The Robert Gordon University, Aberdeen

School of Engineering

MSc Oil and Gas Engineering

Challenges and developments in direct measurement of down hole forces

affecting drilling efficiency

Duncan J Junor (0210305) September 2007

Challenges and developments in direct measurement of down hole forces affecting drilling

efficiency

Duncan James Junor

This report is submitted in partial fulfillment of the requirements for the degree of Master of Science in

Oil and Gas Engineering at the Robert Gordon University, Aberdeen

i

Robert Gordon University

A b s t r a c t

Challenges and developments in direct measurement of down hole forces affecting drilling efficiency

Duncan James Junor

A thesis presented on the techniques deployed to measure forces experienced by

the bottom hole assembly (BHA) during drilling operations and their effects on

drilling efficiency.

The primary forces under investigation include weight, torque and bending on bit

which are parameters known to be important factors in determining the direction,

rotation, and rate of drilling.

The analysis and modeling of drilling dynamics and associated dysfunctions is

presented along with the impact on drilling efficiency and methods to detect and

remedy these issues to optimize drilling efficiency.

Strain and derived stress relationships are reviewed, along with the application of

strain gauge technology to measure the lateral, axial, and torsional strains

experienced during rotary drilling operations. Further review is presented on the

application of strain gauges to measurement subs within the BHA which are

specifically designed to accurately measure the specified strains, and derive the

associated forces through calculation.

An assessment in development of down hole telemetry techniques is briefly

presented, along with potential implications on improving predictive modeling

accuracy through enhanced real time data availability at the surface and the

possibility for future automated drilling techniques.

ii

ACKNOWLEDGMENTS

The author wishes to express sincere appreciation to Ken McDonald, Jez

Greenwood and Kevin Glass for their assistance and guidance in the preparation

of this thesis. In addition, special thanks to Rick Hay and John Snyder whose

familiarity with the needs and ideas of the area of study was helpful during the

early research phase of this undertaking. Thanks also to my family and colleagues

for their encouragement and understanding during preparation of this thesis.

iii

TABLE OF CONTENTS

Abstract............................................................................................................................ i Acknowledgments....................................................................................................... ii Table of Contents ....................................................................................................... iii List of figures ............................................................................................................... iv List of Tables ................................................................................................................ v List of symbols, abbreviations, nomenclature.................................................. vi Chapter 1......................................................................................................................... 1

1.0 Introduction ............................................................................................... 1 1.1 Statement of the problem................................................................. 1 1.2 Research Approach............................................................................ 1

Chapter 2 ........................................................................................................................ 3 2.0 Drilling Efficiency and Dynamics .......................................................... 3

2.1 Overview.............................................................................................. 3 2.2 Evaluation of Drilling Dynamics and Associated Challenges ... 3 2.3 Drilling Hydraulics........................................................................... 12 2.4 Bit Cutting Efficiency...................................................................... 13 2.5 Surface measurement techniques .................................................. 24

Chapter 3 ...................................................................................................................... 26 3.0 Principles of strain/stress and measurement techniques................. 26

3.1 Definitions of Strain and Stress..................................................... 26 3.2 Mohr’s Circles ................................................................................... 34 3.3 Strain Gauges .................................................................................... 35

Chapter 4 ...................................................................................................................... 43 4.0 Application to Downhole measurement............................................. 43

4.1 WOB/TOB/BOB measurement devices. .................................. 43 Chapter 5 ...................................................................................................................... 54

5.0 The impact of advanced telemetry on drilling efficiency................. 54 5.1 Traditional Down-hole telemetry methods................................. 55 5.2 Intelligent/Wired Pipe .................................................................... 56 5.3 Implications on drilling dynamics, MWD and LWD................ 57

Chapter 6 ...................................................................................................................... 60 6.0 Findings and Discussion ........................................................................ 60

6.1 Description of Findings .................................................................. 60 6.2 Thesis.................................................................................................. 63

List of Equations ....................................................................................................... 65 References & Bibliography.................................................................................... 69

iv

LIST OF FIGURES

Figure 2-1: Examples of twist-off failures of the drill string.................................. 4

Figure 2-2: Problems associated with wellbore stability while drilling. ................ 5

Figure 2-3: Triaxial shock and vibration .................................................................... 6

Figure 2-4: Forward and Backward Bit whirl............................................................ 7

Figure 2-5: Examples of PDC bit damage from backward whirl ......................... 8

Figure 2-6: Balled Bit ................................................................................................... 12

Figure 2-7: Worn Bit Examples................................................................................. 13

Figure 2-8: Example Drill-Off test data .................................................................. 18

Figure 2-9: Example of Founder point and relationship to bit performance .. 20

Figure 2-10: Example analysis of MSE and Drilling Efficiency attributes (Rock Strength and Bit work/Torque (Halliburton SPARTA output - © All rights reserved).............................................................. 22

Figure 2-11: Example analysis of MSE and Drilling Efficiency attributes (Bit efficiency and Optimal WOB/RPM/ROP) (Halliburton SPARTA output © All rights reserved) .............................................. 23

Figure 3-1: Basic strain ................................................................................................ 27

Figure 3-2: Poisson Strain........................................................................................... 28

Figure 3-3: Shearing Strain ......................................................................................... 28

Figure 3-4: Normal Stress........................................................................................... 29

Figure 3-5: Stress/Strain relationship and elasticity............................................... 30

Figure 3-6: Mohr’s circle representation of Normal, Biaxial and Triaxial stress systems............................................................................................ 34

Figure 3-7: Metallic foil gauge.................................................................................... 35

Figure 3-8 Wheatstone bridge circuit ....................................................................... 38

Figure 3-9: Axial strain configurations ..................................................................... 41

Figure 3-10: Bending Strain configurations............................................................. 42

v

Figure 3-11: Torsional/Shear strain configurations............................................... 42

Figure 4-1: Diagram showing layout of force measuring sleeve/loop............... 45

Figure 4-2: Layout showing load cell insert configuration of DAS patent........ 46

Figure 4-3: Example of radial pocket and strain gauge insert configuration. ... 47

Figure 4-4: Effect on gauges during pure axial compressive load (WOB Measurement)........................................................................................... 47

Figure 4-5: Effect on gauges during pure axial tension load (WOB Measurement)........................................................................................... 48

