Note: Descriptions are shown in the official language in which they were submitted.
METHOD FOR PRODUCING AN OIL WELL
Technical Field
[0001] The present disclosure relates to the field drilling.
In particular, the present
disclosure relates to drilling parameters and their effect on drill string
vibrations.
=
Background
[00021 To achieve improved drilling efficiency and better
productivity of the driller,
.there.'is a need for real-time optimization of drilling parameters during
drilling operations
through each formation in order to optimize weight on bit and bit rotation
speed to increase
drilling rate as well as reduce the drilling cost, The driller only sees the
surface data but there
is usually a deviation in the downhole drilling parameters. The driller needs
to make better
decisions as he manipulates the drilling variables to improve drilling and
deal With various
issues thatmay arise during drilling operations,
=
10003] The drilling data collected during drilling include
weight on bit (W01=), rotary =
speed (RPM), pump, parameters (SPM), depth, inclination, azimuth and rate of
penetration
(ROP). These parameters have a significaiit impact on the entire optimization
process of the =
= WOR and RPM. The success of drilling optimization is closely related with
the quality of the
recorded drilling data. I Towever, the driller has to 'make those important
decisions in real time
when drilling problems arise.
100041 Several methods have been used to optithize the
drilling parameters. In 1975,
Tansev explained how to improve drilling performance. His method inVolves the
interaction of
= = raw data, regression and an optimization technique in order
to predict ROP and the life of the
bit (Tansev .1975). Karlsson et al. in 1985, observed the use of a RITA design
that included a
=
navigation sub. They noticed that.the tool allowed the driller to always know
the direction of
I .the well and make required trajectory changes while drilling
(Karlsson et al, 1985), In 1997,
== Kamata et al. explained a drill-bit seismic technique, which
provides important subsurface
structure information by using acoustic energy radiated during drilling
operations. Sensors,
placed at the top of drill siring, were used to record the inlOnnation. They
achieved drilling
optimization from the information gathered thereby improving safety records
and saving cost
=
- 1 -
=
=
CA 3019996 2018-10-05
= =
(Kamata et al. 1997). Paes et al in 2005, focused on the use or sensors !hr
pressure-while-
.
= drilling (PWD) and vibration sensors to reduce the drilling cost, non-
productive time (NPT),
and improve drilling effectiveness without adding more cost to the cost of the
routine
measurement while drilling (Paes et al 2005). Elshafei et al in 2015
determined the right -
combination of drilling parameters to reduce drilling time and minimize
deviation from planned
drilling path by inputting control commands on angular velocity and torque for
a quad bit
drilling =system (Elshafei et al 2015). In 2017, Torres-Cabrera et al observed
the difficulty in
predicting BHA behaviour which leads to low ROP, unnecessary tripping, and
occasionally lost
pipe in hole. '[hey addressed the issues through a series of drilling
improvements based on real-
time and post-well analyses (Torres-Cabrera et al 2017).
= [00051 Another method that can be applied to optimize drillbt
'parameters is "machine
learning." Machine learning isn't new; it has been around at least since the
1970s, when the first
related algorithms appeared. The general idea behind most machine learning is
that a computer
learns to perform a task by studying a training set of examples. The computer
(or system of
distributed or embedded computers and controllers) then performs the same task
with data it
hasn't encountered belbre (Louridas et al 2016), Machine learning has been
applied to other
aspects in the oil industry. -Zhang ct al in 1991, applied machine learning to
rock. mechanics
and observed that all of the factors governing the rock mass behaviors could
be considered as
= input variables to predict the varying rock behaviors. They made these
observations without
. limiting the amount of input variables that could be used (Zhang
et al 1991). Alvarado et al in
2002 used machine learning in their aim to adapt EOR/IOR (enhanced oil
recovery/improved
oil recovery) technologies to rejuvenate a large number of the mature fields
in Venezuela. They
used machine learning algorithms to draw rules for screening (Alvarado .et al
2002). In 2016,
Cao et al used machine learning algorithms to predict production for several
wells using
pressure and production data, geological maps, and constraints during
operations, They used a
=
well-known machine learning method ¨ Artificial Neural Network (ANN). Without
assuming
a prearranged model, ANN learns from large volume of data points and can
change based on
the flexibility of the data available (Cao et at 2016). hi 2017, 1Bangert
proposed the use of
machine learning in order to conduct smart condition monitoring. He realized
that his proposed
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=
=
=
CA 3019996 2018-10-05
method was more successful than standard condition monitoring thus preventing
false alarms
= and always alarming unhealthy states of plants or equipment (Bangert et
al 2017).
[0006] Frequent vibrations of the drill string may lead to
poor drilling performance and
non-productive time. The cOncerns arising from drilling vibration are: wasted
energy input, low
ROI', lengthy drilling time, spoilt bit, damage to the stecrable motor leading
to unintended trips,
damaged Measurement-While-Drilling (MWD)/Logging-While-Drilling (LWD) tools
causing
lost data, increased fatigue in the drill string, higher caving due to
borehole = wall damage,
discrepancy in data due to Meddling with downhole tool telemetry during
vibrations, increased
cost of equipment repairs and increased downtime.
10007] Two kinds of vibration are of significant concern.
First is Stick-Slip. In this case,
the bit periodically stops rotating in a torque up moment then spins freely,
this goes on through
a non-uniform rotation of the drill string. During stick slip, the downhole
RPM can be 3x to
15x the average surface RPM. The consequences of Stick-slip are bit damage,
lower ROP,
connection over-torque, back-off and drill string twist-offs. Stick slip
occurrence also leads to =
wear on bit gauge and stabilizer as well as in ter-rup Lion in mud pulse
telemetry.
[0008] The second vibration type is drill string whirling. The
bulk of drill string
whirling happens in the BHA. During whirling, parts of the BHA face lateral
displacements
which generate bending stresses and lateral shocks when the BHA contacts the
borehole wall
OPT Staff 1998). I-Living the drill string moving around the wellbore and not
rotating about its
centerline is the whirling phenomenon. Three types of whirling can occur;
forward whirling is =
.scenario where the drill string is rotating around the vvellbore in the same
direction with its
rotation around its own centerline; backward whirling is a. situation where
the drill string is =
rotating around the wellhore in a direction opposite the direction of its
rotation around its own.
centerline. Chaotic whirling occurs where the bits moves in a zig-zag manner
with no consistent
= direction. Whirling creates an over gauge hole reinforcing the tendency
for the bit and BHA to =
whirl.
