U.S. patent application number 10/766494 was filed with the patent office on 2004-09-30 for roller-cone bits, systems, drilling methods, and design methods with optimization of tooth orientation.
This patent application is currently assigned to Halliburton Energy Service, Inc.. Invention is credited to Chen, Shilin.
Application Number | 20040188148 10/766494 |
Document ID | / |
Family ID | 32719414 |
Filed Date | 2004-09-30 |
United States Patent
Application |
20040188148 |
Kind Code |
A1 |
Chen, Shilin |
September 30, 2004 |
Roller-cone bits, systems, drilling methods, and design methods
with optimization of tooth orientation
Abstract
A novel and improved roller cone drill bit and method of design
are disclosed. A roller cone drill bit for drilling through
subterranean formations having an upper connection for attachment
to a drill string, and a plurality cutting structures rotatably
mounted on arms extending downward from the connection. A number of
teeth are located in generally concentric rows on each cutting
structure. The actual trajectory by which the teeth engage the
formation is mathematically determined. A straight-line trajectory
is calculated based on the actual trajectory. The teeth are
positioned in the cutting structures such each tooth having a
designed engagement surface is oriented perpendicular to the
calculated straight-line trajectory.
Inventors: |
Chen, Shilin; (Dallas,
TX) |
Correspondence
Address: |
BAKER BOTTS L.L.P.
Suite 600
2001 Ross Avenue
Dallas
TX
75201
US
|
Assignee: |
Halliburton Energy Service,
Inc.
|
Family ID: |
32719414 |
Appl. No.: |
10/766494 |
Filed: |
January 28, 2004 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10766494 |
Jan 28, 2004 |
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10189305 |
Jul 2, 2002 |
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10189305 |
Jul 2, 2002 |
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09629344 |
Aug 1, 2000 |
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6412577 |
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09629344 |
Aug 1, 2000 |
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09387304 |
Aug 31, 1999 |
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6095262 |
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Current U.S.
Class: |
175/341 ;
175/379 |
Current CPC
Class: |
E21B 10/16 20130101;
G06F 16/258 20190101 |
Class at
Publication: |
175/341 ;
175/379 |
International
Class: |
E21B 010/18 |
Claims
What is claimed is:
1. A drill bit comprising: a bit body; at least one roller cone
attached to the bit body and able to rotate with respect to the bit
body; and a plurality of cutting elements disposed on the at least
one roller cone, at least one bit design parameter selected so that
the cutting elements wear in a selected manner when drilling an
earth formation.
2. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to optimize a rate of penetration over the
life of the drill bit.
3. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to maximize a total life of the drill
bit.
4. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to optimize a rate of penetration and
maximize a total life of the drill bit.
5. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to substantially optimize a distribution of
axial forces over the drill bit over the life of the drill bit.
6. The drill bit of claim 1, wherein the drill bit comprises a
plurality of roller cones having cutting elements thereon, the at
least one bit design parameter selected to substantially balance
axial forces between roller cones over the life of the drill
bit.
7. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to substantially optimize work performed over
the drill bit over the life of the drill bit.
8. The drill bit of claim 1, wherein the drill bit comprises a
plurality of roller cones having cutting elements thereon, the at
least one bit design parameter selected to substantially balance
work performed between roller cones over the life of the drill
bit.
9. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to substantially optimize a volume of
formation cut by cutting elements over the drill bit over the life
of the drill bit.
10. The drill bit of claim 1, wherein the drill bit comprises a
plurality of roller cones having cutting elements thereon, the at
least one bit design parameter selected to substantially balance a
volume of formation cut by cutting elements between roller cones
over the life of the drill bit.
11. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to increase durability of the drill bit.
12. The drill bit of claim 11, wherein the at least one bit design
parameter comprises cutting element material.
13. The drill bit of claim 12, wherein the cutting element material
comprises tungsten carbide.
14. The drill bit of claim 12, wherein the cutting elements are
formed from at least two different materials.
15. The drill bit of claim 14, wherein at least one of the at least
two different materials comprises a hardfacing material.
16. The drill bit of claim 11, wherein the at least one bit design
parameter comprises a number of cutting elements.
17. The drill bit of claim 11, wherein the at least one bit design
parameter comprises a hardness of a cutting element material.
18. The drill bit of claim 11, wherein the at least one bit design
parameter comprises cutting element geometry.
19. The drill bit of claim 1, wherein the at least one bit design
parameter is selected to minimize wear of the cutting elements.
20. The drill bit of claim 19, wherein the at least one bit design
parameter comprises cutting element material.
21. The drill bit of claim 20, wherein the cutting element material
comprises tungsten carbide.
22. The drill bit of claim 20, wherein the cutting elements are
formed from at least two different materials.
23. The drill bit of claim 22, wherein at least one of the at least
two different materials comprises a hardfacing material.
24. The drill bit of claim 19, wherein the at least one bit design
parameter comprises a number of cutting elements.
25. The drill bit of claim 19, wherein the at least one bit design
parameter comprises a hardness of a cutting element material.
26. The drill bit of claim 19, wherein the at least one bit design
parameter comprises cutting element geometry.
27. The drill bit of claim 1, wherein the at least one bit design
parameter comprises cutting element material.
28. The drill bit of claim 27, wherein the cutting element material
comprises tungsten carbide.
29. The drill bit of claim 27, wherein the cutting elements are
formed from at least two different materials.
30. The drill bit of claim 29, wherein at least one of the at least
two different materials comprises a hardfacing material.
31. The drill bit of claim 1, wherein the at least one bit design
parameter comprises a number of cutting elements.
32. The drill bit of claim 31, wherein the at least one bit design
parameter comprises a hardness of a cutting element material.
33. The drill bit of claim 31, wherein the at least one bit design
parameter comprises cutting element geometry.
34. The drill bit of claim 1, wherein the at least one bit design
parameter comprises a number of cutting elements on each roller
cone.
35. The drill bit of claim 1, wherein the cutting element material
comprises tungsten carbide.
36. The drill bit of claim 1, wherein the at least one bit design
parameter comprises cutting element geometry.
Description
CROSS-REFERENCE TO OTHER APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/189,305 filed by Shilin Chen on Jul. 2,
2002, which is a continuation of U.S. Pat. application Ser. No.
