SYSTEM AND METHOD FOR IMPROVING STABILITY OF DRILLING TOOLS

SYSTEME ET PROCEDE POUR AMELIORER LA STABILITE D'OUTILS DE FORAGE

English Abstract

According to some embodiments of the present disclosure, a method for configuring a drill bit comprises determining a number of blades of a drill bit. If the number of blades of the drill bit equals five, the method further comprises disposing each of a plurality of depth of cut controllers (DOCCs) on one of the blades of the drill bit such that each group of three radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced. If the number of blades of the drill bit is greater than five, the method further comprises disposing each of the plurality of DOCCs on one of the blades of the drill bit such that each group of four radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.

French Abstract

La présente invention concerne un procédé pour configurer un foret. Ledit procédé comprend la détermination d'un nombre de lames d'un foret. Si le nombre de lames du foret est égal à cinq, le procédé comprend en outre la disposition de chacun parmi une pluralité de dispositifs de commande de profondeur de coupe (« Depth Of Cut Controllers » ou DOCC) sur une des lames du foret de sorte que chaque groupe de trois DOCC consécutifs radialement parmi la pluralité de DOCC soit sensiblement équilibré en force. Si le nombre de lames du foret est supérieur à cinq, le procédé comprend en outre la disposition de chacun parmi la pluralité de DOCC sur une des lames du foret de sorte que chaque groupe de quatre DOCC consécutifs radialement parmi la pluralité de DOCC soit sensiblement équilibré en force.

Claims

38
WHAT IS CLAIMED IS:
1. A method for configuring a drill bit comprising:
determining a number of blades of a drill bit;
if the number of blades of the drill bit equals five, disposing each of a
plurality of
depth of cut controllers (DOCCs) on one of the blades of the drill bit such
that each group
of three radially consecutive DOCCs of the plurality of DOCCs is substantially
force
balanced; and
if the number of blades of the drill bit is greater than five, disposing each
of the
plurality of DOCCs on one of the blades of the drill bit such that each group
of four
radially consecutive DOCCs of the plurality of DOCCs is substantially force
balanced.
2. The method of Claim 1, further comprising adjusting an axial position of

at least one of the plurality of DOCCs such that the plurality of DOCCs are in
contact
with a formation to be drilled at substantially the same time.
3. The method of Claim 2, further comprising adjusting the axial position
of
the at least one DOCC based on a critical depth of cut control curve.
4. The method of Claim 1, further comprising:
determining a desired radial position for each of the plurality of DOCCs; and
disposing each of the plurality of DOCCs on one of the blades based on the
desired radial position of the respective DOCC.
5. The method of Claim 4, further comprising determining the desired radial

position for each of the plurality of DOCCs such that the desired radial
position of each of
the plurality of DOCCs at least partially overlaps the desired radial position
of its
respective neighbor DOCC in a radial plane.
6. The method of Claim 1, further comprising disposing each of the
plurality
of DOCCs on one of the blades such that each DOCC of each group of three
radially
consecutive DOCCs is generally spaced symmetrically from the other DOCCs of
the
respective group on a face of the drill bit.

39
7. The method of Claim 1, further comprising disposing each of the
plurality
of DOCCs on one of the blades such that each DOCC of each group of four
radially
consecutive DOCCs is generally spaced symmetrically from the other DOCCs of
the
respective group on a face of the drill bit.
8. The method of Claim 1, further comprising disposing each of the
plurality
of DOCCs on one of the blades such that each DOCC of each group of three
radially
consecutive DOCCs is spaced from the other DOCCs of the respective group by
between
approximately 100 degrees and 140 degrees with respect to a rotational axis of
the drill
bit.
9. The method of Claim 1, further comprising disposing each of the
plurality
of DOCCs on one of the blades such that each DOCC of each group of four
radially
consecutive DOCCs is spaced from the other DOCCs of the respective group by
between
approximately 75 degrees and 105 degrees with respect to a rotational axis of
the drill bit.
10. The method of Claim 1, wherein if the number of blades of the drill bit
is
five, the method further comprises:
disposing each DOCC of a first group of three radially consecutive DOCCs on
one of the blades such that the first group is substantially force balanced,
the first group
of three radially consecutive DOCCs including a first DOCC, a second DOCC
neighboring the first DOCC in a radial plane, and a third DOCC neighboring the
second
DOCC in the radial plane; and
disposing a fourth DOCC on one of the blades such that a second group of three

radially consecutive DOCCs is substantially force balanced, the fourth DOCC
neighboring the third DOCC in the radial plane, and the second group of three
radially
consecutive DOCCs including the second DOCC, the third DOCC, and the fourth
DOCC.
11. The method of Claim 1, wherein if the number of blades of the drill bit
is
greater than five, the method further comprises:
disposing each DOCC of a first group of four radially consecutive DOCCs on one

of the blades such that the first group is substantially force balanced, the
first group of
four radially consecutive DOCCs including a first DOCC, a second DOCC
neighboring




40
the first DOCC in a radial plane, a third DOCC neighboring the second DOCC in
the
radial plan, and a fourth DOCC neighboring the third DOCC in the radial plane;
and
disposing a fifth DOCC on one of the blades such that a second group of four
radially consecutive DOCCs is substantially force balanced, the fifth DOCC
neighboring
the fourth DOCC in the radial plane and the second group of four radially
consecutive
DOCCs including the second DOCC, the third DOCC, the fourth DOCC, and the
fifth
DOCC.
12. A drill bit comprising:
a bit body including a rotational axis extending therethrough;
five blades disposed on the bit body that form a bit face;
a plurality of cutting elements each disposed on one of the blades; and
a plurality of depth of cut controllers (DOCCs) configured to control a depth
of
cut of at least one of the cutting elements, each of the plurality of DOCCs
disposed on
one of the blades such that each group of three radially consecutive DOCCs of
the
plurality of DOCCs is substantially force balanced.
13. The drill bit of Claim 12, wherein each DOCC of the plurality of DOCCs
has an axial position such that the plurality of DOCCs are in contact with a
formation to
be drilled at substantially the same time.
14. The drill bit of Claim 13, wherein the axial position of the plurality
of
DOCCs is based on a critical depth of cut control curve.
15. The drill bit of Claim 12, wherein each DOCC of the plurality of DOCCs
has a desired radial position and each of the plurality of DOCCs is disposed
on one of the
blades based on the desired radial position of the respective DOCC.
16. The drill bit of Claim 15, wherein the desired radial position for each
of
the plurality of DOCCs is such that the desired radial position of each of the
plurality of
DOCCs at least partially overlaps the desired radial position of its
respective neighbor
DOCC in a radial plane.




41
17. The drill bit of Claim 12, wherein each of the plurality of DOCCs is
disposed on one of the blades such that each DOCC of each group of three
radially
consecutive DOCCs is generally spaced symmetrically from the other DOCCs of
the
respective group on a face of the drill bit.
18. The drill bit of Claim 12, wherein each of the plurality of DOCCs is
disposed on one of the blades such that each DOCC of each group of three
radially
consecutive DOCCs is spaced from the other DOCCs of the respective group by
between
approximately 100 degrees and 140 degrees with respect to the rotational axis
of the drill
bit.
19. A drill bit comprising:
a bit body including a rotational axis extending therethrough;
more than five blades disposed on the bit body to form a bit face;
a plurality of cutting elements each disposed on one of the blades; and
a plurality of depth of cut controllers (DOCCs) configured to control a depth
of
cut of at least one of the cutting elements, each of the plurality of DOCCS
disposed on
one of the blades such that each group of four radially consecutive DOCCs of
the
plurality of DOCCs is substantially force balanced.
20. The drill bit of Claim 19, wherein each DOCC of the plurality of DOCCs
has an axial position such that the plurality of DOCCs are in contact with a
formation to
be drilled at substantially the same time.
21. The drill bit of Claim 20, wherein the axial position of the plurality
of
DOCCs is based on a critical depth of cut control curve.
22. The drill bit of Claim 19, wherein each DOCC of the plurality of DOCCs
has a desired radial position and each of the plurality of DOCCs is disposed
on one of the
blades based on the desired radial position of the respective DOCC.
23. The drill bit of Claim 22, wherein the desired radial position for each
of
the plurality of DOCCs is such that the desired radial position of each of the
plurality of




42
DOCCs at least partially overlaps the desired radial position of its
respective neighbor
DOCC in a radial plane.
24. The drill bit of Claim 19, wherein each of the plurality of DOCCs is
disposed on one of the blades such that each DOCC of each group of four
radially
consecutive DOCCs is generally spaced symmetrically from the other DOCCs of
the
respective group on a face of the drill bit.
25. The drill bit of Claim 19, wherein each of the plurality of DOCCs is
disposed on one of the blades such that each DOCC of each group of four
radially
consecutive DOCCs is spaced from the other DOCCs of the respective group by
between
approximately 75 degrees and 105 degrees with respect to the rotational axis
of the drill
bit.

Description

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1
SYSTEM AND METHOD FOR IMPROVING STABILITY OF DRILLING TOOLS
TECHNICAL FIELD
The present disclosure relates generally to downhole drilling tools and, more
particularly, to a system and method for improving the stability of drilling
tools.
BACKGROUND
Various types of downhole drilling tools including, but not limited to, rotary
drill
bits, reamers, core bits, and other downhole tools have been used to form
wellbores in
associated downhole formations. Examples of such rotary drill bits include,
but are not
limited to, fixed cutter drill bits, drag bits, polycrystalline diamond
compact (PDC) drill
bits, and matrix drill bits associated with forming oil and gas wells
extending through one
or more downhole formations. Fixed cutter drill bits such as a PDC bit may
include
multiple blades that each include multiple cutting elements.
In typical drilling applications, a PDC bit may be used to drill through
various
levels or types of geological formations with longer bit life than non-PDC
bits. Typical
formations may generally have a relatively low compressive strength in the
upper
portions (e.g., shallower drilling depths) of the formation and a relatively
high
compressive strength in the lower portions (e.g., deeper drilling depths) of
the formation.
A drilling tool may include one or more depth of cut controllers (DOCCs)
configured to control the amount that a drilling tool cuts into the side of a
geological
formation. However, conventional DOCC configurations may be such that all the
DOCCs
configured to control the depth of cut of a drilling tool for a desired depth
of cut may not
be in contact with the formation at the same time. Accordingly, the DOCCs may
not
control the depth of cut of the cutting tools to the desired depth of cut and
may unevenly
control the depth of cut with respect to each other. Such uneven depth of cut
control may
result in imbalance forces and vibrations. Further, traditional layouts of
DOCCs on a
drilling tool may add to these imbalance forces.
SUMMARY
According to some embodiments of the present disclosure, a method for
configuring a drill bit comprises determining a number of blades of a drill
bit. If the
number of blades of the drill bit equals five, the method further comprises
disposing each
of a plurality of depth of cut controllers (DOCCs) on one of the blades of the
drill bit such
that each group of three radially consecutive DOCCs of the plurality of DOCCs
is