[00091 The driller has to constantly manipulate available
parameters to mitigate
vibration problems, A driller's dilemma .emerges when increasing the WOB
induces stick-slip
whereas increasing the RPM induces.whirl. Keeping both WOB and RPM low reduces
vibration =
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CA 3019996 2018-10-05
=
levels but it negatively affects ROP. As a result, the drilling operation
either suffers low ROP
or experiences higher ROP but with severe vibrations (Wu et al 2010).
[00010] Therefore, improvements in determining optimized parameters for
drilling are
desirable.
SUMMARY
[00011] In a first aspect, the present disclosure provides a method for
producing an oil
well. The method comprises: drilling into the Earth, the drilling being
effected by a drill =
string, the drill string having a drill bit; obtaining real-time data from the
drill string, the real-
time data comprising, Measured depth, drilling time, drill bit depth, weight
on drill bit (WOB)
,data, revolution per minute (RPM) data, torque (TOR) data and rate of
penetration (ROP)
data; in accordance with the real-time data and in accordance with pre-
determined rules,
obtaining a drill string data classification scheme, which defines an optimum
drilling
= parameter zone; performing a principal component analysis (PCA) of the
real-time data, to
. obtain a set of principle components associated to the real-time data;
selecting a subset of the
set of principle components; in accordance with the subset of principles
components,
performing an inverse of the PCA, to obtain modified data; classifying the
modified data in
accordance with the drill string data classification scheme, to obtain
classified modified data;
. comparing the classified modified data to the optimum drilling parameter
zone, to obtain a
comparison result; and adjusting at least one of the WOB and the RPM in
accordance with the
comparison result.
[00012] Other aspects and features of the present disclosure will
'become apparent to
those ordinarily skilled in the art upon review or the following description
of specific
embodiments in conjunction with the accompanying figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[00013] Figure 1 shows prior art examples ofmachine learning methods.
¨100014] Figure 2 shows an example of a prior art optimum Zone Chart.
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CA 3019996 2018-10-05
[000151 Figure 3A shows a block diagram representation of an
embodiment of a method
in accordance with the present disclosure.
[00016] Figure 3B shows a flowchart of an embodiment of a method
in accordance with
the present disclosure.
[00017] . Figure 3C shows an embodiment of a classification tree in accOrdanee
with an
= embodiment of the present disclosure.
[00018] Figure 4 shows an example of an operational process to
determine the upper =
limit of RPM, in accordance with the present disclosure.
=
[00019] Figurc.5 shows an example of how change in ROP and
change in time 'versus
time plot might to look like.
[00020] Figure 6 shows the ideal position the upper and lower
limits of WOB and RPM
in the optimum zone plot, in accordance with an embodiment of the present
disclosure.
= [00021] Figure 7 shows the plotting of principal
components on data set on the X-Y
coordinate system. = =
[00022] Figure 8 shows the effect of dimension reduction using
Principal Components
, Analysis
=
100023] Figures 9A and 9B show that principal components are
actually the eigen vectors
of the covalent matrix of the original data in the X-Y coordinate system.
[00024] Figure 9C shows a plot of WOB vs. RPM, as determined !Or
real-time data in an
experiment in accordance with the present disclosure, also shown is an optimum
zone as
determined for the real-time data.
1.00025] Figure 91) shows a plot of W013 vs. RPM, for the data of
:Figure 9C, after PCA
of that data.
=
[00026] Figure 10 shows how the safety factors affect the
optimum zone to form the safe
zone in the optimum zone chart, in accordance with an embodiment of the
present disclosure.
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=
CA 3019996 2018-10-05
[00027] Figure 11 shows a .centroid in the safety zone of
Figure 10, in accordance with
the present disclosure. =
[00028] Figure 1 2 shows a plot of bit depth, measured depth
versus time for the portion of
a well under study.
[00029] Figure 13 shows the first 3.5 minutes of depth versus
time plot in stand one
(shallow depth).
[00030] Figure 14 shows the first 3.5 minutes of depth versus
time plot in stand two
(intermediate depth).
[00031] Figure 15 shows the first 3.5 minutes of depth versus
time plot in stand three
(deep depth). =
[00032] Figure 16 shows the Torque versus WOB plot for Stand
Two Update One which
helps to obtain the corresponding constants.
=
[00033]. Figure 17 shows the Depth of Cut versus WOB plot for
Stand Two Update One
which helps to obtain the corresponding constants.,
. [00034] . Figure 18 shows a combined plot of change in ROP
divided by Change in Time
= versus Time and also ROP and WOB versus Time in order to get the minimum
W013 for stand
two update one.
=
. [00035] Figure 19 shows the optimuni zone plot for stand two
update one. =
= =
DETAILED DESCRIPTION
=
[00036] The present disclosure enables a driller, drilling an
oil well, to assess, during
. drilling, the appropriateness of the drilling parameters being used and to
correct these during
.drilling. The drilling parameters are monitored/measured during drilling and
the yalu.es of those
measured parameters are used to define an optimum drilling zone in the WOB-RPM
spade. The
optimum zone is displayed to the user in addition to WOB-RPM data points. The
displayed
WOB-RPM data points are obtained by subjecting the measured parameter values
to a principal
1 component analysis in order to obtain only the most significant
WOB-RPM data points, which
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CA 3019996 2018-10-05
=
=
are the ones displayed. The principle component analysis essentially niters
out less important
data, which in turn provides the driller better insight into the drilling
process and the best drilling' =
parameters to use,
=
Abbreviations
[00037] Abbreviations used throughout the present disclosure
include:
ANN Artificial Neural Network
=
BHA Bottom Hole Assembly
LWD Logging While Drilling =
MSE Mechanical Specific Energy
=
MWD Measurement-While-prilling
NPT Non-productive Time =
. PCA Principal Component Analysis
PDC Polycrystalline Diamond Compact =
=
= PWD Pressure-While-Drilling
=
ROP Rate of Penetration
RPM Revolutions per Minute
W013 Weight on Bit
TOR Torque = =
DOC Depth of Cut
QRA Quantitative Risk Analysis
F
=
The Concept of Machine Learning
=
[00038] Machine learning =gives computers the ability to
optimize performance criterion
based on sample data or past knowledge. The goal of machine learning is to
identify and reveal
c.;
CA 3019996 2018-10-05
= bidden patterns linked with the data being analyzed. The world today is
circled with
= = applications ()I-machine learning. A perfect example is the
usc of GoolcTM search which learns
to display the best results. Another example is the anti-spam software which
filters email
messages. =
[00039]
As shown in Figure 1, there are two major types of machine learning.