Figure 4-6: Effects on gauges of pure torsional load (TOB measurement)...... 49

Figure 4-7: Summary definition of Woloson ‘Drilling Efficiency Sensor’ apparatus. .................................................................................................. 50

Figure 5-1: Example real-time data analysis application. ...................................... 54

Figure 5-2: Configuration of IntelliServ™ Network wired pipe......................... 56

LIST OF TABLES

Table 2-1: Summary of drilling dysfunctions, detection and mitigation actions. ....................................................................................................... 10

Table 3-1: Example bonding adhesives based on temperature ranges .............. 37

vi

LIST OF SYMBOLS, ABBREVIATIONS, NOMENCLATURE

Abbreviations

BHA – Bottom-Hole Assembly RTD – Resistive Temperature Detector

BOB – Bending On Bit SPE – Society of Petroleum Engineers

BUR – Build Up Rate SPP – Standpipe Pressure

DDS – Drilling Dynamics Sensor TOB – Torque On Bit

DES – Drilling Efficiency Sensor TD – Total Depth (well)

DLS – Dog Leg Severity WBM – Water Based Mud

DOC – Depth of Cut WOB – Weight On Bit

ECD – Equivalent Circulating Density WTB – WOB/TOB/BOB

EM – Electro-Magnetic (Telemetry)

FDP – Exxon Fast Drill Process

IADC – International Association of Drilling Contractors

KB – Kelly Bushing

LWD – Logging While Drilling

MWD – Measurement While Drilling

NPT – Non Productive Time

OBM – Oil Based Mud

PDC – Polycrystalline Diamond Compact bit

RC – Roller Cone Bit

RPM – Revolutions Per Minute

ROP – Rate of Penetration

RSS – Rotary Steerable System (Drilling)

vii

Symbols

π - Mathematical Constant (3.14159)

µ - Coefficient of friction

σ - Stress

ε - Strain

ν - Poisson Ratio

γ - Shearing Strain

τ - Shear Stress

G - Shear Modulus

Z - Section Modulus

MB - Bending Moment

F - Force

I - Second moment of area

J - Polar second moment of area

V - Voltage

1

C h a p t e r 1

1.0 INTRODUCTION

The purpose of this thesis is to examine the forces exerted on the drill string BHA

and methods utilized to measure Weight, Torque and Bending on bit as required

to better understand and influence drilling dysfunctions which often increase non

productive time (NPT) and limit efficient drilling of the well.

1.1 Statement of the problem.

The forces on the BHA components are known to be important factors in

maintaining drilling efficiency and in determining the direction, rotation, and rate

of drilling. Weight On Bit, (WOB) Torque On Bit, (TOB) and Bending On Bit,

(BOB) are specific forces which act on the BHA. Methods of measuring these

attributes range from implied calculations from surface data (for WOB/TOB) to

direct real time down hole measurement with sensors located close to the bit in

drill string subs. Accurate real time measurements allow monitoring of attributes

and direct correlation to predictive models. Interpretation of real time results

improves efficiency of the directional drilling process which is becoming prevalent

in a larger percentage of wells being drilled today. Present methods rely largely on

WOB and TOB measurements which are calculated from hook loads and surface

measurements of torque. These measures offer an indication of what is actually

happening at the drill face, but not accurately enough to consistently manage and

optimize ROP and hole quality.

1.2 Research Approach

A thorough literature search was undertaken to examine current understanding

associated with drilling dynamics and associated measurement techniques.

Sources included services and technology company web sites, society papers

(predominantly Society of Petroleum Engineers SPE), patent and patent

2

applications (describing variants of measurement devices), specific strain gauge

vendor literature , Halliburton company prior knowledge and learning materials on

the elements and technology used to combat vibration and improve drilling

efficiency.

A key element of measurement revolves around real-time data capture and

analysis. Prior knowledge and experience in this field has developed significantly in

the past 10 years and is now a de facto standard in the industry. The availability of

real-time transmission of data to the surface is a pre-requisite to enabling a near bit

WOB/TOB/BOB (WTB) solution. Prior methods of delivering real-time data

capture techniques are discussed in terms of the current restrictions affecting the

desired measurement. Significant advances have been made recently in the field of

enhanced bandwidth data transmissions techniques with wired pipe offerings

which have been researched in terms of the potential applicability to enhanced

WTB and therefore drilling efficiency capabilities.

It became evident in early research that simple metal or foil strain gauge

technology and know how has proven effective to date in measuring the desired

forces. Focus was therefore placed on detailed research of Wheatstone bridge

configurations and latest thinking on orientation, configuration and attachment of

these gauges to the drill string to optimize effective and accurate measurements.

Research was undertaken around the elements of configuration, reliability,

accuracy, and overall operating parameters for strain gauge technology and

application to WTB measurement. Known challenges include the management and

compensation for temperature and differential pressure fluctuations, gauge

mounting techniques, and general methods of calibration

3

C h a p t e r 2

2.0 DRILLING EFFICIENCY AND DYNAMICS

2.1 Overview

Although the primary focus of the thesis applies to WOB/TOB/BOB, wider

research was required on drilling efficiency/dynamics, measurement while drilling

(MWD) and real-time data capture and analysis techniques. Sources of data

included service company websites, gauge and down hole equipment vendor

literature, SPE and IADC published papers and published patents and patent

applications.

2.2 Evaluation of Drilling Dynamics and Associated Challenges

Given the increasing cost of daily rig rates, operators, service companies and

drilling contractors alike are increasingly analyzing methods to improve drilling

efficiency by reducing non productive time (NPT), and maximizing the rate of

penetration (ROP) through the formations being drilled. Drillstring vibration is a

significant contributor to NPT.

Drill string vibration reflects the basic physics of resonance at the natural

frequency of the object (in this case the drill string and associated bottom-hole

assembly (BHA)) along with the subsequent harmonics which cause natural

vibration. Understanding the natural frequency for each element of the drill string

determines which frequencies to recognize and manage during the drilling

operation. Changing drilling parameters serves to change the frequency away from

the natural frequency of the element which is causing undesired vibration.

The drill string and BHA configuration can be designed to minimize anticipated

resonance, for example through the use of stabilizers located at certain points

along the BHA, these however can cause their own issues in terms of sticking and

increasing down hole torque. It is often difficult to recognize what the cause of the

4

down hole issue is without accurate measurements of the forces on the drill string

at the BHA.