09/629,344 filed by Shilin Chen on Aug. 1, 2000, now U.S. Pat. No.
6,412,577, which is a continuation of U.S. patent application Ser.
No. 09/387,304 filed by Shilin Chen on Aug. 31, 1999, now U.S. Pat.
No. 6,095,262, which claims the benefit of U.S. Provisional
Application Serial No. 60/098,422 filed on Aug. 31, 1998, which is
hereby incorporated by reference.
BACKGROUND AND SUMMARY OF THE INVENTION
[0002] The present invention relates generally to the drilling of
oil and gas wells, or similar drilling operations, and in
particular to orientation of tooth angles on a roller cone drill
bit.
[0003] Background: Rotary Drilling
[0004] Oil wells and gas wells are drilled by a process of rotary
drilling, using a drill rig such as is shown in FIG. 10. In
conventional vertical drilling, a drill bit 10 is mounted on the
end of a drill string 12 (drill pipe plus drill collars), which may
be more than a mile long, while at the surface a rotary drive (not
shown) turns the drill string, including the bit at the bottom of
the hole.
[0005] Two main types of drill bits are in use, one being the
roller cone bit, an example of which is seen in FIG. 11. In this
bit a set of cones 16 (two are visible) having teeth or cutting
inserts 18 are arranged on rugged bearings on the arms of the bit.
As the drill string is rotated, the cones will roll on the bottom
of the hole, and the teeth or cutting inserts will crush the
formation beneath them. (The broken fragments of rock are swept
uphole by the flow of drilling fluid.) The second type of drill bit
is a drag bit, having no moving parts, seen in FIG. 12.
[0006] Drag bits are becoming increasingly popular for drilling
soft and medium formations, but roller cone bits are still very
popular, especially for drilling medium and medium-hard rock. There
are various types of roller cone bits: insert-type bits, which are
normally used for drilling harder formations, will have teeth of
tungsten carbide or some other hard material mounted on their
cones. As the drill string rotates, and the cones roll along the
bottom of the hole, the individual hard teeth will induce
compressive failure in the formation.
[0007] The bit's teeth must crush or cut rock, with the necessary
forces supplied by the "weight on bit" (WOB) which presses the bit
down into the rock, and by the torque applied at the rotary drive.
While the WOB may in some cases be 100,000 pounds or more, the
forces actually seen at the drill bit are not constant: the rock
being cut may have harder and softer portions (and may break
unevenly), and the drill string itself can oscillate in many
different modes. Thus the drill bit must be able to operate for
long periods under high stresses in a remote environment.
[0008] When the bit wears out or breaks during drilling, it must be
brought up out of the hole. This requires a process called
"tripping": a heavy hoist pulls the entire drill string out of the
hole, in stages of (for example) about ninety feet at a time. After
each stage of lifting, one "stand" of pipe is unscrewed and laid
aside for reassembly (while the weight of the drill string is
temporarily supported by another mechanism). Since the total weight
of the drill string may be hundreds of tons, and the length of the
drill string may be tens of thousands of feet, this is not a
trivial job. One trip can require tens of hours and is a
significant expense in the drilling budget. To resume drilling the
entire process must be reversed. Thus the bit's durability is very
important, to minimize round trips for bit replacement during
drilling.
[0009] Background: Drill String Oscillation
[0010] The individual elements of a drill string appear heavy and
rigid. However, in the complete drill string (which can be more
than a mile long), the individual elements are quite flexible
enough to allow oscillation at frequencies near the rotary speed.
In fact, many different modes of oscillation are possible. (A
simple demonstration of modes of oscillation can be done by
twirling a piece of rope or chain: the rope can be twirled in a
flat slow circle, or, at faster speeds, so that it appears to cross
itself one or more times.) The drill string is actually a much more
complex system than a hanging rope, and can oscillate in many
different ways; see WAVE PROPAGATION IN PETROLEUM ENGINEERING,
Wilson C. Chin, (1994).
[0011] The oscillations are damped somewhat by the drilling mud, or
by friction where the drill pipe rubs against the walls, or by the
energy absorbed in fracturing the formation: but often these
sources of damping are not enough to prevent oscillation. Since
these oscillations occur down in the wellbore, they can be hard to
detect, but they are generally undesirable. Drill string
oscillations change the instantaneous force on the bit, and that
means that the bit will not operate as designed. For example, the
bit may drill oversize, or off-center, or may wear out much sooner
than expected. Oscillations are hard to predict, since different
mechanical forces can combine to produce "coupled modes"; the
problems of gyration and whirl are an example of this.
[0012] Background: Roller Cone Bit Design
[0013] The "cones" in a roller cone bit need not be perfectly
conical (nor perfectly frustroconical), but often have a slightly
swollen axial profile. Moreover, the axes of the cones do not have
to intersect the centerline of the borehole. (The angular
difference is referred to as the "offset" angle.) Another variable
is the angle by which the centerline of the bearings intersects the
horizontal plane of the bottom of the hole, and this angle is known
as the journal angle. Thus as the drill bit is rotated, the cones
typically do not roll true, and a certain amount of gouging and
scraping takes place. The gouging and scraping action is complex in
nature, and varies in magnitude and direction depending on a number
of variables.
[0014] Conventional roller cone bits can be divided into two broad
categories: Insert bits and steel-tooth bits. Steel tooth bits are
utilized most frequently in softer formation drilling, whereas
insert bits are utilized most frequently in medium and hard
formation drilling.
[0015] Steel-tooth bits have steel teeth formed integral to the
cone. (A hardmetal is typically applied to the surface of the teeth
to improve the wear resistance of the structure.) Insert bits have
very hard inserts (e.g. specially selected grades of tungsten
carbide) pressed into holes drilled into the cone surfaces. The
inserts extend outwardly beyond the surface of the cones to form
the "teeth" that comprise the cutting structures of the drill
bit.
[0016] The design of the component elements in a rock bit are
interrelated (together with the size limitations imposed by the
overall diameter of the bit), and some of the design parameters are
driven by the intended use of the product. For example, cone angle
and offset can be modified to increase or decrease the amount of
bottom hole scraping. Many other design parameters are limited in
that an increase in one parameter may necessarily result in a
decrease of another. For example, increases in tooth length may
cause interference with the adjacent cones.