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substantially force balanced. If the number of blades of the drill bit is
greater than five,
the method further comprises disposing each of the plurality of DOCCs on one
of the
blades of the drill bit such that each group of four radially consecutive
DOCCs of the
plurality of DOCCs is substantially force balanced.
BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of the present disclosure and its features
and
advantages, reference is now made to the following description, taken in
conjunction with
the accompanying drawings, in which:
FIGURE 1 illustrates an example embodiment of a drilling system in accordance
with some embodiments of the present disclosure;
FIGURE 2 illustrates a bit face profile of a drill bit forming a wellbore, in
accordance with some embodiments of the present disclosure;
FIGURE 3 illustrates a blade profile that may represent a cross-sectional view
of a
blade of a drill bit, in accordance with some embodiments of the present
disclosure;
FIGURE 4A illustrates the face of a drill bit including a depth of cut
controller
(DOCC) having forces acting upon it during drilling, in accordance with some
embodiments of the present disclosure;
FIGURE 4B illustrates a bit face profile of the drill bit of FIGURE 4A;
FIGURE 5A illustrates the face of an example drill bit including DOCCs that
may
be substantially force balanced, in accordance with some embodiments of the
present
disclosure;
FIGURE 5B illustrates a bit face profile of the drill bit of FIGURE 5A;
FIGURE 6A illustrates the face of another example drill bit including DOCCs
that
may be substantially force balanced, in accordance with some embodiments of
the present
disclosure;
FIGURE 68 illustrates a bit face profile of the drill bit of FIGURE 6A;
FIGURE 7A illustrates the face of an example drill bit including five blades
having DOCCs disposed thereon and force balanced in accordance with some
embodiments of the present disclosure;
FIGURE 7B illustrates a bit face profile of the drill bit of FIGURE 7A;
FIGURE 8A illustrates the face of an example drill bit including six blades
having
DOCCs disposed thereon and force balanced in accordance with some embodiments
of
the present disclosure;

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FIGURE 8B illustrates a bit face profile of the drill bit of FIGURE 8A;
FIGURE 9A illustrates the face of an example drill bit including seven blades
having DOCCs disposed thereon and force balanced in accordance with some
embodiments of the present disclosure;
FIGURE 9B illustrates a bit face profile of the drill bit of FIGURE 9A;
FIGURE 10 illustrates the face of an example drill bit including eight blades
having DOCCs disposed thereon and force balanced in accordance with some
embodiments of the present disclosure;
FIGURE 11 illustrates the face of an example drill bit including nine blades
having DOCCs disposed thereon and force balanced in accordance with some
embodiments of the present disclosure;
FIGURE 12 illustrates an example method for disposing DOCCs on a drill bit
such that the imbalance forces associated with the DOCCs acting on the drill
bit may be
reduced in accordance with some embodiments of the present disclosure;
FIGURE 13 illustrates another example method for disposing DOCCs on a drill
bit such that the imbalance forces associated with the DOCCs acting on the
drill bit may
be reduced in accordance with some embodiments of the present disclosure;
FIGURE 14A illustrates the face of a drill bit for which a critical depth of
cut
control curve (CDCCC) may be determined, in accordance with some embodiments
of
the present disclosure;
FIGURE 14B illustrates a bit face profile of the drill bit of FIGURE 14A;
FIGURES 14C and 14D illustrate critical depth of cut control curves of the
drill
bit of FIGURE 14A; and
FIGURE 15 illustrates an example method of determining and generating a
CDCCC in accordance with some embodiments of the present disclosure.
DETAILED DESCRIPTION
Embodiments of the present disclosure and its advantages are best understood
by
referring to FIGURES 1 through 15, where like numbers are used to indicate
like and
corresponding parts.
FIGURE 1 illustrates an example embodiment of a drilling system 100 configured
to drill into one or more geological formations, in accordance with some
embodiments of
the present disclosure. While drilling through geological formations, a
variety of forces
may act on components of a drilling tool such as the cutting elements and
depth of cut

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controllers (DOCCs) of the drilling tool. Accordingly, a drilling tool may
experience
imbalance forces if the forces acting on each of the components of the
drilling tool are not
sufficiently balanced.
Imbalance forces may be created by a variety of factors associated with non-
uniform downhole drilling conditions. For example, imbalance forces may be
created
when a drilling tool transitions from a first downhole formation to a second
downhole
formation that is harder than the first formation. Imbalance forces may also
be created by
drilling from a first downhole formation into a second downhole formation
where the
second downhole formation may be at an angle other than normal to the wellbore
being
formed by a downhole drilling tool. Further, imbalance forces may be created
by different
DOCCs coming in contact with the formation at different times. Such imbalance
forces
may result in vibrations to a drill string that may damage one or more
components of the
drill string. Accordingly, drilling system 100 may include downhole drilling
tools (e.g., a
drill bit, a reamer, a hole opener, etc.) configured to reduce imbalance
forces applied to
one or more components of drilling system 100 to improve the performance of
drilling
system 100.
As disclosed in further detail below and according to some embodiments of the
present disclosure, a drilling tool may include DOCCs oriented on a drilling
tool to
improve the balance of forces acting on the drilling tool. Additionally, the
DOCCs
configured for a particular desired depth of cut may be configured such that
they are in
contact with the formation at substantially the same time to further improve
the balance of
forces acting on the drilling tool. Consequently, imbalance forces of a
drilling tool
associated with the DOCCs may be reduced or eliminated.
Drilling system 100 may include a well surface or well site 106. Various types
of
drilling equipment such as a rotary table, mud pumps and mud tanks (not
expressly
shown) may be located at a well surface or well site 106. For example, well
site 106 may
include a drilling rig 102 that may have various characteristics and features
associated
with a "land drilling rig." However, downhole drilling tools incorporating
teachings of the
present disclosure may be satisfactorily used with drilling equipment located
on offshore
platforms, drill ships, semi-submersibles and drilling barges (not expressly
shown).
Drilling system 100 may include a drill string 103 associated with drill bit
101 that
may be used to form a wide variety of wellbores or bore holes such as
generally vertical
wellbore 114a or generally horizontal wellbore 114b as shown in FIGURE 1.
Various

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directional drilling techniques and associated components of a bottom hole
assembly
(BHA) 120 of drill string 103 may be used to form horizontal wellbore 114b.
For
example, lateral forces may be applied to BHA 120 proximate kickoff location
113 to
form horizontal wellbore 114b extending from generally vertical wellbore 114a.
5 BHA 120 may be formed from a wide variety of components configured to
form
a wellbore 114. For example, components 122a, 122b and 122c of BHA 120 may
include,
but are not limited to, drill bits (e.g., drill bit 101), drill collars,
rotary steering tools,
directional drilling tools, downhole drilling motors, reamers, hole enlargers
or stabilizers.
The number of components such as drill collars and different types of
components 122
included in BHA 120 may depend upon anticipated downhole drilling conditions
and the
type of wellbore that will be formed by drill string 103 and rotary drill bit
101.
A wellbore 114 may be defined in part by a casing string 110 that may extend
from well surface 106 to a selected downhole location. Portions of a wellbore
114, as
shown in FIGURE 1, that do not include casing string 110 may be described as
"open
hole." Various types of drilling fluid may be pumped from well surface 106
through drill
string 103 to attached drill bit 101. Such drilling fluids may be directed to
flow from drill
string 103 to respective nozzles (not expressly shown) passing through rotary
drill bit
101. The drilling fluid may be circulated back to well surface 106 through an
annulus 108
defined in part by outside diameter 112 of drill string 103 and inside
diameter 118 of
wellbore 114a. Inside diameter 118 may be referred to as the "sidewall" of
wellbore 114a.
Annulus 108 may also be defined by outside diameter 112 of drill string 103
and inside
diameter 111 of casing string 110.
Drilling system 100 may also include a rotary drill bit ("drill bit") 101.
Drill bit
101 May be any of various types of fixed cutter drill bits, including PDC
bits, drag bits,
matrix drill bits, and/or steel body drill bits operable to form wellbore 114
extending
through one or more downhole formations. Drill bit 101 may be designed and
formed in
accordance with teachings of the present disclosure and may have many
different designs,
configurations, and/or dimensions according to the particular application of
drill bit 101.
Drill bit 101 may include one or more blades 126 (e.g., blades 126a-126i) that
may be disposed outwardly from exterior portions of bit body 124 of drill bit
101. Bit
body 124 may have a generally cylindrical shape and blades 126 disposed on bit
body
124 may be any suitable type of projections extending outwardly from rotary
bit body
124. For example, a portion of blade 126 may be directly or indirectly coupled
to an

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exterior portion of bit body 124, while another portion of blade 126 may be
projected
away from the exterior portion of bit body 124. Blades 126 formed in
accordance with
teachings of the present disclosure may have a wide variety of configurations
including,
but not limited to, substantially arched, helical, spiraling, tapered,
converging, diverging,
symmetrical, and/or asymmetrical.
In some cases, blades 126 may have substantially arched configurations,
generally
helical configurations, spiral shaped configurations, or any other
configuration
satisfactory for use with each downhole drilling tool. One or more blades 126
may have a
substantially arched configuration extending from proximate rotational axis
104 of bit
101. The arched configuration may be defined in part by a generally concave,
recessed
shaped portion extending from proximate bit rotational axis (or rotational
axis) 104. The
arched configuration may also be defined in part by a generally convex,
outwardly curved
portion disposed between the concave, recessed portion and exterior portions
of each
blade which correspond generally with the outside diameter of the rotary drill
bit.
In an embodiment of drill bit 101, blades 126 may include primary blades
disposed generally symmetrically about rotational axis 104. For example, one
embodiment may include three primary blades oriented approximately 120 degrees

relative to each other with respect to rotational axis 104 in order to provide
stability for
drill bit 101. In some embodiments, blades 126 may also include at least one
secondary
blade disposed between the primary blades. The number and location of
secondary blades
and primary blades may vary substantially. Blades 126 may be disposed
symmetrically or
asymmetrically with regard to each other and rotational axis 104 where the
disposition
may be based on the downhole drilling conditions of the drilling environment.
Each of blades 126 may include a first end disposed proximate or toward
rotational axis 104 and a second end disposed proximate or toward exterior
portions of
drill bit 101 (i.e., disposed generally away from rotational axis 104 and
toward uphole
portions of drill bit 101). The terms "downhole" and "uphole" may be used in
this
application to describe the location of various components of drilling system
100 relative
to the bottom or end of a wellbore. For example, a first component described
as "uphole"
from a second component may be further away from the end of the wellbore than
the
second component. Similarly, a first component described as being "downhole"
from a
second component may be located closer to the end of the wellbore than the
second
component.