First is
supervised (predictive) learning where for a given input variables (x) and
output variables (Y),
=
= one can use an algorithm to learn the mapping function from the input to
the output: Y = f(x).
The goal is to approximate the mapping function so well that when there is a
new input data
(x), accurate predictions can be made to obtain the output variables (Y) for
that data.
[00040]
Unsupervised (descriptive) learning is the second major type of machine
=
learning. Unsupervised learning is where for a given input data (x) there are
no corresponding
output variables. The concept behind unsupervised learning is identify the
underlying pattern
in the data in order to learn more about the data.
I-Tow Machine Learning is utilized for Vibration Problems
=
=
[00041]
WOB and RPM. causing whirling and stick slip can be predetermined if the
(Olaf
drilling conditions are known (Wu et al 2010), A boundary condition for stable
drilling can be
obtained in a plot with WOB on the Y axis and RPM on the X axis, as shown in
Figure 2. This =
means ii the driller maintains the drilling parameters such as to keep the bit
in the optimum
zone, then drilling will be stable depending on the hit and mechanical
properties of the rock.
[00042]
The boundaries of the optimum zone help determine the best combination of
WOB and RPM for optimuni ROP. The hard question to answer is if the stick slip
and whirling
zone is predicted accurately.
[00043]
= Tn order to identify the optimum zone effectively, an exemplary
embodiment of -
a method, in accordance with the present disclosure, is shown in Figure 3A.
This method is
adopted to ensure that all the monitored/measured drilling parameters have an.
impact on the
optimum zone. The method represented at Figure 3A uses available real-time
data 100 obtained
from a drilling rig 102. The exemplary method performs a variable
transformation and reduction
- 8 - =
=
CA 3019996 2018-10-05
(e.g., at steps 104, 106, 108, 110, 112, 114), and then utilizes machine
learning algorithms to
identify the optimum drilling parameter zone and display it to the driller.
[00044]
Figure 3B shows a flowchart of an embodiment of a method in accordance
with
the present disclosure. The method 01Figure 3B has drilling --into the Earth -
being carried out,
at action 300. As the drilling is carried out, Measured Depth, Drilling Time,
Bit Depth, WOB,
ROP, RPM and TOR are obtained (e.g., measured or determined), in real-time, at
action 302.
. All these can be referred to as surface parameters in that they can be
obtained as the drilling
progresses, in realTtime, without requiring physical access to the. bottom
hole assembly. In . .
addition to Measured Depth, Drilling Time, Bit Depth, WOB, ROP, RPM and TOR,
any other
parameter that can be measured in real-time is to be considered within the
scope of the present
disclosure. For example, MSE can also he measured. At action 304, the real-
time data is
processed, in accordance with pre-determined rules, in order to obtain a
classification schem.e
for the real-time data. The classification scheme defines an optimum drilling
parameter zone.
As will be described further below, the pre-determined rules produce upper and
lower limits for
the WOB and for the RPM. These rules are based accepted practices in the art
of drilling.
[00045]
As will be understood by the skilled worker, the measured depth is the
length of
the path of the drill string, including the bends. The hit depth is the same
as the measured depth
during drilling. When drilling stops, the bit depth will be less when pulled
up from the bottom
=
of the well being drilled.
=
[00046]
At action 305, a principal component analysis (PCA) of the real-time data
is
.
= performed to obtain a set of principle components associated to the
real-time data.
Subsequently, at action 307, a subset of the principal components is selected_
For example, only
the principal components that account tbr 99% (or any other suitable
percentage) of the data
points can be selected to be part of the subset. At action 309, using only the
subset 0 fprincipal
, .
components, an inverse PCA is perfbmied to obtain a modified data, which no
longer includes
the original real-time data related to the principal, components that were not
identified as
important (for example, the principal components that accounted for the
remaining 1% of the
data points).
=
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CA 3019996 2018-10-05
[00047] At action 311, the modified data is classified in
accordance with the
classification scheme obtained at 304, to obtain classified modified data,
which is then
compared, at action 313, to the optimum drilling parameter zone. This results
in a comparison
result on which an adjustment of the W013. and/or the RPM can be effected, at
action 315.
Visualization of the data points in the optimum zone chart will show the
driller which zones
have most of the data points. Regardless of whether there are data points in
the optimum zone
or not, the upper and the lower limits of' RPM and WOB are the boundaries
within which the
= driller can
run the operations with =
100048] Subsequently, after waiting for a pre-determincd
amount of time at action 317
(for example, 3.5 minutes or any other suitable time duration), the method
loops hack to action
304 where the classification scheme is defined (re-defined) in accordance with
real-time data
acquired since the definition ol the previous classification scheme. As will
be understood by =
the skilled worker, this re-defines the optimum drilling parameter zone. In
addition to looping
back to action 304, the method also loops hack to action 305 where a PCA is
performed on in
accordance with real-time data acquired since the previous PCA.
=
[00049] As will be understood by the skilled worker, the
aforementioned comparison can= = =
= be automated through any conventional means. The automata process can
include the step of
= identifying. data points that have values comprised within the
optimum'zone, compare those
= points to the current WOB and RPM settings, and automatically adjust
those settings so that
they correspond to one of the data points identified as being within the
optimum zone.
[00050] in other embodiments, as will be detailed Further
below, a safe zone within the
optimum zone can be determined by quantitative risk analysis (QRA) and the
comparison action . .
can entail comparing post-PCA data comprised within the sale zone with the
current settings of
WOB and RPM, and automatically adjust those settings so that they correspond
to one of the
data points identified as being within the optimum zone.
[00051] In Further embodiments, and as will be detailed
Further below, a centroid of the
post-PCA data points that are within the safe zone, or within the optimum
zone, can be
calculated by, for example, a clustering operation, and the current settings
of' the WOB and
RPM can be compared to the WOB and RPM values of the eentroid. The drilling
WOR and
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,
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CA 3019996 2018-10-05
RPM settings can automatically be set to the W013 and RPM values of the
centroid if they differ
=
Iron] those values.