[0017] Background: Tooth Design
[0018] The teeth of steel tooth bits are predominantly of the
inverted "V" shape. The included angle (i.e. the sharpness of the
tip) and the length of the tooth will vary with the design of the
bit. In bits designed for harder formations the teeth will be
shorter and the included angle will be greater. Gage row teeth
(i.e. the teeth in the outermost row of the cone, next to the outer
diameter of the borehole) may have a "T" shaped crest for
additional wear resistance.
[0019] The most common shapes of inserts are spherical, conical,
and chisel. Spherical inserts have a very small protrusion and are
used for drilling the hardest formations. Conical inserts have a
greater protrusion and a natural resistance to breakage, and are
often used for drilling medium hard formations.
[0020] Chisel shaped inserts have opposing flats and a broad
elongated crest, resembling the teeth of a steel tooth bit. Chisel
shaped inserts are used for drilling soft to medium formations. The
elongated crest of the chisel insert is normally oriented in
alignment with the axis of cone rotation. Thus, unlike spherical
and conical inserts, the chisel insert may be directionally
oriented about its center axis. (This is true of any tooth which is
not axially symmetric.) The axial angle of orientation is measured
from the plane intersecting the center of the cone and the center
of the tooth.
[0021] Background: Rock Mechanics and Formations
[0022] There are many factors that determine the drillability of a
formation. These include, for example, compressive strength,
hardness and/or abrasivity, elasticity, mineral content
(stickiness), permeability, porosity, fluid content and
interstitial pressure, and state of under-ground stress.
[0023] Soft formations were originally drilled with "fish-tail"
drag bits, which sheared the formation away. Roller cone bits
designed for drilling soft formations are designed to maximize the
gouging and scraping action. To accomplish this, cones are offset
to induce the largest allowable deviation from rolling on their
true centers. Journal angles are small and cone-profile angles will
have relatively large variations. Teeth are long, sharp, and
widely-spaced to allow for the greatest possible penetration.
Drilling in soft formations is characterized by low weight and high
rotary speeds.
[0024] Hard formations are drilled by applying high weights on the
drill bits and crushing the formation in compressive failure. The
rock will fail when the applied load exceeds the strength of the
rock. Roller cone bits designed for drilling hard formations are
designed to roll as close as possible to a true roll, with little
gouging or scraping action. Offset will be zero and journal angles
will be higher. Teeth are short and closely spaced to prevent
breakage under the high loads. Drilling in hard formations is
characterized by high weight and low rotary speeds.
[0025] Medium formations are drilled by combining the features of
soft and hard formation bits. The rock breaks away (is failed) by
combining compressive forces with limited shearing and gouging
action that is achieved by designing drill bits with a moderate
amount of offset. Tooth length is designed for medium extensions as
well. Drilling in medium formations is most often done with weights
and rotary speeds between that of the hard and soft formations.
Area drilling practices are evaluated to determine the optimum
combinations.
[0026] Background: Roller Cone Bit Interaction with the
Formation
[0027] In addition to improving drilling efficiency, the study of
bottom hole patterns has allowed engineers to prevent detrimental
phenomena such as those known as tracking, and gyration. The
impressions a tooth makes into the formation depend largely on the
design of the tooth, the tangential and radial scraping motions of
the tooth, the force and speed with which the tooth impacts the
formation, and the characteristics of the formation. Tracking
occurs when the teeth of a drill bit fall into the impressions in
the formation formed by other teeth at a preceding moment in time
during the revolution of the drill bit. Gyration occurs when a
drill bit fails to drill on-center. Both phenomena result in slow
rates of penetration, detrimental wear of the cutting structures
and premature failure of bits. Other detrimental conditions include
excessive uncut rings in the bottom hole pattern. This condition
can cause gyration, result in slow rates of penetration,
detrimental wear of the cutting structures and premature failure of
the bits. Another detrimental phenomenon is bit lateral vibration,
which can be caused by radial force imbalances, bit mass imbalance,
and bit/formation interaction among other things. This condition
includes directional reversals and gyration about the hole center
often known as whirl. Lateral vibration results in poor bit
performance, overgage hole drilling, out-of-round, or "lobed"
wellbores, and premature failure of both the cutting structures and
bearing systems of bits. (Kenner and Isbell, DYNAMIC ANALYSIS
REVEALS STABILITY OF ROLLER CONE ROCK BITS, SPE 28314, 1994).
[0028] Background: Bit Design Currently, roller cone bit designs
remain the result of generations of modifications made to original
designs. The modifications are based on years of experience in
evaluating bit records, dull bit conditions, and bottom hole
patterns.
[0029] One method commonly used to discourage bit tracking is known
as a staggered tooth design. In this design the teeth are located
at unequal intervals along the circumference of the cone. This is
intended to interrupt the recurrent pattern of impressions on the
bottom of the hole. Examples of this are shown in U.S. Pat. No.
4,187,922 and UK application 2,241,266.
[0030] Background: Shortcomings of Existing Bit Designs
[0031] The economics of drilling a well are strongly reliant on
rate of penetration. Since the design of the cutting structure of a
drill bit controls the bit's ability to achieve a high rate of
penetration, cutting structure design plays a significant role in
the overall economics of drilling a well. Current bit designs have
not solved the issue of tracking. Complex mathematical models can
simulate bottom hole patterns to a limited extent, but they do not
suggest a solution to the ever-present problem of tracking. The
known angular orientations of teeth designed to improve tooth
impact strength leave excessive uncut bottom hole patterns and do
not solve the problem of tracking. The known angular orientations
of teeth designed to increase bottom hole coverage, fail to
optimize tooth orientation and do not solve the problem of
tracking. Staggered tooth designs do not prevent tracking of the
outermost rows of teeth. On the outermost rows of each cone, the
teeth are encountering impressions in the formation left by teeth
on other cones. The staggered teeth are just as likely to track an
impression as any other tooth. Another disadvantage to staggered
designs is that they may cause fluctuations in cone rotational
speed, resulting in fluctuations in tooth impact force and
increased bit vibration. Bit vibration is very harmful to the life
of the bit and the life of the entire drill string.
