U.S. patent application number 12/984473 was filed with the patent office on 2011-07-07 for reamer and bit interaction model system and method.
Invention is credited to Shilin Chen, John Ransford Hardin, JR., Eric Lauret, Stefano Mancini, Luk Servaes.
Application Number | 20110166837 12/984473 |
Document ID | / |
Family ID | 42315247 |
Filed Date | 2011-07-07 |
United States Patent
Application |
20110166837 |
Kind Code |
A1 |
Servaes; Luk ; et
al. |
July 7, 2011 |
Reamer and Bit Interaction Model System and Method
Abstract
Teachings of the disclosure are directed to a reamer and/or bit
interaction model system and method. The method may include
receiving performance data regarding a cutting structure, and
calculating a characteristic curve, using the performance data. The
characteristic curve may be weight-based and/or torque-based. The
method may also include storing the characteristic curve. In
particular embodiments, the characteristic curve may include either
weight on cutting structure or torque on the cutting structure, as
a function of the rate of penetration.
Inventors: |
Servaes; Luk; (Lafayette,
LA) ; Hardin, JR.; John Ransford; (Spring, TX)
; Mancini; Stefano; (Ravenna, IT) ; Lauret;
Eric; (Tubize, BE) ; Chen; Shilin; (The
Woodlands, TX) |
Family ID: |
42315247 |
Appl. No.: |
12/984473 |
Filed: |
January 4, 2011 |
Current U.S.
Class: |
703/2 ; 703/7;
715/764 |
Current CPC
Class: |
E21B 41/0092 20130101;
E21B 44/00 20130101; E21B 10/26 20130101; G06F 17/10 20130101; E21B
10/00 20130101 |
Class at
Publication: |
703/2 ; 715/764;
703/7 |
International
Class: |
G06F 17/10 20060101
G06F017/10; G06F 3/048 20060101 G06F003/048; G06G 7/48 20060101
G06G007/48 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 5, 2010 |
IT |
PCT/IT2010/000002 |
Claims
1. A method, comprising: receiving performance data regarding a
cutting structure; calculating, using the performance data, a
characteristic curve regarding the cutting structure, the
characteristic curve being either weight-based, or torque-based;
and storing the characteristic curve.
2. The method of claim 1, wherein the characteristic curve includes
either (weight on cutting structure/rock strength) or (torque on
the cutting structure/weight on the cutting structure), as a
function of (rate of penetration/rotary speed).
3. The method of claim 1, wherein calculating the characteristic
curve comprises calculating a weight-based characteristic curve
including varying weight on the cutting structure as a function of
a rate of penetration of the cutting structure.
4. The method of claim 1, wherein calculating the characteristic
curve comprises calculating a torque-based characteristic curve
including varying torque on the cutting structure as a function of
a rate of penetration of the cutting structure.
5. The method of claim 1, wherein calculating the characteristic
curve comprises: calculating a weight-based characteristic curve
including varying weight on the cutting structure as a function of
a rate of penetration of the cutting structure; and calculating a
torque-based characteristic curve including varying torque on the
cutting structure as a function of a rate of penetration of the
cutting structure.
6. The method of claim 1, wherein calculating the characteristic
curve comprises calculating a two dimensional curve fit that
estimates values of performance of the cutting structure across a
range of respective rates of penetration.
7. The method of claim 6, wherein the two dimensional curve fit
comprises a polynomial curve.
8. The method of claim 6, wherein storing the characteristic curve
comprises storing coefficients of the curve fit.
9. The method of claim 1, wherein the performance data is derived
from a plurality of different types of information selected from
the group consisting of computer models, actual downhole
measurements, actual surface measurements, and marketing data.
10. The method of claim 1, further comprising using the
characteristic curve to compare a first bottom hole assembly that
includes the first cutting structure, with a second bottom hole
assembly.
11. The method of claim 1, further comprising using the
characteristic curve to compare a first bottom hole assembly that
includes the first cutting structure, with a plurality of other
bottom hole assemblies.
12. The method of claim 11, wherein the second bottom hole assembly
includes a drill bit.
13. The method of claim 11, wherein the second bottom hole assembly
includes a drill bit and a reamer.
14. The method of claim 11, wherein the first cutting structure is
associated with a first drill bit and the first bottom hole
assembly further comprises a first reamer, and the second bottom
hole assembly includes a second drill bit.
15. The method of claim 14, wherein the second bottom hole assembly
further comprises a second reamer.
16. The method of claim 11, wherein the first bottom hole assembly
comprises a first drill bit of a first diameter, and the second
bottom hole assembly comprises a second drill bit of a second
diameter that is not equal to the first diameter.
17. The method of claim 1, wherein the cutting structure is
associated with a bottom hole assembly that includes a drill bit
and a plurality of independent reamers.
18. The method of claim 1, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising: calculating weight on bit as a function of weight on
the bottom hole assembly; and calculating weight on reamer as a
function of weight on the bottom hole assembly.
19. The method of claim 1, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising: displaying weight on bit as a function of weight on the
bottom hole assembly; and displaying weight on reamer as a function
of weight on the bottom hole assembly.
20. The method of claim 1, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising calculating a plurality of neutral point locations along
the bottom hole assembly.
21. The method of claim 1, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising displaying a plurality of neutral point locations along
the bottom hole assembly.
22. A method, comprising: receiving a first characteristic curve
regarding a first cutting structure; receiving a second
characteristic curve regarding a second cutting structure;
calculating a system characteristic curve that combines the first
characteristic curve and the second characteristic curve; comparing
the system characteristic curve with other characteristic curves;
and selecting a bottom hole assembly based upon the comparison.
23. The method of claim 22, wherein the system characteristic curve
includes weight on a system that includes the first and second
cutting structures, as a function of a rate of penetration.
24. The method of claim 22, wherein: the first characteristic curve
includes a weight on the first cutting structure, as a function of
a rate of penetration of the first cutting structure; the second
characteristic curve includes a weight on the second cutting
structure as a function of a rate of penetration of the second
cutting structure; and the system characteristic curve comprises a
sum of the first and second characteristic curves.
25. The method of claim 22, further comprising receiving lithology
information regarding an earth formation, and wherein comparing the
system characteristic curve with other characteristic curves
comprises predicting, using the lithology information, relative
performance of (i) a system that includes the first and second
cutting structures, and (ii) other cutting structures associated
with the other characteristic curves.
26. The method of claim 22, wherein the first cutting structure
comprises a drill bit disposed adjacent an end of a drill string
and the second cutting structure comprises a reamer disposed along
the drill string.
27. The method of claim 22, wherein calculating the system
characteristic curve comprises calculating a weight-based system
characteristic curve including varying a weight on the system as a
function of a rate of penetration of a system that includes the
first and second cutting structures.
28. The method of claim 22, wherein calculating the system
characteristic curve comprises calculating a torque based
characteristic curve of the system that includes varying a torque
of the system as a function of a rate of penetration of the
system.
29. The method of claim 22, wherein calculating the system
characteristic curve comprises: calculating a weight-based system
characteristic curve including varying a weight on the system as a
function of a rate of penetration of a system that includes the
first and second cutting structures; and calculating a torque based
characteristic curve of the system that includes varying a torque
on the system as a function of a rate of penetration of the
system.
30. The method of claim 22, wherein calculating the system
characteristic curve comprises calculating a two dimensional curve
fit that estimates values of performance of the system across a
range of respective rates of penetration.
31. The method of claim 30, wherein the two dimensional curve fit
comprises a polynomial curve.
32. The method of claim 30, wherein storing the system
characteristic curve comprises storing coefficients of the curve
fit.
33. The method of claim 22, wherein the first and second
characteristic curves are derived from performance data that is
derived from a plurality of different types of information selected
from the group consisting of computer models, actual downhole
measurements, actual surface measurements, and marketing data.
34. The method of claim 22, further comprising using the system
characteristic curve to compare a first bottom hole assembly that
includes the first and second cutting structures, with a second
bottom hole assembly.
35. The method of claim 34, wherein the second bottom hole assembly
includes a drill bit.
36. The method of claim 34, wherein the second bottom hole assembly
includes a drill bit and a reamer.
37. The method of claim 34, wherein the first bottom hole assembly
comprises a first drill bit of a first diameter, and the second
bottom hole assembly comprises a second drill bit of a second
diameter that is not equal to the first diameter.
38. A method, comprising: receiving cutting structure selection
criteria, the cutting structure selection criteria selected from
the group consisting of Bit Series, Bit Class, Bit Application, Bit
Technology, Bit Blade Count, Bit Cutter Size, Bit Profile Shape,
Bit Diameter, Bit Chamfer Type, Bit Chamfer Size, Bit Material
Number, Bit Type, Bit Cutting Structure Number, Reamer Type, Reamer
Body, Reamer Opening Diameter, Reamer Pilot Hole Diameter, Reamer
Arm Count, Reamer Blade Count, Reamer Layout, Reamer Cutter Size,
Reamer Material Number, Reamer Project Name, connection size and
connection Type; displaying a plurality of cutting structures to a
user that meet some or all of the cutting structure selection
criteria; receiving a selection from the user, the selection
including a plurality of the displayed cutting structures for
comparison; comparing each cutting structure of the selection,
using respective characteristic curves, the characteristic curves
being either weight-based or torque-based; and displaying results
of the comparison to the user.
39. The method of claim 38, further comprising receiving lithology
information regarding an earth formation, and wherein comparing
each cutting structure of the selection comprises predicting
relative performance of each cutting structure of the selection,
with respect to the lithology information.
40. The method of claim 38, further comprising receiving a
plurality of constraints for a proposed well, and wherein
displaying results of the comparison to the user includes
identifying each cutting structure of the selection that violates
one or more of the constraints.
41. The method of claim 38, wherein each characteristic curve
comprises a weight-based characteristic curve including varying a
weight on the cutting structure as a function of a rate of
penetration of the respective cutting structure.
42. The method of claim 38, wherein each characteristic curve
comprises a torque based characteristic curve including varying a
torque on the cutting structure as a function of a rate of
penetration of the respective cutting structure.
43. The method of claim 38, wherein each characteristic curve
comprises: a weight-based characteristic curve including varying a
weight on the cutting structure as a function of a rate of
penetration of the respective cutting structure; and a torque based
characteristic curve including varying a torque on the cutting
structure as a function of a rate of penetration of the respective
cutting structure.
44. The method of claim 38, wherein each characteristic curve
comprises a two dimensional curve fit that estimates values of
performance of the respective cutting structures across a range of
respective rates of penetration.
45. The method of claim 44, wherein the two dimensional curve fit
comprises a polynomial curve.
46. The method of claim 44, wherein each characteristic curve is
retrieved for comparison using the coefficients of the curve
fit.
47. The method of claim 38, wherein each characteristic curve is
derived from performance data that is derived from a plurality of
different types of information selected from the group consisting
of computer models, actual downhole measurements, actual surface
measurements, and marketing data.
48. The method of claim 38, comparing each cutting structure of the
selection using the respective characteristic curve comprises using
the respective characteristic curves to compare a first bottom hole
assembly that includes a particular cutting structure, with a
second bottom hole assembly.
49. The method of claim 48, wherein the second bottom hole assembly
includes a drill bit.
50. The method of claim 48, wherein the second bottom hole assembly
includes a drill bit and a reamer.
51. The method of claim 48, wherein the first cutting structure is
associated with a first drill bit and the first bottom hole
assembly further comprises a first reamer, and the second bottom
hole assembly includes a second drill bit.
52. The method of claim 51, wherein the second bottom hole assembly
further comprises a second reamer.
53. The method of claim 48, wherein the first bottom hole assembly
comprises a first drill bit of a first diameter, and the second
bottom hole assembly comprises a second drill bit of a second
diameter that is not equal to the first diameter.
54. The method of claim 48, wherein the first bottom hole assembly
comprises a drill bit and a reamer, and further comprising:
calculating weight on bit as a function of weight on the first
bottom hole assembly; and calculating weight on reamer as a
function of weight on the first bottom hole assembly.
55. The method of claim 48, wherein the first bottom hole assembly
comprises a drill bit and a reamer, and further comprising:
displaying weight on bit as a function of weight on the first
bottom hole assembly; and displaying weight on reamer as a function
of weight on the first bottom hole assembly.
56. The method of claim 48, further comprising calculating a
plurality of neutral point locations along the first bottom hole
assembly.
57. The method of claim 48, further comprising displaying a
plurality of neutral point locations along the first bottom hole
assembly.