= [00052] In instances where the process is not automated, the
driller in charge of the
drilling operation can be provided with a display showing a plot of the WOP
versus RPM post-
,
PCA data and the optimum zone (for an example of Such a plot, see Figure 9D
further below) =
and, based on the displayed data, the driller can set the WOB and the RPM to
any suitable value
found in the optimum zone. Similarly, the driller can be provided with a
display showing a plot
, .
of the WOP versus RPM post-PC A data and the safe zone and, based on the
displayed data, the
driller can set the WOB and the RPM to any suitable value found in the safe
some. Further, the
driller can be provided with a display showing the albrementioned centroid
and, based on the
WOR and RPM values of the centroid, the driller can set the drilling
parameters to those values.
= =
Classification Scheme
[00053] The following relates to action 302 in Figure 313.
[00054] Classification is a kind of arrangement where like
data are classed together and
separated from unlike data; the main reasons behind elassification is to (a)
put knowledge in
shape and storage, (b) do structural analysis of the data being stored; and
(c) figure out the
relationship existing among different parts of' the structure found (Mirkin
1996).
[00055] A decision tree classification is used, as an example
in the present disclosure.
Decision trees are based on algorithms which split data into branches. Unlike
a tree where the
= root is at the bottom, a decision tree has its root node at the apex of
the tree (Ville et al 2013).
The basis ibr building the decision tree is echoed in this root node: the name
of the field of data
=
and the arrangement of the values that are contained in that field.
=
[00056] There are 3 types. of nodes in a decision tree
= Decision nodes;
=
,! = Chance nodes;
=
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=
CA 3019996 2018-10-05
=
= Leaf or terminal or end nodes (HloomsburY Publishing 2013).
[00057] In each internal node of the tree reflects certain
characteristics of the system, and
each leaf node represents a class label. There are 3 'steps to contrasting the
decision tree:
= Step 1: At the root of the tree, place the most defining feature of the
dataset
= = Step 2: The training set is then split into subsets with
values corresponding to their
respective attributes.
= Step 3: Redo step 1 and step 2 on each subset till there are terminal
nodes in all the .
branches of the tree.
[00058] In the generic classification tree in Figure 3C, there are four
key values: the =
upper limit of WOB, the lower limit of W013, the upper limit of RPM and the
lower limit or
RPM. These values represent the houndari 'es for stick slip, forward whirling,
backward whirling
and low ROP zones respectively. These values change for each stand on a 3.5
minutes basis.
Obtainim the Upper and Lower Limits or RPM and W013
Ulmer limit of RPM
[00059] Conventionally, the upper limit of RPM is calculated by first
determining the
mean RPM value and then inCreasing that value by 10% three times. 8ee Figure
4.
[00060] Increasing the average RPM by 10% three times means
=
RP/Vlupp,õ = (1.1)3 (Mean RPM) = 1.331 (Mean RPM)
[000611 After several iterations with field data, the need to further
reduce this value
arose, hence a new formula for the upper limit of RPM,
RPMi ipper1.331*mcan(RPM)-((0.95*mean(RPM))/3))
=
=
.Lower limit of RPM =
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=
=
CA 3019996 2018-10-05
=
[00062] The lower limit of RPM (RPM lower) can be obtained by
first finding the
= minimum depth of cut, which can be obtained based on equation below,
which was derived
from the mechanical specific energy (MSE) equation 'introduced by Teale (Teale
1965).
=
B2 * WOB4 + 2B1)32 WOB3 + + 282B0 ¨ 271-AIB2) *
WOE'
+ (2.81B0 47r.A0./32) * WOB + (B4 +2111B0 ¨ 2irA0131) = 0
=
[00063] Four values of WOB would be gotten from this quark
equation, only the
positive value has physical meaning. The positive value of WOB can he plugged
into the known
equation for depth ()I' cut to obtain the optimum* depth of cut. The constants
in the equation
above can be calculated from their source equations below (Hamrick 2011),
Depth of Cut DOC .= g(WOB) = B2 * WOB2 B * WOB + Bo
= = =
=
Torque = f (YOB) Ao -F * WOR
[00064] By plotting a chart ofincoming torque, depth of cut
and WOB data, the constants
,= .A and B can be calculated. The minimum depth of cut would then be
50% of the optimum depth
of cut, Just by unit conversion using ROP, the minimum RPM can be calculated.
= =
(DOC)opt
=
2
= _________________________________________________________
= (DOC),iõ.
Upper limit WOB =
[00065] The upper limit of WOB is determined based on stick
slip index.. It is expected .
1 that the optimum zone chart would be updated every 3.5 minutes or
210 seconds. The stick slip
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=
index would be calculated every 20 seconds. This makes 10 test of stick slip
index within each =
update of the optimum zone.
=
= =
Stick Slip index _____
(Torquemax ¨ Torquemin)
= %
Torqueõõ
= [000661 Based on that calculation, the severity of the stick slip
calculation can he
estimated which is shown in the table 3 below:
Table 1 .Vibration Severity Levels Based on. Downhole Measurements (Al
Dashaishi ct al =
2015)
Lateral Ace Lateral RIM Ace Stick-Slip
- =
.Severity Level Severity Level Severity
Level
(g's) = (g's)
0-15 Normal 0-0.5 , Low
15-35 Moderate 0-2.5 Normal 0,5-1
Moderate
= =
35+ Severe = 2.5+ Severe
Severe
[000671 The upper limit of WOB can then he deriVecl based on
the following rules:
= when one test has stick 5Iip index greater than 0.5, make the upper limit
of W013
=
equal to the minimum W013 of the test
!I =
=
= = - 14 -
=
CA 3019996 2018-10-05
=
=
= when two or mote tests have stick slip index greater than 0.5, make the
upper limit
of WOB equal to the least minimum WOB dull the tests with stick slip index
greater than 0.5
= when all the tests have stick slip index less than 0,5, make upper limit
of WOB
=
= equal the maximum WOB of all the tests
=
Lower limit WOB =
100068] The lower limit of WOB can be based on the hardness of
the formation being
drilled. This is the WOE which corresponds to the time when the slope of the
ROP versus =
time plot becomes constant. 'This is shown in Figure 5,
Rules of the Classification 'free to Obtain the Optimum Zone
[00069] The optimum zone, and the lower and upper limits for
RPM and WOB are =
. = shown at Figure 6. In this figure:
= Zone I. is the Stick = Slip Zone
= = Zone 4 is the Low ROP Zone
= Zone
5 is the Forward Whirling Zone = =
= Zone 3 is the Backward Whirling 7one
= Zone 2. is the Optimum Zone
=
= WOE upper limit is based on stick slip index calculations
= WOB lower limit is based on formation hardness (ROP change)
= RPM lower Limit is based on minimum depth fait calculations
= RPM upper limit is still based on reversal of conventional operational
processes
= leading to
vibrations =
[00070] With this knowledge, a decision tree can hc formed
based on the fact that any
data point above the stick slip line is in the stick slip zone and would most
likely be experiencing
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= =
CA 3019996 2018-10-05
stick slip, any data point behind the low ROP line, is in the low ROP zone and
would be
experiencing less. efficient drilling, any data point ahead of the backward
whirling line would =
be in the backward whirling zone and would be experiencing backward whirling
and finally
= any data point below the forward whirling line would. be in the forward
whirling zone and most
likely be experiencing forward whirling. Figure 3C, discussed above, is based
on Figure 6.
