U.S. patent application number 09/990177 was filed with the patent office on 2002-08-08 for method of and system for controlling directional drilling.
Invention is credited to Nettles, Kenneth L., Pinckard, Mitchell D..
Application Number | 20020104685 09/990177 |
Document ID | / |
Family ID | 22957385 |
Filed Date | 2002-08-08 |
United States Patent
Application |
20020104685 |
Kind Code |
A1 |
Pinckard, Mitchell D. ; et
al. |
August 8, 2002 |
Method of and system for controlling directional drilling
Abstract
A method of and system for controlling directional drilling
determines a relationship between surface drill string orientation
angle and drill bit face angle. The method uses the relationship to
determine a predicted drill bit face angle. The method then uses
the predicted drill bit face angle to achieve a target drill bit
face angle by calculating a surface drill string correction angle.
The correction angle may be displayed to a human driller.
Alternatively, the correction angle may be provided as an input to
an automated drilling machine.
Inventors: |
Pinckard, Mitchell D.;
(Houston, TX) ; Nettles, Kenneth L.; (Richmond,
TX) |
Correspondence
Address: |
Pillsbury Winthrop LLP
Intellectual Property Group
50 Fremont Street
P.O. Box 7880
San Francisco
CA
94105
US
|
Family ID: |
22957385 |
Appl. No.: |
09/990177 |
Filed: |
November 21, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60252752 |
Nov 21, 2000 |
|
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Current U.S.
Class: |
175/61 ;
175/26 |
Current CPC
Class: |
E21B 47/02 20130101;
E21B 7/068 20130101 |
Class at
Publication: |
175/61 ;
175/26 |
International
Class: |
E21B 044/00; E21B
007/04 |
Claims
What is claimed is:
1. A method of controlling directional drilling, which comprises:
determining a relationship between a first drilling control
variable and drill bit face angle; determining, based upon said
relationship, a target first control variable value to achieve a
target face angle; and, correcting current first drilling control
variable to said target first drilling control variable to achieve
said target face angle.
2. The method as claimed in claim 1, wherein determining said
relationship between said first drilling control variable and said
drill bit face angle comprises: collecting drill bit face angle and
first drilling control variable data.
3. The method as claimed in claim 2, wherein determining said
relationship between said first drilling control variable and said
drill bit face angle comprises: performing linear regression of
said drill bit face angle and said first drilling control variable
data, to obtain a mathematical model with drill bit face angle as a
response variable and first drilling control variable as an
explanatory variable.
4. The method as claimed in claim 3, wherein determining a target
first control variable value to achieve a target face angle
includes: solving said mathematical model for a measured first
drilling control variable value.
5. The method as claimed in claim 1, wherein correcting a current
first drilling control variable to said target first drilling
control variable to achieve a target face angle. calculating a
surface drill string correction angle to achieve said target face
angle.
6. The method as claimed in claim 5, including displaying said
correction angle.
7. The method as claimed in claim 5, including inputting said
correction angle to an automatic drilling machine.
8. The method as claimed in claim 1, wherein said control variable
is surface drill string orientation.
9. The method as claimed in claim 1, including: determining a
relationship between rate of penetration and a second drilling
control variable; determining a target second drilling control
variable value, based upon said relationship between rate of
penetration and said second drilling control variable, to achieve
an optimum rate of penetration; and, maintaining said second
drilling control variable at said target second drilling control
variable value.
10. The method as claimed in claim 9, wherein determining said
relationship between rate of penetration and said second drilling
control variable includes: collecting rate of penetration data.
11. The method as claimed in claim 10, wherein determining a
relationship between rate of penetration and said second drilling
control variable includes: performing linear regression of said
rate of penetration data and said second drilling control variable
data, to obtain a mathematical model with rate of penetration as
response variable and second drilling control variable as an
explanatory variable.
12. The method as claimed in claim 9, wherein maintaining said
second drilling control variable at said target second drilling
control variable value includes: displaying said target second
drilling control variable value.