58. A system, comprising: an interface for receiving performance
data regarding a cutting structure; a processor for calculating,
using the performance data, a characteristic curve regarding the
cutting structure, the characteristic curve being either
weight-based, or torque-based; and a memory for storing the
characteristic curve.
59. The system of claim 58, wherein the characteristic curve
includes either (weight on cutting structure/rock strength) or
(torque on the cutting structure/weight on the cutting structure),
as a function of (rate of penetration/rotary speed).
60. The system of claim 58, wherein calculating the characteristic
curve comprises calculating a weight-based characteristic curve
including varying weight on the cutting structure as a function of
a rate of penetration of the cutting structure.
61. The system of claim 58, wherein calculating the characteristic
curve comprises calculating a torque-based characteristic curve
including varying torque on the cutting structure as a function of
a rate of penetration of the cutting structure.
62. The system of claim 58, wherein calculating the characteristic
curve comprises: calculating a weight-based characteristic curve
including varying weight on the cutting structure as a function of
a rate of penetration of the cutting structure; and calculating a
torque-based characteristic curve including varying torque on the
cutting structure as a function of a rate of penetration of the
cutting structure.
63. The system of claim 58, wherein the processor is further
operable to use the characteristic curve to compare a first bottom
hole assembly that includes the first cutting structure, with a
second bottom hole assembly.
64. The system of claim 58, wherein the processor is further
operable to use the characteristic curve to compare a first bottom
hole assembly that includes the first cutting structure, with a
plurality of other bottom hole assemblies.
65. The system of claim 58, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and wherein the
processor is further operable to: calculate weight on bit as a
function of weight on the bottom hole assembly; and calculate
weight on reamer as a function of weight on the bottom hole
assembly.
66. The system of claim 58, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising a graphical user interface operable to: display weight
on bit as a function of weight on the bottom hole assembly; and
display weight on reamer as a function of weight on the bottom hole
assembly.
67. The system of claim 58, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and wherein the
processor is further operable to calculate a plurality of neutral
point locations along the bottom hole assembly.
68. The system of claim 58, wherein the first cutting structure is
associated with a drill bit of a bottom hole assembly, and the
bottom hole assembly further comprises a reamer, and further
comprising a graphical user interface being operable to display a
plurality of neutral point locations along the bottom hole
assembly.
69. A system, comprising: an interface being operable to receive a
first characteristic curve regarding a first cutting structure; the
interface being operable to receive a second characteristic curve
regarding a second cutting structure; a processor being operable to
calculate a system characteristic curve that combines the first
characteristic curve and the second characteristic curve; the
processor being further operable to compare the system
characteristic curve with other characteristic curves; and the
processor being further operable to select a bottom hole assembly
based upon the comparison.
70. The system of claim 69, wherein the system characteristic curve
includes weight on a system that includes the first and second
cutting structures, as a function of a rate of penetration.
71. The system of claim 69, wherein: the first characteristic curve
includes a weight on the first cutting structure, as a function of
a rate of penetration of the first cutting structure; the second
characteristic curve includes a weight on the second cutting
structure as a function of a rate of penetration of the second
cutting structure; and the system characteristic curve comprises a
sum of the first and second characteristic curves.
72. The system of claim 69, wherein calculating the system
characteristic curve comprises calculating a weight-based system
characteristic curve including varying a weight on the system as a
function of a rate of penetration of a system that includes the
first and second cutting structures.
73. The system of claim 69, wherein calculating the system
characteristic curve comprises calculating a torque based
characteristic curve of the system that includes varying a torque
of the system as a function of a rate of penetration of the
system.
74. The system of claim 69, wherein calculating the system
characteristic curve comprises: calculating a weight-based system
characteristic curve including varying a weight on the system as a
function of a rate of penetration of a system that includes the
first and second cutting structures; and calculating a torque based
characteristic curve of the system that includes varying a torque
on the system as a function of a rate of penetration of the
system.
75. A system, comprising: an interface being operable to receive
cutting structure selection criteria, the cutting structure
selection criteria selected from the group consisting of Bit
Series, Bit Class, Bit Application, Bit Technology, Bit Blade
Count, Bit Cutter Size, Bit Profile Shape, Bit Diameter, Bit
Chamfer Type, Bit Chamfer Size, Bit Material Number, Bit Type, Bit
Cutting Structure Number, Reamer Type, Reamer Body, Reamer Opening
Diameter, Reamer Pilot Hole Diameter, Reamer Arm Count, Reamer
Blade Count, Reamer Layout, Reamer Cutter Size, Reamer Material
Number, Reamer Project Name, connection size and connection Type; a
graphical user interface being operable to display a plurality of
cutting structures to a user that meet some or all of the cutting
structure selection criteria; the interface being further operable
to receive a selection from the user, the selection including a
plurality of the displayed cutting structures for comparison; a
processor being operable to compare each cutting structure of the
selection, using respective characteristic curves, the
characteristic curves being either weight-based or torque-based;
and the graphical user interface being further operable to display
results of the comparison to the user.
76. The system of claim 75, wherein the interface is further
operable to receive lithology information regarding an earth
formation, and wherein comparing each cutting structure of the
selection comprises predicting relative performance of each cutting
structure of the selection, with respect to the lithology
information.
77. The system of claim 75, wherein the interface is further
operable to receive a plurality of constraints for a proposed well,
and wherein displaying results of the comparison to the user
includes identifying each cutting structure of the selection that
violates one or more of the constraints.
Description
RELATED APPLICATIONS
[0001] This application claims the benefit under 35 U.S.C.
.sctn.119 of International Patent Application No. PCT/IT2010/00002
filed Jan. 5, 2010.
TECHNICAL FIELD
[0002] The teachings of the present disclosure relate to the
selection, analysis and evaluation of cutting structures and more
particularly, to a reamer and bit interaction model system and
method.
BACKGROUND
[0003] A drill bit at the end of a bottom hole assembly (BHA) is
used to drill a hole through earth formations. The drill bit has a
design with a cutting structure to accomplish this task. Models of
the cutting structure can predict performance in terms of rate of
penetration (ROP), force, torque, side force, vibration, walk
tendencies, steerability etc. A drill bit may contain a secondary
cutting structure that is intended to further enlarge the hole,
such as a bi-center bit. For purposes of this disclosure, these
secondary cutting structures may be considered to be part of the
drill bit and not part of a reamer.
[0004] A reamer is utilized to enlarge a borehole through earth
formations. The reamer has a design with a cutting structure to
accomplish this task. Models of the cutting structure can predict
performance in terms of rate of penetration (ROP), force, torque,
side force, vibration, walk tendencies, steerability, etc.
[0005] A reamer may exist at the end of a BHA (without a drill bit)
if the pilot hole formed by a drill bit already exists. Typically a
reamer is utilized above a drill bit in the same BHA. Multiple
reamers can also be deployed, each enlarging a different increment
of hole size (with our without a drill bit). Multiple reamers of
the same enlargement increment might also be used for redundancy in
case of a failure of one cutting structure. Reaming can occur both
in the downward and upward directions along the borehole.
[0006] A reamer may employ a fixed cutting structure, such as a
single piece hole opener, or an expandable/retractable cutting
structure for passing through restrictions in the wellbore
completion, or to enlarge only specific sections of a borehole for
specific purposes. Selective control of an expandable/retractable
reamer could also be used to keep a reamer dormant as a backup in
case of failure of a primary reamer cutting structure.
[0007] A simple way to characterize the performance of the drill
bit and reamer cutting structures is needed. With a simple
characterization, the performance of these cutting structures can
be easily compared across a range of lithology and drilling
parameters and evaluated against a set of constraints.
SUMMARY
[0008] The teachings of the present disclosure are directed to a
reamer and/or bit interaction model system and method. In
accordance with a particular embodiment, the method includes
receiving performance data regarding a cutting structure, and
calculating a characteristic curve, using the performance data. The
characteristic curve may be weight-based and/or torque-based. The
method further includes storing the characteristic curve.
[0009] In a particular embodiment of the present disclosure, the
characteristic curve includes either (weight on cutting
structure/rock strength) or (torque on the cutting structure/weight
on the cutting structure), as a function of (rate of
penetration/rotary speed).
[0010] In another embodiment of the present disclosure, the
characteristic curve includes varying weight or torque on the
cutting structure as a function of a rate of penetration of the
cutting structure.
[0011] In accordance with yet another embodiment of the present
disclosure, a method includes receiving first and second
characteristic curves regarding first and second cutting
structures, respectively. A system characteristic curve is
calculated that combines the first characteristic curve and the
second characteristic curve. The system characteristic curve may
then be compared with other characteristic curves, and a bottom
hole assembly may be selected, based upon the comparison.
[0012] In accordance with still another embodiment of the present
disclosure a method includes receiving cutting structure selection
criteria and displaying several cutting structures that meet some
or all of the criteria to a user. The method may further include
receiving a selection of cutting structures for comparison, from
the user. In accordance with a particular embodiment of the present
disclosure, the cutting structures of the selection may be compared
using their respective characteristic curves. The results of the
comparison may be displayed to the user.
[0013] Technical advantages of particular embodiments of the
present disclosure include a reamer and bit interaction model
system and method that allows for the collection of minimal data
regarding a cutting structure(s), and the calculation, storage
and/or display of a characteristic curve that reflects the
anticipated performance of such cutting structure(s).
[0014] Another technical advantage of particular embodiments of the
present disclosure includes a reamer and bit interaction model that
enables quick selection of a particularly suitable drill bit,
reamer, and/or combined reamer(s)/bit cutting structures using data
from multiple source(s). In accordance with particular embodiments,
the selection may meet a set of constraints across a spectrum of
lithology and drilling parameters.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] For a more complete understanding of the present disclosure
and its advantages, reference is now made to the following
descriptions, taken in conjunction with the accompanying drawings,
in which:
[0016] FIG. 1 illustrates reamer and bit cutting structures in an
operating well, that may be selected in accordance with particular
embodiments of the present disclosure;
[0017] FIGS. 2-3 illustrate weight-based characteristic curves, in
accordance with particular embodiments of the present
disclosure;
[0018] FIGS. 4-5 illustrate torque-based characteristic curves, in
accordance with particular embodiments of the present
disclosure;
[0019] FIGS. 6-7 illustrate weight distribution graphs, in
accordance with particular embodiments of the present
disclosure;
[0020] FIGS. 8-9 illustrate torque distribution graphs, in
accordance with particular embodiments of the present
disclosure;
[0021] FIG. 10 illustrates a weight distribution graph, in
accordance with particular embodiments of the present
disclosure;
[0022] FIG. 11 illustrates a torque distribution graph, in
accordance with particular embodiments of the present
disclosure;
[0023] FIGS. 12a-12h illustrate characteristic curves, in
accordance with particular embodiments of the present
disclosure;
[0024] FIGS. 13-25 illustrate screen shots of a graphical user
interface associated with a computer system that may be used to run
software embodying instructions of the method of the present
disclosure, in accordance with particular embodiments of the
present disclosure;
[0025] FIGS. 26-27 illustrate particular embodiments of flow charts
describing an algorithm(s) that may be used in accordance with a
particular embodiment of the present disclosure;
[0026] FIG. 28 illustrates an iterative process(es) that may be
used in the calculation of a characteristic curve, in accordance
with particular embodiments of the present disclosure;
[0027] FIG. 29 illustrates representations of a BHA, varying
lithology and an illustrations of the "cases" encountered by the
BHA, in accordance with a particular embodiment of the present
disclosure; and
[0028] FIG. 30 illustrates a computer system that may be used to
implement aspects of the teachings of the present disclosure.
DETAILED DESCRIPTION
[0029] The teachings of the present disclosure provide a system and
method that enables an efficient and rapid selection of a
particularly suitable drill bit, reamer, and/or combined
reamer(s)/bit cutting structures. The selection may be intended to
meet a set of constraints and may address one or more of a spectrum
of lithology and drilling parameters. Data from multiple source(s)
may be used in the selection process. In accordance with a
particular embodiment, systems or methods of the present disclosure
may employ a software algorithm and/or a methodology that
characterizes and analyzes drill bit and reamer cutting structure
performance in a variety of ways.
[0030] FIG. 1 illustrates a bottom hole assembly 30 that includes
multiple cutting structures including a cutting structure(s)
associated with a drill bit 32 at the end of the bottom hole
assembly BHA, and a cutting structure(s) associated with a reamer
34 located uphole from drill bit 30. Drill bit 32 at the end of the
(BHA) is typically used to drill a hole through earth formations.