The term “Drilling Dynamics” is often used to refer to these ‘triaxial’ vibration

forces in motion during the drilling activity. These vibrations cause significant

damage to drillstring components and reduce the efficiency of drilling in terms of

hole quality and rate of penetration.

The effects of vibration can be categorized in two broad areas:

• Damage to the drillstring components

• Damage to the wellbore

Damage to drillstring components incur lost drilling time associated with tripping

out to repair and or replace components and include:

• Damage to sensitive electronic Measurement While Drilling (MWD) and

Logging While Drilling (LWD) equipment

• Premature Bit Failure (Excessive wear, broken cutters and/or cones)

• Wear on tool joints, stabilizers and other down hole assemblies in the drill

string

• Twist-offs where the drillstring breaks down hole due to fatigue or

excessive torque (Refer to Figure 2-1 below)

• Poor control of the deviation/direction of the well due to a lack of

accurate understanding of the tool face position and stresses.

Figure 2-1: Examples of twist-off failures of the drill string1

1 Courtesy of Halliburton – Sperry Drilling Services ©All rights reserved

5

Damage to the wellbore itself, which can reduce ROP and restrict the ability to

complete the drilling of the well to total depth (TD). Examples include:

• Breakout

• Washouts

• Fracturing

• Sloughing and caving

• Hole enlargement

Figure 2-2: Problems associated with wellbore stability while drilling.

Figure 2-2 demonstrates examples of wellbore instability along with their stress

field locations within the Mohr-Coulomb failure envelope2. The careful modeling

and prediction of stress fields assists the drilling process by planning actions to

minimize failure, unplanned vibration events therefore significantly impact the

anticipated wellbore stability characteristics, for example hole enlargement

associated with excessive bit and BHA whirl, or washouts and fracturing due to

contact of the drillstring with the wellbore or high localized pressures.

2 Economides M J, et al, 'Petroleum Well Construction', John Wiley and Sons, 1998 ISBN: 0-471-96938-9

6

It is important therefore to review each element of vibration, their effects,

methods of detection and actions to control the specific vibration when

encountered. Figure 2-3 shows the three types of vibration experienced during

drilling.

Figure 2-3: Triaxial shock and vibration

2.2.1 Axial Vibrations (Bit Bounce/Chatter)

This occurs when axial vibrations cause the bit, (and therefore drill string), to

vibrate or bounce on the formation. It can be due to several things including

variation on the WOB, changes in mud pressure and the interaction of the bit

cutting structure on the formation (i.e. interaction with stringers, ledges, hard rock

formations etc.) Bit bounce is typically encountered with roller cone bits which

exhibit an unstable bottom hole pattern.

Bit Chatter refers to the high-frequency resonance of the bit and BHA typically

caused by PDC bits due to blade and or cutter interaction with the formation.

Bit Bounce frequency is between 1 and 10 Hz and Bit Chatter frequency is

between 50 and 350 Hz

Axial Vibration

Lateral Vibration Torsional

Vibration

7

2.2.2 Lateral Vibrations (Bit/BHA Whirl)

Lateral vibrations are experienced at right angles to the drillstring and are

commonly referenced as ‘Bit Whirl’ or ‘BHA Whirl’ where the lateral vibration

causes a bending vibration in the BHA. Whirl can manifest itself in both forward

and backward directions.

Figure 2-4: Forward and Backward Bit whirl.

Bit Whirl is described as an eccentric rotation of the bit about a point other than

its geometric center and is shown in figure 2-4. Bit whirl can be further categorized

as forward whirl or backward whirl. Forward whirl is where the vibration causes

movement of the bit around the hole in the same direction as the rotation of the

bit (i.e. clockwise).

Backward whirl is more complex and results in the backward rotation of

circumferential points of contact, (e.g. the back of the fixed cutter blade), which

creates a rotation around the hole in the opposite direction to the rotation of the

bit, (i.e. anticlockwise, whilst the drill string rotates clockwise). The right hand

section of figure 2-4 shows the pattern created by the path of the blade tip as the

irregular force on the back of the blade causes the blade to briefly rotate

anticlockwise before the next blade engages the formation.

Whirl creates an over gauge bore hole which further propagates the detrimental

effects if not detected and remedied. Bit whirl, particularly backward whirl, causes

Eccentric Rotation about a point other than the geometric center

Forward Whirl – In direction of bit rotation (Clockwise)

Backward Whirl – blade tips rotate opposite direction of bit rotation (Anticlockwise)

Clockwise rotation of bit (viewed from below)

Over gaugewellbore

Path of blade on impact

Path of blade tip around wellbore

8

significant damage to PDC bits due to high and irregular impact loads, also it will

exhibit off center wear in roller cone bits. Figure 2-5 shows examples of the cutter

damage which can be attributable to backward whirl as well as other factors such

as excessive torque. Damage to the rear of the blades is also a telltale sign of bit

whirl.

Figure 2-5: Examples of PDC bit damage from backward whirl3

BHA Whirl is described as an eccentric rotation of the BHA about a point other

than its geometric center and is related to onset of Bit whirl or visa versa. BHA

whirl can also change the tilt or orientation of the bit causing the bit to whirl. BHA

whirl causes the BHA to buckle in a sinusoidal shape and has several detrimental

effects including fatigue or failure of the components, additional friction forces

due to borehole contact, (leading to hole enlargement, washouts and potential lost

circulation) and significant shock and vibration of sensitive LWD /MWD sensors.

Whirl frequency is between 10-100 Hz for the bit, and 5-20 Hz for the BHA.

2.2.3 Torsional Vibrations (Stick Slip)

Stick-slip describes the situation where the drillstring stops or slows down rotation

to a point where the drill string torques up and rapid releases energy once the BHA

and bit free up and begin rotation again. Due to the built up torque the string

rotates significantly faster than the nominal rpm during the slip phase. Stick-Slip is

3 Courtesy of Halliburton – Security DBS © All rights reserved

Chipped CutterBroken

Cutters

9

caused largely by interaction with the formation and frictional forces between the

drillstring, BHA and the Wellbore, environments which become increasingly

common in highly deviated and deep wells.

Stick-Slip frequency is less than 1 Hz

2.2.4 Coupling

Coupling describes the process where the presence of one vibration mode

instigates another, to the extent that all 3 modes can be exhibited in the string at

the same time. This can often happen where the initial vibration mode is not

detected or managed, leading to undesirable effects on the drilling process and

potential for catastrophic failure of the drill string.

