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PAPER 2004-007
Optimization of Well Placement and/or
Borehole Trajectory for Minimum Drilling Cost
(A Critical Review of Field Case Studies)O.R. AYODELEUniversity of Alberta
This paper is to be presented at the Petroleum Societys 5thCanadian International Petroleum Conference (55
thAnnual Technica
Meeting), Calgary, Alberta, Canada, June 8 10, 2004. Discussion of this paper is invited and may be presented at the meeting iffiled in writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed wilbe considered for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject tocorrection.
Abstract
This paper provides a brief explanation of the factors that
affect optimal well placement and/or borehole trajectory andhow these factors can be controlled or selected to giveoptimized well trajectories. Review of some of the general
techniques used in achieving optimal well placement and/orborehole trajectory, with a view to minimizing drilling cost, arepresented and some field case studies/field examples selected
from lit erature are given. Limi tat ions of some of thesetechniques are also discussed.
Introduction
Drilling of wells for optimal placement within the reservoir
or target is one of the most important challenges in modern day
drilling problems. The cost associated with drilling operations
can run into several millions of dollars in land, swamp and
offshore environments. With the advent of deep-offshore
drilling, with its associated higher cost, the need for optimal
well placement cannot be over-emphasized. Good drilling
practices and planning, that bring about accurate or near
accurate well placement or accurate borehole trajectory tracking
can significantly reduce drilling cost by eliminating the need to
plan or drill additional wells. Several factors come into play
during drilling that can affect optimal well placement or well
trajectory. Many of these factors can be controlled easily while
others are particularly difficult to control. Also, a previous
knowledge of the drilling environment, in terms of formation
type, BHA behaviour and hole stability, can be helpful in
making better planning for optimal well placement.
Previous knowledge can be used to simulate well trajectory
torque, BHA frictional resistance, expected build or turning
rate, etc. Planning for a directional or horizontal wel
encompasses hitting the target point(s) with precision and
accuracy at low cost. Factors to be considered include; well
total depth, target inclination and direction, curvature and
turning sections, and kick-off points. Other issues include the
type of tools used in monitoring and the error associated with
such tools, method of well planning and how the well is actually
drilled. The purpose of this paper is to briefly discuss factors
that affect optimal well placement and/or borehole trajectory
and review several techniques, available in the literature for
optimizing well placement and/or borehole trajectory. Some
relevant field case studies/field examples are also discussed in
the paper.
PETROLEUM SOCIETYCANADIAN INSTITUTE OF MINING, METALLURGY & PETROLEUM
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Factors that Affect Well Placement
Many factors that affect bore hole trajectory and accurate
well placements are directly related to the factor affecting hole
angle and inclinations. These include the type of bottom hole
assembly (BHA) in terms of size and elastic properties;
borehole shape and curvature; bit-type; formation strength and
anisotropy; and drilling parameters and conditions(1)
.
BHA Type
The stiffness property of BHA components plays a major role in
critical well placement. The stiffness property is dependent on
the modulus of elasticity and the moment of inertial of the BHA
components. BHA components should be selected in such a
way that the stiffness property can withstand borehole
conditions for effective bore control. The weights of the BHA
components also affect the BHA stability and well control
behaviour. The weights depend on the sizes and densities of the
components as well as the buoyancy effect of the drilling mud.
Also, the locations and sizes of the stabilizers and the downhole
measurements systems like MWD tools play a critical role in
trajectory control.
Bore Shape, Curvature and Size
The shape and curvature of the borehole can make the BHA
behave or deflect in a manner that is independent of the BHA
components. Hence, the shape of well can be a vital controlling
factor in accurate well placement. The borehole size, which can
be obtained from real-time caliper log, can also be a major
trajectory control factor. In well sections where there is
borehole washout, there is tendency for the well trajectory to
become more difficult to control for optimal well placement.
Bit Type
Diamond, mill-tooth and rock bits all have different effects
on well bore trajectory. Generally, this is relative to rate of
penetration and other drilling deviation factors and directional
drilling tools being used. Directionally, roller bits tend to
walk to the right, whereas diamond and diamond compact bits
do not(1)
. Also, bit interaction with the formation can be adetermining factor in trajectory well control.
Formation Strength and Anisotropy
The hardness of a formation affects the rate of penetration
and also the bit deviation pattern. The rate of penetration
determines how often the bit or the stabilizer touches the well
bore at any point. High frequency of contact with the boreholemay wear out the stabilizers and the bit. This may also cause
borehole enlargement by cutting into the formation. Formation
with dipping bed planes affects the borehole path. Bits tends to
drill up dip when the bedding planes have dips of less than 450
and tend to drill down dip when bedding dips are greater than
600
(1)
.
Drilling Parameters and Conditions
Several drilling parameters come into play while drilling.
These parameters play a crucial role in well bore trajectory
control and placement. The effect of parameters such as rotating
speed, weight-on-bit, torque, standpipe pressure, flow rate, etc.
is best studied through available drillstring models. Isolating the
effects of the individual parameters might be a cumbersome
task to undertake, hence, using the drill string models provide
an appropriate means of quantifying such effects. The effects of
these parameters on BHA behaviour and well bore control are
also still the subject of intense on-going research.