Drill bit 32 has a particular design including a drill bit cutting
structure(s) to accomplish this task. Models of the drill bit
cutting structure may be used to predict performance in terms of
rate of penetration (ROP), force, torque, side force, vibration,
walk tendencies, steerability etc. In particular embodiments, drill
bit 32 may contain one or more secondary cutting structures that
are intended to further enlarge the hole, such as a bi-center bit.
For purposes of this specification, these secondary cutting
structures may be considered to be part of the drill bit and not
part of a reamer.
[0031] Reamer 34 is typically utilized to enlarge a borehole
through earth formations. Reamer 34 has a design with a reamer
cutting structure(s) to accomplish this task. Models of the cutting
structure can predict performance in terms of rate of penetration
(ROP), force, torque, side force, vibration, walk tendencies,
steerability, etc.
[0032] In alternative embodiments of the present disclosure, reamer
34 may be located at the end of a BHA (without a drill bit), for
example, if the pilot hole formed by a drill bit already exists. A
reamer can also be located higher up in a BHA without a drill bit
if a pilot hole formed by a drill bit already exists. Typically, a
reamer is utilized above a drill bit in the same BHA. Multiple
reamers can also be deployed, each enlarging a different increment
of hole size (with or without a drill bit). Multiple reamers of the
same enlargement increment might also be used for redundancy in
case of a failure of one cutting structure. Reaming can occur both
in the downward and upward directions along the borehole.
[0033] A reamer may employ a fixed cutting structure, such as a
single piece hole opener, or an expandable/retractable cutting
structure for passing through restrictions in the wellbore
completion, or to enlarge only specific sections of a borehole for
specific purposes. Selective control of an expandable/retractable
reamer may also be used to keep a reamer dormant as a backup in
case of failure of a primary reamer cutting structure.
[0034] For the purposes of this specification, "cutting structure"
refers to one or more structures on a BHA that accomplish a cutting
or drilling operation. For example, a drill bit may include a
single cutting structure, or multiple cutting structures.
Similarly, a reamer will typically include only a single cutting
structure, but a single reamer may also include multiple cutting
structures.
[0035] The teachings of the present disclosure also provide a
simplified system and method for characterizing the performance of
the drill bit and/or reamer(s) cutting structures. With a simple
characterization, the performance of these cutting structures can
be easily compared with other cutting structures or combinations of
cutting structures, across a range of lithology and drilling
parameters, and evaluated against a set of constraints.
[0036] In accordance with the present disclosure, characteristic
curves may be used to characterize the performance of a cutting
structure or a system of cutting structures (e.g., drill bit 32
and/or reamer 34) in their relation to dominant environmental and
operating factors such as: applied axial weight, torque, rock
strength, rotation rate, and rate of penetration through rock. Once
a characteristic curve is generated for a cutting structure, the
details of cutter size, cutter position, cutter back rake angle,
cutter side rake angle and other physical characteristics are not
needed in order to predict its performance in any given lithology.
For example, characteristic curves that are generated from actual,
measured field performance data instead of models, do not require
knowledge of such cutter details. The existence of characteristic
curves allows individual cutting structures to be easily analyzed
alone, or together in a system of cutting structures, to predict
the performance of the system and/or select a particularly
appropriate system for a given set of constraints.
[0037] Weight based and torque based simple characteristic curves
of reamer and bit cutting structures are illustrated and described
below.
[0038] For the purposes of this specification, the definition of
the term "weight on bit" (WOB) includes the axial weight or force
applied to a drill bit cutting structure, and the units may be
given in pounds (lbs).
[0039] For the purposes of this specification, the definition of
"weight on reamer" (WOR) includes the axial weight or force applied
to a reamer cutting structure, and the units may be given in pounds
(lbs).
[0040] For the purposes of this specification, the definition of
"torque on bit" (TOB) includes the rotational torque generated at
the drill bit cutting structure in response to the applied WOB, and
the units may be given in foot pounds (ft lbs).
[0041] For the purposes of this specification, the definition of
"torque on reamer" (TOR) includes the rotational torque generated
at the reamer cutting structure in response applied WOR, and the
units may be given in foot pounds (ft lbs).
[0042] For the purposes of this specification, the definition of
"rock strength" (.sigma.) includes the rock compressive strength
and the units may be given in pounds per square inch (psi).
[0043] For the purposes of this specification, the definition of
"rate of penetration" (ROP) includes the axial rate of penetration
of a cutting structure through rock, and the units may be given in
feet per hour (ft/hr).
[0044] For the purposes of this specification, the definition of
"rotary speed" includes the rotation rate of a cutting structure,
and the units may be given in revolutions per minute (RPM).
[0045] For the purposes of this specification, the definition of
"weight on system" (WSYS) includes the axial weight or force
applied to a BHA system of cutting structures, and the units may be
given in pounds (lbs).
[0046] For the purposes of this specification, the definition of
"torque on system" (TSYS) includes the resulting rotational torque
generated from the BHA system of cutting structures in response to
the applied WSYS, and the units may be given in foot pounds (ft
lbs).
[0047] For the purposes of this specification, the definition of d
is the depth of penetration per revolution of a cutting structure
or system of cutting structures, and the units may be given in
inches per revolution (in/rev) of the cutting structure or system
of cutting structures.
[0048] Units used can differ from above. However, to the extent
that calculations and/or comparisons are to be made, or graphs
and/or data are to be combined (as described below), units should
be used consistently.
[0049] In accordance with a particular embodiment of the present
disclosure, the following methodology may be employed, and/or
industry standards and literature accessed and relied upon, in
deriving the characteristic curves describing earth boring cutting
structures (e.g., fixed cutter drill bits, roller cone drill bits,
and fixed or expandable under-reaming devices, whether concentric
or eccentric in design).
[0050] One purpose of these characteristic curves is to assist in
providing a solution to the Bit-Reamer Interaction question: "what
are the performance capabilities of a drill bit-and-reamer
combination used in real-life, and how could a given combination
produce improved performance downhole?" Over the recent years this
has proven an increasingly difficult question to answer whenever
performing or attempting to optimize or improve performance during
a simultaneous enlarging-while-drilling operation.
[0051] Without attempting to cover a transient (time-dependant)
solution to this question at this point, it was decided to first
identify a viable steady-state solution. In order to accommodate
this and allow its integration into a stand-alone evaluation tool,
not directly linked to advanced finite element analysis (FEA) style
engineering platforms (capable of only analyzing each component
individually) some form of characteristic curve(s) is
beneficial.
[0052] This reference information may be compiled directly from the
calculation results of such high-end engineering platforms, but at
the same time could be derived from real-life performance data
(whether they're based on historical or real-time drilling
information).
[0053] While deriving this (these) characteristic curve(s) and
developing a solution to the Bit-Reamer Interaction question it's
beneficial to ensure the following parameters are contained within
them: (a) the rotary speed, (b) the drilling weight, (c) the
drilling torque, (d) the rate of penetration and (e) the
compressive rock strength.
[0054] Presumably one of, if not the most well-known equations
within the oilfield recently is Teale's formula defining Specific
Energy.sup.1--the work done per volume of rock excavated, E.sub.s,
and the units may be given in pounds per square inch (psi). This
equation is illustrated below for a drill bit: .sup.1"The Concept
of Specific Energy in Rock Drilling", Teale, International Journal
Rock Mechanics Mining Science, 1964.
E S = WOB A + 120 .pi. R P M TOB A ROP ##EQU00001##
where "A" is the borehole cross-sectional area and the units may be
given in square inches (in.sup.2).
[0055] Since this equation is well known and accepted across the
industry it appeared a good starting point in developing the
required characteristic curve(s), although it did not initially
cover all the required parameters.
[0056] Pessier et al..sup.2 further describes how Teale introduced
the concept of minimum specific energy (or maximum mechanical
efficiency). The minimum specific energy is reached when the
specific energy approaches, or is roughly equal to, the compressive
strength of the rock being drilled (meaning the maximum mechanical
efficiency is achieved), i.e., .sup.2"Quantifying Common Drilling
Problems with Mechanical Specific Energy and a Bit-Specific
Coefficient of Sliding Friction, Pessier et al., SPE #24584,
1992.
E S = E S Min .apprxeq. .sigma. ##EQU00002## thus , E S Min =
.sigma. = WOB A + 120 .pi. RPM TOB A ROP ##EQU00002.2##
[0057] This form of the specific energy equation now contains all
the desired parameters that should ultimately be present within the
characteristic curves: (a) the rotary speed, (b) the drilling
weight, (c) the drilling torque, (d) the rate of penetration and
(e) the compressive rock strength.
[0058] To find a suitable characteristic equation, in accordance
with particular embodiments of the present disclosure, some
manipulation of this equation is required. Rearranging the equation
at minimum specific energy,
A = WOB .sigma. + 120 .pi. RPM TOB .sigma. ROP ##EQU00003##
[0059] The depth of penetration per revolution is,
d = ROP 5 R P M ##EQU00004##
[0060] Substituting into the equation for "A" gives,
A = WOB .sigma. + 120 .pi. TOB .sigma. 5 d ##EQU00005##
reducing to,
A = WOB .sigma. + 24 .pi. TOB .sigma. d ##EQU00006##
[0061] Further review of Pessier reveals the definition of the
sliding coefficient of friction, .mu., which is dimensionless:
TOB = .mu. D WOB 36 ##EQU00007##
where D is the borehole diameter and units may be expressed in
inches (in).
[0062] This sliding coefficient of friction was initially
introduced to express the drilling torque as a function of the
drilling weight. This sliding coefficient of friction can be
inserted into the equation for A:
A = WOB .sigma. + 24 .pi. .mu. D WOB .sigma. d 36 ##EQU00008##
rearranging and reducing,
A = WOB .sigma. [ 1 + 24 .pi. .mu. D 36 d ] ##EQU00009## A = WOB
.sigma. [ 1 + 2 .pi. .mu. D 3 d ] ##EQU00009.2## WOB .sigma. = A [
1 + 2 .pi. .mu. D 3 d ] ##EQU00009.3## Effective Area = WOB .sigma.
= A [ 1 + 2 .pi. .mu. D 3 d ] ##EQU00009.4##
[0063] This equation was taken to be a suitable form for a
characteristic equation in that WOB/.sigma. could be related to
something tangible (borehole cross-sectional area, A) through a
non-dimensional transform (within the brackets) that was dependant
on the depth of penetration per revolution, d. This relationship
for WOB/.sigma. is called the "Effective Area" and the units may be
given in square inches (in.sup.2).
[0064] The value of the sliding coefficient of friction, .mu.,
and/or the value of WOB/.sigma. can be provided by models or data
for a given value of d. Thus the form of this "weight based"
characteristic equation is what is important (as opposed to the
equation itself) where the Effective Area is a function of d.
Effective Area = WOB .sigma. = f ( d ) ##EQU00010##
[0065] Having a characteristic curve that defines the weight on a
cutting structure required to advance at a given depth of
penetration per revolution, d, in a given rock strength is very
useful. The equations above can be applied to any cutting
structure, for example a reamer cutting structure, by replacing WOB
with WOR, and TOB with TOR.
[0066] This form of the characteristic equation effectively
captures four out of the five desired parameters (rotary speed,
drilling weight, rate of penetration, and compressive rock
strength) excepting the drilling torque. In accordance with
particular embodiments, a second "torque based" characteristic
equation was needed as a function of the depth of penetration per
revolution, d, as well. It was noted that TOB/WOB, having units in
inches (in), might be a desirable characteristic to complement
WOB/.sigma. (having units in square inches (in.sup.2)). Such a
characteristic can be derived by going back to the equation for
borehole area at minimum specific energy, A:
A = WOB .sigma. + 24 .pi. TOB .sigma. d ##EQU00011##
with further manipulation,
A = WOB .sigma. + 24 .pi. d WOB .sigma. TOB WOB ##EQU00012## A =
WOB .sigma. [ 1 + 24 .pi. d TOB WOB ] ##EQU00012.2## 24 .pi. d TOB
WOB = A WOB .sigma. - 1 ##EQU00012.3## TOB WOB = d 24 .pi. [ A WOB
.sigma. - 1 ] ##EQU00012.4##
For a circular borehole,
A=.pi.R.sup.2
where R is the radius of the borehole and units may be given in
inches (in). Thus,
TOB WOB = d 24 .pi. [ .pi. R 2 WOB .sigma. - 1 ] ##EQU00013## TOB
WOB = d 24 [ R 2 WOB .sigma. - 1 .pi. ] ##EQU00013.2## Effective
Radius = TOB WOB = d 24 [ R 2 WOB .sigma. - 1 .pi. ]
##EQU00013.3##
[0067] This equation was taken to be a suitable form for a second
characteristic equation in that TOB/WOB was dependant on the depth
of penetration per revolution, d, and the first characteristic
Effective Area (WOB/.sigma.), which itself is dependent on the
depth of penetration per revolution, d. This relationship for
TOB/WOB is called the "Effective Radius" and the units may be given
in inches (in). Warren.sup.3 shows a somewhat similar relationship
for torque of a roller cone bit, but the focus was on trying to use
roller cone bit torque as an indicator of formation properties. The
equations above can be applied to any cutting structure, for
example a reamer cutting structure, by replacing WOB with WOR, and
TOB with TOR. .sup.3"Factors Affecting Torque for a Roller Cone
Bit", Warren, SPE#11994, 1984.