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Each of blades 126 may have a leading (or front) surface disposed on one side
of
the blade in the direction of rotation of drill bit 101 and a trailing (or
back) surface
disposed on an opposite side of the blade away from the direction of rotation
of drill bit
101. Blades 126 may be positioned along bit body 124 such that they have a
spiral
configuration relative to rotational axis 104. In other embodiments, blades
126 may be
positioned along bit body 124 in a generally parallel configuration with
respect to each
other and rotational axis 104.
Blades 126 may have a general arcuate configuration extending radially from
rotational axis 104. The arcuate configurations of blades 126 may cooperate
with each
other to define, in part, a generally cone shaped or recessed portion disposed
adjacent to
and extending radially outward from the rotational axis.
Blades 126 may include one or more cutting elements 128 disposed outwardly
from exterior portions of each blade 126. For example, a portion of a cutting
element 128
may be directly or indirectly coupled to an exterior portion of a blade 126
while another
portion of the cutting element 128 may be projected away from the exterior
portion of the
blade 126. Cutting elements 128 may be any suitable device configured to cut
into a
formation, including but not limited to, primary cutting elements, backup
cutting elements
or any combination thereof. By way of example and not limitation, cutting
elements 128
may be various types of cutters, compacts, buttons, inserts, and gage cutters
satisfactory
for use with a wide variety of drill bits 101.
In some embodiments of the present disclosure, cutting elements 128 may be
disposed on blades 126 to improve the balance of forces acting on cutting
elements 128.
Therefore, imbalance forces associated with cutting elements 128 may be
reduced in
addition to reducing the imbalance forces associated with DOCCs.
Cutting elements 128 may include respective substrates with a layer of hard
cutting material disposed on one end of each respective substrate. The hard
layer of
cutting elements 128 may provide a cutting surface that may engage adjacent
portions of
a downholc formation to form a wellbore 114. The contact of the cutting
surface with the
formation may form a cutting zone associated with each of cutting elements
128. The
edge of the cutting surface located within the cutting zone may be referred to
as the
cutting edge of a cutting element 128.
Each substrate of cutting elements 128 may have various configurations and may

be formed from tungsten carbide or other materials associated with forming
cutting

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elements for rotary drill bits. Tungsten carbides may include, but are not
limited to,
monotungsten carbide (WC), ditungsten carbide (W2C), macrocrystalline tungsten
carbide
and cemented or sintered tungsten carbide. Substrates may also be formed using
other
hard materials, which may include various metal alloys and cements such as
metal
borides, metal carbides, metal oxides and metal nitrides. For some
applications, the hard
cutting layer may be formed from substantially the same materials as the
substrate. In
other applications, the hard cutting layer may be formed from different
materials than the
substrate. Examples of materials used to form hard cutting layers may include
polycrystalline diamond materials, including synthetic polycrystalline
diamonds.
Blades 126 may also include one or more DOCCs (not expressly shown)
configured to control the depth of cut of cutting elements 128. A DOCC may
comprise an
impact arrestor, a backup cutter and/or an MDR (Modified Diamond
Reinforcement).
Exterior portions of blades 126, cutting elements 128 and DOCCs may be
described as
forming portions of the bit face. As mentioned above and detailed below, the
layout and
disposition of the DOCCs on the face of drill bit 101 and blades 126 may be
such that
imbalance forces associated with the DOCCs may be reduced.
Blades 126 may further include one or more gage pads (not expressly shown)
disposed on blades 126. A gage pad may be a gage, gage segment, or gage
portion
disposed on exterior portion of a blade 126. Gage pads may often contact
adjacent
portions of a wellbore 114 formed by drill bit 101. Exterior portions of
blades 126 and/or
associated gage pads may be disposed at various angles, either positive,
negative, and/or
parallel, relative to adjacent portions of a straight wellbore (e.g., wellbore
114a). A gage
pad may include one or more layers of hardfacing material.
The rate of penetration (ROP) of drill bit 101 is often a function of both
weight on
bit (WOB) and revolutions per minute (RPM). Drill string 103 may apply weight
on drill
bit 101 and may also rotate drill bit 101 about rotational axis 104 to form a
wellbore 114
(e.g., wellbore 114a or wellbore 114b). For some applications a downhole motor
(not
expressly shown) may be provided as part of BHA 120 to also rotate drill bit
101. The
depth of cut controlled by DOCCs (not expressly shown) and blades 126 may also
be
based on the ROP and RPM of a particular bit. Accordingly, as described in
further detail
below, the configuration of the DOCCs to provide an improved depth of cut of
cutting
elements 128 may be based in part on the desired ROP and RPM of a particular
drill bit
101.

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FIGURE 2 illustrates bit face profile 200 that may represent a cross-sectional
view
of drill bit 101. In the present embodiment, drill bit 101 may be configured
to form a
wellbore through a first formation layer 202 into a second formation layer
204, in
accordance with some embodiments of the present disclosure. Exterior portions
of blades
(not expressly shown), cutting elements 128 and DOCCs (not expressly shown)
may be
projected rotationally onto a radial plane to form bit face profile 200. In
the illustrated
embodiment, formation layer 202 may be described as "softer" or "less hard"
when
compared to downhole formation layer 204. As mentioned above and discussed in
further
detail below, the placement of DOCCs on blades 126 of drill bit 101 may be
such that
imbalance forces that may result from a transition from formation layer 202 to
formation
layer 204 may be reduced.
As shown in FIGURE 2, exterior portions of drill bit 101 that contact adjacent

portions of a downhole formation may be described as a "bit face." Bit face
profile 200 of
drill bit 101 may include various zones or segments. Bit face profile 200 may
be
substantially symmetric about rotational axis 104 due to the rotational
projection of bit
face profile 200, such that the zones or segments on one side of rotational
axis 104 may
be substantially similar to the zones or segments on the opposite side of
rotational axis
104.
For example, bit face profile 200 may include gage zone 206a located opposite
gage zone 206b, shoulder zone 208a located opposite shoulder zone 208b, nose
zone 210a
located opposite nose zone 210b, and cone zone 212a located opposite cone zone
212b.
Cutting elements 128 included in each zone may be referred to as cutting
elements of that
zone. For example, cutting elements 128g included in gage zones 206 may be
referred to
as gage cutting elements, cutting elements 128, included in shoulder zones 208
may be
referred to as shoulder cutting elements, cutting elements 128i, included in
nose zones 210
may be referred to as nose cutting elements, and cutting elements 128c
included in cone
zones 212 may be referred to as cone cutting elements. As discussed in further
detail
below with respect to FIGURE 3, each zone or segment along bit face profile
200 may be
defined in part by respective portions of associated blades 126.
Cone zones 212 may be generally convex and may be formed on exterior portions
of each blade (e.g., blades 126 as illustrated in FIGURE 1) of drill bit 101,
adjacent to and
extending out from rotational axis 104. Nose zones 210 may be generally convex
and
may be formed on exterior portions of each blade of drill bit 101, adjacent to
and

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extending from each cone zone 212. Shoulder zones 208 may be formed on
exterior
portions of each blade 126 extending from respective nose zones 210 and may
terminate
proximate to a respective gage zone 206.
FIGURE 3 illustrates bit face profile 300 that represents another cross-
sectional
5 view of drill bit 101. Bit face profile 300 may represent drill bit 101.
A comparison of
FIGURES 2 and 3 shows that bit face profile 300 of FIGURE 3 is inverted with
respect to
bit face profile 200 of FIGURE 2.
A coordinate on the graph in FIGURE 3 corresponding to rotational axis 104 may

be referred to as an axial coordinate or position. A coordinate on the graph
in FIGURE 3
10 corresponding to reference line 301 may be referred to as a radial
coordinate or radial
position that may indicate a distance extending orthogonally from rotational
axis 104 in a
radial plane passing through rotational axis 104. For example, in FIGURE 3
rotational
axis 104 may be placed along a z-axis and reference line 301 may indicate the
distance
(R) extending orthogonally from rotational axis 104 to a point on a radial
plane that may
be defined as the ZR plane.
According to the present disclosure and as detailed below, DOCCs (not
expressly
shown) disposed along bit face profiles 200 and 300 may be disposed on blades
126 and
oriented on the face of drill bit 101 to reduce the imbalance of forces acting
on drill bit
101. As discussed further with respect to FIGURES 4-11, the placement of each
DOCC
on the face of drill bit 101 to reduce the imbalance forces may be such that
groups of
DOCCs consecutively placed in the radial plane may be substantially force
balanced.
Such force balancing may be based on the number of blades 126, the number of
DOCCs
and the number of DOCCs in each group of radially consecutive DOCCs.
Additionally,
the axial position of the each DOCC may be adjusted such that each DOCC
configured
for a desired depth of cut of drill bit 101 may be in contact with the
formation at
substantially the same time to reduce imbalance forces associated with the
DOCCs.
FIGURES 2 and 3 are for illustrative purposes only and modifications,
additions
or omissions may be made to FIGURES 2 and 3 without departing from the scope
of the
present disclosure. For example, the actual locations of the various zones
with respect to
the bit face profile may vary and may not be exactly as depicted.
FIGURE 4A illustrates the face of drill bit 401 including DOCC 402 having
forces acting upon it during drilling, in accordance with some embodiments of
the present
disclosure. FIGURE 4B illustrates a bit face profile of drill bit 401 of
FIGURE 4A. To

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11
provide a frame of reference, FIGURE 4B may include a coordinate system
similar to that
of FIGURE 3 and includes a z-axis that may represent rotational axis 404 of
drill bit 401.
Accordingly, a coordinate or position corresponding to the z-axis of FIGURE 4B
may be
referred to as an axial coordinate or axial position of the bit face profile
depicted in
FIGURE 4B. FIGURE 4B also includes a radial axis (R) that indicates the
orthogonal
distance from rotational axis 404 of drill bit 401.
Additionally, a location along the bit face of drill bit 401 as shown in
FIGURE 4A
may be described by x and y coordinates of an xy-plane of FIGURE 4A. The xy-
plane of
FIGURE 4A may be substantially perpendicular to the z-axis of FIGURE 4B such
that the
xy-plane of FIGURE 4A may be substantially perpendicular to rotational axis
404 of drill
bit 401. Additionally, the x-axis and y-axis of FIGURE 4A may intersect each
other at the
z-axis of FIGURE 4B such that the x-axis and y-axis may intersect each other
at
rotational axis 404 of drill bit 401.
The distance from rotational axis 404 of the drill bit 401 to a point in the
xy plane
of the bit face of FIGURE 4A may indicate the radial coordinate or radial
position of the
point on the bit face profile depicted in FIGURE 4B. For example, the radial
coordinate,
r, of a point in the xy plane having an x coordinate, x, and a y coordinate,
y, may be
expressed by the following equation:
1 I X2 + y2
Additionally, a point in the xy plane (of FIGURE 4A) may have an angular
coordinate that may be an angle between a line extending orthogonally from
rotational
axis 404 of drill bit 401 to the point and the x-axis. For example, the
angular coordinate
(0) of a point in the xy plane (of FIGURE 4B) having an x-coordinate, x, and a
y-
coordinate, y, may be expressed by the following equation:
0 = arctan (y/x)
The cited coordinates and coordinate systems are used for illustrative
purposes
only, and any other suitable coordinate system or configuration, may be used
to provide a
frame of reference of points along the bit face profile and bit face of a
drill bit associated
with FIGURES 4A and 4B, without departing from the scope of the present
disclosure.
Additionally, any suitable units may be used. For example, the angular
position may be
expressed in degrees or in radians.

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12
Returning to FIGURE 4A, drill bit 401 may include DOCC 402 disposed on
blades 426. In the present illustration, one DOCC 402 is depicted but drill
bit 401 may
include additional DOCCs disposed on any one of blades 426. Additionally,
blades 426
may also include cutting elements (not expressly shown) and DOCC 402 may
control the
depth of cut of one or more of these cutting elements.
As mentioned above, a variety of forces may act on DOCC 402 when DOCC 402
is in contact with a formation while drilling. These forces may include
frictional force (Ff)
405 (also referred to as drag force), radial force (Fr) 407, both of which are
depicted in
FIGURE 4A, and normal force (Fa) 411, which is depicted in FIGURE 4B.
The combination of frictional force 405 and radial force 407 may result in
lateral
force 409 acting upon drill bit 401 such that frictional force 405 and radial
force 407 may
be vector components of lateral force 409 of drill bit 401. The sum of
frictional forces
405 and radial forces 407 acting on each DOCC 402 may represent the overall
lateral
force 409 acting on drill bit 401 due to DOCCs 402. Lateral force 409 may, if
unbalanced, cause a lateral moment to be exerted on drill bit 401, which may
cause drill
bit 401 to vibrate, veer in an undesirable direction or any combination
thereof.
Accordingly, as detailed below, DOCCs 402 may be disposed on blades 426 to
improve
the balance of their respective frictional forces 405 and radial forces 407
such that lateral
force 409 and its associated lateral moment may be reduced.
Normal force 411 associated with DOCC 402 may include the forces acting on
DOCC 402 that are perpendicular to the surface of DOCC 402, as shown in FIGURE
4B.
Normal force 411 may include a vector component radial force (Fr) 415 (which
may be
part of the sum of forces that equals radial force 407 of FIGURE 4A) and
vector
component axial force (Fa) 413. Axial force 413 may represent the forces
acting on
DOCC 402 that are parallel to rotational axis 404 of drill bit 401. Axial
force 413 may
generate an axial moment acting on drill bit 401 that may be represented by
multiplying
axial force 413 by the radial distance of DOCC 402 from rotational axis 404.
For
example, in the present illustration, DOCC 402 may have a radial distance of
"L" from
rotational axis 404 such that the axial moment (Ma) associated with DOCC 402
acting on
drill bit 401 may be expressed by the following equation:
Ma = Fa* L.
DOCCs 402 may be disposed on blades 426 such that the axial moments of
DOCCs 402 may be substantially balanced to reduce an overall axial moment of
drill bit