13. The method as claimed in claim 9, wherein maintaining said
second drilling control variable at said target second drilling
control variable value includes: inputting said target drilling
control variable value to an automatic drilling machine.
14. The method as claimed in claim 9, wherein said second drilling
control variable is pressure differential.
15. A directional drilling control system, which comprises: means
for determining a relationship between a first drilling control
variable and a drill bit face angle; means for predicting, based
upon said relationship, a target first drilling control variable to
achieve a target drill bit face angle; and, means for determining a
correction to said target first drilling control variable to
achieve a target face angle.
16. The system as claimed in claim 15, wherein said means for
determining said relationship between said drilling control
variable and said drill bit face angle comprises: means for
collecting drill bit face angle and first drilling control variable
data.
17. The system as claimed in claim 16, wherein said means for
determining said relationship between said first drilling control
variable and said drill bit face angle comprises: means for
performing linear regression of said drill bit face angle and said
first drilling control variable data, to obtain a mathematical
model with drill bit face angle as response variable and first
drilling control variable as an explanatory variable.
18. The system as claimed in claim 17, wherein said means for
predicting said predicted drill bit face angle includes: means for
solving said mathematical model for said first drilling control
variable value.
19. The system as claimed in claim 15, wherein said means for
determining a correction to said target first drilling control
variable to achieve a target face angle includes: means for
calculating a surface drill string correction angle to achieve said
target face angle.
20. The system as claimed in claim 19, including a display for
displaying said correction angle.
21. The system as claimed in claim 15, including: means for
determining a relationship between rate of penetration and a second
drilling control variable; means for determining a target control
variable value, based upon said relationship between rate of
penetration and said second drilling control variable, to achieve
an optimum rate of penetration.
22. The system as claimed in claim 21, wherein said means for
determining said relationship between rate of penetration and said
second drilling control variable includes: means for collecting
rate of penetration data.
23. The system as claimed in claim 22, wherein said means for
determining a relationship between rate of penetration and said
second drilling control variable includes: means for performing
linear regression of said rate of penetration data and said second
drilling control variable data, to obtain a mathematical model with
rate of penetration as response variable and second drilling
control variable as an explanatory variable.
24. The system as claimed in claim 21, including a display for
displaying said target second drilling control variable value.
25. The system as claimed in claim 21, including: an automatic
drilling machine arranged to receive said target control variable
value.
26. A method of drilling, which comprises: determining a
relationship between surface drill string angular orientation and
drill bit face angle; determining, based upon said relationship, a
target surface drill string angular orientation to achieve a target
face angle; correcting current surface drill string angular
orientation to said target surface drill string angular orientation
to achieve said target face angle; determining a relationship
between rate of penetration and a drilling control variable;
determining a target drilling control variable value, based upon
said relationship between rate of penetration and said drilling
control variable, to achieve an optimum rate of penetration; and,
maintaining said drilling control variable at said target second
drilling control variable value.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] The present application claims the benefit of U.S.
Provisional Application No. 60/252,752, filed Nov. 21, 2000, titled
Method of and System for Controlling Directional Drilling.
FIELD OF THE INVENTION
[0002] The present invention relates generally to the field of oil
and gas well drilling. More particularly, the present invention
relates to a method of and system for controlling directional
drilling.
DESCRIPTION OF THE PRIOR ART
[0003] It is very expensive to drill bore holes in the earth such
as those made in connection with oil and gas wells. Oil and gas
bearing formations are typically located thousands of feet below
the surface of the earth. Accordingly, thousands of feet of rock
must be drilled through in order to reach the producing formations.
Additionally, many wells are drilled directionally, wherein the
target formations may be spaced laterally thousands of feet from
the well's surface location. Thus, in directional drilling, not
only must the depth but also the lateral distance of rock must be
penetrated.
[0004] The cost of drilling a well is primarily time dependent.
Accordingly, the faster the desired penetration location, both in
terms of depth and lateral location, is achieved, the lower the
cost in completing the well.
