Optimization of Well Placement Andor Borehole Trajectory for Minimum Drilling Cost- GOOD

8/10/2019 Optimization of Well Placement Andor Borehole Trajectory for Minimum Drilling Cost- GOOD

1/19

1

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


2/19

2

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:


3/19

3

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


4/19

4

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.


5/19

5

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


6/19

6

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


7/19

7

(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.


8/19

8

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.


9/19

9

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)


10/19

10

Figure 1: Horizontal View Transformation. Source: Maldia et al . (1991)[3]

QL

QL

Table 4: Calculated position uncertainty error. Source: Williamson (2000)[6]


11/19

11

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]

.


12/19

12

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)


13/19

13

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]


14/19

14

Figure 8: Azimuth Comparison: Single-Axis and Multiple Survey Corrections. Source: Wilson and Brook (2001)[7]


15/19

15

Figure 9(a) and 9(b): Positions of Accelerometers. Source: McElhinney et al. (2000)[9]

Figure 9(a):

Figure 9(b):


16/19

16

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]


17/19

17

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]


18/19

18

Figure 14: Views of Planned and Actual Trajectories. Source: Downton et al. (2000)[11]


19/19

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]

Date post:	02-Jun-2018
Category:	Documents
Upload:	drilling-moneytree
View:	216 times
Download:	0 times

Optimization of Well Placement Andor Borehole Trajectory for Minimum Drilling Cost- GOOD

Documents