[00071] At every 3.5 minutes or 3 feet. interval (or any other
suitable time interval or
distance), the optimum zone cab updated by calculating, based on real-time
data obtained at
action 302, Figure 3B, new lower and upper limits for WOB and RPM: All the
data points will
= belong to one or the zones.
[000721 As will be understood by the skilled worker, the real-
time data could be
classified and represented in the same plot as the optimum zone. However,
representing all
acquired data in in the same plot as the optimum zone would result in a very
dense plot and
provide little or no insight to the driller, when the real-time data is
acquired at any reasonable
=
rate (e.g., 100 data points per. second). As such, the present disclosure uses
a dimensionality
reduction technique to obtain a modified data set that has considerably less
data point.
=
= [00073] . After dimensionality reduction, the
driller can see how much of' the data points
arc in. stick slip or whirling. Based on the arrangement, the driller can
either select the readings
=
= of the data points in the optimum zone or ask the system to generate a
range of data points that
are in the optimum zone. However, if there is a significant change in drilling
parameters, the
optimum zone will shift its location and new sal. ranges would have to be
generated. "f his will
be discussed further below in relation to Figures 9C and 9D.
=
Principal Component Analysis (PCA)
r [00074] hi an example provided in the present disclosure, PCA
is used to form a lean
r, =
data set that best represents the drilling process. A sununarY of PCA is
provided below.
[00075] PCA can be used for searching out veiled patterns in
high dimension. data (i.e.,
I where the number of features exceed the number of observation). In
this research, PCA is used
- 16 -
. =
CA 3019996 2018-10-05
for reducing the dimension of the input data without losing important
information in the original
data (Lindsay 2002). Three steps govern the PCA process.
1000761 The first step is to determine the covariance of the
matrix. Covariance is the
measure how two diffircrit variables relate with each other during changes in
values. The
formula for covariance is an adjustment of the variance formula which only
analysis the dataset
in one variable,
= =
Variance cr2 =-E(K
For the variable x, /2 is the mean and N is quantity of data points in
variable x. This formula is
then modified the give the formula for covariance between two variables.
Consider two
= variables x and y
= X=f) (Yi
Covariance=. cov(x, y)
. n ¨
IF multiple variables are involved, the covariance matrix will be symmetrical;
meaning the
transpose of the matrix will be the same as the original matrix. Assuming
there are four . ,=
variables, w, x, y and z. The covariance matrix will be as follows:
=
cov(w, Iv) cov(w, x) cov(w, y) cov(w, 2) \
= =
= cov(x, w) cov(x, x) cov(x,y) cov(x,z)
C -
=
cov(y,w) cov(y,x) cov(Y,y) cov(y,z)
cov(z,w) cov (z, x) cov(z, y) cov(z,z) /
=
Note that the diagonal arc the variances of each Variable,
[00077] Next would be to estimate the eigen values and
eigenvectors of the covariance
matrix. Let A be an n X it matrix. The number k is an eigenvalue of A if there
exist a non-zero
vector v, such that Av Av The eigen values of -A are the roots of the
characteristic
polynomial
1 0 '0
p(.1) = det(A ¨ Al); where 1 is the identity matrix. I =.( 0 1 0 or!
k0 0.\
0 0 1
=
- 17 -
=
CA 3019996 2018-10-05
1 =
=
,
. .
, .
For each eigenvalue A., the corresponding eigenvectors arc
. .
vit
V2 . .
= v = : obtained by solving the linear system (A ¨ A0v = 0
F
t7,., .
.
[00078] The principal components are the eigenvectors. The
principal components are
.
.
, ranked according to their corresponding ei genval tics: If the
characteristic polynomial of A has
4 as its highest power then there would he 4 eigenvalues. The highest
eigenvalue would produce
= . the first principal component; the second. highest cigcnvaluo would
produce the second
principal component (eigeiwector),
. .
[000791 In Figure 7, the data is first plotted on X and Y
coordinates. The principal
direction is where the highest variance lies. In this case, the U direction is
the principal direction . . .
with the highest importance. The V direction must be orthogonal to the I.1
direction. It is .
expected that when X and Y coordinates are 'transformed into IJ and V
coordinates, the = ,
,
covariance between X and Y variables becomes zero. U and V variables are
called principal
, 'components (Gillies et al). In reality, they are the eigenvectors
of the covariance matrix of the = original dataset. The level of importance is
based on the eigenvalues; the eigenvec,tor with the .
highest eigenvalue is the most significant and is termed the first principal
component. The
,
eigenvector orthogonal to the First principal component with the next highest
eigenvalue is the;
.1
1 .
second principal component and so on (Gillies et al). The reduction aspect is
done alter the -
original dataset has been transformed to principal components. Before inverse
PCA is done to .
get the original variables, some dimensions are zeroed out which have low
eigenvalues. The
,
resulting original dataset is leaner and very distinct on what values arc to
be used as shown in
Figure 8.
.
. [00080] Let's assume that the drilling parameters inputted
into PCA arc WOB, RPM,
,I
. .