[0005] While many operations are required to drill and complete a
well, perhaps the most important is the actual drilling of the bore
hole. In order to achieve the optimum time of completion of a well,
it is necessary to drill at the optimum rate of penetration and to
drill in the minimum practical distance to the target location.
Rate of penetration depends on many factors, but a primary factor
is weight on bit. In mud motor bent sub directional drilling, the
best indication of weight on bit is mud motor differential
pressure.
[0006] As disclosed, for example in Millheim, et al., U.S. Pat. No.
4,535,972, rate of penetration increases with increasing weight on
bit until a certain weight on bit is reached and then decreases
with further weight on bit. Thus, there is generally a particular
weight on bit that will achieve a maximum rate of penetration.
[0007] Drill bit manufacturers provide information with their bits
on the recommended optimum weight on bit. However, the rate of
penetration depends on many factors in addition to weight on bit.
For example, the rate of penetration depends upon characteristics
of the formation being drilled, the speed of rotation of the drill
bit, and the rate of flow of the drilling fluid. Because of the
complex nature of drilling, a weight on bit that is optimum for one
set of conditions may not be optimum for another set of
conditions.
[0008] Directional drilling has been a combination of art and skill
as well as science and engineering. The direction of drilling is
determined by the azimuth or face angle of the drilling bit. Face
angle information is measured downhole by a steering tool. Face
angle information is typically conveyed from the steering tool to
the surface using relatively low bandwidth mud pulse signaling. The
driller attempts to maintain the proper face angle by applying
torque corrections to the drill string. However, because of the
latency in receiving face angle information, the driller typically
over- or under-corrects. The over- or under-correction results in
substantial back and forth wandering of the drill bit, which
increases the distance that must be drilled in order to reach the
target formation. Back and forth wandering also increases the risk
of stuck pipe and makes the running and setting of casing more
difficult.
SUMMARY OF THE INVENTION
[0009] The present invention provides a method of and system for
controlling directional drilling by determining a relationship
between a first drilling control variable and drill bit face angle.
The method and system of the present invention use the relationship
to determine a predicted drill bit face angle. The method and
system then use the predicted drill bit face angle to achieve a
target drill bit face angle by calculating a surface drill string
correction angle. The correction angle may be displayed to a human
driller. Alternatively, the correction angle may be provided as an
input to an automated drilling machine.
[0010] The method and system of the present invention determine the
relationship between the first drilling control variable and the
drill bit face angle by collecting drill bit face angle and control
variable data. The method and system periodically perform linear
regression of the drill bit face angle and first drilling control
variable data, to obtain a mathematical model with drill bit face
angle as response variable and first drilling control variable as
an explanatory variable. The method and system determine the
predicted drill bit face angle by solving the mathematical model
for a measured first drilling control variable value.
[0011] The method and system of the present invention also optimize
rate of penetration. The method and system determine a relationship
between rate of penetration and a second drilling control variable.
The method and system determine a target second drilling control
variable value, based upon the relationship between rate of
penetration and the second drilling control variable. A driller
maintains the control variable at the target control variable
value. As in the case of the correction angle, the target second
drilling control variable may be displayed to a human driller or
inputted to an automated drilling machine.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a pictorial view of a directional drilling
system.
[0013] FIG. 2 is a block diagram of a directional driller control
system according to the present invention.
[0014] FIG. 3 is a pictorial view of a display screen according to
the present invention.
[0015] FIG. 4 is a flowchart of data collection and generation
according to the present invention.
[0016] FIG. 5 is a flowchart of display processing according to the
present invention.
[0017] FIGS. 6A-C comprise a flowchart of rate of penetration
processing according to the present invention.
[0018] FIG. 7 is a flowchart of face angle processing according to
the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0019] Referring now to the drawings and first to FIG. 1, a
drilling rig is designated generally by the numeral 11. Rig 11 in
FIG. 1 is depicted as a land rig. However, as will be apparent to
those skilled in the art, the method and system of the present
invention will find equal application to non-land rigs, such as
jack-up rigs, semisubmersibles, drill ships, and the like.