[0032] Background: Cutting Structure Design
[0033] In the publication A NEW WAY TO CHARACTERIZE THE
GOUGING-SCRAPING ACTION OF ROLLER CONE BITS (Ma, Society of
Petroleum Engineers No. 19448, 1989), the author determines that a
tooth in the first (heel or gage) row of the drill bit evaluated
contacts the formation at -22 degrees (measured with respect to
rotation of the cone about its journal) and begins to separate at
an angle of -6 degrees. The author determines that the contacting
range for the second row of the same cone is from -26 degrees to 6
degrees. The author states that "because the crest of the chisel
inserts are always in the parallel direction with the generatrix of
the roller cone . . . radial scraping will affect the sweep area
only slightly." The author concludes that scraping distance is a
more important than the velocity of the cutter in determining
performance.
[0034] In U.S. Pat. No. 5,197,555, Estes discloses a roller cone
bit having opposite angular axial orientation of chisel shaped
inserts in the first and second rows of a cone. This invention is
premised on the determination that inserts scrape diagonally
inboard and either to the leading side (facing in the direction of
rotation) or to the trailing side (facing opposite to the direction
of rotation). It is noted that the heel row inserts engage the
formation to the leading side, while the second row inserts engage
the formation to the trailing edge. In one embodiment, the inserts
in the heel row are axially oriented at an angle between 30 degrees
and 60 degrees, while the inserts in the second row are axially
oriented between 300 degrees and 330 degrees. This orientation is
designed to provide the inserts with a higher resistance to
breakage. In an alternative embodiment, the inserts in the heel row
are oriented at an axial angle between 300 degrees and 330 degrees,
while the inserts in the second row are axially oriented between 30
degrees and 60 degrees. This orientation is designed to provide the
inserts with a broader contact area with the formation for
increased formation removal, and thereby an increased rate of
penetration of the drill bit into the formation.
[0035] Summary: Roller-Cone Bits, Systems, Drilling Methods, and
Design Methods with Optimization of Tooth Orientation
[0036] The present application describes bit design methods (and
corresponding bits, drilling methods, and systems) in which tooth
orientation is optimized jointly with other parameters, using
software which graphically displays the linearized trajectory of
each tooth row, as translated onto the surface of the cone.
Preferably the speed ratio of each cone is precisely calculated, as
is the curved trajectory of each tooth through the formation.
However, for quick feedback to a design engineer, linear
approximations to the tooth trajectory are preferably
displayed.
[0037] The disclosed innovations, in various embodiments, provide
one or more of at least the following advantages:
[0038] The disclosed methods provide a very convenient way for
designers to take full advantage of the precision of a
computer-implemented calculation of geometries. (The motion over
hole bottom of roller cone bit teeth is so complex that only a
complex mathematical model and associated computer program can
provide accurate design support.)
[0039] The disclosed methods provide convenient calculation of
tooth trajectory over the hole bottom during the period when the
tooth engages into and disengages from the formation.
[0040] The disclosed methods permit the orientation angle of teeth
in all rows to be accurately determined based on the tooth
trajectory.
[0041] The disclosed methods permit the influence of tooth
orientation changes on bit coverage ratio over the hole bottom to
be accurately estimated and compensated.
[0042] The disclosed methods also permit designers to optimally
select different types of teeth for different rows, based on the
tooth trajectory.
[0043] The following patent application describes roller cone drill
bit design methods and optimizations which can be used separately
from or in synergistic combination with the methods disclosed in
the present application. That application, which has common
ownership, inventorship, and effective filing date with the present
application, is:
[0044] application Ser. No. 09/387,737, filed 31 Aug. 1999,
entitled "Force-Balanced Roller-Cone Bits, Systems, Drilling
Methods, and Design Methods" (atty. docket no. SC-9825), now U.S.
Pat. No. 6,213,225, claiming priority from U.S. provisional
application No. 60/098,466 filed 31 Aug. 1998.
[0045] That nonprovisional application, and its provisional
priority application, are both hereby incorporated by
reference.
BRIEF DESCRIPTION OF THE DRAWINGS
[0046] The disclosed inventions will be described with reference to
the accompanying drawings, which show important sample embodiments
of the invention and which are incorporated in the specification
hereof by reference, wherein:
[0047] FIGS. 1A-1C shows a sample embodiment of a bit design
process, using the teachings of the present application.
[0048] FIG. 2 shows the tangential and radial velocity components
of tooth trajectory, viewed through the cutting face (i.e. looking
up).
[0049] FIGS. 3A, 3B, 3C, and 3D show plots of planar tooth
trajectories for teeth in four rows of a single cone, referenced to
the XY coordinates of FIG. 2.
[0050] FIGS. 4A and 4B show tangential and radial distances,
respectively, for the four tooth trajectories shown in FIGS.
3A-3D.
[0051] FIG. 5 is a sectional view of a cone (normal to its axis),
showing how the tooth orientation is defined.
[0052] FIG. 6 shows time-domain plots of tooth tangential speed,
for the five rows of a sample cone, over the duration of the
trajectory for each row.
[0053] FIGS. 7A and 7B show how optimization of tooth orientation
can perturb the width of uncut rings on the hole bottom.
[0054] FIGS. 8A and 8B show how optimization of tooth orientation
can disturb the tooth clearances.
[0055] FIGS. 9A, 9B and 9C show the screen views which a skilled
bit designer would see, according to some embodiments of the
invention, while working on a bit optimization which included
optimization of tooth orientation.
[0056] FIG. 10 shows a drill rig in which bits optimized by the
teachings of the present application can be advantageously
employed.
[0057] FIG. 11 shows a conventional roller cone bit, and FIG. 12
shows a conventional drag bit.
[0058] FIG. 13 shows a sample XYZ plot of a non-axisymmetric tooth
tip.
[0059] FIG. 14 shows axial and sectional views of the i-th cone,
and illustrates the enumeration of rows and teeth.
[0060] FIGS. 15A-15D show how the planarized tooth trajectories
vary as the offset is increased.
[0061] FIGS. 16A-16D show how the ERSD and ETSD values vary for all
rows of a given cone as offset is increased.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0062] The numerous innovative teachings of the present application
will be described with particular reference to the presently
preferred embodiment (by way of example, and not of
limitation).