.1
1 , TOR, TOW or any other drilling parameter desired to have an
impact on the optimum zone, for .
il
:.
example, MSE. If' we represent their values by xi,x2,¨,xx:
11
il From k original variables: x1,x2,....,xk: PCA aims to produce knew
variables: yu2,,,,,yk: where
ii
=
- 18 - =
. . .
.
.
. .
CA 3019996 2018-10-05
=
= aiiri a12x2 + clikxk, =
=
Y2 anxi. + 22.x2 + == = + axk =
=
=
Yk + '" + akkxk =
yk's are uncorrelated (orthogonal) =
=
yi explains as much as possible of original variance in data set
y2 explains as much as possible of remaining variance
=
{a1i,a12,...,a1k} is 1st Eigenvector,
{a21,a22,...,C12k} is 2nd Eigcuvector, 72
=
1000811 Figures 9A and 9R simply refreshes the understanding of
how principal
components relate to each other in PCA.
& X2. are the eigenvectors of the =
correlation/covariance matrix and & k2 are the coefficients or the principal
components. Ifyi
and y2 explains 99% of original data, {a31,a32,...,a3k} up to faki,a142,,.akk)
are equaled to 2,1:TO,
Therefore
=
= = at ixi -F a2x2 -F
aikxk
Y2 = a2x1 + (122x2 + + avdck
y3 = ax + a-,12x2 + === + a3kXk
=
Y4 (141X1 a42x2 + " + 44kxk
y5 asix, + a52x2 = = + askxk
=
= =
=
=
yk aki X1 + ak2 X2 + = = = akkXk
=
becomes =
=
- 19 - CA 3019996 2018-10-05
= = anxi + a.22x2 == = + axk
Y2 = a21x1 + a22x2 + '" + aUXIC
= y3 = (0)xi + (0)x2 + + (0),ck
y4 = (0)x.1 + (0),r2 + = + (0)x1 =
ys = (0)x1 (0)x2 + (0)xk
yk (0)xl + (0)x2 + (0).xk
=
= =
= [00082] Based on the new values of y3 ... yk, inverse PCA is
perRimed to produce new .
sctof xi, X2, ..., Xk. At this point, the reduction has already happened.
[00083] =Figure 9C shows real-time, WOR vs. RPM data points and the
,Optimum zone
(rectangle) determined in accordance with the real-time data. Figure 9D shows,
on an expanded
scale, the PCA data calculated based on the real-time data of Figure 9C, and
the optimum zone.
These figures (9C. and 9D) are the result of a field test conducted on a well
in the continental
Unites States. In Figure 9C, there are data points in every zone even though
more dominant in
the stick slip and forward whirling zones. After PCA, Figure 9D, there is a
clear definition of
where the data points lie. Most of the points are in the stick slip zone while
the forward whirling
zone has more data points than the optimum zone.
= Safe zone within the optimum zone
=
1.000841- The concept of the safe zone is to account for the risk of
having data points lie
.in the optimum zone when they should actually outside the optimum zone, in
vibration prone
zone. The following process takes note of this risk.
[000851 For the stick slip zone, a safety factor is obtained and is
subtracted from the
upper limit of the W013, while for the forward whirling zone, the
corresponding safety factor
- 20 -
=
CA 3019996 2018-10-05
is added to the lower limit of W013. For the backward whirling zone, the
corresponding the
safely Ihetor is subtracted from the upper limit of 'RPM. The safety factor
can be obtained
through quantitative risk analysis.
Quantitative Risk Analysis (QRA)
= =
1000861 ORA has been used widely in the construction industries
and has also been used
in casing design and well planning by the oil and gas industries. The QRA
approach considers
the uncertainty of each input variable and provides comprehensive statistical
properties of =
W011, RPM, ROP, MSE, TOR and other drilling parameters. The parameters needed
for
quantitatively calculating the risks are discussed generally below,
[00087] A mean value, m, is the expected value or the weighted
average of a number N
of data points x,
= x
m _______________________________________________
[00088] Standard deviation, s, is a measure of dispersion or
variability. Standard
.
=
deviation measures the closeness of each random variable to the mean value
pang 2002), It is
given as
=
= jE(xi ¨ m)2
=_- =
=
[00089] Coefficient of Variance (COV) evaluates the
distribution of the standard
deviation over the mean value (Liang 2002) The data is more uncertain as the
COV goes higher,
= = COV ¨ =
=
in
= =
= [00090] To calculate the risk of data points in the
optimum. zone fall into the vibration
prone zones, there is a need to first determine the means and standard
deviations of the stick
= - 21 -
CA 3019996 2018-10-05
=
slip zone (Mss and SW, the backward whirling zone (Maw and Snw), the forward
whirling zone
(MFw and Sim) and the optimum zone (Mop and Sop).
= For normally distributed stick slip and optimum zone data, the margin
between the two
probability density functions (PDFs) has a mean margin of
Mso Mss ¨ MOP
And standard deviation margin of
=
= Sso i/C5s.02 (S0p)2 =
=
H);
ms0
The risk of having optimum zone data points in stick slip zone = Rs()
Sso =
hi order to give the driller some more space to change parameters, 20% of the
risk can be
allowed =
= Therefore, Rso = 80% (1-52.9"); this is the safety factor for the
stieleslip zone_ -
. For normally distributed, optimum zone and forward whirling
data, the margin between
the two probability density functions (PDEs) has a mean margin of
MOP ¨ MFW =
And standard deviation margin of
= =
S OF = (S P)2 fC FW)2
/m
The risk of having forward whirling zone data points in optimum zone = ROF (-
9; =
SOF
In order to give the driller some more space to change parameters, can take
20% of the risk
can be allowed
Moir
Therelbre, Rub- 80% (--); this is the safety factor for the forward whirling
zone.
= For normally distributed backward whirling and optimum zone data, the
margin
between the two probability density functions (PllEs) has a mean margin of
MBO = MBW MOP
= And standard deviation margin of
=
=
SBO "ASRWY (SOP)2 =
=
- 22 -
=
=
CA 3019996 2018-10-05
The risk of having optimum zone data points in backward whirling zone ¨ RB0 =
t )=
Sao
Tn order to give the driller some more space to change parameters, 20% of the
risk can
be allowed
Therefore, Rso -= 80% C-L2n ); this is the safety factor for the backward
whirling zone.