[0020] Rig 11 includes a derrick 13 that is supported on the ground
above a rig floor 15. Rig 11 includes lifting gear, which includes
a crown block 17 mounted to derrick 13 and a traveling block 19.
Crown block 17 and traveling block 19 are interconnected by a cable
21 that is driven by draw works 23 to control the upward and
downward movement of traveling block 19. Traveling block 19 carries
a hook 25 from which is suspended a top drive 27. Top drive 27
supports a drill string, designated generally by the numeral 31, in
a well bore 33. According to an embodiment of the present
invention, drill string 31 is coupled to top drive 27 through an
instrumented sub 29. As will be discussed in detail hereinafter,
instrumented top sub 29 includes sensors that provide torque and
angular position information according to the present
invention.
[0021] Drill string 31 includes a plurality of interconnected
sections of drill pipe 35 a bottom hole assembly (BHA) 37, which
includes stabilizers, drill collars, and a suite of measurement
while drilling (MWD) instruments including a steering tool 53. As
will be explained in detail hereinafter, steering tool 53 provides
bit face angle information according to the present invention.
[0022] A bent sub mud motor drilling tool 41 is connected to the
bottom of DHA 37. As is well known to those skilled in the art, the
face angle of the bit of drilling tool 41 used to control azimuth
and pitch during sliding directional drilling. Drilling fluid is
delivered to drill string 31 by mud pumps 43 through a mud hose 45.
During rotary drilling, drill string 31 is rotated within bore hole
33 by top drive 27. As is well known to those skilled in the art,
top drive 27 is slidingly mounted on parallel vertically extending
rails (not shown) to resist rotation as torque is applied to drill
string 31. During sliding drilling, drill string 31 is held in
place by top drive 27 while the bit is rotated by mud motor 41,
which is supplied with drilling fluid by mud pumps 43. Although a
top drive rig is illustrated, those skilled in the art will
recognize that the present invention may also be used in connection
with systems in which a rotary table and kelly are used to apply
torque to the drill string The cuttings produced as the bit drills
into the earth are carried out of bore hole 33 by drilling mud
supplied by mud pumps 43.
[0023] Referring now to FIG. 2, there is shown a block diagram of a
preferred system of the present invention. The system includes a
mud pump pressure sensor 51. Pump pressure sensors are well known
in the art. Preferably, they produce a digital pressure value at a
convenient sampling rate, which in the preferred embodiment is five
times per second although other sampling rates may be used. Pump
pressure provides an indication of weight on bit. In relatively
straight holes, weight on bit can be measured or computed directly.
However, in highly deviated holes, direct measurement or
computation of weight on bit is difficult if not impossible.
Therefore, in the present invention, weight on bit is inferred from
pump pressure or pressure differential (Delta_P). The driller
applies weight to the bit effectively by controlling the height or
position of hook 25 in derrick 13. The driller controls the
position of hook 25 by operating a brake to control the paying out
of cable from drawworks 23.
[0024] Referring still to FIG. 2, the system of the present
invention includes a hook speed/position sensor 52. Hook speed
sensors are well known to those skilled in the art. An example of a
hook speed sensor is a rotation sensor coupled to crown block 17. A
rotation sensor produces a digital indication of the magnitude and
direction of rotation of crown block 17 at the desired sampling
rate. The direction and linear travel of cable 21 can be calculated
from the output of the hook position sensor. The speed of travel
and position of traveling block 19 and hook 25 can be easily
calculated based upon the linear speed of cable 21 and the number
of cables between crown block 17 and traveling block 19. According
to the present invention, hook speed provides an indication of rate
of penetration (ROP).
[0025] The system of the present invention includes a steering tool
53, which produces a signal indicative of drill bit face angle.
Typically, steering tool uses mud pulse telemetry to send signals
to a surface receiver (not shown), which outputs a digital face
angle signal. However, because of the limited bandwidth of mud
pulse telemetry, the face angle signal is produced at a rate of
once every several seconds, rather than at the preferred five times
per second sampling rate. For example, the sampling rate for the
face angle signal may be about once every Twenty seconds.