Borehole Trajectory / Well PlacementOptimization Techniques
Optimization issues can be addressed from several angles
depending on the professional dealing with the issues. To the
drilling engineer, well trajectory optimization can be seen as a
way to place the well on the right path to hit the right target(s)
with minimal cost by avoiding unnecessary surface trips and
borehole problems like wall collapse and stuck pipe. To the
reservoir engineer, it involves hitting the right sand in a
specified spot in order to maximize recovery (See reference 2).
Whatever the objective of the professionals dealing with such
issues, the common message is that the well should be drilled
for cost effectiveness without compromising good engineeringpractices and environmental concerns. This section contains
optimization issues as presented in the literature from different
perspectives.
Optimization Technique for Well Planningand Development of Accurate Well PathEstimation Methods
Maldia et al.(3)
developed a well planning technique for dual
targets with significant bit walk. The technique is a
generalization of the well planning method for two targets with
a computerized approach. Targets points are given in Cartesian
co-ordinates. After calculating the first estimate of the surfacelocation (point S in Figure 1), the planned survey is computed
(measured depth, inclination and azimuth) at a specified
interval. In reality, only one azimuth value is needed since all
trajectory points are contained in the same vertical plane.
A bit work-model is used to estimate the azimuth change at
each survey station. In the approach developed by Maldia et al,
the bit work model presented by Maldia and Hygino is used.
Given a build-up rate (BUR), departure and a Kick-off-point
(KOP) or measured depth (MD), the bit walk rate and new
azimuth at each station are estimate assuming an inclination
greater than or equal to 200
using the equations below,
respectively,:
( )ii Sinfaa
K
331+= .................(1)
and
MDKiii += +1 ...........(2)
where 1 is the inclination rate constant, 3 is the azimuth
rate constant, is the inclination and i refers to the survey
station. The parameter, 3f , is the variation of inclination with
measured depth and it is given as:
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dMD
df
=3 ........................(3)
The bit walk below 200 inclination is neglected. After
computing the parameters in Equations (1), (2) and (3), the
coordinates (x, y, z) at each survey station are computed using
the minimum curvature method. The top view of the calculated
trajectory is shown in Figure 1, passing through points S, Cand D. Due to the fact that the bit walk below 20
0inclination is
neglected, error is introduced into the computation and this hasto be corrected for. The targets are points A and B in Figure 1.
The next step involves using techniques commonly used in
computer graphics to match the predicted 3-D trajectory to the
actual targets. Points on the SCD are translated so that point D
matches point B (FEB in Figure 1). This translation makes use
of homogeneous coordinates and matrix operations. The lead
angle, L , is then computed by using the dot product of EB and
AB shown in Figure 1.
The curve FEB and points A and B are translated so that
point B matches the origin. Curve FEB is rotated about the
origin by the amount, L , to match point E to A. Translation
and rotation are done simultaneously. Finally, the curve O2AB
and point A are translated so that the origin of the co-ordinate
system that will appear on the computer monitor matches point
O2.
The above procedure ensures the best surface location, the
necessary lead angle to account for bit-walk and calculates the
planned well trajectory. A computer program was developed to
do all the calculations in the procedure as well as display the
graphical output to the computer monitor to help visualize the
spatial trajectory of the planned well. The program was written
in Turbo-Pascal (version 5.5) for microcomputers.
Field Example 1: Accurate Wellbore Survey calculations
One of the examples presented by Maldia(3)
is shown to
illustrate the generality and ease of use of the program
developed. Well B (Figure 2(a)) was drilled offshore Brazilwith a maximum inclination angle of 380. The program was
used to plan the well. The actual surface location and the two
targets are aligned and, due to bit- walk, the first target was not
intercepted within the pre-established 164ft radius. Figure 2(b)
shows that the best surface co-ordinates to intersect both targets
are 31,8804.69E m and 7477911N m (See circled point in
Figure 2(b)). For this situation the calculated error between the
first target match is 2 ft.
Argun and Kuru(4)
developed a technique for approximating
the trajectory between two consecutive survey points using a
curve defined in three-dimensional space (3D Space Curve
Method). This technique determines the coordinates of any
point along the borehole accurately leading to accurate survey
estimations and, hence optimized well placements. The methodis based on the fact that a 3D curve better represents the shape
of the borehole between two consecutive points. They show that
polynomial expressions of order two, (quadratic), can be used to
better represent the distance between the coordinates of points
along the well paths. They showed that that the data (measured
depth, inclination and azimuth) between consecutive surveys
can be used to obtained the coefficients ( 1a , 2a , 3a , 1b , 2b and
3b ) of the expressions in the equation of a tangent vector given
as follows:
( ) ( ) ( )
( ) ( ) ( )2
332
222
11
332211
222
222
btabtabta
kbtajbtaibtau
+++++
+++++= .....(4
where
112
1/ ctbtaSN ++= .............................(5)
222
2/ ctbtaWE ++= .......................(6)
332
3 ctbtaTVD ++= .............................(7)
and u is the tangent unit vector while tin the measured depthfrom the surface. Another expression for u as given by theauthors is:
( ) ( ) kCosjSinSiniCosSinu ++= ......(8
where is the inclination and is the azimuth (direction). By
using Equations (5), (6) and (7), by equating Equations (4) and
(8) with the denominator of Equation (4) being equal to 1 and
by using the available data between two points, the coefficients
in Equations (4) to (7) and the inclination and azimuth can be
obtained. Such computations usually start from a referencepoint (say at the surface) where all the relevant data are known
and the survey point after the reference point, where relevant
data are not available. After the first computation, subsequen
computations can be made, since the equation of the path
between the first two survey points is known explicitly. "It i
then possible to determine the co-ordinates of any point along
the course length between survey points[4]
. The main
advantage of the method presented by Argun and Kuru is that it
is well suited for target intersections. Most of the methods
available in the industry are not suitable to hit the target with
the specified inclination and the direction(4)
. The method
presented above provides a way to hit the target at the specified
coordinates, inclination and direction.