2.2.5 Mitigation

In general the occurrence of drilling dysfunctions can be mitigated either through

surface techniques or changes to down hole configurations.

Surface techniques include changing WOB or RPM parameters, modifying mud

rheology or utilizing top drive soft torque systems which monitor and increase

RPM to reduce torque. (It should be noted that soft torque systems can also prove

problematic in the management of drilling dysfunctions as the attempt to

automatically manage stick/slip conditions, for example soft torque adjustment,

can over/under compensate and further propagate vibration and therefore the

original slick/slip condition)

Down hole configuration techniques require tripping out of the hole and changing

BHA configurations including bits, stabilizers, changing from RSS to mud motor

configurations adding vibration subs etc, all of which are costly in terms of NPT

and want to be avoided wherever possible.

Table 2-1 on pages 10 and 11 show details of each of the drilling dysfunctions

along with typical actions to mitigate the problem once identified.

10

Table 2-1: Summary of drilling dysfunctions, detection and mitigation actions.

Drilling

Dysfunction

Attributable

Conditions

Detection &

Damage

Mitigation

Action

Bit Whirl

(Lateral Vibration)

(Freq. 10-100 Hz)

Predominantly due to Bit/BHA interaction with

wellbore.

Also high ROP/low WOB, misalignment,

imbalance, changes in formation hardness/bit

formation interaction

Detected thru increased torque, high frequency

lateral or torsional vibration and reduced ROP.

Leads to cutter damage, over-gauge hole

Increase WOB

Reduce RPM

Pickup off bottom and re-start with lower RPM

BHA Whirl

(Lateral Vibration)

(Freq. 5-20 Hz)

Predominantly mass imbalance and resonance of

BHA at critical RPM’s

Detected thru increased torque, increased MWD

shocks, high frequency lateral or torsional

vibration and reduced/erratic ROP

Leads to twist offs, washout, tool joint wear and

stabilizer damage.

Adjust RPM to reduce harmonic resonance.

Pickup off bottom and re-start with lower RPM

Stick-Slip

(Torsional Vibration)

(Freq. <1 Hz)

Predominantly due to Bit/BHA interaction with

wellbore.

Also use of aggressive PDC bit and high WOB

and hard formations

Detected thru reduced/erratic ROP, poor

directional control, torque fluctuation/cyclicity

and MWD shocks

Leads to over-torque or back-off of connections,

twist off, washouts, cutter impact damage

Decrease WOB

Increase RPM

Increase mud lubricity

Pickup off bottom to allow torsional energy to release and drill with higher RPM / Lower WOB

11

Bit Bounce

(Axial Vibration)

(Freq. 1 - 10 Hz)

Predominantly associated with roller cone bits

exhibiting unstable tri-lobe bottom hole pattern

Also hard rock environments, stringers, and

under gauge holes

Detected thru reduced ROP, fluctuation in WOB

and surface/KB vibration.

Leads to twist off, washout and cutter impact

damage

Reduce RPM

Increase WOB

Pickup off bottom and restart to re-establish preferable bottom-hole pattern

Utilize shock tool in drillstring

Bit Chatter

(Lateral Vibration)

(Freq. 50-350Hz)

Predominantly associated with PDC bits in high

compressive strength formations.

Not detectable at surface

Leads to cutter damage, failure of sensitive

electronics in MWD/LWD equipment and the

onset of bit whirl

Adjust RPM/WOB to reduce harmonic resonance.

Coupling

(Axial, Lateral,

Torsional Vibration)

(Freq. 0-20 Hz)

Predominantly associated with the failure to

identify and control one of the above vibration

conditions to the extent that other vibrations are

initiated simultaneously

Increase in torque, poor directional control,

reduced or erratic ROP and mud pulse telemetry

interference.

Leads to M/LWD Failure, cutter damage,

drillstring wear/fatigue & twist off/washouts

Pickup off bottom and restart with modified WOB/RPM

Reconfigure BHA and/or stabilization methods

12

2.3 Drilling Hydraulics

Other attributes which have a significant effect in drilling efficiency include mud

hydraulics and rheology including ECD measurement, hole cleaning efficiency,

washouts, and optimization at the bit for hydraulic horsepower or impact force. It

is important in terms of WOB, TOB and ROP measurement to determine if the

dysfunction is vibration related, hydraulic related or a combination thereof. In

addition, the mud type and rheology can influence the onset of certain drilling

dysfunctions, such as stick-slip for example.

2.3.1 Bit/Bottom Balling

One of the most common issues associated with hydraulics is bit/bottom balling.

Bit Balling is often a phenomenon when drilling shale formations with Water

Based Mud (WBM) a reduction in ROP is experienced due to the bit being clogged

with clay cuttings.

Figure 2-6: Balled Bit

Figure 2-6 shows an example of a balled PDC bit.4 Bottom hole

balling can occur in conditions with high WOB and high

bottom hole pressure/high mud weight where a layer of

hydrated shale prevents cutting action on the formation.

Methods of identifying balling include:

• Application of increased WOB does not realize a change in ROP or

reduces ROP

• Increased stand pipe pressure (SPP) without associated increase in flow

• Comparing actual vs predicted Mechanical Specific Energy (MSE) (which

is explained in more detail later in the thesis), or identifying a reduction in

torque at the bit.

Bit and bottom hole balling can be mitigated through design of WBM with greater

lubricity or selection of appropriately designed PDC bits optimized for hydraulic

4 Courtesy of Halliburton – Security DBS © All rights reserved

13

horsepower. Once ROP reduction is identified WOB should be reduced and the

bit picked up off bottom as soon as possible. Actions should be taken to clear the

bit such as increasing flow rate, or spinning the bit off bottom at a relatively high

RPM to remove the caking of cuttings and formation materials.

2.4 Bit Cutting Efficiency

When the bit is actually cutting the rock formation it is important to predict and

monitor the bit performance and determine when the bit has reached its useful life

expectancy. The understanding of cutting performance and therefore the

associated ROP depends on a number of factors. Figure 2-7 shows examples of

worn PDC and RC bits.