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13
401. Such reduction in the axial moment may reduce vibrations and maintain the
desired
trajectory of drill bit 401.
Modifications, additions, or omissions may be made to FIGURES 4A and 4B
without departing from the scope of the present disclosure. For example, as
mentioned
previously, drill bit 401 may include any number of DOCCs 402, disposed on any
number
of blades 426 in a manner that improves the balance of forces acting on drill
bit 401. As
discussed in further detail below, DOCCs 402 may be organized into groups of
radially
consecutive DOCCs 402 that may be in contact with a formation being drilled to
balance
the forces acting on drill bit 401. Additionally, although not expressly
shown, drill bit 401
may include one or more cutting elements.
FIGURE 5A illustrates the face of drill bit 501 including DOCCs 502a, 502b,
and
502c that may be a group of three radially consecutive DOCCs that are
substantially force
balanced, in accordance with some embodiments of the present disclosure.
FIGURE 5B
illustrates a bit face profile of drill bit 501 of FIGURE 5A. The orientation
of DOCCs
502a-502c on drill bit 501 of FIGURES 5A and 5B may include a coordinate
system
similar to that of FIGURES 4A and 48. Drill bit 501 may also include one or
more
cutting elements not expressly shown.
Drill bit 501 may include blades 526a-526e. Blade 526a may include DOCC 502a
disposed thereon, blade 526b may include DOCC 502b disposed thereon, and blade
526d
may include DOCC 502c disposed thereon. DOCC 502a may have a radial location
closest to rotational axis 504 of drill bit 501. The radial location of DOCC
502b may
overlap the radial location of DOCC 502a by less than 100% and may be further
from
rotational axis 504 in the radial plane than DOCC 502a. In the present
embodiment,
DOCC 502b may be an adjacent or "neighbor" DOCC to DOCC 502a in the radial
direction because DOCCs 502a and 502b may be next to each other in the radial
plane.
The radial location of DOCC 502b may overlap the radial location of DOCC 502a
by less
than 100% and may be further from rotational axis 504 and cone zone 512 in the
radial
plane than DOCC 502b. DOCC 502c may be an adjacent or "neighbor" DOCC to DOCC
502b because DOCCs 502b and 502c may be next to each other in the radial
plane. With
DOCCs 502a-502c being placed outward radially from rotational axis 504 toward
the
edge of drill bit 501, DOCCs 502a, 502b, and 502c may be referred to as
radially
consecutive DOCCs going from DOCC 502a to DOCC 502c.

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14
In the illustrated embodiment of FIGURE 5A, DOCCs 502a, 502b, and 502c may
be disposed on blades 526a, 526b, and 526d, respectively, such that DOCCs
502a, 502b
and 502c are spaced approximately 120 degrees from each other with respect to
rotational
axis 504. In such a configuration where DOCCs 502a-502c are spaced in a
generally
symmetrical manner on the face of drill bit 501 the imbalance forces
associated with
DOCCs 502a, 502b, and 502c may at least partially counteract each other.
For example, DOCCs 502a, 502b, and 502c may have associated radial forces
507a, 507b, and 507c, respectively and associated frictional forces 505a,
505b, and 505c,
respectively. Frictional forces 505a, 505b, and 505c and radial forces 507a,
507b, and
507c may result in lateral forces 509a, 509b, and 509c acting on drill bit
501, similarly to
lateral forces 409 acting on drill bit 401 described above with respect to
FIGURE 4A. As
shown in FIGURE 5A, the directions of lateral forces 509a, 509b, and 509c may
at least
partially oppose each other such that lateral forces 509a, 509b, and 509c may
at least
partially cancel each other out. Accordingly, the overall lateral force and
its associated
lateral moment associated with DOCCs 502a-502c acting on drill bit 501 may be
reduced
and/or minimized. Such a configuration may be desirable because as the overall
lateral
forces and lateral moments approach zero, vibrations of drill bit 501 and its
associated
BHA and drill string may also be reduced, which may reduce wear on the
components
and improve drilling performance.
Further, as shown in FIGURE 5B, axial forces 513a, 513b, and 513c may be
associated with DOCCs 502a, 502b, and 502c, respectively. With DOCCs 502a,
502b,
and 502c disposed on drill bit 501 in a generally symmetrical manner as
depicted in
FIGURE 5A, axial forces 513a, 513b, and 513c may be acting on different areas
of the
face of drill bit 501 such that the axial moments associated with axial forces
513a, 513b,
and 513c may at least partially counteract each other.
Therefore, the overall imbalance forces and moments (e.g., lateral and axial
forces
and moments) associated with DOCCs 502a-502c acting on drill bit 501 may be
reduced
and/or minimized. DOCCs 502a, 502b, and 502c configured as shown and described
in
FIGURES 5A and 5B may be referred to as a force balanced group of three
radially
consecutive DOCCs.
Additionally, as detailed below with respect to FIGURES 12, 14A-14D, and 15,
the axial positions of DOCCs 502a, 502b, and 502c may be configured such that
each of
DOCCs 502a, 502b, and 502c are in contact with a formation at approximately
the same

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time for a desired depth of cut. Accordingly, imbalance forces associated with
DOCCS
502a-502c not being in contact with the formation at approximately the same
time may be
reduced.
Modifications, additions, or omissions may be made to drill bit 501 without
5
departing from the scope of the present disclosure. For example, a group of
DOCCs 502
may be located within and/or overlap with a different zone (e.g., cone zone
512, shoulder
zone 508, gage zone 506a, etc.) of drill bit 501. Additionally, a drill bit
may include more
or fewer blades and/or DOCCs that may be force balanced according to the
particular
number of blades and DOCCs that may be in contact with a formation at a time.
10 For
example, FIGURE 6A illustrates the face of drill bit 601 including DOCCs
602a, 602b, 602c, and 602d that may be a group of four radially consecutive
DOCCs that
are substantially force balanced, in accordance with some embodiments of the
present
disclosure. FIGURE 6B illustrates a bit face profile of drill bit 601 of
FIGURE 6A. The
orientation of DOCCs 602a-602d on drill bit 601 of FIGURES 6A and 6B may be
15 referred
to using a coordinate system similar to that of FIGURES 4A and 4B. Drill bit
601 may also include one or more cutting elements not expressly shown.
Drill bit 601 may include blades 626a-626d with DOCCs 602a-602d respectively
disposed thereon. In the illustrated embodiment, DOCCs 602a-602d may be placed

outward radially with DOCC 602a disposed closest to rotational axis 604 in the
radial
direction and DOCC 602d disposed closest to the edge of drill bit 601.
Accordingly,
similar to DOCCs 502a-502c of FIGURES 5A and 5B, DOCCs 602a-602d may be
referred to as radially consecutive DOCCs going from DOCC 602a to DOCC 602d.
In the illustrated embodiment in FIGURE 6A, DOCCs 602a-602d may be
disposed on blades 626a-626d, respectively, such that DOCCs 602a-602d are
spaced
approximately 90 degrees from each other with respect to rotational axis 604.
Similar to
described above with respect to DOCCs 502a-502c of FIGURES 5A and 5B, in such
a
configuration where DOCCs 602a-602d are spaced in a generally symmetrical
manner on
the face of drill bit 601 the imbalance forces and moments associated with
DOCCs 602a-
602d may at least partially counteract each other.
For example, DOCCs 602a, 602b, 602c, and 602d may have associated radial
forces 607a, 607b, 607c, and 607c, respectively and associated frictional
forces 605a,
605b, 605c, and 605d, respectively. Frictional forces 605a, 605b, 605c, and
605d and
radial forces 607a, 607b, 607c, and 607c, may result in lateral forces 609a,
609b, 609c,

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16
and 609d acting on drill bit 601, similarly to lateral forces 409 acting on
drill bit 401
described above with respect to FIGURE 4A and lateral forces 509a-509c acting
on drill
bit 501 described above with respect to FIGURE 5A. As shown in FIGURE 6A, the
directions of lateral forces 609a, 609b, 609c, and 609d may at least partially
oppose each
other such that lateral forces 609a, 609b, 609c, and 609d may at least
partially cancel
each other out. Accordingly, the overall lateral force and its associated
lateral moment
associated with DOCCs 602a-602d acting on drill bit 601 may be reduced and/or
minimized.
Further, as shown in FIGURE 6B, axial forces 613a, 613b, 613c, and 613d may be
associated with DOCCs 602a, 602b, 602c, and 602d, respectively. With DOCCs
602a,
602b, 602c, and 602d disposed on drill bit 601 in a generally symmetrical
manner as
depicted in FIGURE 6A, axial forces 613a, 613b, 613c, and 613d may be acting
on
different areas of the face of drill bit 601 such that the axial moments
associated with
axial forces 613a, 613b, 613c, and 613d may at least partially counteract each
other.
Therefore, the overall imbalance forces and moments (e.g., lateral and axial
forces
and moments) associated with DOCCs 602a-602d acting on drill bit 601 may be
reduced
and/or minimized. DOCCs 602a, 602b, 602c, and 602d configured as shown and
described in FIGURES 6A and 6B may be referred to as a force balanced group of
four
radially consecutive DOCCs.
Additionally, as described below with respect to FIGURES 13, 14A-14D, and 15,
the axial positions of DOCCs 602a-602d may be configured such that each of
DOCCs
602a, 602b, 602c, and 602d are in contact with a formation at approximately
the same
time at a desired depth of cut. Accordingly, imbalance forces associated with
DOCCS
602a-602d not being in contact with the formation at approximately the same
time may be
reduced.
Modifications, additions, or omissions may be made to drill bit 601 without
departing from the scope of the present disclosure. For example, a group of
DOCCs 602
may be located within and/or overlap with a different zone (e.g., cone zone
612, shoulder
zone 608, gage zone 606a, etc.) of drill bit 601. Additionally, a drill bit
may include more
or fewer blades and/or DOCCs that may be force balanced according to the
particular
number of blades and DOCCs that may be in contact with a formation at a time.
Further,
FIGURES 6A and 6B are used to show a layout of four radially consecutive DOCCs
that
are substantially force balanced on drill bit 601 with four blades. However,
as described

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17
in further detail below with respect to FIGURES 8A-11, and 13, drill bits
having more
than five blades may also have one or more force balanced groups of four
radially
consecutive DOCCs.
As described above, DOCCs of drill bits may be configured in force balanced
groups of three radially consecutive DOCCs and force balanced groups of four
radially
consecutive DOCCs (among other force balanced groups of N number of radially
consecutive DOCCs). As described in detail below with respect to FIGURES 7A,
7B, and
12, imbalance forces associated with DOCCs of a drill bit having five blades
may be
reduced and/or minimized by disposing the DOCCs on the five bladed drill bit
such that
every group of three radially consecutive DOCCs of the drill bit is
substantially force
balanced. Additionally, as described below with respect to FIGURES 8A-11 and
13,
imbalance forces associated with DOCCs of a drill bit having more than five
blades may
be reduced and/or minimized by disposing the DOCCs such that every group of
four
radially consecutive DOCCs is substantially force balanced. Additionally, the
axial
positions of the DOCCs may be determined according to the present disclosure
such that
each DOCC associated with a desired depth of cut is in contact with a
formation at
approximately the same time. Therefore, drill bits designed in accordance with
the
teachings of the present disclosure may have improved force balancing and a
reduction in
vibrations, which may reduce strain and wear on one or more components of an
associated drill string.
FIGURE 7A illustrates the face of drill bit 701 including five blades (blades
726a-
726e) having DOCCs (DOCCs 702a-702j) disposed thereon and force balanced in
accordance with some embodiments of the present disclosure. FIGURE 7B
illustrates a
bit face profile of drill bit 701 of FIGURE 7A. Drill bit 701 may also include
one or more
cutting elements not expressly shown.
In the illustrated embodiment as shown in FIGURES 7A and 7B, DOCCs 702a-
702j may be increasingly disposed outward from a rotational axis 704 of drill
bit 701 such
that DOCCs 702a-702j may be considered radially consecutive DOCCs going from
DOCC 702a to DOCC 702j. As described in detail below, DOCCs 702a-702j may be
disposed on blades 726a-726e such that any group of three radially consecutive
DOCCs
702 may be forced balanced. Such a configuration may allow for increased
balance and
stability of drill bit 701.