[0063] Overview of Sample Design Process
[0064] FIG. 1A-1C show a sample embodiment of a bit design process,
using the teachings of the present application. Specifically, FIG.
1A shows an overview of the design process, and FIGS. 1B and 1C
expand specific parts of the process.
[0065] First, the bit geometry, rock properties, and bit
operational parameters are input (step 102). Then the 3D tooth
shape, cone profile, cone layout, 3D cone, 3D bit, and 2D hole
profile are displayed (step 104).
[0066] Since there are two types of rotation relevant to the
calculation of the hole bottom (cone rotation and bit rotation),
transformation matrices from cone to bit coordinates must be
calculated (step 106). (See FIG. 1B.) The number of bit revolutions
is input (step 108), and each cone is counted (step 110), followed
by each row of teeth for each cone (step 112). Next, the type of
teeth of each row is identified (step 114), and the teeth are
counted (step 116). Next, a time interval delta is set (step 118),
and the position of each tooth is calculated at this time interval
(step 120). If a given tooth is not "cutting" (i.e., in contact
with the hole bottom), then the algorithm continues counting until
a cutting tooth is reached (step 122). The tooth trajectory, speed,
scraping distance, crater distribution, coverage ratio and tracking
ratios for all rows, cones, and the bit are calculated (step 124).
This section of the process (depicted in FIG. 1B) gives the teeth
motion over the hole bottom, and displays the results (step
126).
[0067] Next the bit mechanics are calculated. (See FIG. 1C.) Again
transformation matrices from cone to bit coordinates are calculated
(step 128), and the number of bit revolutions and maximum time
steps, delta, are input (step 130). The cones are then counted
(step 132), the bit and cone rotation angles are calculated at the
given time step (step 134), and the rows are counted (step 136).
Next, the 3d tooth surface matrices for the teeth on a given row
are calculated (step 138). The teeth are then counted (step 140),
and the 3d position of the tooth on the hole bottom is calculated
at the given time interval (step 142). If a tooth is not cutting,
counting continues until a cutting tooth is reached (step 144). The
cutting depth, area, volume and forces for each tooth are
calculated, and the hole bottom model is updated (based on the
crater model for the type of rock being drilled). Next the number
of teeth cutting at any given time step is counted. The tooth force
is projected into cone and bit coordinates, yielding the total cone
and bit forces and moments. Finally the specific energy of the bit
is calculated (step 146).
[0068] Finally, all results are outputted (step 148). The process
can then be reiterated if needed.
[0069] Four Coordinate Systems
[0070] Four coordinate systems are used, in the presently preferred
embodiment, to define the crest point of a tooth in three
dimensional space. All the coordinate system obey the "Right Hand
Rule". These coordinate systems--tooth, cone, bit, and hole--are
described below.
[0071] Local Tooth Coordinates
[0072] FIG. 13 shows a sample XYZ plot of a tooth tip (in tooth
local coordinates). Tooth coordinates will be indicated here by the
subscript t. (Of course, each tooth has its own tooth coordinate
system.) The center of the X.sub.tY.sub.tZ.sub.t coordinate system,
in the presently preferred embodiment, is located at the tooth
center. The coordinate of a tooth's crest point P.sub.t will be
defined by parameters of the tooth profile (e.g. tooth diameter,
extension, etc.).
[0073] Cone Coordinates
[0074] FIG. 14 shows axial and sectional views of the i-th cone,
and illustrates the enumeration of rows and teeth. Cone coordinates
will be indicated here by the subscript c. The center of the cone
coordinates is located in the center of backface of the cone. The
cone body is fixed with respect to these coordinates, and hence
THESE COORDINATES ROTATE WITH THE CONE. (Of course, each cone has
its own cone coordinate system.) The axis Z.sub.c coincides with
the cone axis, and is oriented towards to the bit center. Cone axes
Y.sub.c and X.sub.c, together with axis Z.sub.c, follow the right
hand rule. As shown in FIG. 13, four parameters are enough to
completely define the coordinate of the crest point of a tooth on
cone profile. These four parameters are H.sub.c, R.sub.c,
.PHI..sub.c and .theta..sub.c. For all the teeth on the same row,
H.sub.c, R.sub.c, and .PHI..sub.c are the same.
[0075] Bit Coordinates
[0076] Similarly, a set of bit axes X.sub.bY.sub.bZ.sub.b,
indicated by the subscript b, is aligned to the bit. The bit is
fixed with respect to these coordinates, and hence THESE
COORDINATES ROTATE WITH THE BIT. Axis Z.sub.b preferably points
toward the cutting face, and axes X.sub.b and Y.sub.b are normal to
Z.sub.b (and follow the right-hand rule).
[0077] Hole Coordinates
[0078] The simplest coordinate system is defined by the hole axes
X.sub.hY.sub.hZ.sub.h, which are fixed in space. Note however that
axes Z.sub.b and Z.sub.h may not be coincident if the bit is
tilted. FIG. 2 shows the tangential and radial velocity components
of tooth trajectory, viewed through the cutting face (i.e. looking
up). Illustrated is a small portion of a tooth trajectory, wherein
a tooth's crest (projected into an X.sub.hY.sub.h plane which
approximates the bottom of the hole) moves from point A to point B,
over an arc distance ds and a radial distance dr.
[0079] Transformations
[0080] Since all of these coordinate systems are xyz systems, they
can be interrelated by simple matrix transformations.
[0081] Both the bit and the cones are rotating with-time. In order
to calculate the position on hole bottom where the crest point of a
tooth engages into formation, and the position that the crest point
of a tooth disengages from formation, all the teeth positions at
any time must be described in hole coordinate system XhYhZh.
[0082] The transformation from tooth coordinates
X.sub.tY.sub.tZ.sub.t to cone coordinates X.sub.cY.sub.cZ.sub.c can
be defined by a matrix Rtc, which is a matrix function of teeth
parameters:
Rtc=f(H.sub.c, R.sub.c, .theta..sub.c, .PHI..sub.c),
[0083] so that any point P.sub.t in X.sub.tY.sub.tZ.sub.t can be
transformed into local cone coordinates X.sub.cY.sub.cZ.sub.c
by:
P.sub.c=R.sub.tc*P.sub.t.