[0068] Again, the form of this "torque based" characteristic
equation is what is important (as opposed to the equation itself)
where the Effective Radius is a function of d.
Effective Radius = TOB WOB = f ( d ) ##EQU00014##
[0069] Collecting various datasets (containing the five mentioned
parameters) allows for the determination of two characteristic
trends/curves while implementing some form of curve-fitting upon
them. These datasets may be generated from the previously mentioned
state-of-the-art FEA-style engineering platforms for a given earth
boring device, or may just as well be compiled using real-life
drilling information.
[0070] These characteristic curves now define the global
steady-state drilling response of an earth boring device without
being required to evaluate a certain design within a high-end
engineering platform and this for a limitless amount of drilling
environment combinations.
[0071] FIG. 2 illustrates a weight based characteristic curve
pertaining to a drill bit, for example drill bit 32. The
characteristic curve includes a graphical depiction of the cutting
structure(s) predicted performance. In the illustrated embodiment
of FIG. 2, the horizontal, or x-axis reflects the depth of
penetration per revolution, d (measured in inches per revolution of
the drill bit). The vertical axis, or y-axis reflects the weight on
bit divided by rock strength (the Effective Area). In the
illustrated embodiment of FIG. 2, drill bit 32 is an eight and
one-half inch drill bit. As discussed in more detail below, the
data used to generate the characteristic curve of FIG. 2 may be
derived from a variety of sources, including actual data, or data
derived from a computer model.
[0072] FIG. 3 illustrates a weight based characteristic curve
similar to FIG. 2, except that the characteristic curve of FIG. 3
pertains to a reamer, for example reamer 34. The characteristic
curve includes a graphical depiction of the cutting structure(s)
performance. In the illustrated embodiment of FIG. 3, the
horizontal, or x-axis reflects the depth of penetration (measured
in inches) per revolution, d, of the reamer. The vertical axis, or
y-axis reflects the weight on reamer divided by rock strength (the
Effective Area). In the illustrated embodiment of FIG. 3, reamer 34
is an eight and one-half inch by twelve and one-quarter inch
reamer.
[0073] FIG. 4 illustrates a torque based characteristic curve
pertaining to a drill bit, for example drill bit 32. The
characteristic curve includes a graphical depiction of the cutting
structure(s) performance. In the illustrated embodiment of FIG. 4,
the horizontal, or x-axis reflects the depth of penetration
(measured in inches) per revolution, d, of the drill bit. The
vertical axis, or y-axis reflects the torque on bit divided by
weight on bit (the Effective Radius). In the illustrated embodiment
of FIG. 4, drill bit 32 is an eight and one-half inch drill
bit.
[0074] FIG. 5 illustrates a torque based characteristic curve
similar to FIG. 4, except that the characteristic curve of FIG. 5
pertains to a reamer, for example reamer 34. The characteristic
curve includes a graphical depiction of the cutting structure(s)
performance. In the illustrated embodiment of FIG. 5, the
horizontal, or x-axis reflects the depth of penetration (measured
in inches) per revolution, d, of the reamer. The vertical axis, or
y-axis reflects the torque on reamer divided by weight on reamer
(the Effective Radius). In the illustrated embodiment of FIG. 5,
reamer 34 is an eight and one-half inch by twelve and one-quarter
inch reamer.
[0075] According to the teachings of the present disclosure, the
weight based characteristic curves for a drill bit and reamer(s) in
a given BHA can be combined as illustrated in FIG. 6. As
illustrated in FIG. 6, each of the drill bit and reamer
characteristic curves are reflected upon a common graph, with
common axes. The characteristic curve includes a graphical
depiction of the cutting structures performance. In the illustrated
embodiment of FIG. 6, the horizontal, or x-axis reflects the depth
of penetration (measured in inches) per revolution, d, of the
cutting structures (e.g., drill bit 32 and reamer 34). The vertical
axis, or y-axis reflects the weight on the cutting structure (e.g.,
drill bit or reamer) divided by the rock strength (.sigma.) (the
Effective Area). In the illustrated embodiment of FIG. 6, drill bit
32 is an eight and one-half inch drill bit and reamer 34 is an
eight and one-half inch by twelve and one-quarter inch reamer.
[0076] As depicted in FIG. 6, the combined characteristic curves
allow for a user to select any desired ROP/RPM for a BHA that
includes bit 32 and reamer 34, and quickly calculate (or at least
approximate) the associated weight on bit/rock strength for the
drill bit 32 ("Resulting WOB/.sigma.") and the associated weight on
reamer/rock strength for the reamer 34 ("Resulting WOR/.sigma.").
The drill bit cutting structure and the reamer cutting structure
may be in different lithologies with different rock strength,
.sigma.. The appropriate rock strength, .sigma., for each cutting
structure must be used, such as .sigma..sub.b for the rock strength
associated with the drill bit and a .sigma..sub.r for the rock
strength associated with the reamer.
[0077] In addition, the weight based characteristic curve for the
combined BHA system of a drill bit and reamer cutting structures
can be generated as illustrated in FIG. 7. Similar to FIG. 6, FIG.
7 reflects the characteristic curve of drill bit 32 and reamer 34.
However, FIG. 7 also includes the characteristic curve of the
system (combined drill bit and reamer cutting structure
characteristic curves). The characteristic curve of the system
reflects the sum of the drill bit characteristic curve and the
reamer characteristic curve. The system characteristic curve allows
a user to determine the weight required for the system, for any
desired ROP. In FIG. 7, drill bit 32 is an eight and one-half inch
drill bit and reamer 34 is an eight and one-half inch by twelve and
one-quarter inch reamer.
[0078] It is worth noting that two weight-based characteristic
curves may only be "added" together to obtain the system curve fit,
if the rock strengths that the two cutting structures are
encountering are equal, or approximately equal. This is true
because rock strength appears in the denominator of the y-axis of
the weight based characteristic curves.
[0079] In a similar manner, according to the teachings of the
present disclosure, the torque based characteristic curves for a
system that includes a drill bit and reamer(s) in a given BHA can
be illustrated on a common graph as illustrated in FIG. 8. As shown
in FIG. 8, each of the drill bit and reamer characteristic curves
are reflected upon a common graph, with common axes. The
characteristic curve includes a graphical depiction of the
respective cutting structures performance. In the illustrated
embodiment of FIG. 8, the horizontal, or x-axis reflects the depth
of penetration (measured in inches) per revolution, d, of the
cutting structures (e.g., drill bit 32 and reamer 34). The vertical
axis, or y-axis reflects the torque on the cutting structure (e.g.,
drill bit 32 and reamer 34) divided by the weight on the cutting
structure (the Effective Radius). In the illustrated embodiment of
FIG. 8, drill bit 32 is an eight and one-half inch drill bit and
reamer 34 is an eight and one-half inch by twelve and one-quarter
inch reamer.
[0080] As depicted in FIG. 8, the combined characteristic curves
allow for a user to select any desired ROP/RPM for a BHA that
includes bit 32 and reamer 34, and quickly calculate (or at least
approximate) the associated torque on bit/weight on bit for the
drill bit 32 ("Resulting TOB/WOB") and the associated torque on
reamer/weight on reamer for the reamer 34 ("Resulting
TOR/WOR").
[0081] Likewise, a torque based characteristic curve for the
combined BHA system (including the drill bit 32 and reamer 34
cutting structures) can be generated as illustrated in FIG. 9.
[0082] The y-axis of this curve represents TSYS/WSYS and the x-axis
is the depth of penetration per revolution, d, that has been
consistently used in all the characteristic curves. Thus, values
from the previous characteristic curves can be combined as follows
at a given ROP/RPM and rock strength, .sigma., to achieve the
desired characteristic:
TOB .times. 12 WOB .times. WOB .sigma. + TOR .times. 12 WOR .times.
WOR .sigma. WOB + WOR .sigma. = ( TOB + TOR ) .times. 12 WOB + WOR
= TSYS .times. 12 WSYS ##EQU00015##
where TOB, TOR, and TSYS units are [ft lb]; WOB, WOR, and WSYS
units are [lb]; and .sigma. units are [psi]. Other units can be
applied as well as long as appropriate conversion factors are
used.
[0083] It is often desired to know the BHA system applied weight,
WSYS, (e.g., in FIG. 7) required to drill at a desired ROP (in a
given rock at a desired RPM) as well as the distribution of that
BHA system applied weight to the cutting structures in the BHA.
Since the drill bit and reamer(s) in a BHA have the same nominal
ROP, the combined characteristic curves make it easier to see how
the weight distribution and torque distribution between drill bit
and reamer(s) cutting structures must exist to sustain that ROP in
a given rock and RPM.
[0084] The sum of the weights that are distributed to each of the
cutting structures equals the weight applied on the system of
cutting structures, according to the following equation:
WSYS[lb]=WOB[lb]+WOR(s)[lb]
[0085] Likewise, the sum of the torques generated by each of the
cutting structures equals the torque generated by the system of
cutting structures, according to the following equation:
TSYS[ft lb]=TOB[ft lb]+TOR(s)[ft lb]
[0086] A weight based characteristic curve for the BHA system of
cutting structures can be generated by simply adding together the
curves for each cutting structure (see e.g., FIG. 7 that combines a
drill bit weight based characteristic curve and a reamer weight
based characteristic curve, into a system weight based
characteristic curve). However, the same is not true of the torque
based characteristic curves. Torque based characteristic curves
cannot be added together in the same way as weight based
characteristic curves, because the measure of weight in the
denominator is different between the two (i.e., weight on reamer
and weight on bit are not equal).
[0087] Combined characteristic curves reflect the individual weight
on bit and weight on reamer(s) that correspond to a desired
drilling ROP (in a given rock and desired RPM) as well as the
weight on the system WSYS of drill bit and reamer cutting
structures in the BHA that correspond with a desired ROP. Likewise,
the combined characteristic curves show the individual torque on
bit and torque on reamer(s) generated by the individual weight on
bit and weight on reamer(s) at the desired ROP (in a given rock and
desired RPM).
[0088] It is worth noting that the RPM of the cutting structures in
a BHA may be different (but are typically the same). For example, a
given BHA may include a mud motor between the drill bit and reamer,
that may drive the drill bit cutting structure at a higher RPM than
the reamer cutting structure. In this embodiment, the reamer may be
driven at the drill pipe RPM directly from the drilling rig at
surface. In this case, nominal ROP will still be the same for each
cutting structure, but ROP/RPM, hence the depth of penetration per
revolution, d, will be different for the different cutting
structures. The cutting structure turning at a higher RPM has to
have a lower value of d in order to progress at the same ROP as
another cutting structure in the same BHA turning at a lower RPM.
The individual characteristic curves for each cutting structure are
still valid in this case but the system curves are not, since the
RPM in the respective denominators are not equal.
[0089] In lieu of, or in addition to determining the BHA system
applied weight/rock strength (WSYS/.sigma.) required to drill at a
desired ROP, it may be desirable to determine the ROP that can be
achieved with a given available WSYS. Here the system level curve
is valuable to find the ROP that can be sustained by a given WSYS
(in a given rock and desired RPM). See for example, FIG. 10. Once
the system ROP is determined, the weight and torque distributions
can be obtained as before along with the system torque TSYS.
[0090] Likewise, it may be desired to determine the ROP that can be
achieved with a given desired limit of system torque TSYS. Again,
the system level curve is valuable to find the ROP that can be
sustained at a given level of TSYS (in a given rock and desired RPM
and WSYS). See for example, FIG. 11. After the system ROP is
determined, the weight and torque distributions can be obtained as
described above.