= S fj()
[000911 Figure 10 shows a safety zone (safe zone) within the
optimum zone of Figure 6. =
The safety factor is calculated based on the real-time data, not on data
obtained post PCA.
Clustering and centroid of optimum zone
[000921 Clustering is a process forming groups whose objects
are somewhat siinilar. A .
cluster is grouping of objects which are alike and different from objects in
other clusters. K-
means clustering is a known type of clustering used, as an example, in the
present disclosure.
Widely used in data mining, K-means algorithm is a type of' clustering
analysis based on
partitioning. The centre, of each cluster represents the cluster as the
algorithm ensures
convergence towards stable centroids of clusters. The centroid is the centre
or mean point, of
the cluster. K is the number of clusters. After initialization, there are 3
steps in the K-means
process.
1000931 Initialization: set seed points (randomly) =
= Step 1: Each object (compressed: data point) is placed in a cluster of
the nearest seed
point (centroid) measured with a specific distance metric (Euclidean distance)
= ' Step 2: Estimate new centroid for each cluster in the current
partitioning
= Step 3: Repeat Step 1; continue iterating until there are no more changes
in membership
in each cluster.
[000941 A centroid obtained from Kmeans Clustering (or any
other suitable method) can
be used to obtain the recommended WOB and RPM Values of the safe zone which
the driller
= can operate with when there are vibration issues. The centroid of the
safe zone is shown in
Figure ii. The centroid in Figure 11 is obtained by clustering the data points
in the optimum
= zone. If the optimum zone has no data points, the centroid would be based
on the polygon
=
= - 23 -
= =
CA 3019996 2018-10-05
=
formed by the upper and lower limits of WOR and RPM. Referring now to Figure
9D above,.
the centroid there was determined by clustering the post-PCA data points in
the optimum zone.
Example
[00095] In the following example, the data is drawn from a well
in Western Canada,
The results presented here are the outcome of each step in the machine
learning process. The
first set of results relate to PCA done on all the field data fed to the
system. The principal
components and their respective percentage of significance are derived. The
principal
components that make up at least 99% of the data were chosen while the other.,
principal =
= components are zeroed out before an inverse PCA is performed to obtain
the leaner original
data. Based on the decision tree classification, each data point is then
classified into one of the .
five _zones in the WOB and RPM plot. The quantitative risk analysis results
are shown and then
applied to the optimum zone chart to. produce the safe zone plot.
1-000961 This analysis was done on the first 3.5 minutes of three
stands o drill string (that
= is the first 3 updates of three stands). For this well, a depth. of 3..5
feet is drilled in 3.5 minutes.
For this post. analysis, the entire data for the tegion for the selected stand
would he analysed lifr
vibration issues and classified into the five zones. The stand chosen is one
with no obvious =
issues. The visible signs ofproblems with the data from a stand are
inequalities between the bit
depth and the measured depth. It is the bit depth that is very important; it
tells that the drill . =
string is moving into the formation and not just rotating at a spot. Any stand
that has a constant
depth for a while is an indication of stoppage in drilling or pause in
drilling forward. Figure 12 =
shows the plot of bit depth, measured depth versus time for the portion of the
well being studied.
Results
=
[00097] Figures 13 to 15 show the first 3.5 minutes of the three
stands. Each 3.5 minutes
of each stand is called the .first update of that stand. Usually each stand
would have an average.
of 5 updates. Results from Stand 2 Update 1 are the lbetts of this example.
RPMupper Calculations
- 24 -
=
CA 3019996 2018-10-05
=
=
[000931 The upper limit of RPM was calculated in accordance with the
details provided
further above.
= For stand one, RPMõppõ = 58.4993rpm
=
For stand two, RP/14õppõ 59:84577-pm
For stand three, RPMumõ,. 30.4300rprn
=
RPMõ,/J1 (rev/min) Calculations
=
[00099] In order tci find the constants Ibr the depth of cut and
torques equations, graphs
of torque versus WOB and depth of cut versus WOB were plotted and the
constants were
obtained for the first update from stand two.
1000100] The value for the constants in the Torque equation are shown
in the table 2 below
are obtained from Figure 16, the Torque versus WOB plot.
Table 2 Constants Obtained from the Torque Equation
Constants from
Torque = f(WOB) = An + A1* WOB. .
Data Source A0 '
= Stand Two Update One 3.7345 0.54.47
[0001011 The value for the constants in the Depth of Cut equation are
shown in the table
3 below are from Figure 17, Depth of Cut versus WOB plot.
Table 3 Constants Obtined from the Depth of Cut Equation
=
Constants from
Depth of Cut = DOG = g(WOB)
* WOB2 Bi*W0.13 + 130
- -
=
=
CA 3019996 2018-10-05
=
Data Source 82 BO .
Stand Two Update One ¨6.0002 0.0049 0.0015
=
[000102] The constants from the Torque and Depth of Cut equations are now
substituted
to find the WORopt, DOCopt which will then be combined with the ROPayg to find
RP hinitn.
Four solutions will always be gotten from the WOR opt equation, only the
positive value has a
= physical meaning and only that value Would be used in the DOC,,pr
equation.
82 * WOR:pt + 2B1Bz WOBgpt + (3? + 2/32130 ¨ 27tA1B2) WOBgpt
. + (2R1R0 ¨ 471110B7) WOB,rt + (B(I + 2AiL?0 ¨ 27TF10.81) = 0
Depth of Cut = DOCopt g(WO) = B2 * WOB02pt * WOBõpe +
=
Table 4-Calculations Breakdown fbr Obtaining Minimum RPM =
Parameters Stand Two Update One
/32 * WORg.pt 0.0002W0B4
Opt
2B1B2 0.00000196WOB'
opt
=
* WOB4r
=
(1312 + 282B0 ¨0.000659969W.08,,pt
¨ 2n-Ai/32) =
=
=
* WOHLt =
=
=
(2.131.130 = ¨0.0093723392WOR0pt
82)
=
* WOBõpc
=
=
=
- 26 -
= =
=
= =
CA 3019996 2018-10-05
.; (11(1 + 2/11B0 .. -0.1133548802
¨ 2RA0B1)
=
WOBõrt 5 .5130417559i=-775.¨
solution 1
WOBopt -0.493839345416.8616
solution 2 Ii* 4.735475187016882
WOBopt -0.4938393454168616 -
solution 3 i* 4.735475187016882
WOBopt -4.535170454764039 -
solution 4
Relevant 5.513049145597762
WOBopt
D 0 Copt 0.0345926827
DO Cõii 0.0172963414
R 0 P 47.0425
RP Mmin = 2719.794834762.