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18
For example, DOCCs 702a-702j may be organized into the following groups of
three radially consecutive DOCCs: (702a, 702b, 702c); (702b, 702c, 702d);
(702c, 702d,
702e); (702d, 702e, 702f); (702e, 702f, 702g); (702f, 702g, 702h); (702g,
702h, 702i);
and (702h, 702i, 702j). As shown in FIGURE 7A, each DOCC 702 in the groups of
three
radially consecutive DOCCs is spaced from the other DOCCs in its respective
group in a
generally symmetrical manner (e.g., spaced from each other between
approximately 100
degrees and 140 degrees with respect to rotational axis 704) such that the
imbalance
forces associated with each DOCC 702 of a particular group of three radially
consecutive
DOCCs 702 may at least partially counteract each other. For example, DOCCs
702a,
702b, and 702c are spaced such that the imbalance forces associated with each
of DOCCs
702a, 702b and 702c may at least partially counteract each other. Accordingly,
the overall
imbalance forces associated with DOCCs 702a-702j as experienced by drill bit
701 may
be reduced or minimized. The placement of DOCCs 702a-702j on the face of drill
bit 701
such that each radially consecutive group of three DOCCs may be force balanced
according to method 1200 described with respect to FIGURE 12 below.
Additionally, the axial positions of DOCCs 702a-702j may be configured such
that each of DOCCs 702a-702j is in contact with the formation being drilled at

approximately the same time. Such adjustments may be made by calculating a
critical
depth of cut control curve (CDCCC) with respect to drill bit 701. Calculation
of the
CDCCC is described in detail with respect to FIGURES 14 and 15 below.
Modifications, additions, or omissions may be made to FIGURES 7A and 7B
without departing from the scope of the present disclosure. For example,
various
configurations of DOCCs 702a-702j disposed on blades 726a-726e may result in
each
group of three radially consecutive DOCCs being force balanced. The
illustrated
disposition of DOCCs 702a-702j on drill bit 701 is merely one example of DOCCs
702a-
702j disposed in force balance groups of three radially consecutive DOCCs on a
drill bit
including five blades.
FIGURE 8A illustrates the face of a drill bit 801 including six blades (blades

826a-826f) having twelve DOCCs (DOCCs 802a-8021) disposed thereon and force
balanced in accordance with some embodiments of the present disclosure. FIGURE
8B
illustrates a bit face profile of drill bit 801 of FIGURE 8A. Drill bit 801
may also include
one or more cutting elements not expressly shown.

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19
In the present embodiment as shown in FIGURES 8A and 8B, DOCCs 802a-8021
may be increasingly disposed outward from a rotational axis 804 of drill bit
801 such that
DOCCs 802a-8021 may be considered radially consecutive DOCCs going from DOCC
802a to DOCC 8021. As described in detail below, DOCCs 802a-8021 may be
disposed on
blades 826a-826f such that any group of four radially consecutive DOCCs 802
may be
forced balanced. Such a configuration may allow for increased balance and
stability of
drill bit 801.
For example, DOCCs 802a-8021 may be organized into the following groups of
four radially consecutive DOCCs 802: (802a, 802b, 802c, 802d); (802b, 802c,
802d,
802e); (802c, 802d, 802e, 8020; (802d, 802e, 802f, 802g); (802e, 802f, 802g,
802h);
(802f, 802g, 802h, 802i); (802g, 802h, 802i, 802j); (802h, 802i, 802j, 802k);
and (802i,
802j, 802k, 8021). As shown in FIGURE 8A, each DOCC 802 in the groups of four
radially consecutive DOCCs is spaced from the other DOCCs 802 in its
respective group
in a generally symmetrical manner (e.g., spaced from each other between
approximately
75 degrees and 105 degrees with respect to rotational axis 804)such that the
imbalance
forces associated with each DOCC 802 of a particular group of four DOCCs 802
may at
least partially counteract each other. For example, DOCCs 802a, 802b, 802c,
and 802d
are spaced such that the imbalance forces associated with each of DOCCs 802a,
802b,
802c, and 802d may at least partially counteract each other. Accordingly, the
overall
imbalance forces associated with DOCCs 802a-8021 as experienced by drill bit
801 may
be reduced or minimized. The placement of DOCCs 802a-8021 on the face of drill
bit 801
such that each radially consecutive group of four DOCCs may be force balanced
may be
done according to method 1300 described with respect to FIGURE 13 below.
Additionally, the axial positions of DOCCs 802a-8021 may be configured such
that each of DOCCs 802a-8021 is in contact with the formation being drilled at
approximately the same time. Such adjustments may be made by calculating a
critical
depth of cut control curve (CDCCC) with respect to drill bit 801. Calculation
of the
CDCCC is described in detail with respect to FIGURES 14 and 15 below.
Modifications, additions, or omissions may be made to FIGURES 8A and 8B
without departing from the scope of the present disclosure. For example,
various
configurations of DOCCs 802a-8021 disposed on blades 826a-826f may result in
each
group of four radially consecutive DOCCs being force balanced. The illustrated

disposition of DOCCs 802a-8021 on drill bit 801 is merely one example of DOCCs
802a-

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8021 disposed in force balance groups of four radially consecutive DOCCs on a
drill bit
including six blades.
FIGURE 9A illustrates the face of a drill bit 901 including seven blades
(blades
926a-926g) having fourteen DOCCs (DOCCs 902a-902n) disposed thereon and force
5 balanced in accordance with some embodiments of the present disclosure.
FIGURE 9B
illustrates a bit face profile of drill bit 901 of FIGURE 9A. Drill bit 901
may also include
one or more cutting elements not expressly shown.
In the present embodiment as shown in FIGURES 9A and 9B, DOCCs 902a-902n
may be increasingly disposed outward from a rotational axis 904 of drill bit
901 such that
10 DOCCs 902a-902n may be considered radially consecutive DOCCs going from
DOCC
902a to DOCC 902n. As described in detail below, DOCCs 902a-902n may be
disposed
on blades 926a-926g such that any group of four radially consecutive DOCCs 902
may be
forced balanced. Such a configuration may allow for increased balance and
stability of
drill bit 901.
15 For example, as shown in FIGURE 9A, each DOCC 902 in the groups of four
radially consecutive DOCCs is spaced from the other DOCCs 902 in its
respective group
in a generally symmetrical manner (e.g., spaced from each other between
approximately
75 degrees and 105 degrees with respect to rotational axis 904) such that the
imbalance
forces associated with each DOCC 902 of a particular group of four DOCCs 902
may at
20 least partially counteract each other. For example, DOCCs 902a, 902b,
902c, and 902d
are spaced such that the imbalance forces associated with each of DOCCs 902a,
902b,
902c, and 902d may at least partially counteract each other. Accordingly, the
overall
imbalance forces associated with DOCCs 902a-902n as experienced by drill bit
901 may
be reduced or minimized. The placement of DOCCs 902a-902n on the face of drill
bit 901
such that each radially consecutive group of four DOCCs may be force balanced
may be
done according to method 1300 described with respect to FIGURE 13 below.
Additionally, the axial positions of DOCCs 902a-902n may be configured such
that each of DOCCs 902a-902n is in contact with the formation being drilled at

approximately the same time. Such adjustments may be made by calculating a
critical
depth of cut control curve (CDCCC) with respect to drill bit 901. Calculation
of the
CDCCC is described in detail with respect to FIGURES 14 and 15 below.
Modifications, additions, or omissions may be made to FIGURES 9A and 9B
without departing from the scope of the present disclosure. For example,
various

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configurations of DOCCs 902a-902n disposed on blades 926a-926g may result in
each
group of four radially consecutive DOCCs being force balanced. The illustrated

disposition of DOCCs 902a-902n on drill bit 901 is merely one example of DOCCs
902a-
902n disposed in force balance groups of four radially consecutive DOCCs on a
drill bit
including seven blades.
FIGURE 10 illustrates the face of a drill bit 1001 including eight blades
(blades
1026a-1026h) having sixteen DOCCs (DOCCs 1002a-1002p) disposed thereon and
force
balanced in accordance with some embodiments of the present disclosure. Drill
bit 1001
may also include one or more cutting elements not expressly shown.
In the present embodiment as shown in FIGURE 10, DOCCs 1002a-1002p may
be increasingly disposed outward from a rotational axis 1004 of drill bit 1001
such that
DOCCs 1002a-1002p may be considered radially consecutive DOCCs going from DOCC

1002a to DOCC 1002p. As described in detail below, DOCCs 1002a-1002p may be
disposed on blades 1026a-1026h such that any group of four radially
consecutive DOCCs
1002 may be forced balanced. Such a configuration may allow for increased
balance and
stability of drill bit 1001.
For example, as shown in FIGURE 10, each DOCC 1002 in the groups of four
radially consecutive DOCCs is spaced from the other DOCCs 1002 in its
respective group
in a generally symmetrical manner (e.g., spaced from each other between
approximately
75 degrees and 105 degrees with respect to rotational axis 1004) such that the
imbalance
forces associated with each DOCC 1002 of a particular group of four DOCCs 1002
may
at least partially counteract each other. For example, DOCCs 1002a, 1002b,
1002c, and
1002d are spaced such that the imbalance forces associated with each of DOCCs
1002a,
1002b, 1002c, and 1002d may at least partially counteract each other.
Accordingly, the
overall imbalance forces associated with DOCCs 1002a-1002p as experienced by
drill bit
1001 may be reduced or minimized. The placement of DOCCs 1002a-1002p on the
face
of drill bit 1001 such that each radially consecutive group of four DOCCs may
be force
balanced may be done according to method 1300 described with respect to FIGURE
13
below.
Additionally, the axial positions of DOCCs 1002a-1002p may be configured such
that each of DOCCs 1002a-1002p is in contact with the formation being drilled
at
approximately the same time. Such adjustments may be made by calculating a
critical

