Lyons W.C. (ed.). Standard handbook of petroleum and natural gas engineering.2001- Volume 1
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Downhole Motors
875
Similarly, the pressure drop across the bit
to
produce the above hydraulic
horsepower at a circulation flowrate of
300
gal/min is
85.05( 1,7 14)
300
APb
=
=
486
psi
The pressure drop across the bit at a circulation flowrate of
400
Ib/gal
is
Apb
=
364
psi
The pressure drop across the bit at a circulation flowrate
of
500
gal/min
Apb
=
292
psi
Total Pressure
LOSS.
Using Table
4-110
and Equations
4-150
and
4-151,
the
pressure loss across the turbine motor can be determined for the various
circulation flowrates and the mud weight of
16.2
lb/gal. These data together
with the above bit pressure loss data are presented in Table
4-1 13.
Also presented
in Table
4-113
are the component pressure losses of the system for the various
circulation
f
lowrates considered. The total pressure loss tabulated in the lower
row represents the surface standpipe pressure when operating at the various
circulation flowrates.
Pump Limitations.
Table
4-1 12
shows there are five possible liner sizes that can
be used on the Model
10-P-130
mud pump. Each liner size must be considered
to obtain the optimum circulation flowrate and appropriate liner size. The
maximum pressure available for each liner size will be reduced by a safety factor
of
0.90.*
The maximum volumetric flowrate available for each liner size
will
also be reduced by a volumetric efficiency factor of 0.80 and an additional safety
factor of
0.90.**
Thus, from Table
4-112,
the allowable maximum pressure and
allowable maximum volume, metric flowrates will be those shown in Figures
4-195
through
4-199,
which are the liner sizes
5
+,
5
fr,
5
j,
6
and
6
in., respectively.
Plotted on each of these figures are the total pressure losses for the various
circulation flowrates considered. The horizontal straight line on each figure
is
the allowable maximum pressure for the particular liner size. The vertical
straight line is the allowable maximum volumetric flowrate for the particular
liner size. Only circulation flowrates that are in the lower left quadrant
of
the
figures are practical. The highest circulation flowrate (which produces the
highest turbine motor horsepower) is found in Figure
4-197,
the 5Q-in. liner.
This optimal circulation flowrate is
340
gal/min.
Turbine Motor Performance.
Using the turbine
motor
performance data in
Table
4-110
and the scaling relationships in Equations
4-145
through
4-151,
the
performance graph for the turbine motor operating with a circulation flowrate
of
340
gal/min and mud weight of
16.2
lb/gal can be prepared. This is given
in Figure
4-200.
*This safety factor is not necessary
for
new, well-maintained equipment
**The volumetric efficiency factor is about
0.95
for precharged pumps.
876
Drilling and Well Completions
Table
4-113
Drill String Component Pressure
Losses
at
Various Circulation Flowrates for Example
2
Pressure
(psi)
Components
200
gpm
300
gpm
400
gpm
500
gpm
Surface Equipment
4
11 19 31
Drill Collar Bore 60 117 118 272
Turbine Motor 536 1207 2145 3352
Drill
Bit
729 486 364 292
Drill Collar Annulus 48 91 144 207
Drill Pipe Annulus 133 39 1 56 1 248
Total Pressure
Loss
1970 3038 4652 6736
Drill Pipe
Bore
460 878 1401
2021
-
-
-
-
Total Flow Area for Bit.
Knowing the optimal circulation flowrate, the actual
pressure loss across the bit can be found as before in the above. This is
85.05( 1,714)
340
APb
=
=
429
psi
With the flowrate and pressure loss across the bit, the total flow area of the
diamond bit
A,
(in.2) can be found using
[88]
(4-153)
where
ROP
=
rate of penetration in ft/hr
Nb
=
bit speed in rpm
The bit speed will be the optimum speed of the turbine motor,
685
rpm. The
total flow area
A,,
for the diamond bit is
1
1/2
(340)' 16.2
Ad
=
[
8795( 429)
]
0.9879
=
0.713
in.2
(text
continued
on
page
882)
Downhole
Motors
877
I
II
pall
=
4586 psi
qa,l
=
283
gpm
I
I
I
I
I
8000
6000
4000
2000
0
200
400
600
Figure
4-195.
5'h-in. liner,
total
pressure
loss
versus flowrate, Example
2.
(Courtesy
Smith
International, Inc.)
878
Drilling
and
Well
Completions
pd
=
4181
psi
q,,
=
310
gpm
8000
6000
4000
2000
0
200
400
600
q
(gpm)
Figure
4-196.
5%-in.
liner,
total pressure
loss
versus flowrate, Example
2.
(Courtesy
Smith
International, Inc.)