[0084] At time t=0, it is assumed that the plane
X.sub.cO.sub.cZ.sub.c is parallel to the bit axis. At time t, the
cone has a rotation angle .lambda. around its negative axis
(-Z.sub.c). Any point on the cone moves to a new position due to
this rotation. The new position of P.sub.c in X.sub.cY.sub.cZ.sub.c
can be determined by combining linear transforms.
[0085] The transform matrix due to cone rotation is R.sub.cone:
R.sub.cone=cos(.lambda.)I+(1-cos(.lambda.))NcNc'+sin(.lambda.)Mc,
[0086] where N.sub.c is the rotation vector and M.sub.c is a 3*3
matrix defined by N.sub.c.
[0087] Therefore, the new position P.sub.crot of P.sub.c due to
cone rotation is:
P.sub.crot=R.sub.cone*P.sub.c
[0088] Let R.sub.cb1, R.sub.cb2, and R.sub.cb3 be respective
transformation matrices (for cones 1, 2, and 3) from cone
coordinate to bit coordinates. (These matrices will be functions of
bit parameters such as pin angle, offset, and back face length.)
Any point P.sub.ci in cone coordinates can then be transformed into
bit coordinates by:
P.sub.b=R.sub.cbi*P.sub.ci+P.sub.c0i for i=1, 2, or 3,
[0089] where P.sub.c0i is the origin of cone coordinates in the bit
coordinate system.
[0090] The bit is rotating around its own axis. Let us assume that
the bit axes and hole axes are coincident at time t=0. At time t,
the bit has a rotation angle .beta.. The transform matrix due to
bit rotation is:
Rbh=cos(.beta.)I+(1-cos(.beta.))NbNb'+sin(.beta.)Mb
[0091] where Nb is the rotation vector and Mb is a 3*3 matrix
defined by Nb. Therefore, any point Pb in bit coordinate system can
be transformed into the hole coordinate system
X.sub.hY.sub.hZ.sub.h by:
Ph=Rbh*Pb.
[0092] Therefore, the position of the crest point of any tooth at
any time in three dimensional space has been fully defined by the
foregoing seven equations. In order to further determine the engage
and disengage point the formation is modeled, in the presently
preferred embodiment, by multiple stepped horizontal planes. (The
number of horizontal planes depends on the total number of rows in
the bit.) In this way, the trajectory of any tooth on hole bottom
can be determined.
[0093] Calculation of Trajectories in Bottomhole Plane
[0094] With the foregoing transformations, the trajectory of the
tooth crest across the bottom of the hole can be calculated. FIGS.
3A, 3B, 3C, and 3d show plots of planar tooth trajectories,
referenced to the hole coordinates X.sub.hY.sub.h, for teeth on
four different rows of a particular roller cone bit. The teeth on
the outermost row (first row) scrapes toward the leading side of
the cone. Its radial and tangential scraping distances are similar,
as can be seen by comparing the first bar in FIG. 4A with the first
bar in FIG. 4B. However for teeth on the second row the radial
scraping motion is much larger than the tangent motion. The teeth
on the third row scrape toward the trailing side of the cone, and
the teeth on the forth row scrape toward the leading side of the
cone.
[0095] FIGS. 4A and 4B show per-bit-revolution tangential and
radial distances, respectively, for the four tooth trajectories
shown in FIGS. 3A-3d. Note that, in this example, the motion of the
second row is almost entirely radial, and not tangential.
[0096] Projection of Trajectories into Cone Coordinates
[0097] The tooth trajectories described above are projected on the
hole bottom which is fixed in space. In this way it is clearly seen
how the tooth scrapes over the bottom. However for the bit
manufacturer or bit designer it is necessary to know the teeth
orientation angle on the cone coordinate, in order either to keep
the elongate side of the tooth perpendicular to the scraping
direction (for maximum cutting rate in softer formations) or to
keep the elongate side of the tooth in line with the scraping
direction (for durability in harder formations). To this end the
tooth trajectories are projected to the cone coordinate system. Let
P.sub.1={x.sub.1, y.sub.1, z.sub.1}.sub.c and P.sub.2={x.sub.2,
y.sub.2, Z.sub.2}.sub.c be the engage and disengage points on cone
coordinate system, respectively, and approximate the tooth
trajectory P.sub.1-P.sub.2 as a straight line. Then the scraping
angle in cone coordinates is:
R.sub.s={square root}{square root over
((x.sub.2-x.sub.1).sup.2+(y.sub.1+y- .sub.2).sup.2)}
[0098] and 1 s = tan - 1 ( R s z 2 - z 1 )
[0099] The teeth can then be oriented appropriately with respect to
this angle gamma. For example, for soft formation drilling the
tooth would preferably be oriented so that its broad side is
perpendicular to the scraping direction, in order to increase its
rate of rock removal. In this case, the direction .gamma..sub.c of
the elongate crest of the tooth, in cone coordinates, is normal to
.gamma..sub.s, i.e. .gamma..sub.c=y.sub.s+.pi./2. Conversely, for
drilling harder formations with a chisel-shaped tooth it might be
preferable to orient the tooth with minimum frontal area in the
direction of scraping, i.e. with y.sub.c
[0100] Derivation of Equivalent Radial and Tangential Scraping
[0101] There are numerous parameters in roller cone design, and
experienced designers already know, qualitatively, that changes in
cone shape (cone angle, heel angle, third angle, and oversize
angle) as well as offset and journal angle will affect the scraping
pattern of teeth in order to get a desired action-on-bottom. One
problem is that it is not easy to describe a desired
action-on-bottom quantitatively. The present application provides
techniques for addressing this need.
[0102] Two new parameters have been defined in order to
quantitatively evaluate the cone shape and offset effects on tooth
scraping motion. Both of these parameters can be applied either to
a bit or to individual cones.
[0103] (1) Equivalent Tangent Scraping Distance (ETSD) is equal to
the total tangent scraping distance of all teeth on a cone (or bit)
divided by the total number of the teeth on the cone (or bit).
[0104] (2) Equivalent Radial Scraping Distance (ERSD) is equal to
the total radial scraping distance of all teeth on a cone (or bit)
divided by the total number of the teeth on the cone (or bit).