[0026] The system of the present invention also includes a drill
string angle sensor 54, which provides an indication of the angular
orientation of the drill string entering the well bore. The drill
string angle sensor is included in instrumented top sub 29
illustrated in FIG. 1. Substantial reactive torque is stored in the
form of twists or wraps in the drill string. Thus, the angular
orientation of the drill string entering the well bore is not the
same as the face angle of the drill bit. Also, due to the elastic
nature of the drill sting and contact with the wall of the well
bore, there are delays between the time torque is applied to the
drill string at the surface and when the face angle changes at the
bottom. Moreover, a particular angular change of drill string
orientation at the surface does not necessarily produce the same
face angle change at the bottom of the hole. The drill string angle
sensor is coupled to the top drive to provide a digital signal at
the preferred sampling rate of five times per second.
[0027] In FIG. 2, the digital outputs of sensors 51-54 are received
at a processor 55. Processor 55 is programmed according to the
present invention to process data received from sensors 51-54.
Processor 55 receives user input from user input devices, such as a
keyboard 57. Other user input devices such as touch screens,
keypads, and the like may also be used. Processor 55 provides
visual output to a display 59. Processor 55 may also provide output
to an automatic driller 61, as will be explained in detail
hereinafter.
[0028] Referring now to FIG. 3, a display screen according to the
present invention is designated by the numeral 63. Display screen
63 includes a target Delta_P display 65 and a current Delta_P
display 67. According to the present invention, a target Delta_P is
calculated to achieve a desired rate of penetration. Target Delta_P
display 65 displays the target Delta_P computed according to the
present invention. Current Delta_P display 67 displays the actual
current Delta_P.
[0029] As will be explained in detail hereinafter, the method and
system of the present invention constructs a mathematical model of
the relationship between Delta_P and rate of penetration for the
current drilling environment. The mathematical model is built from
data obtained from pump pressure sensor 51 and hook speed/position
sensor 53. When a statistically valid model is created, the present
invention calculates a target Delta_P, which is displayed in target
Delta_P display 65. After the system of the present invention has
built the model, the system continually tests the validity of the
model against the data obtained from pressure sensor 51 and hook
speed/position sensor 53. The system of the present invention
continuously updates the model; however, the system of the present
invention uses one model as long as the model is valid. If
conditions change such that the current model is no longer valid,
then the system of the present invention fetches the current
updated model.
[0030] According to one aspect of the present invention, a driller
attempts to match the value displayed in current Delta_P display 67
with the value displayed in target Delta_P display 65. According to
another aspect of the present invention, the driller may turn
control over to automatic driller 61. If the driller has turned
control over to automatic driller 61, the driller continues to
monitor display 63. If the model becomes invalid, then a flag 69
will be displayed. Flag 69 indicates that the model does not match
the current drilling environment. Accordingly, flag 69 indicates
that the drilling environment has changed. The change may be a
normal lithological transition from one rock type to another or the
change may indicate an emergency or potentially catastrophic
condition. When flag 69 is displayed, the driller is alerted to the
change in conditions.
[0031] Display screen 63 also includes a target face angle display
71 and a current face angle display 73. Target face angle is a
value that is input according to the directional drilling plan for
the well. As will be explained in detail hereinafter, current face
angle is either the last face angle measured by the steering tool,
or a face angle value predicted from a mathematical model of face
angle as a function of surface drill string angle.
[0032] Display screen 63 also includes an angular correction
display 77. Angular correction display 77 displays a recommended
angular correction to apply to the drill string with the top drive
in order to bring the current face angle to the target face angle.
The angular correction value is calculated from a model constructed
according to the present invention. The angular correction value is
expressed in degrees from the current angular orientation of the
drill string.