Field Example 2:Accurate Wellbore Prediction
Argun and Kuru presented examples to show the accuracy o
their new methods in predicting well path trajectory. They used
some real field data available in the literature and compared
their results with those of other methods as presented in Table
1. As seen in the table, the results of the 3-D Space Curve
method are similar to those of other methods. Despite this, it is
expected that the 3D Space method would give better results in
longer survey intervals and when the wellbore shape deviated
from being part of a perfect circle(4)
. They also presented data
for a plug-back operation. They used the 3D Space Curve
method through an iterative procedure to obtain the minimum
course length of 500 ft. The course length was from a plug-back
depth (12,095 ft measured depth, 160 inclination, N 15
0W
direction, 11,934 ft TVD, 1,201 ft N and 453 ft E) to a newtarget depth (13,185 ft measured depth, 50 inclination, N 20
0W
direction, 13,000 ft TVD, 1,750 ft N and 750 ft E) using a
specified dogleg-severity of 50/100 ft.
McCann and Suryanarayana(5)
also presented a procedure
that uses nonlinear optimization theory to plan complex, three
dimensional well paths and corrections while drilling. The
procedure helps to place accurately the well on the correc
trajectory. Several well planning programs are available
commercially to solve the problem of finding an appropriate
horizontal or directional well path. However, all of these use a
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trial-and-error procedure to arrive at a solution. Typically, these
programs convert the underdetermined problem into a fully
determined one by requiring the user to select a value for
enough of the parameters, and using a trial-and error procedure,
arrive at a satisfactory well path. This is sometimes augmented
by heuristic rule-bases(5)
.
Such methods are time consuming and more suited for a
simple well path. To overcome these shortcomings McCann and
Suryanarayana developed an approach that uses non-linear
optimization, which is superior to the trial-and-error techniques
in use today. The approach is more rational and intuitive, and
can be extended easily to a wide range of problems, such as
dynamic steering and finding well paths that minimize torque
and drag. The approach uses a criterion that minimizes the
distance between the solution parameters and a preferred set.
With the coordinate system shown in Figure 3 and using a
user-preferred parameter or the minimum length criterion or a
combination of both, the problem of well-path planning was
posed as an optimization problem, using the optimization
procedure that follows:
4
=
x
F
x
FQ
T
............................(9)
121 ...................................(10)
222 ...............................(11)
323 ...................................(12)
5
=
xxP
T
.........................(13)
where F is the augmented objective function defined as:
++++=i
iifF 332211 .........(14)
Other parameters in Equations (9) to (14) are defined asfollows: The parameters s' , are the Lagrange multipliers, is
the vector of inequality constraints converted into equalityconstraints, x is the column vector of well path parameters , is the equality constraints, is the pre-selected errortolerance, Q is the error in optimization condition and P is the
error in satisfaction. Equation (9) results from the standard first-
order condition that the first derivative of the objective
functions or equivalently, the augmented function vanishes at
the minimum. In practice, the satisfaction of this condition isachieved within a pre-selected small tolerance, 4 . Equations
(10), (11) and (12) represent the three equality constraints that
must be satisfied for the end-point of the well path to coincide
with the target. The target is not a fixed point, and there is
always a tolerance within which the target may be reached. The
parameters, 1 , 2 and 3 are the user-selected target
tolerances on the North/South coordinate, East/West coordinate,
and the TVD, respectively. Equation (13) ensures that all the
inequality constraints are satisfied. Hence, the problem here is
to find the x that satisfies all of the above conditions. This
makes the problem of planning a well path or path correction a
non-linear optimization problem.
McCann and Suryanarayana used the sequential gradient-
restoration algorithm (SGRA) for optimization of the problem.