[0091] Constraints other than weight on cutting structure, torque
on cutting structure, rate of penetration and rotary speed may also
be used in the evaluation and/or selection process, in accordance
with other embodiments of the present disclosure. For example, a
maximum or minimum WOB constraint may be used to determine the
maximum or minimum ROP (in a given rock and desired RPM). From the
ROP, weight and torque distributions as well as required system
weight and generated torque can be determined. Similar constraints
can be used for a reamer(s). Still another constraint may include
maximum or minimum depth of penetration per revolution, d [in/rev]
(the x-axis in the characteristic curves).
[0092] In yet another embodiment of the present disclosure, a new
cutting structure may be designed to approximate a desired
characteristic curve. For example, it may be desirable to utilize a
given reamer cutting structure that has a certain characteristic
curve. It may also be desirable to design a new drill bit cutting
structure with a characteristic curve that closely matches the
reamer, so that the reamer and drill bit require similar WOR and
WOB to drill through a given rock formation. Other design goals may
include: maintaining a certain desired ratio of WOR and WOB or TOR
and TOB; maintaining desired WOR and WOB when the reamer and drill
bit are in different formations.
[0093] The characteristic curves for each cutting structure can be
generated using existing models of their performance. Models of
cutting structure performance through a given rock lithology and
drilling parameters are common. For example, models generated by
computer systems employing the IBitS.TM. and IReamS software
(available from Halliburton) may be used to generate, in whole or
in part, or to supplement characteristics curves, according to the
teachings of the present disclosure. However, other sources of
generating characteristic curves are available, and described in
more detail below.
[0094] Characteristic curves for drill bit and reamer cutting
structures can be obtained from a variety of sources including, but
not limited to: (i) computer models of the cutting structures
(e.g., IBitS.TM., IReamS); (ii) downhole measurements of WOB, WOR,
TOB, TOR, RPM, .sigma. (porosity measurement used to determine
.sigma.), and pressure (as it affects .sigma.); (iii) surface
measurements of ROP, RPM, WSYS, TSYS, and mud density; (iv)
publicly available competitor supplied information (spec sheets,
marketing material, white papers, etc); (v) customer supplied
information; (vi) combinations of models and actual measurements;
(vii) models and/or measurements that vary with use through cutter
wear; or (viii) real time generation of characteristic curves.
[0095] Downhole measurements previously taken of WOB, WOR, TOB,
TOR, RPM, .sigma., and pressure (as it affects rock strength) from
logging while drilling (LWD) tools exist and can be used to help
generate "actual" characteristic curves. ROP (a necessary
component) is typically measured at surface. RPM is also typically
measured at surface but can also be measured downhole with LWD
tools. Such "actual" characteristic curves can be used to compare
to, and improve model generated curves, and can also be added to a
database of performance data, for reference as current or offset
well data.
[0096] Surface measurements of ROP, RPM, WSYS, TSYS, and mud
density (downhole pressure) can also be used to generate, in whole
or in part, or supplement the generation of characteristic curves,
and to validate/improve model generated curves.
[0097] Often, drill bit manufacturers will not disclose enough
detail to allow third party modeling of a cutting structure
directly (e.g., via IBitS.TM. or IReamS). However, if the
manufacturer provides performance data such as ROP vs. WOB, or ROP
vs. WOR, for a given RPM and rock strength, characteristic curves
can be constructed. Specification sheets that are published by such
manufacturers may provide such information. Performance data
regarding a particular manufacturer's drill bits, reamers, etc.,
may also be derived from downhole and surface measurements as
described above. Similarly, customers and potential customers may
provide performance data of a particular manufacturer's drill bits
or reamers sufficient to generate characteristic curves.
[0098] Combinations of models and measurements can also be utilized
to generate characteristic curves. Often the measurements can be
used to refine models.
[0099] As cutters on a drill bit or reamer cutting structure wear,
the performance of the cutting structure, and hence the
characteristic curves, will change. These changes are difficult to
predict, although models that attempt to do so, exist. Field data
may be more accurate with regard to the measurement of declining
performance. Characteristic curves can be generated for worn
cutting structures and calibrated to the amount of wear. In this
manner, such characteristic curves may be utilized to
predict/improve performance of the cutting structures, over time
and use.
[0100] "Real-time" data (collected on site during drilling
operations) may also be used to generate characteristic curves
while drilling, in order to see how performance changes over time,
or lithology, or drilling parameters. These changes can be used to
recommend different operating parameters or to pull a drill bit or
reamer from the well once performance has degraded beyond an
acceptable level.
[0101] There are a number of sources available for collecting
performance data, and there is a large number of drill bits and
reamers to be evaluated (a user will benefit if hundreds, or even
thousands of drill bits and/or reamers are evaluated and compared)
for a specific drilling operation. In order to allow for an
accurate calculation of the characteristic curve of a given cutting
structure, a curve fit is calculated that accurately reflects the
performance data, or values of performance. In accordance with a
particular embodiment, the values of performance may include weight
on cutting structure and/or torque on cutting structure. In a
particular embodiment, the curve fit may be a polynomial curve
fit.
[0102] In order to allow comparisons of many configurations at a
time, as well as for speed of calculation, polynomial curve fits of
the characteristic curves are performed and only the coefficients
of the polynomial are stored in the cutting structure database
(along with additional information for each drill bit and reamer
cutting structure). Thus, thousands of drill bit cutting structures
may be stored in the database, and evaluated rapidly for a given
drilling operation.
[0103] In the illustrated embodiments, the characteristic curves
are two-dimensional, and reflect certain values of performance
(weight or torque on cutting structure) versus rate of penetration
per revolution. However, it will be recognized by those of ordinary
skill in the art that other embodiments may employ three
dimensional (e.g., a "Z-axis") or four dimensional (e.g., time
varying), in accordance with the teachings of the present
disclosure.
[0104] In accordance with a particular embodiment of the present
disclosure, up to a 20th degree polynomial (21 parameters) may be
used as a curve fit to reflect the weight based and torque based
characteristic curves (see e.g., FIGS. 12a through 12h). FIGS. 12a
through 12d illustrate a weight based (two segment) and a torque
based (two segment) drill bit curve fit. FIGS. 12e through 12h
illustrate a weight based (two segment) and a torque based (two
segment) reamer curve fit, in accordance with particular
embodiments of the present invention.
[0105] In a particular embodiment, a model such as IBitS (for bits)
or IReamS (for reamers) is used to calculate values of data points
on the characteristic curves ("original" y-values). To enhance
accuracy at low values of depth of penetration per revolution, d,
characteristic curves are generated in two overlapping segments.
The first segment of each characteristic curve is generated using
201 data points, from d=0.00025 [in/rev] to d=0.08025 [in/rev]
(inclusive) in increments of d of 0.00040 [in/rev]. To accomplish
this, the models are run with rotary speed of 120 [rpm] and rock
strength of 18,000 [psi] while incrementing the ROP from 0.15
[ft/hr] to 48.15 [ft/hr] (inclusive) in increments of 0.24
[ft/hr].
[0106] The second segment of each characteristic curve is generated
using 201 data points from d=0.04000 [in/rev] to d=1.00000 [in/rev]
(inclusive) in increments of d of 0.00480 [in/rev]. To accomplish
this, the models are run with rotary speed of 120 [rpm] and rock
strength of 18,000 [psi] while incrementing the ROP from 24.00
[ft/hr] to 600.00 [ft/hr] (inclusive) in increments of 2.88
[ft/hr]. It is important to note that the calculated values of d up
to 1.0 [in] may exceed what is physically possible. But calculating
values of d over such a large range enables the computational
iterations described later to occur in a smooth manner.
[0107] The two segments overlap for values of d between 0.04000
[in/rev] and 0.08025 [in/rev] (inclusive). Polynomial curve fits
are calculated for each segment and the coefficients of the
polynomials are stored in the database of characteristic curves for
each cutting structure. In the application of the program, the
polynomial coefficients of the first segment of each characteristic
curve are used for values of d less than 0.06 [in/rev]. When values
of d are greater than or equal to 0.06 [in/rev], the polynomial
coefficients of the second segment of each characteristic curve are
used. In this manner, curve fitting errors that occur near the ends
of the polynomial curve segments do not impact the results in this
overlap region.
[0108] At each increment, for the weight based characteristic curve
of a drill bit, original values of WOB/.sigma. and depth of
penetration per revolution, d, (derived from the RPM and ROP
values) are calculated. A polynomial curve fit is performed on each
of two segments, each segment containing 201 data points, as
described above. The details of the polynomial curve fit process
are described later.
[0109] At each increment, for the torque based characteristic curve
of a drill bit, original values of TOB/WOB and depth of penetration
per revolution, d, (derived from the RPM and ROP values) are
calculated. A polynomial curve fit is performed on each of two
segments, each segment containing 201 data points, as described
above. The details of the polynomial curve fit process are
described later.
[0110] At each increment, for the weight based characteristic curve
of a reamer, original values of WOR/.sigma. and depth of
penetration per revolution, d, (derived from the RPM and ROP
values) are calculated. A polynomial curve fit is performed on each
of two segments, each segment containing 201 data points as
described above. The details of the polynomial curve fit process
are described later.
[0111] At each increment, for the torque based characteristic curve
of a reamer, original values of TOR/WOR and depth of penetration
per revolution, d, (derived from the RPM and ROP values) are
calculated. A polynomial curve fit is performed on each of two
segments, each segment containing 201 data points as described
above. The details of the polynomial curve fit process are
described later.
[0112] In all these particular embodiments, the polynomial curve
fit of each segment of each characteristic curve is performed by
first recentering and rescaling the x-axis (depth of penetration
per revolution, d) values of the original data points for better
numerical properties of the curve fit. The x-axis values are
transformed (recentered and rescaled) into x' values as
follows:
x ' = x - dAv Std d ##EQU00016##
[0113] where dAv is the average of the 201 values of depth of
penetration per revolution, d, and Std d is the standard deviation
of the 201 values of depth of penetration per revolution, d.
[0114] Then a conventional least squares polynomial curve fit is
applied to the 201 data points of each segment of each
characteristic curve to determine the coefficients of the
polynomial. An example of this polynomial curve fit can be found in
the "polyfit" function of commercially available technical
computing software MATLAB.RTM. available from The MathWorks.TM..
The degree, "n", of the polynomial of each segment of each
characteristic curve is chosen as follows to achieve the desired
level of accuracy:
[0115] for the first segment (0.00025.ltoreq.d
[in/rev].ltoreq.0.08025) for drill bit cutting structures, the
weight based (WOB/.sigma.) characteristic curve segment utilizes a
15.sup.th degree polynomial (16 coefficients);
[0116] for the second segment (0.0400.ltoreq.d
[in/rev].ltoreq.1.0000) for drill bit cutting structures, the
weight based (WOB/.sigma.) characteristic curve segment utilizes a
15.sup.th degree polynomial (16 coefficients);
[0117] for the first segment (0.00025.ltoreq.d
[in/rev].ltoreq.0.08025) for drill bit cutting structures, the
torque based (TOB/WOB) characteristic curve segment utilizes a
20.sup.th degree polynomial (21 coefficients);
[0118] for the second segment (0.0400.ltoreq.d
[in/rev].ltoreq.1.0000) for drill bit cutting structures, the
torque based (TOB/WOB) characteristic curve segment utilizes a
20.sup.th degree polynomial (21 coefficients);
[0119] for the first segment (0.00025.ltoreq.d
[in/rev].ltoreq.0.08025) for reamer cutting structures, the weight
based (WOR/.sigma.) characteristic curve segment utilizes a
13.sup.th degree polynomial (14 coefficients);
[0120] for the second segment (0.0400.ltoreq.d
[in/rev].ltoreq.1.0000) for reamer cutting structures, the weight
based (WOR/.sigma.) characteristic curve segment utilizes a
13.sup.th degree polynomial (14 coefficients);
[0121] for the first segment (0.00025.ltoreq.d
[in/rev].ltoreq.0.08025) for reamer cutting structures, the torque
based (TOR/WOR) characteristic curve segment utilizes a 20.sup.th
degree polynomial (21 coefficients);
[0122] for the second segment (0.0400.ltoreq.d
[in/rev].ltoreq.1.0000) for reamer cutting structures, the torque
based (TOR/WOR) characteristic curve segment utilizes a 20.sup.th
degree polynomial (21 coefficients).