[0105] Both of these two parameters they have much more clear
physical meaning than the offset value and cone shape.
[0106] Surprisingly, the arcuate (or bulged) shape of the cone
primarily affects the ETSD value, and the offset determines the
ERSD value. Also surprisingly, the ERSD is not equal to zero even
at zero offset. In other words, the teeth on a bit without offset
may still have some small radial scraping effects.
[0107] The radial scraping direction for all teeth is always toward
to the hole center (positive). However, the tangential scraping
direction is usually different from row to row.
[0108] In order to use the scraping effects fully and effectively,
the leading side of the elongated teeth crest should be orientated
at an angle to the plane of the cone's axis, which is calculated as
described above for any given row.
[0109] FIG. 2 shows the procedure in which a tooth cuts into (point
A) and out (point B) the formation. Due to bit offset, arcuate cone
shape and bit and cone rotations, the motion from A to B can be
divided into two parts: tangent motion ds and radial motion dr.
Notice the tangent and radial motions are defined in hole
coordinate system XhYh. Because ds and dr vary from row to row and
from cone to cone, we derive an equivalent tangent scraping
distance (ETSD) and an equivalent radial scraping distance (ERSD)
for a whole cone (or for an entire bit).
[0110] For a cone, we have 2 ETSD = j Nr ds j Nt j Nc and ERSD = j
Nr dr j Nt j Nc
[0111] where Nc is the total tooth count of a cone and Nr is the
number of rows of a cone.
[0112] Similarly for a bit, we have 3 ETSD = i 3 j Nr ds ij Nt ij
Nb and ERSD = i 3 j Nr dr ij Nt ij Nb
[0113] where Nb is the total tooth count of the bit.
[0114] FIGS. 15A-15D show how the planarized tooth trajectories
vary as the offset is increased. These figures clearly show that
with the increase of the offset value, the radial scraping distance
is increased. Surprisingly, the radial scraping distance is not
equal to zero even if the offset is zero. This is due to the
arcuate shape of the cone.
[0115] FIGS. 16A-16D show how the ERSD and ETSD values vary for all
rows of a given cone as offset is increased. From these Figures, it
can be seen that the tangent scraping distance of the gage row,
while very small compared to other rows but is not equal to zero.
It means that there is a sliding even for the teeth on the driving
row. This fact may be explained by looking at the tangent speed
during the entry and exit of teeth into and out of the rock. (FIG.
6 shows time-domain plots of tooth tangential speed, for the five
rows of a sample cone, over the duration of the trajectory for each
row.) During the cutting procedure the tangent speed is not equal
to zero except for one instant. Because the sliding speed changes
with time, the instantaneous speed is not the best way to describe
the teeth/rock interaction.
[0116] Note that the tangent scraping directions are different from
row to row for the same cone. FIG. 5 is a sectional view of a cone
(normal to its axis), showing how the tooth orientation is defined
in the present application: the positive direction is defmed as the
same direction as the bit rotation. This means that the leading
side of tooth on one row may be different from that on another
row.
[0117] The ERSD increases almost proportionally with the increase
of the bit offset. However, ERSD is not zero even if the bit offset
is zero. This is because the radial sliding speed is not always
zero during the procedure of tooth cutting into and cutting out the
rock.
[0118] Calculation of Uncut Rings, and Row Position Adjustment
[0119] FIGS. 7A and 7B show how optimization of tooth orientation
can perturb the width of uncut rings on the hole bottom. The width
of uncut rings is one of the design constraints: a sufficiently
narrow uncut ring will be easily fractured by adjacent cutter
action and mud flows, but too large an uncut ring will slow rate of
penetration. Thus one of the significant teachings of the present
application is that tooth orientation should not be adjusted in
isolation, but preferably should be optimized jointly with the
width of uncut rings.
[0120] Interference Check
[0121] Another constraint is tooth interference. In the crowded
geometries of an optimized roller cone design, it is easy for an
adjustment to row position to cause interference between cones.
FIGS. 8A and 8B graphically show how optimization of tooth
orientation can disturb the tooth clearances. Thus optimization of
tooth orientation is preferably followed by an interference check
(especially if row positions are changed).
[0122] Iteration
[0123] Preferably multiple iterations of the various optimizations
are used, to ensure that the various constraints and/or
requirements are all jointly satisfied according to an optimal
tradeoff.
[0124] Graphic Display
[0125] The scraping motion of any tooth on any row is visualized on
the designer's computer screen. The bit designer has a chance to
see quantitatively how large the motion is and in which direction
if bit geometric parameters like cone shape and offset are
changed.
[0126] FIGS. 9A, 9B and 9C show the screen views which a skilled
bit designer would see, according to some embodiments of the
invention, while working on a bit optimization which included
optimization of tooth orientation. These three views show
representations of tooth orientation and scraping direction for
each tooth row on each of the three cones. This simple display
allows the designer to get a feel for the effect of various
parameter variations
[0127] Calculation of Cone/Bit Rotation Ratio
[0128] The present application also teaches that the ratio between
the rotational speeds of cone and bit can be easily checked, in the
context of the detailed force calculations described above, simply
by calculating the torques about the cone axis. If these torques
sum to zero (at a given ratio of cone and bit speed), then the
given ratio is correct. If not, an iterative calculation can be
performed to find the value of this ratio.
[0129] However, it should be noted that the exact calculation of
the torque on the cones is dependent on use of a solid-body tooth
model, as described above, rather than a mere point
approximation.
[0130] Previous simulations of roller cone bits have assumed that
the gage row is the "driving" row, which has no tangential slippage
against the cutting face. However, this is a simplification which
is not completely accurate. Accurate calculation of the ratio of
cone speed to bit speed shows that it is almost never correct, if
multiple rows of teeth are present, to assume that the gage row is
the driver.
[0131] Changes in the tooth orientation angle will not themselves
have a large immediate effect on the cone speed ratio. However, the
tooth orientation affects the width of uncut rings, and excessive
uncut ring width can require the spacing of tooth rows to be
changed. Any changes in the spacing of tooth rows will probably
affect the cone speed ratio.