Figure 2-7: Worn Bit Examples.5

2.4.1 Rock Strength

A significant influence on drilling efficiency is obviously attributable to

understanding and predicting the rock strength and associated rock stresses that

the drillstring will encounter during drilling. The term GeoMechanics is used to

refer to the analysis of rock data derived from various sources including down hole

logs, core analysis and analog geological data. Geomechanical models are

developed to accomplish this prediction/understanding by analyzing expected

lithology, rock strength and shale plasticity of the expected geology and

formations. The understanding of Geomechanics not only improves the drilling

efficiency, but also ensures that the stability of the wellbore is maintained and that

unexpected wellbore collapse events are not encountered. It is not the purpose of

this thesis to describe detailed Geomechanical processes, however there are some

significant elements of this understanding that allows drillers to optimize ROP by

determining appropriate WOB and RPM limits. Mechanical Efficiency is a

5 Courtesy of Halliburton – Security DBS © All rights reserved

14

modeling method which is beginning to gain traction in the industry and to

provide the link between Geomechanical modeling and management of the

numerous drilling dynamics described above.

2.4.2 Mechanical Specific Energy (MSE)

MSE predominantly relates to the efficiency of the bit and is defined as:

o The rock strength divided by specific energy applied to the bit (i.e. the ratio of

input energy to the ROP) or

o The measure of energy required to destruct a given volume of rock;

To determine MSE, the specific energy must first be calculated.

Specific Energy (Es) is defined as the total bit force divided by the cross sectional

area of the bit, in the simplest terms:

Specific Energy = )(in area sectional crossBit

(lbf) ForceBit Total)( 2=psiEs ...........................................(2-1)

Given this Mechanical Efficiency or MSE is defined as:

ROPOutput EnergyInput )( ≈psiMSE ...................................................................................................................(2-2)

In theory the MSE ratio should be constant for a given rock compressive strength

and therefore the energy required to destroy the rock should also be constant

assuming that the bit efficiency remains constant.

The concept of MSE was originally proposed by Teale in 19656 where he defined

the following equations for predicting MSE:

Specific Energy = ROPA

TNA

WOBEsbitbit *

***120 π+= ......................................................................(2-3)

6 Teale, R.: “The Concept of Specific Energy in Rock Drilling”, Intl. J. Rock Mech. Mining Sci. (1965) 2, 57-73

15

Also Specific Energy Es = ⎟⎟⎠

⎞⎜⎜⎝

⎛+

ROPDN

AWOB

bitbit *33.131 µ

..........................................................(2-4)

Where:

Es = Specific Energy, psi

Abit = Bit Area, Sq. Inches

Dbit = Bit Diameter Inches

N = RPM

T= Torque, ft-lbs

ROP = ft/hr

µ = Coefficient of Friction

Torque is an important measurement in the MSE calculations. Given that the

WOB, RPM and ROP calculations are taken at surface, a coefficient of sliding

friction (µ) is determined for each bit. This allows the expression of torque as a

function of WOB. The coefficient of sliding friction (µ) defined as:

Coefficient of Friction =WOBD

Torque

bit *36=µ ..............................................................................(2-5)

And therefore:

36*WOBD

Torque bitµ= ............................................................................................................................(2-6)

And Mechanical Efficiency (EFFM) is defined as:

EsEsEFFM

min= ...............................................................................................................................................(2-7)

Where Esmin approximates the compressive strength (σ) of the rock (psi). (i.e. the

minimum specific energy required to overcome the rock strength)

Therefore Mechanical Efficiency (0-100%) is also equal to

100*Es

EFFMσ

= ........................................................................................................................................(2-8)

16

And maximum efficiency occurs where 1min ≈Es

Es

Teale’s equations considered rotary drilling at atmospheric conditions, subsequent

work undertaken by Pessier et al (described in SPE 245847) validated these findings

when drilling under hydrostatic pressure and by Dupriest et al (described in IPTC

106078) which resulted in the following equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ROPATRPM

AWOBpsiMSE

BITBIT ****120*35.0)( π

................................................................(2-9)

Where 0.35 represents a practical efficiency factor for the bit in field conditions

and is often referred to as the mechanical efficiency factor EFFM

2.4.3 Bit Torque/WOB relationship

The calculation of MSE enables the prediction of how efficient a bit will be in a

particular formation, having understood the rock strengths and associated rock

mechanics. The cutting action and efficiency of the bit is a function of the actual

cutting torque, a bit will be at its most efficient when new (assuming it is designed

correctly) and conversely be least efficient when the bit is dull and the cutting

structure is significantly worn.

Obviously not all of the torque applied to the BHA and bit is directly converted to

cutting action; significant amounts are dissipated as friction either as a result of

insufficient WOB or insufficient cutting capacity of the bit. There are several

thresholds to consider, the first is associated with sufficient WOB to overcome the

initial friction as the bit engages the formation, once this threshold is overcome the

cutting efficiency will increase relative to applied WOB. Once ROP is initiated,

there is a second threshold where the maximum mechanical efficiency and

therefore the maximum cutting action are achieved. At this point further increases

in WOB will not realize corresponding increases in ROP because the bit has

reached its cutting limitation, in fact increases in WOB will increase friction losses

and potentially increase bit wear and reduce MSE.

7 SPE 24584 - Quantifying Common Drilling Problems With Mechanical Specific Energy and a Bit-Specific

Coefficient of Sliding Friction. (R.C. Pessier, Hughes Tool Co., and M.J. Fear, BP Exploration) 8 IPTC 10607 - Maximizing ROP with Real-Time Analysis of Digital Data and MSE. F.E.Dupriest, SPE, Exxon Mobil, and J.W. Witt, SPE, and S.M. Remmert, SPE, Rasgas Co. Ltd.

17

A third threshold relates to the condition where all the torque is applied to

overcoming friction, and therefore none is applied to cutting, increases in WOB

and therefore torque will not realize increased ROP because the bit has no capacity

to cut the formation, or because other drilling dysfunctions are preventing ROP.

Given the above, the behavior of each bit can be modeled to predict the

percentages of torque being applied to cutting vs being lost to friction. Modeling

can predict the maximum theoretical Depth Of Cut (DOC) per revolution and

therefore ROP at a given WOB; this is an important factor in understanding what

the bit performance should be and how to identify trends which are inconsistent

with the predicted performance. (Figure 2-9 on page 20 further describes bit

performance relationships)

2.4.4 Modeling Constraints

As stated previously the MSE calculation is typically made with surface data for

WOB, RPM and ROP as well as calculated torque values.

