Page 596 - Air and Gas Drilling Manual

11-34 Air and Gas Drilling Manual
directly proportional to the volumetric flow rate of the fluid. The torque that the
rotor shaft can produce is nearly directly proportional to the pressure drop through
the motor. Thus, the power the motor can generate is also directly proportional to
the pressure drop through the motor. Figure 11-12 shows the torque and power
outputs versus pressure drop plots for a typical 6 3/4 inch outside diameter, 5:6
lobe, downhole positive displacement motor with a volumetric flow rate of 400
gal/min of drilling mud or other incompressible drilling fluid.
The plots in Figure 11-12 are for the drilling fluid volumetric flow rate of 400
gal/min. This volumetric flow rate gives a nearly constant motor rotor rotation
speed of 200 rpm (the drill bit speed). There are a similar family of plots that can be
prepared for this motor for other drilling fluid volumetric flow rates. Higher
volumetric flow rates yield higher drill bit speeds and lower volumetric flow rates
yield lower drill bit speeds. The torque and power plots are similarly altered for
increases and decreases in volumetric flow rates.
Illustrative Example 11.2 Determine the injection pressure and resulting
compressor fuel consumption when a Baker Oil Tools Model Mach 1, 6 3/4 inch
outside diameter, 5:6 lobe, downhole positive displacement motor is utilized to drill
the openhole interval from 7,000 ft to 10,000 ft of the Illustrative Example 8.3
series in Chapter 8. The positive displacement motor is to use a 7 7/8 inch tri-cone
roller cutter drill bit to drill at 10,000 ft. It is required that the downhole motor
develop 25 horsepower when drilling under load. In the Illustrative Example 8.3
series two semi-trailer mounted Dresser Clark Model CFB-4, four-stage,
reciprocating piston compressors where selected. Each of these compressors where
driven by a Caterpillar Model D398 diesel fueled prime mover. These two
compressor units provide a total of 2,400 acfm to the borehole. The drilling
location is at 4,000 ft above sea level. The annulus solution given in Illustrative
Example 8.3b will be used as the starting point for this example.
In Illustrative Example 8.3b the bottomhole annulus pressure was determined.
This annulus bottomhole pressure was found to be
p a5 204 5 psia
.
P p 144
a5 a5
2
,
P 29 448 lb/ft abs
a5
Using the positive displacement motor to drill the borehole does not alter the
annulus solution obtained in Illustrative Example 8.3b. However, it will alter the
pressure calculations from the bottom of the annulus to the top of the inside of the
drill string (the injection pressure).
Drill Bit Nozzles
The tri-cone roller cutter drill bit used in this example operation has three
nozzles. The nozzle inside diameter is selected by trial and error. Figure 11-12
shows that for a drilling mud flow rate of 400 gal/min, the drill bit speed will be
200 rpm. Thus, the nozzles inside diameter must be selected to give a simulated