[0132] Definitions:
[0133] Following are short definitions of the usual meanings of
some of the technical terms which are used in the present
application. (However, those of ordinary skill will recognize
whether the context requires a different meaning.) Additional
definitions can be found in the standard technical dictionaries and
journals.
[0134] Drag bit: a drill bit with no moving parts that drills by
intrusion and drag.
[0135] Mud: the liquid circulated through the wellbore during
rotary drilling operations, also referred to as drilling fluid.
Originally a suspension of earth solids (especially clays) in
water, modem "mud" is a three-phase mixture of liquids, reactive
solids, and inert solids.
[0136] Nozzle: in a passageway through which the drilling fluid
exits a drill bit, the portion of that passageway which restricts
the cross-section to control the flow of fluid.
[0137] Orientation: the angle of rotation with which a
non-axisymmetric tooth is inserted into a cone. Note that a tooth
which is axisymmetric (e.g. one having a hemispherical tip) cannot
have an orientation.
[0138] Roller cone bit: a drilling bit made of two, three, or four
cones, or cutters, that are mounted on extremely rugged bearings.
Also called rock bits. The surface of each cone is made up of rows
of steel teeth (generally for softer formations) or rows of hard
inserts (typically of tungsten carbide) for harder formations.
[0139] According to a disclosed class of innovative embodiments,
there is provided: A method of designing a roller cone bit,
comprising the steps of: adjusting the orientation of at least one
tooth on a cone, in dependence on an expected trajectory of said
tooth through formation material at the cutting face, in dependence
on an estimated ratio of cone rotation to bit rotation;
recalculating said ratio, if the location of any row of teeth on
said cone changes during optimization; recalculating the trajectory
of said tooth in accordance with a recalculated value of said cone
speed; and adjusting the orientation of said tooth again, in
accordance with a recalculated value of said tooth trajectory.
[0140] According to another disclosed class of innovative
embodiments, there is provided: A method of designing a roller cone
bit, comprising the steps of: calculating the trajectory of at
least one tooth on each cone through formation material at the
cutting face; and jointly optimizing both the orientations of said
teeth and the width of uncut rings on said cutting face, in
dependence on said trajectory.
[0141] According to another disclosed class of innovative
embodiments, there is provided: A method of designing a roller cone
bit comprising the steps of: a) adjusting the orientation of at
least one row of teeth on a cone, in dependence on an expected
trajectory of said tooth through formation material at the cutting
face; b) calculating the width of uncut rings of formation
material, in dependence on the orientation of said row of teeth,
and adjusting the position of said row of teeth in dependence on
said calculated width; and c) recalculating the rotational speed of
said cone, if the position of said row is changed, and accordingly
recalculating said trajectory of teeth in said row.
[0142] According to another disclosed class of innovative
embodiments, there is provided: A method of designing a roller cone
bit, comprising the steps of: calculating the respective
trajectories, of at least two non-axisymmetric teeth in different
rows of a roller cone bit, through formation material at the
cutting face; and graphically displaying, to a design engineer,
both said trajectories and also respective orientation vectors of
said teeth, as the engineer adjusts design parameters.
[0143] According to another disclosed class of innovative
embodiments, there is provided: A method of designing a roller cone
bit, comprising the steps of: calculating the curved trajectory of
a non-axisymmetric tooth through formation material at the cutting
face, as the bit and cones rotate; calculating a straight line
approximation to said curved trajectory; and orienting said tooth
with respect to said approximation, and not with respect to said
curved trajectory.
[0144] According to another disclosed class of innovative
embodiments, there is provided: A roller cone drill bit designed by
any of the methods described above, singly or in combination.
[0145] According to another disclosed class of innovative
embodiments, there is provided: A rotary drilling system,
comprising: a roller cone drill bit designed by any of the methods
described above, singly or in combination. a drill string which is
mechanically connected to said bit; and a rotary drive which
rotates at least part of said drill string together with said
bit.
[0146] According to another disclosed class of innovative
embodiments, there is provided: A method for rotary drilling,
comprising the actions of: applying weight-on-bit and rotary
torque, through a drill string, to a drill bit designed in
accordance with any of the methods described above, singly or in
combination.
[0147] Modifications and Variations
[0148] As will be recognized by those skilled in the art, the
innovative concepts described in the present application can be
modified and varied over a tremendous range of applications, and
accordingly the scope of patented subject matter is not limited by
any of the specific exemplary teachings given.
[0149] For example, the various teachings can optionally be adapted
to two-cone or four-cone bits.
[0150] In the example of FIGS. 9A-9C the crest profiles of all rows
except the gage rows are shown as identical (and their crest
orientations are indicated by simple ellipses). However, this is
not necessary: optionally the designer can be allowed to plug in
different tooth profiles for different rows, and the optimization
routines can easily substitute various tooth profiles as desired.
In particular, various tooth shapes can be selected from a library
of profiles, to fit the scraping motion of each row.
[0151] In one contemplated class of alternative embodiments, the
orientations of teeth can be perturbed about the optimal value, to
induce variation between the gage rows of different cones (or
within an inner row of a single cone), to provide some additional
resistance to tracking.
[0152] Of course the bit will also normally contain many other
features besides those emphasized here, such as gage buttons, wear
pads, lubrication reservoirs, etc. etc.
[0153] Additional general background, which helps to show the
knowledge of those skilled in the art regarding implementations and
the predictability of variations, may be found in the following
publications, all of which are hereby incorporated by reference:
APPLIED DRILLING ENGNIEERING, Adam T. Bourgoyne Jr. et al., Society
of Petroleum Engineers Textbook series (1991), OL AND GAS FIELD
DEVELOPMENT TECHNIQUES: DRILLING, J. -P. Nguyen (translation 1996,
from French original 1993), MAKING HOLE (1983) and DRILLING MUD
(1984), both part of the Rotary Drilling Series, edited by Charles
Kirkley.
[0154] None of the description in the present application should be
read as implying that any particular element, step, or function is
an essential element which must be included in the claim scope: THE
SCOPE OF PATENTED SUBJECT MATTER IS DEFINED ONLY BY THE ALLOWED
CLAIMS. Moreover, none of these claims are intended to invoke
paragraph six of 35 USC section 112 unless the exact words "means
for" are followed by a participle.
* * * * *