(rev/hr)
RPMmin 45,3299139127
(rev/nun)
. .
WOHõpper Calculations
. [000103] The stick slip index is used to find the upper limit
of W013. For stand two update
one, there arc ten test conducted and the results arc as follows
Table 5 Results of' Stick Slip Index Calculations
:
- 27 -
CA 3019996 2018-10-05
=
=
=
Test ." Stick Slip Index =
=
= 0,307
= 2
0.1934 =
= 3 0.1506
. ____________________________________________________________
4 0.1559
=
= 0.1.236
= 6 0.1232
7 0.0936
______________________________________ ¨ ____________________
= 8 0.7406
9 0.2577
. = 10 0.2684
=
10001041 Based on the rules mentioned further above, test 8
shows potentials for stick slip
since the index is above 0.5. Therethre, the.upper limit of WOB would be the
minimum W011
=
in test 8. The minimum WOB in test 8 is 2.2kDaN. Therefore WO Hupp õ = 2.2 kD
aN .
WO Bmiõ Calculations =
[0001051 WOB lower (WOB min) is achieved by taking the slope of
ROP versus time
every 5 seconds for the entire update leading to 43 rims of slope
calculations. The change. in
ROP versus time plot is fairly constant after the point chosen as where
constant change begins.
Tdeally, the change in ROP versus time should remain constant but in reality,
the change keeps
dropping. So the point chosen would be the highest change in ROP helbre a
consistent drop in
!i
= change in ROP. The closest highest peak after this peak can be referred
to as the Founder Point
(that topic is not the focal point of this disclosure). From Figure =18, the W
0 13mit, = 1.8 /CD aN.
=
The Optimum Zone Chart
- 28 -
=
CA 3019996 2018-10-05
=
[000106] A combination ()I' the upper and lower limits for WOB and RPM
Ibnn the box
that makeup the optimum zone plot, Figure 19. The lack ol' data points in the
optimum zone fOr.
this particular update (stand two update one) is the reason why all the safe
factors are zero for =
this case. In this Figure, the dotted lines are the data points. The RPM is
constant based oafeed
data. The start and end is an indication of when ROP starts occurring so the
reader can see what
is happening in relation with the optimum zone till the ROP comes to the last
data point at the
end.
= =
=
10001071 In the preceding description, for purposes of explanation,
numerous details are
set [bah in order to provide a thorough understanding of the embodiments.
However, it will
= be apparent to One skilled in the art that these specific details are not
required. In other
instances, well-known electrical structures and circuits are shown in block
diagram form in =
order not to obscure the understanding. For example, specific details are not
provided as to
. whether the embodiments described herein are implemented as a software
routine, hardware
circuit, firmware, or. a combination thereof
. [000108] Embodiments of the disclosure can be represented as a
computer program =
=
product stored in a machine-readable medium (also referred to as a computer-
readable
medium, a processor-readable medium, or a computer. usable medium having a
computer- =
readable program code embodied therein). The machine-readable medium can be
any suitable
tangible, non-transitory medium, including magnetic, optical, or electrical
storage medium
including a diskette, compact disk read only memory (CD-ROM), memory device
(volatile or . =
non-volatile), or similar storage mechanism. The machine-readable medium can
contain
various sets of instructions, code sequences, configuration in fimnation, or
other data, which,
when exc,cuted, cause a processor to perfortnsteps in a method according to an
embodiment
of the disclosure. Those of ordinary skill in the art will appreciate that
other instructions and
operations necessary to implement the described implementations can also be
stored on the = . =
machine-readable medium. The instructions stored on the machine-readable
medium can be
executed by a processor or other suitable processing device, and can interface
with circuitry to
perform the described tasks.
=
- 29 -
=
CA 3019996 2018-10-05
i; [000109] The above-described embodiments arc intended to be
examples only.
Alterations, modi fications and variations can be effected to the particular
embodiments by =
those of skill in the art. The scope o the claims should not be limited by the
particular
embodiments set forth herein, but should be construed in a manner consistent
with the
specification as a whole.
[000110] As detailed above, the present disclosure enables a
driller to assess, during
drilling, the appropriateness of the drilling parameters being used and to
correct these during =
drilling. The drilling parameters are monitored/measured during drilling and
the values of those
measured parameters are used to define an optimum drilling zone in the WOR-RPM
space. The
optimum zone is displayed to the user in addition to WOR-RPM data. points. The
displayed .
WOB-RPM data points are obtained by subjecting the measured parameter values
to a principal ,
component analysis in order to obtain only the most significant WOB-RPM data
points, which
are the ones displayed. The principle component analysis essentially filters
out less important
data, which in turn provides the driller better insight into the drilling
process and the best drilling
Parameters to use. Tn some embodiments, the method described can be.
automated.
= =
= =
=
=
=
.
=
=
=
=
=
=
- 30 -
=
CA 3019996 2018-10-05
=
References
1, Al Duhuis1ii M,, Nygaard R., Hod l E., Andersen E., & Helivik S. (May
2015). Post Well
Vibration Analysis in the North Sea: A Tool to Ihiderstand Drilling
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Prosperi, N. 2002. Selection of FOR/TOR Opportunities Based on Machine
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European Petroleum Conference, 29-31 October, Aberdeen, United Kingdom.
https://doi,org/10,2118/78332-MS
3. Bangert, P. (2017, May 9). Smart Condition Monitoring Using Machine
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Society of Petroleum Engineers. doi:10,2118/187936-MS
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=
5.. Cao, Q., Banat:ice, R., Gupta, S., Li J., Mon, W., and Jeyachandra, B.
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https://doi.org/10,2118/176759-MS
7. Gillies D., Diesenroth M. (D0C493): Intelligent Data Analysis and
Probabilistic
Inference Lecture 14. Department of Computing, imperial College London.
Retrieved
from h s: www.doc.ic.ac.uk ' = ' = = =
=
8, llanirick T.R. (2011) Optimization of Operating Parameters for Minimum
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