SGRA is composed of the gradient phases and restoration
phases. The first stage, called the restoration phase involves, a
displacement x , leading from the nominal point x to a
varied point x , that is determined such that the varied pointsatisfies all the constraints of the problem, within pre-selectedtolerances (that is, satisfying Equations (10), (11), (12) and
(13)). In the gradient phase, the constraint-satisfying point x is
displaced by x to a varied point y , such that the value of the
objective function is reduced(5)
. The displacement
computation is dependent only on the first derivative at the
nominal point x and an optimal step-size is selected in such a
way that if the step size is big enough, the descent property ismaintained, and constraint violation is small. The value of x at
the end of a restoration phase gives a well path that reaches the
target within stipulated tolerances and in the interval of the
inequality constraints. McCann and Suryanarayana
implemented the above optimization procedure for double-turn
profiles both in terms of well planning and well path correctionusing a PC-based program that was developed based on the new
optimization technique. These field examples are presented as
follows:
Field Example 3:Well Planning with Nonlinear Optimization
A horizontal well to is to be drilled to a target TVD of 7000
ft, 1500 ft N and 1500 ft E of the surface location. Other
information about the target points includes inclination - 900;
azimuth - 900(requiring a 3-D profile); tolerances - 10 ft (TVD)
and KOP - 4000ft (TVD). Table 2 show as a summary of the
selected preferences, range constraints, weights, and the
solution parameters. Figures 4(a), 4(b) and 4(c) show the 3-D
view, a top view, and a vertical section view of the path
respectively. From Table 2, the solution turn rates are the same
as the preferred values, and the other parameters are nearly thesame as the preference. All of the parameters are within the
prescribed interval constraints, and the target is reached at the
desired inclination and azimuth, within the stipulated tolerances.
The program provides this solution very quickly, within five
seconds. Modifying the preferences, weights or the intervals
and then running the program again can bring about a
refinement of the solution.
The expected targets have the same information as that of the
well planning example except that after drilling to a KOP of
4000 ft TVD, a survey revealed that the well was headed in the
wrong direction. The coordinates at this point are -100 ft N/S
and -100 ft E/W at inclination of 250and azimuth of 225
0. The
well was then re-planned to return the path to the target
direction. The aim was to not deviate too much from theoriginal preferences or ranges, since the available tools and
geologic constraints requires low turn rates. Table 3 shows the
selected preferences, range constraints, weights, and the
solution parameters for the path correction. From the table it can
be seen that the procedure gives an excellent solution for the
path correction. Turn rates are low; all parameters are within the
specified intervals and close to the preferences, given their
relative ranking. Figures 5(a), 5(b) and 5(c) show the 3-D view,
a top view, and a vertical section view of the projected path
correction.
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The presented examples show that the optimization
technique is very efficient and robust, and takes seconds to
arrive at the results. The user can refine the solution and explore
possible options. This is an improvement over the traditional
trial-and-error techniques. The procedure can be used during
well planning stages, when feasible paths are planned and when
quick path corrections are needed. It can also be modified to
include other optimality criteria, including cost. It can be used
for planning wells with dynamic steering.
Optimization From the Perspective ofDeveloping New Error CorrectionTechniques
Williamson(6)
developed a new method for predicting
wellbore position uncertainty. The method is based on error
correction of MWD tool measurements. The author discussed
sources of errors in MWD measurements that contribute to the
problem of predicting or knowing the actual wellbore trajectory.
Such problems as discussed by the author are mostly
environmental in nature. These include sensor errors due to
calibration, BHA (bottom-hole-assembly) magnetic
interference, tool misalignment and magnetic field uncertainty.
These errors can be corrected for in the model developed by
Williamson. However, some other errors that affect MWD
measurements are not included in the model. These include tool
electronics and resolution errors, external magnetic errors,
survey interval and calculation method errors, gravity field
uncertainty errors and along-hole depth errors.
The error model that Williamson presented is based on the
following assumptions: errors in a calculated survey station are
caused exclusively by the measurement errors at that station;
survey stations are modeled 3D element vectors (depth,
inclination, azimuth) and tool-face angles are required at each
station (6)
. Other assumptions include: errors from different
sources are statically independent; a linear relationship existbetween errors at each station and the associated change in
calculated well position; the total effect on calculated well
position of any measurements errors at any survey stations is
equal to the vector sum of their individual effects(6)
.
In the model developed, the error due to the presence of thethi error source at the thk survey station in the thl survey leg
is expressed as the sum of the effects on the preceding and
following calculated displacements(6)
. Mathematically, this is
expressed as:
i
k
k
k
k
klikli
p
dp
rd
dp
rde
+
= +1,,, .................................(15)
where
li, = magnitude of thethi error source
kp = instrument measurement vector at thethk survey station
kr = displacement between survey stations 1k and k
i
kp
= weighted function
The weighted function for each error source is a 3 X 1 vector
element (depth, inclination and azimuth). Williamson presented
weighted functions for all the error sources. For example,
weighted functions for constant and horizontal-dependen
magnetic declination errors are, respectively:
=
1
0
0
AZ
p
...................................................................(16)
( )
=
cos/1
0
0
B
p
DBH......................................(17)
Details of the weighted functions for the other error sources
and mathematics involved are presented by the author. Detailed
information about these can be obtained from the relevan
section of the author's paper. The total position error at a
particular survey station in the survey leg is the sum of the
vector errors, klie ,, , taken over all error sources, i , and all
survey stations up to and including K . The uncertainty in thisposition error is expressed in the form of a covariance matrix
given as[6]
:
[ ] ( ) 22112211 ,,.,,.,,,,,21
klklklklC Tii
Kk
ii
Kki
errors
K
= ...(18
where ( )2211 ,,,,, klkl ii is the correlation coefficient
between the value of thethi error source at the 1k th station (in
the 1l th leg) and 2k th station (in the 2l th leg). Error models
for basic and interference-corrected MWD were applied to the
standard well profiles to generate position uncertainties in each
well. The results are presented below.