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22
depth of cut control curve (CDCCC) with respect to drill bit 1001. Calculation
of the
CDCCC is described in detail with respect to FIGURES 14 and 15 below.
Modifications, additions, or omissions may be made to FIGURE 10 without
departing from the scope of the present disclosure. For example, various
configurations of
DOCCs 1002a-1002p disposed on blades 1026a-1026h may result in each group of
four
radially consecutive DOCCs being force balanced. The illustrated disposition
of DOCCs
1002a-1002p on drill bit 1001 is merely one example of DOCCs 1002a-1002p
disposed in
force balance groups of four radially consecutive DOCCs on a drill bit
including eight
blades.
FIGURE 11 illustrates the face of a drill bit 1101 including nine blades
(blades
1126a-1126i) having eighteen DOCCs (DOCCs 1102a-1102r) disposed thereon and
force
balanced in accordance with some embodiments of the present disclosure. Drill
bit 1101
may also include one or more cutting elements not expressly shown.
In the present embodiment as shown in FIGURE 11, DOCCs 1102a-1102r may be
increasingly disposed outward from a rotational axis 1104 of drill bit 1101
such that
DOCCs 1102a-1102r may be considered radially consecutive DOCCs going from DOCC

1102a to DOCC 1102r. As described in detail below, DOCCs 1102a-1102r may be
disposed on blades 1126a-1126i such that any group of four radially
consecutive DOCCs
1102 may be forced balanced. Such a configuration may allow for increased
balance and
stability of drill bit 1101.
For example, as shown in FIGURE 11, each DOCC 1102 in the groups of four
radially consecutive DOCCs is spaced from the other DOCCs 1102 in its
respective group
in a generally symmetrical manner (e.g., spaced from each other between
approximately
75 degrees and 105 degrees with respect to rotational axis 1104) such that the
imbalance
forces associated with each DOCC 1102 of a particular group of four DOCCs 1102
may
at least partially counteract each other. For example, DOCCs 1102a, 1102b,
1102c, and
1102d are spaced such that the imbalance forces associated with each of DOCCs
1102a,
1102b, 1102c, and 1102d may at least partially counteract each other.
Accordingly, the
overall imbalance forces associated with DOCCs 1102a-1102r as experienced by
drill bit
1101 may be reduced or minimized. The placement of DOCCs 1102a-1102r on the
face
of drill bit 1101 such that each radially consecutive group of four DOCCs may
be force
balanced may be done according to method 1300 described with respect to FIGURE
13
below.

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Additionally, the axial positions of DOCCs 1102a-1102r may be configured such
that each of DOCCs 1102a-1102r are in contact with the formation being drilled
at
approximately the same time. Such adjustments may be made by calculating a
critical
depth of cut control curve (CDCCC) with respect to drill bit 1101. Calculation
of the
CDCCC is described in detail with respect to FIGURES 14 and 15 below.
Modifications, additions, or omissions may be made to FIGURE 11 without
departing from the scope of the present disclosure. For example, various
configurations of
DOCCs 1102a-1102r disposed on blades 1126a-1126i may result in each group of
four
radially consecutive DOCCs being force balanced. The illustrated disposition
of DOCCs
1102a-1102r on drill bit 1101 is merely one example of DOCCs 1102a-1102r
disposed in
force balance groups of four radially consecutive DOCCs on a drill bit
including nine
blades.
FIGURE 12 illustrates an example method 1200 for disposing DOCCs on a drill
bit such that the imbalance forces associated with the DOCCs acting on the
drill bit may
be reduced. Method 1200 may be used to dispose DOCCs on a drill bit such that
each
group of three radially consecutive DOCCs may be substantially force balanced.
For
illustrative purposes, method 1200 is described with respect to drill bit 701
of FIGURES
7A and 7B; however, method 1200 may be performed with respect to any suitable
drill
bit.
The steps of method 1200 may be performed by various computer programs,
models or any combination thereof, configured to simulate and design drilling
systems,
apparatuses and devices. The programs and models may include instructions
stored on a
computer readable medium and operable to perform, when executed, one or more
of the
steps described below. The computer readable media may include any system,
apparatus
or device configured to store and retrieve programs or instructions such as a
hard disk
drive, a compact disc, flash memory or any other suitable device. The programs
and
models may be configured to direct a processor or other suitable unit to
retrieve and
execute the instructions from the computer readable media. Collectively, the
computer
programs and models used to simulate and design drilling systems may be
referred to as a
"drilling engineering tool" or "engineering tool."
Method 1200 may start, and at step 1202, the engineering tool may determine
the
desired radial locations of DOCCs 702a-702j. As described above, DOCCs 702a-
702j
may be configured such that the radial location of each DOCC overlaps less
than 100%

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24
with the radial locations of its neighbor DOCCs in the radial plane.
Additionally as
described above with respect to FIGURES 7A and 7B, DOCCs 702a-702j may be
increasingly disposed outward from rotational axis 704 of drill bit 701 such
that DOCCs
702a-702j may be considered radially consecutive DOCCs going from DOCC 702a to
DOCC 702j.
At step 1204, possible layouts of the first group of three radially
consecutive
DOCCs may be determined. For example, one of blades 726a-726e may be selected
to
have DOCC 702a placed thereon. The blade may be selected such that DOCC 702a
may
be placed at the radial location of DOCC 702a determined in step 1202. In the
present
embodiment, blade 726a may be selected for the placement of DOCC 702a, however
any
other suitable blade 726 may also be selected. With DOCC 702a placed on blade
726a
there are twelve different possibilities for placing each of DOCCs 702b and
702c on one
of blades 726b, 726c, 726d, and 726e. However, of the twelve different
possibilities, six
may be selected to form a substantially force balanced group. The six force
balanced
possibilities with DOCC 702a disposed on blade 726a are listed below:
1. DOCC 702a; Blade 726a
DOCC 702b; Blade 726b
DOCC 702c; Blade 726d
2. DOCC 702a; Blade 726a
DOCC 702b; Blade 726c
DOCC 702c; Blade 726d
3. DOCC 702a; Blade 726a
DOCC 702b; Blade 726c
DOCC 702c; Blade 726e
4. DOCC 702a; Blade 726a
DOCC 702b; Blade 726d
DOCC 702c; Blade 726b
5. DOCC 702a; Blade 726a
DOCC 702b; Blade 726d
DOCC 702c; Blade 726c
6. DOCC 702a; Blade 726a
DOCC 702b; Blade 726e
DOCC 702c; Blade 726c
Similar possibilities may be determined with DOCC 702a disposed on one of
blades
726b-726e.
At step 1206, one of the different possible configurations of disposing each
of
DOCCs 702a-702c on one of blades 726a-726e may be selected. For example, one
of the

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configurations may be selected based on the relative symmetry of the placement
of
DOCCs 702a-702c on the face of drill bit 701 because DOCCs 702a-702c placed in
a
generally symmetrical manner may be substantially force balanced.
In the present example, configuration "3" listed above where DOCC 702a may be
5 disposed on blade 726a, DOCC 702b may be disposed on blade 726c and DOCC
702c
may be disposed on blade 726e is selected. At step 1208, the engineering tool
may
determine whether there are additional DOCCs to be disposed on blades 726 of
drill bit
701. If there are additional DOCCs to be placed, method 1200 may proceed to
step 1210.
For example, after determining the disposition of DOCCs 702a, 702b, and 702c
on blades
10 726a, 726c and 726e, respectively, it may be determined that DOCC 702d
is an additional
DOCC that is to be disposed on a blade 726 of drill bit 701.
At step 1210, the disposition on one of blades 726 for the next consecutive
DOCC
in the radial plane may be selected. For example, DOCC 702d may be the next
radially
consecutive DOCC after DOCC 702c. The location for DOCC 702d may be selected
such
15 that DOCCs 702b, 702c, and 702d are a substantially forced balanced
group of three
radially consecutive DOCCs. Blades 726c and 726e may not be selected because
they
include DOCCs 702b and 702c, respectively. Blade 726a may be possible, but
DOCC
702a may prevent the placement of DOCC 702d at its desired radial location as
determined in step 1202. That leaves blades 726b and 726d as potential
locations for
20 DOCC 702d. In the present example, placement of DOCC 702d on blade 726b
may result
in a more symmetrical placement of DOCCs 702b, 702c, and 702d on the face of
drill bit
701 than placement of DOCC 702d on blade 726d. Therefore, DOCC 702d may be
disposed on blade 726b to provide a generally symmetrical placement of DOCCs
702b-
702d, which may reduce and/or minimize imbalance forces associated with DOCCs
702b-
25 702d acting on drill bit 701.
Following step 1210, method 1200 may return to step 1208 to determine if there

are any more DOCCs to be disposed on the drill bit. If no more DOCCs are to be

disposed on the drill bit, method 1200 may proceed to step 1212. For example,
steps 1208
and 1210 may be repeated with respect to drill bit 701 until the disposition
of each of
DOCCs 702a-702j on one of blades 726a-726e is determined and then method 1200
may
proceed to step 1212.
At step 1212, a CDCCC may be determined for drill bit 701. Calculation of a
CDCCC is described in detail below with respect to FIGURES 14 and 15 below. At
step

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26
1214, the engineering tool may help determine based on the CDCCC if DOCCs 702a-

702j are in contact with the formation at substantially the same time. If one
or more
DOCCs are not in contact with the formation at substantially the same time,
method 1200
may proceed to step 1216.
At step 1216, the axial position of one or more DOCCs may be adjusted based on
the CDCCC. Such adjustment based on the CDCCC is described in further detail
below
with respect to FIGURES 14 and 15. Additionally, in some embodiments, the
axial
locations and surfaces of DOCCs 702a-702j may be adjusted such that DOCCs 702a-
702j
provide a substantially constant depth of cut control for the desired depth of
cut as
described in detail in PCT Application No. 2011/060184, filed November 10,
2011 and
titled "SYSTEM AND METHOD OF CONSTANT DEPTH OF CUT CONTROL OF
DRILLING TOOLS" incorporated by reference herein.
Method 1200 may return to steps 1212 and 1214 following step 1216.
Accordingly, the engineering tool may calculate the CDCCC again to determine
if the
DOCCs would be in contact with the formation at substantially the same time
for the
desired depth of cut. If the CDCCC indicates that the DOCCs would be in
contact with
the formation at substantially the same time for the desired depth of cut,
method 1200
may end.
Accordingly, method 1200 may be used to reduce imbalance forces associated
with DOCCs of a drill bit. Method 1200 may be used to reduce the imbalance
forces by
substantially balancing the groups of three radially consecutive DOCCs,
adjusting the
axial positions of the DOCCs or any combination thereof
Modifications, additions or omissions may be made to method 1200 without
departing from the scope of the present disclosure. For example, although
method 1200
has been described with respect to drill bit 701 of FIGURES 7A and 7B, method
1200
may be used to force balance the radially consecutive groups of three DOCCs of
any
suitable drill bit. Additionally, in some embodiments, steps 1212 through 1216
may be
omitted.
FIGURE 13 illustrates an example method 1300 for disposing DOCCs on a drill
bit such that the imbalance forces associated with the DOCCs acting on the
drill bit may
be reduced. Method 1300 may be used to dispose DOCCs on a drill bit such that
each
group of four radially consecutive DOCCs may be substantially force balanced.
The steps
of method 1300 may be performed by the "drilling engineering tool" or
"engineering

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27
tool" described with respect to method 1200. For illustrative purposes, method
1300 is
described with respect to drill bit 801 of FIGURES 8A and 8B; however, method
1300
may be performed with respect to any suitable drill bit.
Method 1300 may start, and at step 1302, the engineering tool may determine
the
desired radial locations of DOCCs 802a-8021. As described above, DOCCs 802a-
8021
may be configured such that the radial location of each DOCC overlaps less
than 100%
with the radial locations of its neighbor DOCCs in the radial plane.
Additionally with
respect to FIGURES 8A and 8B, DOCCs 802a-8021 may be increasingly disposed
outward from rotational axis 804 of drill bit 801 such that DOCCs 802a-8021
may be
considered radially consecutive DOCCs going from DOCC 802a to DOCC 8021.
At step 1304 possible layouts of the first group of four radially consecutive
DOCCs may be determined. For example, one of blades 826a-826f may be selected
to
have DOCC 802a placed thereon. The blade may be selected such that DOCC 802a
may
be placed at the radial location of DOCC 802a determined in step 1302. In the
present
embodiment blade 826a may be selected for the placement of DOCC 802a, however
any
other suitable blade 826 may also be selected. With DOCC 802a placed on blade
826a
there are a multiple different possibilities for placing each of DOCCs 802b,
802c, and
802d, on one of blades 826b, 826c, 826d, 826e, and 826f, similarly to the
availability of
different placement possibilities of DOCCs 702b and 702c on one of blades
726b, 726c,
726d, and 726e described above.
At step 1306, one of the different possible configurations of disposing each
of
DOCCs 802a-802d on one of blades 826a-826f may be selected. For example, one
of the
configurations may be selected based on the relative symmetry of the placement
of
DOCCs 802a-802d on the face of drill bit 801 because DOCCs 802a-802d placed in
a
generally symmetrical manner may be substantially force balanced. In the
present
example, DOCC 802a may be disposed on blade 826a, DOCC 802b may be disposed on

blade 826d, DOCC 802c may be disposed on blade 826c, and DOCC 802d may be
disposed on blade 826f. At step 1308 it may be determined whether there arc
additional
DOCCs to be disposed on one of blades 826 of drill bit 801. If there arc
additional
DOCCs to be placed, method 1300 may proceed to step 1310. For example, after
determining the disposition of DOCCs 802a, 802b, 802c, and 802d on blades
826a, 826d,
826c, and 826f, respectively, it may be determined that DOCC 802e is an
additional
DOCC that is to be disposed on a blade of drill bit 801.