[0033] Display screen 63 also displays a moving plot 79 of rate of
penetration. The target rate of penetration is indicated in plot 79
by circles 81 and the actual rate of penetration is indicated by
triangles 83. By matching actual Delta_P to target Delta_P, the
plot of actual rate of penetration, indicated by triangles 83, will
be closely matched with the plot of target rate of penetration,
indicated by circles 81, as long as the mathematical model is
valid.
[0034] Referring now to FIGS. 4-7, there are shown flow charts of
processing according to the present invention. In the preferred
embodiment, four separate processes run in a multitasking
environment. In FIG. 4 there is shown a flow chart of the data
collection and generation processing of the present invention. The
system receives hook rate of penetration, Delta_P, drill string
orientation and face angle values from sensors 51-54, at block 101.
The preferred sampling rate for hook ROP, drill string orientation
and Delta_P is five times per second. Because of bandwidth
limitations, face angle values are received at the rate of about
once every sixteen seconds. The system calculates average ROP,
drill string orientation and Delta_P over a selected time period,
which in the preferred embodiment is ten seconds, at block 103.
Then the system stores a face angle value and the average ROP,
drill string orientation and Delta_P values with time stamps, at
block 105 and returns to block 101.
[0035] Referring now to FIG. 5, there is shown display processing
according to the present invention. The system displays the current
average Delta_P, which is calculated at block 103, at block 107.
The system displays the current average ROP, which is also
calculated at block 103 of FIG. 4, at block 109. The system
displays the current face angle, which as will be explained in
detail hereinafter is a forecasted current value, at block 111. The
system displays a target Delta_P, which is calculated according to
the present invention, at block 113. The system also displays a
target ROP, which also is calculated according to the present
invention, at block 115. The system also displays a target face
angle, which is input according to the directional drilling plan,
at block 117. Finally, the system displays an angular correction,
which is also calculated according to the present invention, at
block 119. Then, the system tests, at decision block 121, if a flag
is equal to zero. If so, processing returns to block 107. If the
flag is not equal to zero at decision block 121, the system
displays a flag at block 123 and display processing returns to
block 107.
[0036] Referring now to FIG. 6, and particularly to FIG. 6A, there
is shown a flow chart of the building of a drilling model and
calculation of target rate of penetration and Delta_P according to
the present invention. In the preferred embodiment, FIG. 6
processing is performed once every five seconds. First, the system
cleans the data stored according to FIG. 4 processing and populates
a data array, at block 131. Data cleaning involves removing zeroes
and outliers from the data.
[0037] The clean data are stored in a data array. The data array
includes an index column, a Delta_P column, and an ROP column. The
data array also includes a first lagged ROP column and a second
lagged ROP column. The first lagged ROP is denoted ROP(t-1) and the
second lagged ROP is denoted ROP(t-2).
[0038] After populating the data array with clean data, at block
131, the system performs multilinear regression analysis using
ROP(t) as the response variable and ROP(t-1), ROP(t-2) and
Delta_P(t) as the explanatory variables, at block 133. Multiple
linear regression is a well-known technique and tools for
performing multilinear regression are provided in commercially
available spreadsheet programs, such as Microsoft.RTM. Excel.RTM.,
or commercially available mathematical or statistical tool kits,
such as MATLAB.RTM., available from MathWorks, Inc. Multiple linear
regression produces a mathematical model of the drilling
environment. The mathematical model of the drilling environment is
an equation of the form:
ROP(t)=.alpha.+.beta..sub.1ROP(t-1)+.beta..sub.2ROP(t-2)+.beta..sub.3Delta-
.sub.--P(t), (1)
[0039] where .alpha. is the intercept, .beta..sub.1 and
.beta..sub.2 are lagged ROP coefficients and .beta..sub.3 is the
Delta_P coefficient.