Field Example 4: Error Correction in MWD Tools
Williamson applied the error models for basic and
interference-corrected to the standard well profiles to generate
position uncertainties in each well. The resul ts of severacombinations are tabulated in Table 4. The first column in Table
4 shows the serial numbers (1 to 7) of the examples. Examples 1
and 2 compare the basic and interference-corrected models in
well ISCWSA No. 1. The well is an inclination well and the
interference correction actually degrades the accuracy. Figure 6
shows the results. Examples 3 to 6 all represent the basic MWD
error model applied to well ISCWSA No. 2. They have
significant differences in that each uses a different permutation
of the survey station/assigned depth and symmetric error survey
bias calculation options. The results are shown in Figure 7
Example 7 breaks well ISCWSA No. 3 into three depth
intervals, with the basic and interference corrected models being
applied one after one another. This example gives a test of error
term propagation.
By establishing a common standing point for wellbore
posit ion/t rajectory uncertainty and presenting a set of wel
profiles for investigating the developed error models with a se
of results for testing the software implementation, Williamson
showed that accuracy of well trajectory/well placement can be
enhanced or optimized. Williams also observed that by
developing the presented models, only a few of the problems at
hand have been solved. He recommended that collaborative
work should be directed towards standardization of quality
assurance measures, strengthening the link between quality
assurance specifications and error model parameters, and better
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integration of wellbore position uncertainty with the other
aspects of oil field navigation(6)
.
Chia et al.(7)
developed a method, called the MAP - most
accurate position technique, similar to that by Williamson(6)
.
The method entails statistical combination of surveys from
several wellbore survey instruments to generate a single,
composite, more accurate wellbore position. For brevity, details
of the technique are not provided here and can be found in
reference 7. The main advantage the MAP technique is that its
uncertainty is smaller than that of the individual constituents
surveys(7)
. By reducing positional uncertainty associated with
survey trajectories, well can be drilled to geological targets
more accurately and collision with another well can be easily be
avoided.
Wilson and Brook[8]
showed that drilling fluid
contamination could cause wellbore position error. Such drilling
fluids caused azimuth-shift error due to the presence of
steel/magnetic particles from casing and drillstring wear. This
type of error is severe in oil-based and synthetic mud fluids that
are increasingly being recycled due to environmental
regulations on disposal. The effect of drilling fluid
contamination on azimuth-shift is proportional to fluid cross-sectional area and ratio of MWD tool diameter to the borehole
diameter. Attempts to use a magnet to remove the magnetic
materials have proved unsuccessful. Multiple surveys or
modified-single survey correction may be used for correction.
Wilson and Brook[8]
presented an equation for single-survey
correction. This equation is given as:
+
=
GyByGxBx
GxByGyBx
SinISinCosACosICos
SinACos
refcorrref
corrref
..
..
...
(19)
where I is the i nclination, ref is the independently supplied
dip angle, corrA is the corrected azimuth, B is the magnetic fieldstrength and G is the gravity field strength. The
subscriptsx andy refer to the horizontal and vertical
components of the magnetic and gravity field strength
respectively. The above single-survey correction breaks down
in some situations. It breaks down as the direction approaches
the plane of the magnetic field vector and the horizontal E/W
vector. For brevity, multiple-survey correction equations are not
given here.
Field Example 5: Correction of Error Due To Mud
Typical examples of surveys in which multiple-survey and
single-survey corrections are applied are shown in Figure 8. The
data in the figure are from a North Sea well. Surveys in the
figure were acquired at about 400
inclination. Application of aconventional single-survey correction produced a result that was
further from the inertial navigation survey than the uncorrected
data. A multiple-survey correction indicated negative xyB scale
-factor errors of approximately 1.5%, and gave corrected
azimuth readings in good agreement with the inertial tool.
Gravity Azimuth Correction TechniqueMcElhinney et al.
(9)proposed the use of only gravity-based
measurements for azimuth determination in geothermal wells.
In the region of the world (especially in Iceland) where drilling
is done in volcanic areas with a high geothermal gradient,
incorrect determination of azimuth can hardly be avoided due to
the presence of magnetic materials (pyrites, magnetite, etc.).
McElhinney et al. used a gravity-based MWD measurement and
computed gravity-derived azimuth (based sorely on
accelerometer readings). The results show that accelerometer-
based azimuth can be used with some degree of confidence to
optimize well trajectory by reducing error introduced into the
surveys by magnetic materials. The authors do not present
details of the mathematics of computation, but they are
presented in "Surveying a Subter ranean Borehole using
Accelerometers, US Patent No 98181117.5, 1999"(9)
.