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At step 1310 the disposition on one of blades 826 for the next consecutive
DOCC
in the radial plane may be selected. For example, DOCC 802e may be the next
radially
consecutive DOCC after DOCC 802d. The location for DOCC 802e may be selected
such
that DOCCs 802b, 802c, 802d, and 802e are spaced in a generally symmetrical
manner on
the face of drill bit 801 such that DOCCs 802b-802e may be a substantially
forced
balanced group of four radially consecutive DOCCs. Blades 826d, 826c, and 826f
may
not be selected because they include DOCCs 802b, 802c, and 802d, respectively.
Blade
826a may be possible, but DOCC 802a may prevent the placement of DOCC 802e at
its
desired radial location as determined in step 1302. That leaves blades 826b
and 826e as
potential locations for DOCC 802e. In the present example, placement of DOCC
802e on
blade 826b may result in a more symmetrical placement of DOCCs 802b-802e on
the face
of drill bit 801 than placement of DOCC 802e on blade 826e. Therefore, DOCC
802e
may be disposed on blade 826b to provide a generally symmetrical placement of
DOCCs
802b-802e, which may reduce and/or minimize imbalance forces associated with
DOCCs
802b-802e. Following step 1310 method 1300 may return to step 1308 to
determine if
there are any more DOCCs to be disposed on the drill bit. If no more DOCCs are
to be
disposed on the drill bit, method 1300 may proceed to step 1312. For example,
steps 1308
and 1310 may be repeated with respect to drill bit 801 until the disposition
of each of
DOCCs 802a-8021 on one of blades 826a-826f is determined and then method 1300
may
proceed to step 1312.
At step 1312 a CDCCC may be determined for drill bit 801. Calculation of a
CDCCC is described in detail below with respect to FIGURES 14 and 15. At step
1314,
the engineering tool may help determine based on the CDCCC if DOCCs 802a-8021
are
in contact with the formation at substantially the same time for a desired
depth of cut. If
one or more DOCCs are not in contact with the formation at substantially the
same time,
method 1300 may proceed to step 1316.
At step 1316, the axial position of one or more DOCCs may be adjusted based on

the CDCCC. Such adjustment based on the CDCCC is described in further detail
below
with respect to FIGURES 14 and 15. Additionally, in some embodiments, the
axial
locations and surfaces of DOCCs 802a-8021 may be adjusted such that DOCCs 802a-
8021
provide a substantially constant depth of cut control for the desired depth of
cut as
described in detail in PCT Application No. 2011/060184, filed November 10,
2011 and

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29
titled "SYSTEM AND METHOD OF CONSTANT DEPTH OF CUT CONTROL OF
DRILLING TOOLS" incorporated by reference herein.
Method 1300 may return to steps 1312 and 1314 following step 1316.
Accordingly, the engineering tool may calculate the CDCCC again to determine
if the
DOCCs would be in contact with the formation at substantially the same time
for the
desired depth of cut. If the CDCCC indicates that the DOCCs would be in
contact with
the formation at substantially the same time for the desired depth of cut,
method 1300
may end.
Accordingly, method 1300 may be used to reduce imbalance forces associated
with DOCCs of a drill bit. Method 1300 may be used to reduce the imbalance
forces by
substantially balancing the groups of four radially consecutive DOCCs,
adjusting the
axial positions of the DOCCs or any combination thereof.
Modifications, additions or omissions may be made to method 1300 without
departing from the scope of the present disclosure. For example, although
method 1300
has been described with respect to drill bit 801 of FIGURES 8A and 8B, method
1200
may be used to force balance the radially consecutive groups of four DOCCs of
any
suitable drill bit, such as drill bits 901, 1001, and 1101. Additionally, in
some
embodiments, steps 1312 through 1316 may be omitted.
As mentioned above, a critical depth of cut control curve may be determined
such
that the axial positions of DOCCs may be adjusted to improve the balance of a
drill bit.
FIGURE 14A illustrates the face of a drill bit 1401 for which a critical depth
of cut
control curve (CDCCC) may be determined, in accordance with some embodiments
of
the present disclosure. FIGURE 14B illustrates a bit face profile of drill bit
1401 of
FIGURE 14A.
Drill bit 1401 may include a plurality of blades 1426 that may include cutting
elements 1428 and 1429. Additionally, blades 1426b, 1426d and 1426f may
include
DOCC 1402b, DOCC 1402d and DOCC 1402f, respectively, that may be configured to

control the depth of cut of drill bit 1401. The critical depth of cut of drill
bit 1401 may be
determined for a radial location along drill bit 1401. For example, drill bit
1401 may
include a radial coordinate RF that may intersect with DOCC 1402b at a control
point
P140213, DOCC 1402d at a control point P1402d, and DOCC 1402f at a control
point P1402f.
Additionally, radial coordinate RF may intersect cutting elements 1428a,
1428b, 1428c,

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and 1429f at cutlet points 1430a, 1430b, 1430c, and 1430f, respectively, of
the cutting
edges of cutting elements 1428a, 1428b, 1428c, and 1429f, respectively.
The angular coordinates of control points P14021), P1402d and P1402f (0P1402b,
0P1402d
and OP1402f, respectively) may be determined along with the angular
coordinates of cutlet
5 points
1430a, 1430b, 1430c and 1430f (01430a, 01430b, 01430c and 01430f,
respectively). A
depth of cut control provided by each of control points P14021), P1402d and
P1402f with
respect to each of cutlet points 1430a, 1430b, 1430c and 1430f may be
determined. The
depth of cut control provided by each of control points P14021), P1402d and
P1402f may be
based on the underexposure (61407, depicted in FIGURE 14B) of each of points
P14021 with
10 respect
to each of cutlet points 1430 and the angular coordinates of points P1402 with
respect to cutlet points 1430.
For example, the depth of cut of cutting element 1428b at cutlet point 1430b
controlled by point P1402b of DOCC 1402b (A1430b) may be determined using the
angular
coordinates of point P1402b and cutlet point 1430b (Op1402b and 01430b,
respectively), which
15 arc
depicted in FIGURE 14A. Additionally, A1430b may be based on the axial
underexposure (61407b) of the axial coordinate of point P1402b (Zp1402b) with
respect to the
axial coordinate of intersection point 1430b (Z14300, as depicted in FIGURE
143. In
some embodiments, A14301, may be determined using the following equations:
A14306 = O1407b * 360/(360 - (0p1402b - 014300); and
20 8140m = Z1430b ZP1402b=
In the first of the above equations, 0P1402b and 014306 may be expressed in
degrees
and "360" may represent a full rotation about the face of drill bit 1401.
Therefore, in
instances where 0P14026 and 014306 are expressed in radians, the numbers "360"
in the first
of the above equations may be changed to "27c." Further, in the above
equation, the
25
resultant angle of "(Opi4o2b - 014300 (AO may be defined as always being
positive.
Therefore, if resultant angle A0 is negative, then Ao may be made positive by
adding 360
degrees (or 2n radians) to Ao. Similar equations may be used to determine the
depth of cut
of cutting elements 1428a, 1428c, and 1429f as controlled by control point
P14026 at cutlet
points 1430a, 1430c and 1430f, respectively (A1430a, A1430 and A1430f,
respectively).
30 The
critical depth of cut provided by point 131402b (AP1402b) may be the maximum
of
A1430a5 A1430b, A1430 and A14301' and may be expressed by the following
equation:
AP1402b = max [A1430a, A1430b, A1430, A143011

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The critical depth of out provided by points P1402d and P1402f (AP1402d and
AP1402f,
respectively) at radial coordinate RE may be similarly determined. The overall
critical
depth of cut of drill bit 1401 at radial coordinate RE (ARE) may be based on
the minimum
of AP1402b, AP1402d and Api402f and may be expressed by the following
equation:
AM? = mm [AP1402b, AP1402d) AP14021].
Accordingly, the overall critical depth of cut of drill bit 1401 at radial
coordinate
RE (ARE) may be determined based on the points where DOCCs 1402 and cutting
elements 1428/1429 intersect RE. Although not expressly shown here, it is
understood that
the overall critical depth of cut of drill bit 1401 at radial coordinate RE
(ARF) may also be
affected by control points P14261 (not expressly shown in FIGURES 14A and 14B)
that
may be associated with blades 1426 configured to control the depth of cut of
drill bit 1401
at radial coordinate RF. In such instances, a critical depth of cut provided
by each control
point P1426/ (Ap14261) may be determined. Each critical depth of cut Ap1426/
for each control
point P1426/ may be included with critical depth of cuts AP14021 in
determining the
minimum critical depth of cut at RF to calculate the overall critical depth of
cut A RF at
radial location R.
To determine a critical depth of cut control curve of drill bit 1401, the
overall
critical depth of cut at a series of radial locations Rf (Au) anywhere from
the center of
drill bit 1401 to the edge of drill bit 1401 may be determined to generate a
curve that
represents the critical depth of cut as a function of the radius of drill bit
1401. In the
illustrated embodiment, DOCCs 1402b, 1402d, and 1402f may be configured to
control
the depth of cut of drill bit 1401 for a radial swath 1408 defined as being
located between
a first radial coordinate RA and a second radial coordinate RB. Accordingly,
the overall
critical depth of cut may be determined for a series of radial coordinates Rf
that are within
radial swath 1408 and located between RA and RB, as disclosed above. Once the
overall
critical depths of cuts for a sufficient number of radial coordinates Rf are
determined, the
overall critical depth of cut may be graphed as a function of the radial
coordinates R.
FIGURES 14C and 14D illustrate critical depth of cut control curves where the
critical
depth of cut is plotted as a function of the bit radius, in accordance with
some
embodiments of the present disclosure.
The critical depth of cut control curve may be used to determine the minimum
critical depth of cut control as provided by the DOCCs and/or blades of a
drill bit.

