.5a, and 5.6a describe the implementation of the
basic planning steps Nos. 1 through 6 given in Section 5.1.
Illustrative Example 5.4 Using the basic equations above, determine the
reverse circulation minimum volumetric flow rate required to drill a well with a 12
1/4 inch openhole borehole (12 1/4 inch drill bit diameter) and a uniform drill string
composed of API 5 1/2 inch, 24.70 lb/ft nominal, IEU, FH, Grade E drill pipe (see
Table B-4). The inside diameter of the drill pipe body is 4.670 inches. The
anticipated drilling rate in a competent unfractured limestone sequence (sedimentary
rock) is assumed to be 78.4 ft/hr and the drilling depth is 1,000 ft.
In order to be able to calculate air drilling conditions at other surface elevations
above sea level, all calculations for basic values like the minimum volumetric flow
rate are carried out for a baseline reference atmosphere. For these calculations and
most of those in this treatise the reference atmosphere is the API Mechanical
Equipment Standards standard atmospheric conditions (see Chapter 4). These
conditions are a pressure of 14.696 psia and a temperature of 60˚F. Thus, the
pressure of the gas (in this case air) that will flow into the compressor, P at, is
.
p at = 14 696 psia