Using this technique, the gravity fields at two separate
positions are measured along six axes, two pairs of three
mutually perpendicular axes, at the same time (Figure 9).
Provided the accelerometers are arranged to align with one
another for the axis to be parallel, certain conditions can be
prescribed. If the well path were straight, the accelerometers
(Gx, Gy and Gz) would have the same readings. When the well
inclination changes the values of the Gzs change
correspondingly and the Gx/Gy ratios remain constant, while a
change in direction would result in no change in the Gz values.
The Gx/Gy ratio would change. A change of both inclinationand direction would cause a change in the values of Gx, Gy and
Gz(9)
.
Field Example 6: Azimuthal-Based Computations
Examples shown in Figures 10 and 11 give the comparisons
of gravity-derived azimuths and azimuth derived with other
methods. Some of these results compared favourably.
Rotary Steerable Drilling for Optimal WellPlacement
The most recent approach to optimizing well trajectory
employs the rotary steerable drilling system. Unlike in a
conventional drilling system where angles can be built, dropped
or turns made, only by employing steerable downhole system in
sliding mode without rotating, rotary steerable systems have no
such limitations. Most of the problems that affect directional
wells occur when the drillstring is not rotating, for example,
while sliding. Rotary steerable downhole motor eliminates such
problems. A rotary steerable systems drill smoother and less
tortuous wellbores(10)
, thereby eliminating potential drilling
problems and making possible accurate well placement.
With rotary steerable drilling systems, the equivalent
circulating density (ECD) and the mud weight can be kept more
stable and closer to the formation pressure(10)
. This generally
has the effect of generating a smooth wellbore and a higher
success rate of achieving the desired well path. The rotary
steerable drilling system also greatly helps in depth controlduring drilling. An incorrect well depth (measured depth) might
result in an inaccurate survey computation thereby leading to
wrong well placement. When using the conventional steerable
motor in sliding mode, unknown quantity of static friction
between the well bore and the drill ing has to be overcome,
leading to inaccurate depth control.
In addition to directly helping in achieving optimal well
placement, rotary steerable drilling system can also indirectly
assist in achieving accurate well trajectory due to its smaller
environmental effect on logging/measurement-while drilling
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(MWD/LWD) logs. The smoother borehole that is created with
the rotary steerable system has a positive impact on the quality
of the formation-evaluation/measurement-while-drilling
(FE/MWD) logs(10)
. Due to the less rugose hole created with
the rotary steerable drilling system, the MWD signals, data and
measurements that come to the surface are cleaner and less
affected by noise and are more accurate, making possible the
steering of the well in the correct trajectory. Also, some of the
MWD/LWD data generally help the directional drillers in
avoiding trouble spots during drilling. For example, gamma ray
(formation indicator) and ECD (packed annulus) indicator can
be used with some degree of reliability at the surface by both
the driller and the directional drillers, when there is less noise
corrupting the MWD/LWD signals and data.
The rotary steerable drilling system is relatively new. It has
been deployed in several parts of the world in directional well
operations and the operators have noticed most of the
advantages highlighted. The major limitation of the system is
the cost. It is expensive to run. Hopefully in the future, as more
of such system becomes available, the cost will go down and it
will become widely accepted in the industry. The two most
popular rotary steerable systems (tools) in the market are Bakers
Hughes INTEQs AutoTrak system and the Schlumberger'sPowerDrive system (Figure 12).
Field Example 7: Rotary Steerable System
Field examplesFrom the North Sea and Malaysia are shown
in Figures 13 and 14(11)
. These two examples gave some of the
advantages described above. "In 1998, the Wytch Farm M-17
well was drilled through the narrow Sherwood sandstone
reservoir and between two faults using the PowerDrive tool.
This well set the current record for a bit run, drilling 1287 m in
84 hours while achieving a 110 turn at high inclination(11)
(See Figure 13).
In Malaysia, the PowerDrive rotary steerable system was
used to drill two wells in the Bekok field. In one of the wells
(Bekok A7 ST) 1389 m were drilled at an average of 51 m/hr atabout inclinations varying from 40 to 70 degrees. Builds and
turns averaged 3/30 m. The PowerDrive achieved a 45%
higher ROP saving five days of rig time. Valuable rig time was
also saved because of fewer wiper trips. Only two-thirds of the
time specified in the drilling plan was actually used for drilling.
This resulted in major cost savings (See Figure 14).
Near Bit Inclination Measurement forOptimal Well Placement
Another recent innovation aimed at accurate placement of
the wellbore is the introduction of near-bit inclination
measurement sensors by industrial vendors. Such measurement
sensors, which form an integral part of the MWD/LWD system,
can help to target thin oil intervals sandwiched in between gas
and water boundaries. MWD/LWD systems with this capability
are available for both medium and small well bore sections.
Examples are, Schlumbergers 4-3/4 -in At-Bit Inclination
Measurement tool AIM[12]
for 6-in hole sections and Geo-
Steering tool - GST(13)
for bigger hole sections. Figure 15
shows the relative position of the GST in different drillstring
arrangements. The GST tool can also be used for geo-steering
purposes when landing a well.