[0123] For the 201 original data points of each segment of each
characteristic curve, the x-axis values are set equal to the depth
of penetration per revolution, d. For any given value of x, x' is
calculated to rescale and recenter the values of x by:
x ' = x - dAv Std d ##EQU00017##
[0124] For each value of x, hence x', an associated original
y-value is known. The coefficients of the polynomial curve fit are
determined using the data set (x', y) of the 201 original data
points of each segment of each characteristic curve. The
coefficients of the polynomial curve fit are determined using
mathematical routines equivalent to the polyfit function from
MATLAB.RTM..
[0125] "Fitted" y-values, y', can be calculated using the
coefficients applied to the x' values:
y'=A0+A1x'+A2x'.sup.2+A3x'.sup.3+ . . . Anx'.sup.n
[0126] where y' is the calculated fitted result (WOB/.sigma.,
TOB/WOB, WOR/.sigma., TOR/WOR) for any given x, hence x'; and Ao,
A1, A2, A3 . . . An are the coefficients of an nth degree
polynomial for the appropriate segment of the characteristic curve
at the desired degree n.
[0127] For error checking purposes, this fitted series of values
can be compared to the corresponding original series of values to
determine if the polynomial curve fit adequately represents the
original characteristic curve. A least squares fit comparison is
performed between the original data series and the new fitted
values whereby a coefficient of correlation R is determined as:
R = m i = 1 m y i y i ' - ( i = 1 m y i ) ( i = 1 m y i ' ) [ m i =
1 m y i 2 ( i = 1 m y i ) 2 ] 1 2 [ m i = 1 m y i '2 - ( i = 1 m y
i ' ) 2 ] 1 2 ##EQU00018##
[0128] where m is the number of data values in a series, for
example 201; y.sub.i is the original y-value (WOB/.sigma., TOB/WOB,
WOR/.sigma., TOR/WOR) from the model of i.sup.th data point in the
series of m data points; and y'.sub.i is the fitted y-value
(WOB/.sigma., TOB/WOB, WOR/.sigma., TOR/WOR) calculated from the
polynomial curve fit. The coefficient of correlation R is squared
to obtain the coefficient of determination.
[0129] In a particular embodiment, the coefficient of determination
R.sup.2 should be preferably greater than or equal to 0.9998 for
the polynomial curve fit to have an acceptable error condition.
[0130] A visual indication of the suitability of the polynomial
curve fit with coefficient of correlation R as described above can
be seen in FIG. 12a through FIG. 12h where the fitted y' values are
plotted on top of the characteristic curve through the original y
values.
[0131] Moreover, other curve fits could be used, within the
teachings of the present disclosure. For example, linear, power
law, logarithmic, and/or exponential curve fits may be used to
calculate, or store the characteristic curve fit(s).
[0132] It will be appreciated by those having ordinary skill in the
art, that many cutting structure configurations are possible in a
BHA. In accordance with the teachings of the present invention,
performance of cutting structures can be compared across all
combinations and permutations of (i) drill bit; (ii) reamer; (iii)
drill bit plus reamer; (iv) drill bit plus multiple reamers; and/or
multiple reamers. For example, a single drill bit can be compared
against another drill bit, but a single drill bit can also be
compared against another drill bit plus reamer configuration.
Moreover, drill bit and reamer performance can be compared across
different sizes and types. It may be desirable to compare up to
thousands of combinations at a time to find the best performing
solution across a range of lithology and drilling parameters and
evaluated against a set of constraints.
[0133] The teachings of the present invention allow a user to
collect and analyze data regarding thousands of drill bits and/or
reamer cutting structures. As discussed above, in accordance with a
particular embodiment, such data may be stored in a cutting
structure database of characteristic curve fit polynomial
coefficients. Thus, a system and method are provided to quickly and
easily (i) choose candidate cutting structures and/or cutting
structure combinations, (ii) compare their performance in a given
scenario of lithology and drilling parameters, and/or (iii) select
the best configurations through the use of a Performance Index.
[0134] In accordance with a particular embodiment of the present
invention, a computer algorithm allows a user to accomplish these
tasks. FIG. 26 and FIG. 27 illustrate a particular embodiment flow
chart of the algorithm. The data base of characteristic curve fit
polynomial coefficients is represented in FIG. 26 in the boxes
labeled CHARACTERISTIC, PARAMETER TYPE, and ADDITIONAL DATA.
CHARACTERISTIC holds: the polynomial coefficients of each segment
of each characteristic curve as well as the degree of the
polynomial, n, for each segment; dAv, the average of the 201 values
of depth of penetration per revolution for each segment; and Std d,
the standard deviation of the 201 values of depth of penetration
per revolution for each segment. PARAMETER TYPE stores information
about whether the polynomial coefficients were generated from a
model or from a log of performance from an actual bit run.
ADDITIONAL DATA stores additional identifying information about the
cutting structures such as: (for drill bits) Bit Series, Bit Class,
Bit Application, Bit Technology, Bit Blade Count, Bit Cutter Size,
Bit Profile Shape, Bit Diameter, Bit Chamfer Type, Bit Chamfer
Size, Bit Material Number, Bit Type, Bit Cutting Structure Number,
etc.; (for reamers) Type, Body, Opening Diameter, Pilot Hole
Diameter, Arm Count, Blade Count, Layout, Cutter Size, Material
Number, Project Name, etc. The utility of this additional
information in selecting cutting structures for analysis is
discussed below.
[0135] FIG. 13 illustrates a screen shot of a computer program that
may be employed to select bits, reamers, other cutting structures,
or combinations thereof, in accordance with a particular embodiment
of the present disclosure. The "initial screen" of FIG. 13 allows a
user to select an operation to perform, including: (i) Select Bits;
(ii) Select Reamers; (iii) Select Configurations; (iv) Define
Lithology; (v) Set Drilling Parameters; and/or (vi) Run Selection
Algorithm.
[0136] FIG. 14 illustrates a bit selection screen that allows a
user to apply filters regarding various features of the drill bit
in order to filter out less suitable drill bits for the given
operation. The drill bit selection screen allows a user to select
and/or identify potential drill bits by Bit Series, Bit Class, Bit
Application, Bit Technology, Bit Blade Count, Bit Cutter Size, Bit
Profile Shape, Bit Diameter, Bit Chamfer Type, Bit Chamfer Size,
Bit Material Number, Bit Type, Bit Cutting Structure Number, etc.
In the example of FIG. 14, such filters effectively reduced the
number of drill bits under consideration to one hundred and three.
The computer program also allows the user to select one or more of
the one hundred and three drill bits to be used in later
calculations. As illustrated in FIG. 14, the user selected three
such drill bits for further consideration. The portion of the
computer algorithm corresponding with the functionality shown in
FIG. 14 is shown in FIG. 26 in the box labeled CUTTING STRUCTURE
where cutting structures are selected for further analysis.
[0137] FIG. 15 illustrates a reamer selection screen that allows a
user to apply filters regarding various features of the reamer in
order to filter out less suitable reamers for the given operation.
The reamer selection screen allows a user to select and/or identify
potential reamers by Type, Body, Opening Diameter, Pilot Hole
Diameter, Arm Count, Blade Count, Layout, Cutter Size, Material
Number, Project Name, etc. For example, one filter is the pilot
hole diameter that will normally be selected to match bits that
were previously selected. This allows the user to filter out less
suitable reamers for the given operation. In the example of FIG.
15, filters effectively reduced the number of reamers under
consideration to eleven. The computer program also allows the user
to select one or more of the eleven reamers to be used in later
calculations. As illustrated in FIG. 15, the user selected two such
reamers for further consideration. These two reamers have different
opening diameters to allow the user to evaluate different opening
diameters in the system. The portion of the computer algorithm
corresponding with the functionality shown in FIG. 15 is shown in
FIG. 26 in the box labeled CUTTING STRUCTURE where cutting
structures are selected for further analysis.
[0138] The selected bits and reamers may then be displayed in a
list along with as many as every valid combination/permutation. The
user can select individual bits, individual reamers, combinations
of drill bit and reamer, or every bit, every reamer, and every
combination for analysis.
[0139] FIG. 16 allows the user to select the configurations to be
evaluated. All possible configurations of bits, reamers and bits
plus reamers from the previous selections of bits and reamers are
displayed to the user. In the illustrated embodiment, the user
selects only the bit plus reamer configurations for further
analysis. The portion of the computer algorithm corresponding with
the functionality shown in FIG. 16 is shown in FIG. 26 in the box
labeled CONFIGURATION where cutting structures and cutting
structure combinations are selected for further analysis. The
selected items are called "configurations."
[0140] FIG. 17 illustrates a screen shot from the computer program
that allows the user to define the lithology to be drilled. In
accordance with this embodiment, zones may be defined by depth,
length and rock strength. Any number of zones may be defined to
reflect the lithology of the formation to be drilled. During normal
drilling operations, the drill bit and reamer cutting structures on
a BHA encounter different lithologies (represented by rock
strength) at different times because the cutting structures exist
at different locations along the BHA. The left figure of FIG. 29
shows a representation of a BHA where CS.sub.1 is a drill bit
cutting structure, CS.sub.2 is a reamer cutting structure at
distance h1 above the drill bit, and CS.sub.n represents additional
reamer cutting structures if present in the BHA. The middle figure
of FIG. 29 shows adjacent views of the lithology encountered by the
drill bit and reamer at the same points in time as the well is
drilled in the downward direction. The drill bit CS.sub.1
encounters each new rock strength (.sigma..sub.1, .sigma..sub.2,
.sigma..sub.3, .sigma..sub.4 before the reamer CS.sub.2. The
analysis of bit and reamer(s) performance starts when all cutting
structures are in a defined lithology (the uppermost reamer cutting
structure just touching the top of the uppermost defined
lithology). In FIG. 29, the analysis starts when the drill bit is a
distance h1 below the top of rock strength .sigma..sub.1 and the
reamer is at the top of rock strength .sigma..sub.1. At this time
both the drill bit and reamer are within the same rock strength
.sigma..sub.1 which defines CASE 1 in the analysis shown on the
right figure of FIG. 29. As the BHA drills further down the
lithological column, the drill bit cutting structure encounters new
rock strength .sigma..sub.2 before the reamer cutting structure.
This defines a new case, CASE 2, in the analysis where the drill
bit is in rock strength .sigma..sub.2 and the reamer is still in
rock strength .sigma..sub.1. Drilling further in this example, the
reamer encounters rock strength .sigma..sub.2 while the drill bit
is still in rock strength .sigma..sub.2 which defines CASE 3. Every
time one of the cutting structures in the BHA encounters a new rock
strength, a new case is defined. Each case has a thickness or
length (CASELENGTH) associated with it from the depth where one
cutting structure encounters a new rock strength to the depth where
any of the cutting structures encounters a new rock strength. In
the example in FIG. 29, the four rock strengths and two cutting
structures at a distance h1 apart define seven cases for analysis.
In general, the last case terminates when the drill bit reaches the
bottom of the lowermost defined lithology. The portion of the
computer algorithm corresponding with the functionality shown in
FIG. 17 and FIG. 29 is shown in FIG. 27 in the box labeled CASE
where the lithology is entered in the program and parsed into
"cases" for further analysis and the length or thickness of each
case is calculated and stored.
[0141] FIG. 18 illustrates a screen shot from the computer program
that allows the user to define drilling parameters to be used. In
accordance with this embodiment, a user may define the RPM, and
certain dimensions of the BHA, including the length, bit\reamer
spacing (necessary for defining "cases" of lithology as well as
neutral point locations), and inclination. Using the inclination,
the buoyancy effect of the drilling mud on the BHA for neutral
point calculations can be calculated with the inputs of mud
density, linear weight of the BHA and BHA material density below
the reamer, and linear weight of the BHA and BHA material density
above the reamer. Neutral point will be discussed later in more
detail. Low, medium and high weights on system (WSYS) can be
defined by the user to calculate three different performances
indexes as described later. The weight on system is the drilling
weight applied to the system of cutting structures in the BHA. This
weight is typically supplied by the weight of drill collars in the
BHA. The buoyant weight of the entire drill string (less friction
and reaction between the drill string and the well) including the
drill collars is supported by the hookload of the drilling rig at
surface when the cutting structures are not engaged with the
formation. By the action of the drilling rig lowering the cutting
structures into engagement with the formation and drilling, some of
the weight of the BHA is transferred to the cutting structures and
reacted by the rock at those cutting structures, reducing the
hookload by the same amount. This reduction in hookload is the
weight applied to the system of cutting structures. If a drill bit
or reamer is the only cutting structure in the BHA, all of the
weight on system is applied to the drill bit or reamer. If a
reamer(s) is added to the BHA above the drill bit, the weight on
system is shared between the cutting structures. One of the primary
aims of the computer program of the particular embodiment is to
determine the distribution of the weight on system to the cutting
structures that exist in the BHA. The portion of the computer
algorithm corresponding with the functionality shown in FIG. 18 is
shown in FIG. 27 in the box labeled DRILLING PARAMETERS.