Given drilling dynamics, friction and associated conditions down hole, the actual

MSE value can change significantly from the calculated value.

In addition there are a number of operational rig constraints that impact MSE

including maximum available WOB/TOB, maximum ROP and minimum RPM.

With these constraints considered, there is a practical WOB maximum threshold

that, if exceeded, will reduce mechanical efficiency and increase friction rather than

cutting torque. This practical WOB maximum is significantly less than the

theoretical maximum, and as described earlier, will change as the condition of the

bit changes and other drilling dysfunctions present themselves.

2.4.5 Drill-Off Test

As described previously, there is an expected optimum weight on bit for each well

and specific formation being drilled. The determination of this optimal WOB can

be achieved through several methods, some of which are more reliable than others.

The “drill off” test is a process that involves the application of a high WOB with

the brake locked to prevent the top of the drillstring string from advancing while

continuing to circulate and rotate. This procedure allows the bit to make hole and

18

stretch the string which in turn reduces the WOB. Based on Hooke’s law of

elasticity the ROP response is calculated from the change in the rate of drill string

elongation as the weight declines9. This is based on the following equation:

tEAWL

tWROP

S ∆∆

=∆∆

=*

* .............................................................................................. (2-10)

Where:

W = WOB,

t = time,

L = length of drill pipe,

E = Modulus of Elasticity of drill pipe,

AS = Cross sectional area of the drill pipe

Figure 2-8: Example Drill-Off test data 10

9 SPE/IADC 92194 - Maximizing Drill Rates with Real-Time Surveillance of Mechanical Specific Energy. Fred

E. Dupriest, SPE, ExxonMobil and William L. Koederitz, SPE, M/D Totco, a Varco Company 10 SPE/IADC 92194 - Maximizing Drill Rates with Real-Time Surveillance of Mechanical Specific Energy.

Fred E. Dupriest, SPE, ExxonMobil and William L. Koederitz, SPE, M/D Totco, a Varco Company

Drill Off Test Data

0

5

10

15

20

25

30

35

40

45

42 44 46 48 50 52 54

WOB (klbs)

RO

P (f

t/hr)

80 RPM 70 RPM 60 RPM

Optimal WOB (Founder Point)

19

By measuring the time it takes to drill off the weight on bit at regular intervals (e.g.

2,000lbs) and plotting ROP against WOB or WOB against time (seconds) an

optimal WOB can be derived.

The tests are repeated at varying RPM settings in order to assess the optimal RPM

and WOB settings for the given formation.

Figure 2-8 show plots of data taken at 2,000 lbs WOB intervals and indicates a

linear response up to the optimal WOB point where the ROP stops responding

linearly to increases in WOB.

The drill off test allows a driller to test the drillability of the formation and

calculate the required WOB to optimize ROP as well and predict the expected bit

wear. Although this process is functional, it is time consuming and can provide

varied results.

2.4.6 Founder Point

The “flounder” or “founder” point refers to the point during drilling11 at which the

ROP stops responding linearly with increasing WOB, i.e. where the increase in

WOB does not realize equivalent increases in ROP.

It is important to understand the founder point in order to minimize the bit wear

and maximize the ROP. The causes of founder are predominantly inefficiencies

associated with the drilling dysfunctions described above including hydraulics (hole

cleaning/cuttings), balling, vibration, damaged/worn bits and rig constraints.

Founder point thresholds can be predicted and when encountered, raised to allow

more efficient drilling by understanding the attribute leading to the founder and

adjusting accordingly. For example, by increasing pump rate and flow the

associated improvement in hole cleaning will lead to a reduction in bit balling and

therefore raise the founder point to realize more efficient drilling.

Figure 2-9 describes the relationship of ROP and WOB, respective regions of

performance (described in section 2.4.3) and founder point(s)

11 Proposed by A.Lubinski – January 1958 edition of “The Petroleum Engineer” – Proposal for future tests.

20

Figure 2-9: Example of Founder point and relationship to bit performance 12

2.4.7 MSE summary

Over the years MSE has gathered momentum as a best practice in terms of

predicting, monitoring and improving drilling efficiency, ExxonMobil, for

example, places significant emphasis on understanding MSE within their Fast Drill

Process (FDP) for ROP efficiency13. The advent and acceptance of real-time

monitoring techniques at surface has improved the automation and control of the

various rig attributes to manage WOB, TOB and RPM and therefore maximize

potential ROP.

The opportunity being realized today is the next wave in accuracy associated with

real-time down hole measurement of actual WOB/TOB and BOB as close to the

bit as possible. These measurements significantly improve the predictive model

12 SPE/IADC 92194 - Maximizing Drill Rates with Real-Time Surveillance of Mechanical Specific Energy.

Fred E. Dupriest, SPE, ExxonMobil and William L. Koederitz, SPE, M/D Totco, a Varco Company 13 SPE 102210 - Comprehensive Drill Rate Management Process to Maximize Rate of Penetration.

F.E.Dupriest, Exxon Mobil Development Co.

ROP

WOB

Region II: Efficient Bit

Region I: Inadequate Depth of Cut (DOC)

Enhanced performance

achieved by altering design to raise founder point

Region III: Founder, due to various drilling dysfunctions

Potential Performance: Assuming optimized

efficiency

21

accuracy and allow real time identification and management of drilling

dysfunctions as they present themselves.

Figures 2-10 and 2-11 on the following pages show example analysis of input and

modeling/prediction of MSE and associated attributes from Halliburton’s

SPARTA integrated suite of modeling applications14.

Explanation of each column is given in the notes of each track of information

from derived rock strength parameters through predicted bit performance and

optimal WOB, TOB, RPM and ROP parameters necessary to optimize drilling

efficiency.

These models predict and monitor performance based on surface derived

calculations of WOB and TOB values rather than down hole measured values. As

will become evident later in this thesis, accurate real-time down hole WOB/TOB

measurements will deliver a stepped change efficiency gain in application of MSE

prediction theory.