Field Example 8: Near-Bit Inclination Measurement System
The 4-3/4-in At-Bit Inclination Measurement tool has been
used in Alaska to drill complex 3D directional wells. The too
was used to land wells within 1 ft TVD of the required targe
and then drill for lengths of over 5000 ft with directional
precision previously available only in larger hole sections (12)
With near-bit sensors, the time for sliding, required for accurate
wellbore placement is reduced because a very short time
interval (lag) is required to see the result of sliding. This
generally has the effect of increasing the rate of penetration
(ROP), especially in the horizontal sections that are known to
have low drilling ROP. The near-bit inclination tool can also
help in initiating wellbore sidetracking when a wellbore i
plugged and sidetracking at the kick-off-point. Establishing tha
a small trench has been made and that the sidetrack has been
initiated is easier with an AIM tool since survey points are
much closer to the bit.
The tool also gives better survey projections while drilling
Unlike the conventional MWD tools, where projected surveys
are determined from inclinations measured at several feet (30 to
80 ft) behind the bit, the near-bit tool projected surveys are
more reliable since they are based on measurements a few fee
(4 to 5 ft) behind the bit. Hence, the bit-projected trajectoryestimates is more reliable and can be used with more confidence
when landing a well. This is actually more relevant when
dealing with high-angle wells and build rates greater than
100/100ft
[12]. Figure 16 shows the correlation between the
inclination measurements made with a conventional MWD too
(called Impulse) and the near-bit sensor (AIM) of
Schlumberger. The figure shows that the measurements of the
two tools are almost the same, making the AIM measurement
very reliable.
In summary, with near-bit sensors, the precision of drilling
and landing a well is improved, a higher ROP is achievable
landing a well with a smaller TVD tolerance is possible and
sidetracking can be much more easily initiated. The main
limitations of the near-bit inclination measurement tools includethe cost associated with running the tools, which is quite
expensive.
Concluding Remark
A brief introduction of the need to optimize well bore
trajectory has been presented. Factors affecting borehole
trajectory/well placement are briefly discussed also. This is
followed by a review of the techniques available in the literature
that are used for optimizing well bore trajectory/placement
Some relevant field examples (field case studies) presented in
the literature are given under each technique. The technique
presented do not include all available techniques but cover some
useful techniques. It is hoped that this paper would providefurther insight into other ways of optimizing wellbore
placement/borehole trajectory.
Acknowledgement
The author thanks Dr. E. Kuru, an associate professor of
petroleum engineering at the University of Alberta, for initiating
the subject matter of this paper.
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REFERENCES
1. WALKER, B.H, Factors Controlling Hole Angle and
Direction.Journal of Petroleum Technology, pp. 1171-
1173, November 1986.
2. GUYAGULER, B. and HORNE R., Optimization ofWell Placement. Journal of Energy Resources
Technology. A Transaction of the ASME, Vol. 122, pp.
64-70, June 2000.
3.
MALDIA, E.E., CORDOVIL, A.G., PEREIRA, J.J. andFALCAO, J.L., Computerized Directional Well
Planning for a Dual-Target Objective. SPE paper
number 22315 presented at the Sixth SPE Petroleum
Conference held in Dallas, Texas, June 17-20, 1991.
4. ARGUN, F. and KURU, E., An Improved Method for
Borehole Trajectory Estimation and Target Intersection.
Oil Gas European Magazine, Vol. 23, pp. 1171-1173,
1997.
5. MCCANN, R.C and SURYANARAYANA P.V.R.,
Horizontal Well Path Planning and Correction using
Optimization Techniques. Journal of Energy Resources
Technology. A Transaction of the ASME, Vol. 123, pp.
187-193. September 2001.
6. WILLIAMSON, H.S., Accuracy Prediction for
Directional Measurement While Drilling. SPE Drillingand Completion Journal. Vol. 15, No. 4, pp. 221-233,
December 2000.
7. CHIA, C.R., PHILLIPS, W.J. and AKLESTAD, D.L., ANew Wellbore Posi tion Calculation Method. SP E
Dri ll ing and Completion Journa l, pp. 209 -213,
September 2003.
8. WILSON, H. and BROOKS, A.G., Wellbore Position
Errors Caused by Drilling-Fluid Contamination. SP E
Drilling and Completion Journal, Vol. 16, No. 4, pp.
210-213, November 2001.
9. MCELHINNEY, G.A., MARGEIRSSON, A. and
JAROBORANIR, H.F., Gravity Azimuth: A New
Technique to Determine Your Well Path. SPE paper
number 59200 presented at the 2000 IADC/SPE Drilling
Conference held in New Orleans, Louisiana, February
23-25, 2000.
10. BERGER, P.E., HELGESEN, T.B. and KISMUL, J.K.,
Rotary Steerable Systems Aid Logging. Har t s
Exploration and Production, pp. 71-72, February 2001.
11. DOWNTON G., HENDRICKS, A., KLAUSEN, T.S.
and PAFITIS, D., New Directions in Rotary Steerable
Drilling. Schlumberger Oilfield Review, pp. 18-29,
Spring 2000.