[0040] After the system has performed multilinear regression at
block 133, the system searches for a potential optimum weight on
bit based upon the Delta_P coefficient .beta..sub.3. The Delta_P
coefficient .beta..sub.3 represents the slope of the line in the
hyper plane that relates Delta_P to rate of penetration. In the
neighborhood around the optimum weight on bit, the slope
.beta..sub.3 is about equal to zero. Thus, it is a goal of the
present invention to drill such that the Delta_P coefficient
.beta..sub.3 is close to zero. However, negative Delta_P
coefficients .beta..sub.3 are to be avoided. The greater the
positive value of Delta_P coefficient .beta..sub.3, the further the
system searches into the data array to find a potential optimum
weight on bit. The system tests, at decision block 135, if Delta_P
coefficient .beta..sub.3 is strongly negative, which in the
preferred embodiment is less than -0.5. If so, the system sets the
maximum data array search depth at 1, at block 137. Then the system
sets Delta_P equal to the Delta_P corresponding to the maximum ROP
value in the search depth, at block 139. Since the search depth is
1, there is only one candidate Delta_P. If at decision block 135,
the Delta_P coefficient .beta..sub.3 is not strongly negative, the
system tests, at decision block 141, if the Delta_P coefficient
.beta..sub.3 is weakly negative, which in the preferred embodiment
is between 0 and -0.5. If so, the system sets the maximum data
array search depth equal to 5, at block 143. If not, the system
tests, at decision block 145, if the coefficient .beta..sub.3 is
weakly to moderately positive, which in the preferred embodiment is
between 0 and 1. If so, the system sets the maximum data array
search depth equal to 10, at block 147. If not, which indicates
that the Delta_P coefficient .beta..sub.3 is strongly positive, the
system sets the maximum data array search depth equal to 15, at
block 149. Then, the system uses the maximum data array search
depth set at blocks 143, 147, or 149 to find the indices with the
four highest ROP(t), at block 151. Then, the system sets the
Delta_P equal to the average Delta_P(t) for the four highest ROP(t)
values, at block 153. The system then uses the Delta_P value
determined at block 139 or block 153 to determine a target Delta_P
based upon the Delta_P coefficient .beta..sub.3.
[0041] Referring to FIG. 6E, the system tests, at decision block
155, if Delta_P coefficient .beta..sub.3 is greater than a positive
Delta_P incrementer determiner. The incrementer determiner is
selected to keep the Delta_P coefficient .beta..sub.3 in the
neighborhood of zero. If the Delta_P coefficient .beta..sub.3 is
greater than the incrementer determiner, then the system sets the
target Delta_P equal to the Delta P determined at block 139 or
block 153 plus a Delta_P increment value, at block 157. If not, the
system tests, at decision block 159 if the Delta_P coefficient
.beta..sub.3 is less than (more negative) than the negative Delta_P
incrementer determiner. If so, the system sets the target Delta_P
equal to the Delta_P determined at blocks 139 or 153 minus the
Delta_P increment value, at block 161. If the Delta_P coefficient
.beta..sub.3 is between the positive Delta_P incrementer determiner
and the negative Delta_P incrementer determiner, the system sets,
at block 163, target Delta_P equal to the Delta_P determined at
blocks 139 or 153. The target Delta_P determined at blocks 157, 161
or 163, may be higher than a preset Delta_P limit. Delta_P limit is
set according to engineering and mechanical considerations. The
system tests, at decision block 165, if target Delta_P is greater
than the Delta_P limit. If so, system sets target Delta_P equal to
the Delta_P limit, at block 167.
[0042] Referring now to FIG. 6C, after determining target Delta_P,
the system calculates a target rate of penetration based upon the
target Delta_P and the model of equation (1), at block 171. There
are engineering reasons for limiting rate of penetration. For
example, the drilling fluid system may be able to remove cuttings
at only a certain rate. Drilling above a certain rate of
penetration may produce cuttings at a rate greater than the ability
of the fluid system to remove them. Accordingly, in the present
invention, there is a preset rate of penetration limit. The rate of
penetration limit may be a theoretical maximum rate of penetration,
or some percentage, for example 95% of the theoretical maximum. The
system tests, at decision block 173, if the target ROP is greater
than the ROP limit. If not, the system sets the target ROP equal to
the calculated target ROP, at block 175. If the calculated target
ROP is greater than the ROP limit, then the system sets the target
ROP equal to the ROP limit, at block 177. Then, the system
calculates target Delta_P based upon the ROP limit and the model of
equation (1), at block 179. The system then tests, at decision
block 181, if the target Delta_P calculated at block 179 is greater
than the Delta_P limit. If so, the system sets target Delta_P equal
to the Delta_P limit, at block 183.