[0142] Constraints may be built into the algorithm for every
cutting structure, and may include: (i) Minimum WOB; (ii) Maximum
WOB; (iii) Maximum torque on drill bit connection; (iv) Minimum
WOR; (v) Maximum WOR; (vi) Maximum torque on reamer body; (vii)
Maximum Depth of Penetration Per Revolution (drill bit and reamer);
and/or (viii) Minimum Depth of Penetration Per Revolution (drill
bit and reamer).
[0143] In accordance with the teachings of the present disclosure,
the computer program performs an analysis to calculate a
Performance Index for each BHA cutting structure "configuration"
that is representative of the aggregate performance through all
"cases" of all the lithology increments at the specified RPM at
each WSYS. The Performance Index for each configuration, set of
cases, and WSYS may be represented by a symbol on a chart. In
accordance with a particular embodiment, each configuration will
show three symbols in a vertical column, one each for Low WSYS
(lowest), Medium WSYS (middle), and High WSYS (highest). Many
configurations may be displayed together, column by column. It will
often be the case, that many of the symbols are red as they violate
at least one constraint for at least one case. It is possible that
only a few green symbols may exist; these can be compared and are
candidates for further study and potential selection for use in a
BHA. Each configuration may consist of one or more cutting
structures. The Performance Index is used to compare them all
together.
[0144] In the illustrated embodiment, three WSYS levels are used to
generate three values of Performance Index for each configuration,
but more or fewer WSYS levels can potentially be used, even real
time WSYS in a real time analysis while drilling. In the
illustrated embodiment, the Performance Index is set equal to the
calculated overall ROP of the configuration through the lithology
at the given RPM at each WSYS. ROP may be calculated using the
characteristic curves for each cutting structure through an
iterative process. The portion of the computer algorithm where ROP
is calculated is shown in FIG. 27. Here a "weight analysis" is
performed for each case, configuration and WSYS. In the weight
analysis, the weight from WSYS that is distributed to each cutting
structure (e.g. WOB, WOR) in the BHA is determined such that the
depth of penetration per revolution, d, is the same for all cutting
structures in the BHA. Knowing the value of d that satisfies this
condition, the ROP can be easily determined along with duration of
drilling. For a given WSYS and configuration, the duration of
drilling for all the cases can be summed, with the lowest duration
having the highest overall ROP through all the cases. This overall
ROP is equated to the Performance Index.
[0145] The details of this iterative process are shown in FIG. 28.
The characteristic curves for the cutting structures in a given BHA
are defined over a range of depth of penetration per revolution, d,
from dmin equals 0.00025 inches per revolution to dmax equals one
inch per revolution, in two segments. The initial starting point of
the iterative process is the average of dmin=0 [in/rev] and
dmin=1.0 [in/rev], or d=0.5 [in/rev] (where d=(dmin+dmax)/2).
Recall that d is the x-axis of the weight based characteristic
curve and that the x-axis of each segment of the characteristic
curve has been recentered and rescaled through the use of dAv and
Std d. Recall also that WOB/.sigma. is the y-axis of the weight
based characteristic curve for a drill bit and WOR/G is the y-axis
of the weight based characteristic curve for a reamer. Recall also
that the coefficients (A0, A1, A2, . . . An) of a polynomial curve
fit for each segment of each characteristic curve are stored in a
database of cutting structure characteristic curves along with dAv
and Std d for each segment of each characteristic curve. Thus, to
calculate weight on a cutting structure at a given value of d the
algorithm only needs to know rock strength .sigma. for the case at
hand:
WOB .sigma. = A 0 + A 1 ( d - dAv Std d ) + A 2 ( d - dAv Std d ) 2
+ + An ( d - dAv Std d ) n ##EQU00019## or , WOB = .sigma. [ A 0 +
A 1 ( d - dAv Std d ) + A 2 ( d - dAv Std d ) 2 + + An ( d - dAv
Std d ) n ] ##EQU00019.2##
where the weight on the drill bit cutting structure (WOB) is shown
for the rock strength .sigma. encountered by the drill bit in the
given case. In particular embodiments, the appropriate parameters
of polynomial coefficients, dAv, and Std d must be used for the
value of d in the calculation. The first segment parameters are
used for d<0.06 [in/rev] and the second segment parameters are
used for d.gtoreq.0.06 [in/rev]. A similar equation is used to
calculate the weight on a reamer cutting structure (WOR) using the
polynomial coefficients of each segment of the reamer
characteristic curve, replacing WOB with WOR, and the rock strength
.sigma. that the reamer encounters in the given case.
[0146] FIG. 28 shows the details of the weight analysis for a BHA
with a drill bit and one reamer. Starting with the initial value of
d=(dmin+dmax)/2, the rock strength encountered by the drill bit
.sigma..sub.B, and the rock strength encountered by the reamer
.sigma..sub.R in the given case, the weight on bit and weight on
reamer are calculated, summed, and the summed weight compared to
the system weight. If the summed weight is less than the system
weight, dmin is reset to the current value of d, dmax is kept the
same, and a new value of d=(dmin+dmax)/2 is used in the weight
calculations. If the summed weight is greater than the system
weight, dmax is reset to the current value of d, dmin is kept the
same, and a new value of d=(dmin+dmax)/2 is used in the weight
calculations. This iterative process is repeated until the summed
weight equals the system weight within a tolerance of 0.1 [lb] or
until a limit of 1000 iterations is reached. If a solution is
found, the current value of d in the last iteration is the valid
value of d for all cutting structures and for the system of cutting
structures in the BHA. The current value of the weight on bit (WOB)
and weight on reamer (WOR) in the last iteration are also the valid
values for those parameters and are consistent with the valid value
of d and the system weight WSYS. If 1000 iterations are reached
before convergence, an error condition exists and an error message
is displayed to the user. Other error tolerance conditions, such as
summed weight being within a percentage of system weight, say
within a tolerance of 0.1%, or 1.0%, could also be implemented.
[0147] Once the valid values of d, WOB and WOR are determined for
the case, configuration, and WSYS, values for TOB and TOR can be
determined through the use of the torque based characteristic curve
for each cutting structure without further iteration. Recall that d
is the x-axis of the torque based characteristic curve and that the
x-axis of each segment of the characteristic curve has been
recentered and rescaled through the use of dAv and Std d. Recall
also that TOB/WOB is the y-axis of the torque based characteristic
curve for a drill bit and TOR/WOR is the y-axis of the torque based
characteristic curve for a reamer. Recall also that the
coefficients (B0, B1, B2, . . . Bn) of a polynomial curve fit for
each segment of each characteristic curve are stored in a database
of cutting structure characteristic curves along with dAv and Std d
for each segment of each characteristic curve. The appropriate
parameters of polynomial coefficients, dAv, and Std d must be used
for the value of d in the calculation. The first segment parameters
are used for d<0.06 [in/rev] and the second segment parameters
are used for d.gtoreq.0.06 [in/rev]. Thus, to calculate torque on a
cutting structure at the known valid value of d the algorithm only
needs to know WOB or WOR for the case at hand from the previous
weight analysis:
TOB WOB = B 0 + B 1 ( d - dAv Std d ) + B 2 ( d - dAv Std d ) 2 + +
Bn ( d - dAv Std d ) n ##EQU00020## or , TOB = WOB [ B 0 + B 1 ( d
- dAv Std d ) + B 2 ( d - dAv Std d ) 2 + + Bn ( d - dAv Std d ) n
] ##EQU00020.2##
where the torque on the drill bit cutting structure (TOB) is shown
for the weight on bit (WOB) applied to the drill bit in the given
case, configuration, and WSYS. A similar equation is used to
calculate the torque on a reamer cutting structure (TOR) using the
polynomial coefficients of the reamer characteristic curve, and
replacing TOB with TOR and WOB with WOR in the above equations. The
system torque TSYS is determined by summing the torques of all the
cutting structures in the BHA as previously discussed. In this
example where the system contains one drill bit and one reamer
cutting structure:
TSYS[ftlb]=TOB[ftlb]+TOR[ftlb]
[0148] In addition, once the valid value of d is determined for the
case, configuration, and WSYS it is straightforward to calculate
the ROP and duration for that scenario using the RPM value entered
in the Drilling Parameters screen (FIG. 18) and the drilled length
of the case, where:
ROP ( ft / hr ] = RPM [ rev / min ] .times. d [ in / rev ] .times.
( 60 [ min / hr ] 12 [ in / ft ] ) ##EQU00021## DURATION [ hr ] =
Caselength [ ft ] / ROP [ ft / hr ] ##EQU00021.2##
[0149] The case lengths for a given configuration and WSYS are
summed for all the cases (total length drilled) and divided by the
sum of all the durations (total time to drill) to provide an
overall ROP. This overall ROP value is set equal to the Performance
Index for that scenario. Other measures of Performance Index could
be used instead or in addition: preferred WOB/WOR ratios or range
of ratios, preferred WOB values or range, preferred WOR values or
range, preferred d values or range, preferred torque values or
range, lowest specific energy required, and the like. The
Performance Index can be represented with a symbol on a chart. For
example, FIG. 19 illustrates the display of relative performance of
each configuration, at each "weight on system." In FIG. 19, higher
on the screen reflects better performance (e.g., ROP). Moreover, a
color scheme may be used to identify compliance with constraints.
For example, green symbols may be used if the configuration does
not violate any constraint at any point in the lithology, at the
given drilling parameters (in particular, weight on system).
Conversely, red symbols are used to indicate that one or more
constraints are violated. Also, some symbols may represent
"invalid" conditions, those where there was a computational problem
or where the model results exceed physically possible conditions
(such as excessive depth of advancement per revolution, d). Invalid
symbols, when they occur, are given a gray color and are placed at
the bottom of the Performance Index chart FIG. 19 in a segregated
area that is labeled "Invalid."
[0150] If the configuration violates a constraint at any case
across the lithology, an indication of that violation (red symbol)
may be displayed. If the configuration passes all the way through
all the case analyses without violating any constraint, a green
symbol is displayed. Symbols may be "clicked on" to display more
detailed information, such as to determine which cases might
violate a constraint and why.
[0151] Accordingly, when a red symbol identifies that a constraint
is violated, the computer program allows the user to investigate
and obtain additional information regarding the violation. For
example, in FIG. 20, the user has moved a cursor over a red symbol
to determine what caused the violation. For example, the user can
identify that the load on bit (WOB) is too low in Case 4; the load
on reamer (WOR) is too low in Case 4; and the load on bit (WOB) is
too low in Case 5. The computer program also gives the values that
violated the constraint(s) as well as the value of the
constraint(s) itself to allow the user to assess the significance
of the violation.
[0152] In accordance with the teachings of the present invention, a
substantial amount of information is available, regarding each BHA
configuration. For example, the user interface may be used to
display (i) weight sharing between cutting structures (WOB, WOR and
percentage of WSYS); (ii) torque sharing between cutting structures
(TOB, TOR and percentage of TSYS); and/or (iii) neutral point
locations along the BHA.
[0153] For weight sharing, FIG. 21 illustrates the screen shot that
a user obtains from "clicking on" the highest green symbol of FIG.
19. This weight distribution chart is divided into the cases
defined by the lithology and cutting structure locations. Each case
has a line or box around it creating rows of cases stacked on top
of each other down through the lithology. By moving the cursor into
one of the cases, the user interface illustrates the weight
distribution between the bit and reamer for that case. Within the
teachings of the present invention, the user interface could
display the percent weight distribution. As illustrated in FIG. 21,
each "case" is defined by a change in lithology at the reamer or
the bit. The particular lithology experienced by the bit or the
reamer is illustrated in two columns on the right hand side of FIG.
21.
[0154] In accordance with a particular embodiment of the present
invention, a lithological column of rock strength .sigma. is
defined by the user by depth interval. In alternative embodiments,
this information may be derived from other sources such as logs
derived from modeling (see SPARTA.TM. software, available from
Halliburton) and "real-time" log monitoring (see INSITE.TM.
software, available from Halliburton).