Downhole
Motors
879
pal,
=
3825
psi
qal,
=
340
gpm
8000
6000
4000
2000
0
200
400
600
Flgure
4-197.
5%-in. liner, total pressure
loss
versus flowrate, Example
2.
(Courtesy
Smith
International, Inc.)
Drilling and Well Completions
8000
6000
4000
2000
0
pal
=
3510
psi
q,,
=
370
gpm
I
I
I
I
-
-
-
-
-
-
-
I
I
I
I
I
-
II
1
200
400
600
Figure
4-198.
6-in. liner, total pressure loss versus flowrate, Example
2.
(Courtesy Smith International, Inc.)
Downhole
Motors
881
8000
6000
4000
2000
0
p,,
=
3236
psi
q,,
=
401
gpm
I
I
I
I
-
-
-
-
-
- -
-
7
-
200
400
600
9
(QPm)
Figure
4-199.
6'h-in. liner, total pressure
loss
versus flowrate, Example
2.
(Courtesy
Smith
International,
Inc.)
882
-
v
Q
I-
t
Drilling and Well Completions
4oM)
3000
ZOO0
IO00
0
Circulation
Rate
340
gpm
Mud
WeQht
16.2
pW
-
4
--D
Pressure
400
300
200
100
2000
1500
G
B
f
i
1000
E
c
5
u)
E
0
500
500
lo00
1500
2000
Bit
Speed
(rpm)
Figure 4-200.
Turbine motor, 6Wn. outside diameter, two motor sections,
212 stages,
340
galhin, 16.2-lb/gal mud weight, Example 2.
(Courtesy
Smith
International, Inc.)
(text
continued
from
page
876)
Positive Displacement Motor
Figure
4-201
shows the typical rigid rotor and flexible elastomer stator
configuration for a single chamber of a multichambered downhole positive
displacement motor section. All the positive displacement motors presently in
commercial use are of Moineau type, which uses a stator made of an elastomer.
The rotor is made of a rigid material such as steel and is fabricated in a helical
shape. The activating drilling mud, freshwater, aerated mud, foam or misted air
is pumped at rather high velocity through the motor section, which, because of
the eccentricity
of
the rotor and stator configuration, and the flexibility
of
the
stator, allows the hydraulic pressure of the flowing fluid to impart a torque to
the rotor. As the rotor rotates the fluid is passed from chamber to chamber (a
chamber is a lengthwise repeat of the motor). These chambers are separate
entities and as one opens up to accept fluid from the preceding, the preceding
closes up. This is the concept of the positive displacement motor.
Design
The rotational energy of the positive displacement motor is provided by the
flowing fluid, which rotates and imparts torque to the drill bit. Figure
4-202
shows
the typical complete downhole positive displacement motor.
Downhole Motors
883
Flow
Figure
4-201.
Basic positive displacement
motor
design principle. (Courtesy
Smith International, Inc.)
In general, the downhole positive displacement motor constructed on the
Moineau principle is composed of four sections:
(1)
the dump valve section,
(2)
the multistage motor section,
(3)
the connecting rod section and
(4)
the thrust
and radial-bearing section. These sections are shown in Figure
4-202.
Usually
the positive displacement motor has multichambers, however, the number
of chambers in a positive displacement motor is much less than the number of
stages in a turbine motor. A typical positive displacement motor has from two
to seven chambers.
The dump valve
is
a very important feature of the positive displacement motor.
The positive displacement motor does not permit fluid to flow through the
motor unless the motor is rotating. Therefore, a dump valve at the top of the
motor allows drilling fluid to be circulated to the annulus even if the motor
is not rotating. Most dump valve designs allow the fluid to circulate to the
annulus when the pressure is below a certain threshold, say below
50
psi or
so.
Only when the surface pump is operated does the valve close to force all fluid
through the motor.
The multichambered motor section is composed of only two continuous parts,
the rotor and the stator. Although they are continuous parts, they usually
constitute several chambers. In general, the longer the motor section, the more
chambers. The stator is an elastomer tube formed to be the inside surface of a
rigid cylinder. This elastomer tube stator is of a special material and shape. The
material resists abrasion and damage from drilling muds containing cuttings and
hydrocarbons. The inside surface of the stator is of an oblong, helical shape.
The rotor is a rigid steel rod shaped as a helix. The rotor, when assembled into
the stator and its outside rigid housing, provides continuous seal at contact
points between the outside surface of the rotor and the inside surface of the
stator (see Figure
4-201).
The rotor or driving shaft is made up of n, lodes. The
884
Drilling and Well Completions
Connec
ding
Rod
Section
lhruet
and Radial
Bearing Section
Figure
4-202.
Downhole positive displacement motor design.
(Courtesy Smith
International, Inc.)