14 Courtesy of Halliburton Company – Security DBS SPARTA analysis. © All rights reserved

22

Figure 2-10: Example analysis of MSE and Drilling Efficiency attributes (Rock Strength and Bit work/Torque (Halliburton SPARTA output - © All rights reserved)

Logs provide the primary data for

deriving rock strength

characteristics and can include NMR,

Gamma Ray, density, sonic etc.

logs

Lithology can be interpreted from

the logs and along with the percentage of each component

present at each respective depth

The porosity of the respective rock

types and column is an important attribute and is typically derived

from NMR, Neutron Density

and sonic porosity logs

Geomechanical analysis and the

understanding of the confined and unconfined rock

strength is a critical element in

determining the energy required at

the bit to cut efficiently

The understanding of shale plasticity

includes analysis of shale volume, type & water content as

derived from several logs. This

assists in prediction of bit balling

potential

The Specific Energy and

cumulative work done by the bit is

shown in this track

The total Torque On Bit and cutting torque are shown in this track, and

allows modeling of the torque-WOB

signature as the bit wears from new to

a dull state.

23

Figure 2-11: Example analysis of MSE and Drilling Efficiency attributes (Bit efficiency and Optimal WOB/RPM/ROP) (Halliburton SPARTA output © All rights reserved)

Mechanical Efficiency describes the cutting torque

as a % of the overall torque the remainder of the torque is lost to

friction or constrained by

operational parameters of the

drilling rig

Operational attributes of the

drilling rig introduce

constraints which limit Mechanical

Efficiency potential

Understanding the maximum power

limit of the bit for a given rock strength will allow optimal

ROP without damage to the bit. The limit may not

be achievable given rig operating constraints

Prediction of the optimal WOB

range recognizes all the bit

performance cutting potential and operating constraints as

required to maximize ROP

without exceeding the founder point

Modeling the optimal RPM can be achieved based on understanding the optimal WOB

potential.

The combination and optimization of MSE attributes can model and predict an optimum ROP for a given rock strength and rig

operational constraints

Bit wear can also be modeled based on understanding

all attributes. Iterative MSE

analysis can predict WOB/TOB/RPM settings based on understanding of

amount of bit wear and remaining

efficiency

24

2.5 Surface measurement techniques

2.5.1 WOB/TOB measurement

WOB can be measured at surface by comparing off-bottom and drilling hook load

weights; measurement of torque applied to the bit is measured at the surface in

terms of the rotary torque provided by the top drive or rotary table motor, typically

through measurement of the current draw on the motor, or in the case of hydraulic

driven systems measurement of pressure changes.

Dynamic measuring subs15, (containing torque meters, accelerometers and in

certain cases strain gauges with wireless connectivity) and similar devices have been

developed and utilized in certain configurations, usually located below the power

swivel or just above the Kelly Bushing, however the complexity and calibration

challenges of these devices have prevented them from seeing common use in the

industry.

Surface measurements are not always reliable, particularly in conditions such as

deviated or extended reach wells where borehole friction losses prevent the

transmission of the surface WOB to the BHA and bit at the formation being

drilled.

Torque and Drag analysis is carried out on the wellbore design in order to predict

the axial forces and expected torque and friction forces along the drill string. This

analysis is utilized to determine the feasibility of the well in terms of potential dog

leg severity (DLS) issues, what additional WOB is required to overcome

anticipated forces and at which point in the drilling process. The drilling of

deviated wells introduces additional challenges in predicting torque and drag

dependent on the actual vs. planned tortuosity and the propensity of the well to

spiral as it is drilled, further complicating friction losses and associated issues.

The objective of the driller is to maintain the optimal WOB and TOB as planned

but also to recognize events which may require a deviation from plan to maintain

efficient drilling. Originally this was achieved by manually controlling the draw

works brake to maintain the weight on the weight indicator at the drill floor.

15 lADC/SPE 23888 - Surface Detection of Vibrations and Drilling Optimization : Field Experience by Henry HENNEUSE

25

Advances in electromagnetic and mechanical sensing devices coupled with

computer control and real-time monitoring techniques, have seen significant

acceptance from the industry with continuous display and alerts directly available

to the driller, reducing the complexity of data analysis and the associated decision

making process.

2.5.2 BOB Measurement

Bending at bit and BHA bending is important to determine the side

forces/stresses being encountered by the BHA and bit. As with MSE, torque and

drag and other important attributes, these forces are predicted and modeled to

ensure that potential issues with BHA reliability and dog leg severity (DLS) are

minimized during drilling.

Understanding bending strain and associated stresses on the bit can assist in

optimizing the design of the BHA in deviated wells, where the design of the gauge

length and depth of the bit and associated BHA configuration can be a limitation

in the build up rate (BUR) potential of the string.

Unlike WOB and TOB, bending forces can not be measured from the surface and

can only be measured down hole, preferably as close to the bit/BHA as possible.

The availability of BOB information also provides higher resolution wellbore

curvature data than traditional degree per 100ft survey techniques. For example

BOB measurement can detect high local doglegs where changes in formation types

are encountered which would not show up on a typical survey.

The measurement of the direction of bending stress in relation to the low side of

the hole is an important attribute to determining the direction of the drilling.

26

C h a p t e r 3

3.0 PRINCIPLES OF STRAIN/STRESS AND MEASUREMENT TECHNIQUES

Developments in MWD/LWD have progressed significantly in the past decade as

the requirement for directional wells and accurate well placement with geosteering

techniques has matured.

These increasingly complex wells exacerbated the drilling dysfunctions issues

described in chapter II and as a result necessitated technology developments in

down hole tools which measure the respective drilling dysfunctions, including

triaxial vibration, (with accelerometers), direction (with magnetometers), ECD with

(pressure sensors) and temperature (with temperature sensors)

These measurement systems are typically contained within a single sub which is

located as part of the BHA. Data is captured and relayed back to the surface in

real-time through Mud Pulse or appropriate EM telemetry methods (described in a

later chapter)

Progress in developing and delivering real-time WTB measurement down hole has

only been made in the past 5 years, however the technology used to measure each

attribute has been proven for decades and is relatively simple, it’s application in

harsh down hole environments is more challenging.

There are in excess of 80 patent applications describing WT or WTB tools, all of

them utilize the same fundamental strain gauge techniques with Wheatstone bridge

circuits.

3.1 Definitions of Strain and Stress.

The following section describes the basic physics of strain and is incorporated in

this thesis as a backgrounder to explain the fundamentals associated with

measurement of strain. The ability to measure strain allows derivation of stress and

therefore the forces experienced by an object. This section is important to the

overall understanding of how down hole force measurement is derived.