[0155] Multiple cutting structures in a BHA means that there will
be intervals where all cutting structures may be in the rock having
the same or substantially similar strength, but often the cutting
structures will be in rock having different rock strengths. The
teachings of the present disclosure employ a computer program that
breaks down the depth intervals into cases or increments of
consistent lithology (even if the cutting structures are in
different rocks) for analysis purposes.
[0156] For torque sharing, FIG. 22 is similar to FIG. 21, but it
displays the torque distribution in lieu of weight distribution.
Thus, by moving the cursor through the different cases of FIG. 22,
the user can identify information regarding torque on bit, torque
on reamer and/or torque on system, for each case.
[0157] For neutral point locations, FIG. 23 and FIG. 25 are
illustrative. A neutral point is a position along the BHA body
structure (not the cutting structure) where the effective axial
loading is neither in tension nor in compression--typically the
crossover point between tension and compression. For example, a BHA
hanging vertically off bottom will be in tension (zero at the
bottom of the drill bit). When the drill bit is placed on bottom
with a certain amount of weight, the length of BHA from the bit
upward that equals that WOB is in compression; above that point it
is in tension. The transition is referred to as the "neutral
point."
[0158] Multiple cutting structures in a BHA can lead to multiple
neutral points, as weight taken by each cutting structure creates a
compressive discontinuity in the BHA. If that compressive
discontinuity is larger than the tension that exists (if tension
exists), then a neutral point will exist in the BHA body near the
cutting structure, and an additional neutral point may exist above
the cutting structure as the BHA shifts back again from compression
to tension. A BHA with a drill bit and a reamer may have up to
three neutral points: (i) one between the drill bit and reamer;
(ii) one adjacent the reamer cutting structure; and (iii) one above
the reamer cutting structure. Recommendations as to the
desirability of a neutral point at the reamer cutting structure vs.
tension vs. compression can be valuable in the selection of a given
configuration.
[0159] The simplest expression of neutral point location is for a
vertical BHA with a drill bit in air:
L NP [ ft ] = WOB [ lb ] .omega. [ lb / ft ] ##EQU00022##
where L.sub.NP is the length from the bottom of the drill bit to
the location of the neutral point in the BHA above the drill bit in
feet; WOB is the weight on bit in pounds; .omega. is the linear
weight of the BHA in pounds per foot of length.
[0160] The BHA is typically immersed in a drilling fluid that is
heavier than air, thus a buoyancy effect occurs that effectively
reduces the weight of the BHA by the weight of the drilling fluid
displaced by the BHA. The effective linear weight of the BHA in
drilling fluid is:
.omega. ' [ lb / ft ] = .omega. [ lb / ft ] .times. ( 1 - .rho. MUD
[ lb / gal ] .rho. BHA [ lg / gal ] ) ##EQU00023##
Where .omega.' is the effective linear weight of the BHA in
drilling fluid in pounds per foot of length; .rho..sub.MUD is the
density of the drilling fluid in pounds per gallon typically
ranging from approximately 7.0 [lb/gal] for oil base drilling fluid
to 20 [lb/gal] for very dense drilling fluid; and .rho..sub.BHA is
the density of the BHA material, typically steel with a density of
approximately 0.28 [lb/in.sup.3] which is approximately equal to
64.7 [lb/gal]. Other BHA materials can be used such as aluminum and
titanium which have a lower density than steel, or beryllium copper
or tungsten weighting in a drill collar which has higher density
than steel.
[0161] Thus the expression for the neutral point location for a
vertical BHA with a drill bit in drilling fluid is:
L NP [ ft ] = WOB [ lb ] .omega. ' [ lb / ft ] ##EQU00024##
where .omega.' has been substituted for .omega..
[0162] This equation is further modified to account for the
inclination, .theta., or deviation of the wellbore/BHA from
vertical in degrees. When the wellbore is deviated from vertical,
the effective component of BHA weight per foot along the BHA axis
in drilling fluid is .omega.' COS(.theta.). Thus, the expression of
the neutral point location in a BHA with a drill bit in drilling
fluid is:
L NP [ ft ] = WOB [ lb ] .omega. ' [ lb / ft ] .times. COS (
.theta. [ deg ] ) ##EQU00025##
The utility of this expression becomes less useful at high
inclinations approaching 90 [deg]. In this event, the calculated
neutral point exceeds the length of a typical BHA and the
application of this expression is beyond the intended scope of
use.
[0163] This latest expression of neutral point is valid for a BHA
with a drill bit. It is also valid for a BHA containing both a
drill bit and a reamer above the drill bit to determine the neutral
point location between the drill bit and the reamer. If the WOB
exceeds the effective weight of the BHA between the drill bit and
reamer (accounting for buoyancy and inclination), then the entire
length of BHA between the drill bit and reamer is in compression
and no neutral point exists in this span of BHA.
[0164] The expression of the axial force along the BHA is:
F[lb]=.omega.'[lb/ft].times.COS(.theta.[deg]).times.L[ft]-WOB[lb]
where F is the axial force within the BHA in pounds at a distance L
in feet above the drill bit. This expression is valid for a BHA
with a drill bit. It is also valid for a BHA containing both a
drill bit and a reamer above the drill bit to determine the axial
force in the BHA between the drill bit and reamer. If F is negative
at a distance L above the drill bit, the BHA is in compression at
that location. If F is positive at a distance L above the drill
bit, the BHA is in tension at that location. If F equals zero at a
distance L above the drill bit, then this location is at a neutral
point in the BHA. This basic expression allows the calculation and
plotting of the curves in FIG. 23 and FIG. 25 and tells the user
the state of axial force along the BHA. Note, that between the
drill bit and reamer, the force F only depends on the WOB and the
effective weight of the BHA between the drill bit and reamer. This
force F does not depend on the WOR or the weight of the BHA above
the reamer.
[0165] In a BHA with a drill bit and a reamer, at the reamer
cutting structure, the WOR that is applied by the BHA creates a
compressive discontinuity in the BHA near the reamer cutting
structure equal in magnitude to the WOR. If the BHA is in tension
just below the reamer cutting structure, the BHA can transition
rapidly to compression near the cutting structure if the WOR
exceeds the state of tension. If the BHA is in compression just
below the reamer cutting structure, the BHA will go further into
compression near the cutting structure due to the WOR. Above this
point, the force F.sub.AR in the BHA above the reamer is expressed
by:
F AR [ lb ] = [ .omega. AR ' [ lb / ft ] .times. COS ( .theta. [
deg ] ) .times. ( L AR [ ft ] - L REAM [ ft ] ) + .omega. BR ' [ lb
/ ft ] .times. COS ( .theta. [ deg ] ) .times. L REAM [ ft ] ] -
WSYS [ lb ] ##EQU00026##
where F.sub.AR is the axial force within the BHA in pounds at a
distance L.sub.AR in feet above the drill bit; .omega.'.sub.AR and
.omega.'.sub.BR are the effective linear weights of the BHA in
drilling fluid above and below the reamer respectively; .theta. is
the wellbore or BHA inclination in degrees; L.sub.REAM is the
distance in feet from the drill bit to the reamer cutting
structure; and WSYS is the weight on system in pounds. Setting
F.sub.AR equal to zero allows the location of a neutral point above
the reamer to be calculated as:
L NPAR [ ft ] = WSYS [ lb ] - .omega. BR ' [ lb / ft ] .times. COS
( .theta. [ deg ] ) .times. L REAM [ ft ] .omega. AR ' [ lb / ft ]
.times. COS ( .theta. [ deg ] ) + L REAM [ ft ] ##EQU00027##
where L.sub.NPAR is the value of L.sub.AR at the location of the
neutral point above the reamer in feet. This equation is only valid
when L.sub.NPAR is greater than L.sub.REAM. If the BHA is in
compression at the reamer cutting structure, another neutral point
can exist above the reamer as the BHA moves from compression to
tension. For this to happen, the applied WSYS has to be larger than
the weight of the BHA below the reamer.
[0166] FIG. 23 illustrates neutral points of the BHA, if any. As
illustrated in FIG. 23, the entire BHA is in compression (i.e., no
"neutral point"--point where the curve crosses the x-axis). It may
not be desirable to have this case where the entire BHA is in
compression, and therefore a user may opt to remove this
configuration from consideration.
[0167] FIG. 25 illustrates neutral points associated with a BHA
that violates constraints at a lower weight on system, where
WSYS=11,250 [lb]. Three neutral points are illustrated for a
particular curve for Case 2 (the uppermost curve) for a BHA
containing one drill bit and one reamer located 100 [ft] above the
drill bit. In this case, the WOB is equal to 7,107 [lb] and that
amount of compression exists in the BHA at the bottom of the drill
bit. Moving up the BHA from the drill bit, less compression is
observed until finally the curve crosses the x-axis into tension at
a distance of 87 [ft] above the drill bit. Continuing upward from
the drill bit above 87 [ft], the BHA moves further into tension. A
little higher up at 100 [ft] above the drill bit, the reamer
cutting structure takes the WOR of 4,143 [lb] and a compressive
discontinuity of this magnitude exists in the body of the reamer
(part of the BHA) near the cutting structure. This compressive
discontinuity is large enough to exceed the 1,038 [lb] of tension
that would otherwise exist at this location in the BHA. As the
curve crosses the x-axis again, this time moving into 3,105 [lb] of
compression, another neutral point is created in the BHA at 100
[ft] above the drill bit. Moving further upward in the BHA above
100 [ft], less compression is observed until the curve once again
crosses the x-axis, creating a third neutral point in the BHA at
138 [ft] above the bottom of the drill bit.
[0168] FIG. 24 illustrates additional detail regarding constraint
violations for a given case. After the user clicks on a red symbol
to obtain information regarding the violations, the user may obtain
this screen. This screen shot illustrates the weight distribution
of the BHA, and illustrates more detail about the constraint
violation of Case 5 of the lithology of this particular
configuration and applied system weight.
[0169] Additional functionality included in the computer program is
the ability to save files containing configurations, lithology, and
drilling parameters that are entered in the program. The files can
then be loaded into the program at will instead of the user
reentering the information. It is also desirable for project files
containing all of the information entered for a project to be saved
and reloaded.
[0170] One of the many uses of the computer program is to help
achieve designs of drill bit and/or reamer cutting structures that
meet desired performance criteria. For example, it may be desired
to achieve certain a WOB/WOR ratio, such a WOB/WOR=1.0 where the
weight distribution between the drill bit and reamer are close to
equal under a given set of conditions. The computer program allows
the user to analyze the result of the designs of both cutting
structures and determine in which direction one or both cutting
structures could be changed to meet the desired result. For
example, if WOB/WOR=2.0 but the desired result is WOB/WOR=1.0, the
user can determine that the drill bit is taking a larger proportion
of the system weight. Changing the design of the drill bit cutting
structure to make it drill faster and/or changing the design of the
reamer cutting structure to make it drill slower will help
accomplish the desired result. After the cutting structure(s) is
redesigned (using IBitS or IReamS), it will have a new
characteristic curve and the polynomial coefficients can be added
to the database. The performance of the redesigned cutting
structure(s) can be reanalyzed using the computer program to see if
it approaches the desired result. This process can be repeated as
necessary until the desired result is achieved.
[0171] By storing coefficients of the characteristic curve fits in
the cutting structure database, extremely fast calculation of the
Performance Index (ROP), WOB, WOR, TOB, TOR can be performed for
each configuration and case. This speed of execution enables the
calculation of thousands of cases in a few seconds, making the
algorithm very useful to find configurations that are suitable and
either don't violate any constraints, or don't substantially
violate any constraints.
[0172] The systems, methods, algorithms and/or software described
within this disclosure may be embodied in a computer system 100 for
example, as illustrated in FIG. 30. Computer system 100 includes a
communication interface 102 that is configured and operable to
receive data, a processor(s) 104 for processing data, tangible
computer readable medium (e.g., memory) 106 for storing data, and a
graphical user interface (e.g., display) 108 for use by a user(s)
of the system 130.
[0173] The teachings of the present disclosure provide a system and
method to identify one or more BHA systems that may be suitable for
a particular application. In some embodiments, a user may opt to
obtain even more detail regarding such systems by analyzing these
selected few configurations (out of many) in a modeling software
(e.g., IBits and IReams), armed with new knowledge of the loads
applied.
* * * * *