12. VARCO, M., Inclination At the Bit Improves
Directional Precision for Slimhole Horizontal Wells:
Locals Case Histories. SPE paper number 54593
presented at the 1999 SPE Western Regional Meeting in
Anchorage, Alaska, 26-28 May 1999.13.
BOYD, A., DAVIDS, B., FLAUM, C., KLEIN, J.,
SNEIDER, R. M., SIBBIT, A. and SINGER, J.,The
Lowdown on Low-Resi sti vity Pay. Schlumberger
Oilfield Review, pp. 4-8, Winter 1992.
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Table 1: Comparison of the results of 3-D Space method developed by Argun and Kuru with
those of other methods using available field data. Source: Argun and Kuru (1997)[4]
Method TVD (ft) E/W (ft) N/S (ft)
Tangential 14,370.70 -495.88 1,438.91
Average Angle 14,371.18 -510.06 1,463.48
Balance Tangential 14,370.40 -509.40 1,460.34
Mercury 14,370.38 -509.52 1,460.20
Circular Arc 14,371.40 -510.00 1,459.90
Helical Arc 14,370.80 -513.50 1,453.00Radius of Curvature 14,370.92 -509.86 1,461.80
Minimum Curvature 14,371.44 -509.96 1,460.46
3D Space Curve 14,370.76 -509.96 1,458.40
Table 2: Results of first field example (well planning). Source: McCann and Suryanarayana (2001)[5]
Parameter Pref. Min. Max. Rank Solution
1(0
/100 ft) 2 2 12 5 21 (
0/30 m) 2 2 12 5 2
2 (0/100 ft) 5 2 12 5 5
2 (0/30 m) 5 2 12 5 5
Lh(ft) 500 0 2000 3 522
Lh(m) 152 0 610 3 159
h(deg) 45 5 85 0 36
Ls(ft) 300 0 1000 2 306
Ls(ft) 91 0 305 2 93
h(deg) Free 0 360 0 3.3
Target error: Negligible (less than 0.5 ft (0.2 m) in all directions)
Table 3: Results of second field example (path correction). Source: McCann and Suryanarayana (2001)[5]
Parameter Pref. Min. Max. Rank Solution
1(0/100 ft) 3 2 5 5 3.2
1 (0/30 m) 3 2 5 5 3.2
2 (0/100 ft) 6 2 12 4 4.6
2 (0/30 m) 6 2 12 4 4.6
Lh(ft) 500 0 2000 5 497
Lh(m) 152 0 610 5 151
h(deg) 45 5 60 3 50.2
Ls(ft) 300 0 1000 5 310
Ls(ft) 91 0 305 5 94
h(deg) Free 0 360 0 20.5
Target error: Negligible (less than 0.5 ft (0.2 m) in all directions)
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Figure 1: Horizontal View Transformation. Source: Maldia et al . (1991)[3]
QL
QL
Table 4: Calculated position uncertainty error. Source: Williamson (2000)[6]
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Figure 2(a): Predicted and Actual Horizontal Views for Well B. Source: Maldia et al. (1991)[3]
Figure 2(b): Program Output for Well B. Source Maldia et al. (1991)[3]
Figure 3: Co-ordinate system for a well path. Source: McCann and Suryanarayana (2001)[5]
.
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Figure 4: Well Planning Example. (a) 3D- view. (b) Top View. c) Vertical Section View. Source: McCann and Suryanarayana (2001)
[5]
Figure 5: Path Correction Example. (a) 3D- view. (b) Top View.
(c) Vertical Section View. Source: McCann and Suryanarayana (2001)
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Figure 6: Comparison of Basic and Interference Corrected MWD Error Models in Well ISCWA No.1.
Source: Williamson (2000)[6]
Figure 7: Variation of Lateral Uncertainty and Ellipsoid Semi-Major Axis in a Fish-Hook Well, ISCWSA No.2.
Source: Williamson (2000)[6]
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Figure 8: Azimuth Comparison: Single-Axis and Multiple Survey Corrections. Source: Wilson and Brook (2001)[7]
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Figure 9(a) and 9(b): Positions of Accelerometers. Source: McElhinney et al. (2000)[9]
Figure 9(a):
Figure 9(b):
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Figure 10: Comparison of Azimuth Gravity, Gyros and MWD Magnetic Survey Devices. Source: McElhinney et al. (2000)[9]
Figure 11: Comparison of Azimuth Gravity, Gyros and Magnetic Survey Devices. Source: McElhinney et al. (2000)[9]
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Figure 12: Schlumberger's PowerDrive Rotary Steerable System. Source: Downton et al. (2000)[11]
Figure 13: Longest Bit Run at Whytch Farm. Source: Downton et al. (2000)[11]
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Figure 14: Views of Planned and Actual Trajectories. Source: Downton et al. (2000)[11]
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Figure 15: Illustration of the Relative Position of the GST Tool in a Drillstring.
Source: Bo d et al. 1992[13]
Figure 16: Comparison of MWD and AIM Surveys for a Section of a Horizontal Well.
Source: Varco 1999[12]