[0043] After completing steps 175 or 183, the system calculates a
predicted ROP(t) and confidence interval at block 185. The
predicted ROP is calculated by solving equation (1) for the actual
current Delta_P, ROP(t-1) and ROP(t-2). The system tests, at
decision block 187, if the current ROP is within the confidence
interval. If so, the system sets the flag equal to zero, at block
189, and processing returns to block 131 of FIG. 6A. If, at
decision block 187, the current ROP is not within the confidence
interval, the system sets the flag equal to 1, at block 153.
[0044] Referring now to FIG. 7, there is shown a flow chart of face
angle processing according to the present invention. A target face
angle is determined according to directional drilling plan to
achieve the desired path through the earth to reach a target
location. The target face angle may be periodically recalculated.
The system of the present invention cleans the face angle and drill
string orientation data and populates a data array, at block 201.
The data array is similar to that used in connection with
determining the rate of penetration model. Then, as indicated at
block 203, the system determines the relationship between surface
drill string orientation and bit face angle. The system of the
present invention may determine the relationship between drill
string orientation and bit face angle by performing multiple linear
regression using Face_Angle(t) as the response variable and
Face_Angle(t-1), and Drill_String_Orientation(t) as explanatory
variables, at block 203. The multiple linear regression step of
block 203 produces an equation similar to equation (1) and of the
form:
Face_Angle(t)=.sigma.+.mu..sub.1Face_Angle(t-1)+.mu..sub.2Drill_String_Ori-
entation(t), (2)
[0045] where .sigma. is the intercept, .mu..sub.1 is the lagged
face angle coefficient, and .mu..sub.2 is the
Drill_String_Orientation coefficient. The system then sets the
current face angle equal to the actual current face angle or a
forecast face angle based upon the model, at block 205.
[0046] Alternatively, the system may forecast a face angle based
upon an Exponentially Weighted Moving Average (EWMA) or Box-Jenkins
technique. As is well known to those skilled in the art, EWMA is a
statistic for monitoring a process that averages the data in a way
that gives less and less weight to data as they are further removed
in time. The EWMA statistic is calculated as follows:
EWMA(t)=.lambda.Y(t)+(1-.lambda.)EWMA(t-1) (3)
[0047] where Y(t) is the observed value at time t, and .lambda. is
a weighting constant having a value greater than zero and equal to
or less than one. The weighting constant .lambda. determines the
rate at which older data enter into the calculation of the EWMA
statistic. A .lambda. value close to one gives more weight to
recent data and less weight to older data. Similarly, a .lambda.
value close to zero gives more weight to older data and less weight
to recent data. Usually a .lambda. value between 0.2 and 0.3 yields
a good balance between more recent and less recent data.
[0048] After the system has determined the relationship between
drill string orientation and face angle, the system calculates an
angular correction necessary to achieve the target face angle, at
block 207. From Equation (2), 1 Drill_String _Orientation ( t ) =
Face_Angle ( t ) - 1 Face_Angle ( t - 1 ) 2 ( 4 )
[0049] According to the present invention, angular correction is
expressed as the difference between the current drill string
orientation and the target drill string orientation calculated by
Equation (4). After calculating the angular correction at block
207, the system displays the angular correction, at block 209.
[0050] From the foregoing, it may be seen that the present
invention is well adapted to overcome the shortcomings of the prior
art. The system of the present invention builds mathematical models
of the relationships between Delta_P and rate of penetration as
well as drill string orientation and face angle, for the current
drilling environment. The system continuously updates the
mathematical models to reflect changes in the drilling environment.
The system of the present invention enables a driller to optimize
rate of penetration and control the direction of drilling
simultaneously.
* * * * *