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Additionally, as mentioned above, the CDCCC may be used to determine if DOCCs
are
in contact with a formation at substantially the same time for a desired depth
of cut. For
example, FIGURES 14C and 14D both illustrate a critical depth of cut control
curve for
drill bit 1401 between radial coordinates RA and RB. The z-axis in FIGURES 14C
and
14D may represent the critical depth of cut per revolution (in/rev) along the
rotational
axis of drill bit 1401, and the radial (R) axis may represent the radial
distance from the
rotational axis of drill bit 1401.
FIGURE 14C illustrates a critical depth of cut control curve where the axial
positions of one or more of DOCCs 1402 of drill bit 1401 have not yet been
configured
by using the CDCCC. As shown in FIGURE 14C the minimum critical depth of cut
provided by DOCCs 1402 may not be the same or even. Accordingly, DOCCs 1402
may
not be in contact with the formation at substantially the same time.
Additionally, in the
illustrated embodiment, the desired minimum critical depth of cut for each
DOCC 1402
may be 0.3 inches/revolution (in/rev). However, FIGURE 14C indicates that only
one of
the three DOCCs 1402 may be substantially close to providing a minimum
critical depth
of cut of 0.3 in/rev. Accordingly, the critical depth of cut control curve of
FIGURE 14C
indicates that a modification may be made to DOCCs 1402 such that the minimum
critical
depth of cut provided by each of DOCCs 1402 may be substantially equal and
such that
DOCCs 1402 may be in contact with the formation at substantially the same
time.
For example, as shown in FIGURE 14A, DOCC 1402f may be radially located
closest to the rotational axis of drill bit 1401 with respect to DOCCs 1402b
and 1402d,
DOCC 1402d may be radially located furthest from the rotational axis of drill
bit 1401
with respect to DOCC 1402b and DOCC 1402f, and DOCC 1402b may be radially
located between the radial locations of DOCCs 1402f and 1402d. Accordingly,
the lowest
point on the bump closest to the z-axis of the CDCCC in FIGURE 14C may
indicate the
minimum depth of cut control provided by DOCC 1402f, the lowest point on the
middle
bump of the CDCCC may indicate the minimum critical depth of cut as provided
by
DOCC 1402b, and the lowest point on the bump furthest from the z-axis of the
CDCCC
may indicate the minimum depth of cut control provided by DOCC 1402d.
As mentioned above, in the current embodiment, the desired minimum depth of
cut control provided by each of DOCCs 1402 may be 0.3 in/rev. Therefore, based
on the
CDCCC of FIGURE 14C, the axial position of DOCCs 1402b and 1402d may be
adjusted
such that DOCCs 1402b and 1402d may provide the desired minimum critical depth
of

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cut of 0.3 in/rev. After adjusting the axial positions of DOCCs 1402b and
1402d, the
CDCCC may be calculated again to determine whether DOCCs 1402b and 1402d have
minimum critical depths of cut that may be substantially equal to the desired
minimum
depth of cut of 0.3 in/rev. The process may be repeated as many times as
necessary to
achieve the desired result. FIGURE 14D illustrates a CDCCC where DOCCs 1402b,
1402d and 1402f of drill bit 1401 have been adjusted accordingly such that
each of
DOCCs 1402b, 1402d, and 1402f have a minimum critical depth of cut that is
substantially equal to the desired minimum depth of cut of 0.3 in/rev of this
particular
embodiment.
FIGURE 14D illustrates that by analyzing a CDCCC and adjusting the axial
position of one or more DOCCs 1402, the minimum critical depths of cut
provided by
each of DOCCs 1402 may be substantially equal. Additionally, such adjustments
may
result in each DOCC 1402 substantially providing a desired minimum critical
depth of
cut. Further, such adjustments may allow for DOCCs 1402 to be in contact with
the
formation at substantially the same time to reduce imbalance forces and
vibrations.
Modifications, additions or omissions may be made to FIGURES 14A-14D
without departing from the scope of the present disclosure. For example, as
discussed
above, blades 1426, DOCCs 1402 or any combination thereof may affect the
critical
depth of cut at one or more radial coordinates and the CDCCC may be determined
accordingly. Further, the above description of the CDCCC calculation may be
used to
determine a CDCCC of any suitable drill bit such as drill bits 401, 501, 601,
701, 801,
901, 1001, and 1101 detailed above.
FIGURE 15 illustrates an example method 1500 of determining and generating a
CDCCC in accordance with some embodiments of the present disclosure. The steps
of
method 1500 may be performed by the "drilling engineering tool" or
"engineering tool"
described above with respect to methods 1200 and 1300.
In the illustrated embodiment, the cutting structures of the drill bit,
including at
least the locations and orientations of all cutting elements and DOCCs, may
have been
previously designed. However in other embodiments, method 1500 may include
steps for
designing the cutting structure of the drill bit. For illustrative purposes,
method 1500 is
described with respect to drill bit 1401 of FIGURES 14A-14D; however, method
1500
may be used to determine the CDCCC of any suitable drill bit.

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Method 1500 may start, and at step 1502, the engineering tool may select a
radial
swath of drill bit 1401 for analyzing the critical depth of cut within the
selected radial
swath. In some instances the selected radial swath may include the entire face
of drill bit
1401 and in other instances the selected radial swath may be a portion of the
face of drill
bit 1401. For example, the engineering tool may select radial swath 1408 as
defined
between radial coordinates RA and RB and controlled by DOCCs 1402b, 1402d and
1402f,
shown in FIGURES 14A-14D.
At step 1504, the engineering tool may divide the selected radial swath (e.g.,

radial swath 1408) into a number, Nb, of radial coordinates (Rf) such as
radial coordinate
RF described in FIGURES 14A and 14B. For example, radial swath 1408 may be
divided
into nine radial coordinates such that Nb for radial swath 1408 may be equal
to nine. The
variable "f' may represent a number from one to Nb for each radial coordinate
within the
radial swath. For example, "RI" may represent the radial coordinate of the
inside edge of
a radial swath. Accordingly, for radial swath 1408, "RI" may be approximately
equal to
RA. As a further example, "RNb" may represent the radial coordinate of the
outside edge
of a radial swath. Therefore, for radial swath 1408, "RNb" may be
approximately equal to
RB.
At step 1506, the engineering tool may select a radial coordinate Rf and may
identify control points (P1) located at the selected radial coordinate Rf and
associated with
a DOCC and/or blade. For example, the engineering tool may select radial
coordinate RF
and may identify control points P14021 and P1426i associated with DOCCs 1402
and/or
blades 1426 and located at radial coordinate RF, as described above with
respect to
FIGURES 14A and 14B.
At step 1508, for the radial coordinate Rf selected in step 1506, the
engineering
tool may identify cutlet points (Cj) each located at the selected radial
coordinate Rf and
associated with the cutting edges of cutting elements. For example, the
engineering tool
may identify cutlet points 1430a, 1430b, 1430c and 1430f located at radial
coordinate RF
and associated with the cutting edges of cutting elements 1428a, 1428b, 1428c,
and
1429f, respectively, as described and shown with respect to FIGURES 14A and
14B.
At step 1510 the engineering tool may select a control point P, and may
calculate a
depth of cut for each cutlet Cj as controlled by the selected control point P,
(AO, as
described above with respect to FIGURES 14A and 14B. For example, the
engineering
tool may determine the depth of cut of cutlets 1430a, 1430b, 1430c, and 1430f
as

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controlled by control point P1402b (A1430a, A1430b, A1430c, and A1430f,
respectively) by using
the following equations:
A1430a = 61407a * 360/(360 - (Orion - 01430a));
61407a= Z1430a ZP1402b;
5 A1430b ¨ 614076 * 360/(360 - (Opi - 014300);
61407b = Z1430b - ZP1402b;
A1430c = 61407c * 360/(360 - (0p1402b - 014300);
61407c= Z1430 ZP1402b;
6,1430f = 61407f * 360/(360 - (01)14o2b - 814300); and
10 61407f= Z1430f ZP1402b=
At step 1512, the engineering tool may calculate the critical depth of cut
provided
by the selected control point (Api) by determining the maximum value of the
depths of cut
of the cutlets ci as controlled by the selected control point Pi (Ac) and
calculated in step
1510. This determination may be expressed by the following equation:
15 Ap, ----- max {AO .
For example, control point P1402b may be selected in step 1510 and the depths
of
cut for cutlets 1430a, 1430b, 1430c, and 1430f as controlled by control point
P1402b
(A1430a3 A1430b, A1430, and A1430f, respectively) may also be determined in
step 1510, as
shown above. Accordingly, the critical depth of cut provided by control point
P1402b
20 (Ap1402b) may be calculated at step 1512 using the following equation:
1\p1402b ¨ max [A1430a, A1430b, A1430c, A1434
The engineering tool may repeat steps 1510 and 1512 for all of the control
points
Pi identified in step 1506 to determine the critical depth of cut provided by
all control
points P, located at radial coordinate Rf. For example, the engineering tool
may perform
25 steps 1510 and 1512 with respect to control points P1402d and P1402- to
determine the
critical depth of cut provided by control points P1402d and P1402f with
respect to cutlets
1430a, 1430b, 1430c, and 1430f at radial coordinate RF shown in FIGURES 14A
and 14B
(e.g., AP1402d and Ap1402f, respectively).
At step 1514, the engineering tool may calculate an overall critical depth of
cut at
30 the radial coordinate Rf Rf) selected in step 1506. The engineering tool
may calculate
the overall critical depth of cut at the selected radial coordinate Rf (AO by
determining a

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36
minimum value of the critical depths of cut of control points P, (An)
determined in steps
1510 and 1512. This determination may be expressed by the following equation:
A1= min {Api}
For example, the engineering tool may determine the overall critical depth of
cut
at radial coordinate RF of FIGURES 14A and 14B by using the following
equation:
A RF = Min [AP1402b, AP1402(19 AP1402d=
The engineering tool may repeat steps 1506 through 1514 to determine the
overall
critical depth of cut at all the radial coordinates Rf generated at step 1504.
At step 1516, the engineering tool may plot the overall critical depth of cut
(ARf)
for each radial coordinate Rf, as a function of each radial coordinate Rf.
Accordingly, a
critical depth of cut control curve may be calculated and plotted for the
radial swath
associated with the radial coordinates Rf. For example, the engineering tool
may plot the
overall critical depth of cut for each radial coordinate Rf located within
radial swath 1408,
such that the critical depth of cut control curve for swath 1408 may be
determined and
plotted, as depicted in FIGURES 14C and 14D. Following step 1516, method 1500
may
end.
Accordingly, method 1500 may be used to calculate and plot a critical depth of
cut
control curve of a drill bit. The critical depth of cut control curve may be
used to
determine whether the drill bit provides a substantially even control of the
depth of cut of
the drill bit and whether DOCCs may be in contact with the formation being
drilled at
substantially the same time. Therefore, the critical depth of cut control
curve may be used
to modify the DOCCs of the drill bit configured to control the depth of cut of
the drill bit
to improve the efficiency and balance of the DOCCs.
Modifications, additions, or omissions may be made to method 1500 without
departing from the scope of the present disclosure. For example, the order of
the steps
may be performed in a different manner than that described and some steps may
be
performed at the same time. Additionally, each individual step may include
additional
steps without departing from the scope of the present disclosure. Further,
although
method 1500 is described with respect to drill bit 1401, method 1500 may be
used to
calculate the CDCCC of any suitable drill bit including drill bits 401, 501,
601, 701, 801,
901, 1001, and 1101 described above.

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Although the present disclosure has been described with several embodiments,
various changes and modifications may be suggested to one skilled in the art.
For
example, although the present disclosure describes the configurations of DOCCs
with
respect to drill bits having specific blade configurations, the same
principles may be used
to reduce the imbalance forces of any suitable drilling tool according to the
present
disclosure. It is intended that the present disclosure encompasses such
changes and
modifications as fall within the scope of the appended claims.

Representative Drawing