27

3.1.1 Strain

Strain ε is defined as deformation per unit length of a material in reaction to a

force.

Strain can either be tensile (positive) or compressive (negative) and can be defined

as the ratio of the change in length over the original length (for a simple object)

Therefore:

Strain = εLL∆

= ............................................................................................................. (3-1)

ε is typically dimensionless or with units of inch/inch or mm/mm, and expressed in terms of micro-strain (i.e. ε x10-6 or µε)

Figure 3-1: Basic strain

3.1.2 Poisson Strain

Poisson Strain refers to the response of an object to uniaxial forces resulting in

stretching of the object to the extent that the object elongates in the direction of

the forces and flattens in the direction transverse to the force. The Poisson ratio is

defined as the negative ratio of the strain in the transverse direction to the strain in

the longitudinal or axial section. i.e. Poisson Ratio =

Poisson Ratio =LLDD

axial

trans

//

straindirection alLongitudinstraindirection Transverse

∆∆

−=−=−=εεν .......(3-2)

Force Force

D

∆L L

εLL∆

=

28

Every material has a given Poisson ratio which ranges from 0.0 to 0.5, with 0.5

representing a material that is perfectly incompressible. For example steel has a

Poisson ratio of between 0.27 and 0.3, copper 0.33 and magnesium 0.35.

Figure 3-2: Poisson Strain

3.1.3 Shearing strain

Shearing strain refers to the measure of angular distortion on an object when a

force is applied and the deformation is perpendicular to original plane. Shear strain

γ is defined as the tangent of the angle created by the deformation from the

normal state.

Shearing Strain = Tan length original

nDeformatio φγ == .........................................................................(3-3)

Whereφ is the angle created by the deformation. Stress is measured in units of

force per unit area.

Figure 3-3: Shearing Strain

Force

φ

Force Force

D

L

L+∆L

D-∆D

29

3.1.4 Normal stress

Normal stress is defined as stress which is perpendicular or vertical to the plane of

the object as shown in figure: 3-4.

Normal Stress =AnFor

AreaForcelar Perpendicu

=σ ....................................................................(3-4)

Figure 3-4: Normal Stress

3.1.5 Shear stress

Shear stress is defined as the stress state where the stress is parallel to the plane:

Shear Stress =Aττ For

AreaForce Parallel

= ..........................................................................................(3-5)

Where both stresses are present, e.g. in a diagonal shear of an object, then both the

normal (σ) and shear (τ) components need to be calculated to reflect the overall

stress. (refer to Mohr’s circle biaxial/triaxial stress systems below)

3.1.6 Young’s Modulus

Young’s Modulus (modulus of elasticity) is a measure of the stiffness of a material

and is defined as the relationship of stress and strain or E.

The normal stress-strain relationship is defined as Hooke’s law where:

Force

Plane Area

Internal resisting Forces

30

Stress (σ)

Strain (ε)

Proportional Limit

Yield Point

Rupture Point

Ultimate Strength

Modulus of Elasticity (Straight Line)

Hooke’s Law: εσ *E= or εσ

=E ......................................................................................................(3-6)

And G = the relationship of shear stress and shear strain, and is referred to as the

modulus of rigidity or shear modulus:

Shear Modulus =γτ

==StrainShear StressShear G .........................................................................................(3-7)

The shear modulus can also be expressed as:

Shear Modulus =)2(1

Eν+

=G ..............................................................................................................(3-8)

(E=Modulus of Elasticity and ratio sPoisson'=ν )

Figure 3-5: Stress/Strain relationship and elasticity

When the stress and strain

measurements of a material are

plotted against each other a

graph is plotted as depicted in

Figure 3-5, the straight line

represents the modulus of

elasticity for the material (up to

the proportional limit), beyond

the yield point the materials

elasticity is exceeded and the

material will be permanently deformed (plastic deformation) until the ultimate

strength is reached after which the breaking point or rupture/failure point is

achieved. It should be noted that a materials modulus of elasticity may vary with

temperature, with each material varying to different amounts, this is important in

the selection of materials for given down hole temperature applications.

Given the basics of stress and strain, relationships can be made and equations

derived for bending strain, axial strain, torsional strain and shear strain, or

conversely if we can measure the strain we can calculate the force being applied to

the material at the point of measurement.

31

3.1.7 Bending forces

Bending strain (Moment Strain):

Bending Strain =E

BB

σε ==Elasticity of ModulusStress Bending

............................................................(3-9)

where σB is the moment stress and is equal to the bending moment (force x

length) divided by the sectional modulus (Z). The sectional modulus is a modulus

of a cross section of the object:

Sectional Modulus =(e)Gravity ofCenter of Distance(I) Inertia ofMoment lGeometrica

=Z (in3) ..........................(3-10)

For a drill string section for example:

Drill String section: String

StringString

ODIDOD

ODIZ

*32)(*2 44 −

== π (in3)........................................(3-11)

Given that:

Bending Stress =Z

M BB ==

modulus SectionalMoment Bendingσ ..............................................................(3-12)

Bending Moment = lFM B *= ..........................................................................................................(3-13)

therefore by substitution :

Bending Stress =Z

lFB

*=σ ..................................................................................................................(3-14)

Rearranging this equation bending Force:

Bending Forces =lZEF B **ε= ....................................................................................................(3-15)

where l is the length of the test object.

3.1.8 Axial forces

Similarly Axial strain:

32

Axial Strain =E

AA

σε ==Elasticity of Modulus

Stress Axial ................................................................(3-16)

And:

Axial Stress =AFA

A ==Area Sectional Cross

Force Axialσ .................................................................(3-17)

This can be rearranged to show that:

Axial Force = AEF AAxial **ε= ........................................................................................................(3-18)

3.1.9 Shear Strain

Shear Strain = Gτγ ==

StressShear of ModulusStressShear

...............................................................(3-19)

Where:

Shear Modulus= GLA

FLLLAF

∆=

∆===

//

StrainShear StressShear

γτ

................................................(3-20)

and is typically measured in GPa or ksi (thousands of psi)

The second moment of area (I) is defined as the capacity of a cross section to resist

bending for example for a drill pipe cross section:

Second Moment of Area= 64

)(* 44idod ddI −

=π (in4) ..............................................................(3-21)

3.1.10 Torsional Strain

Torsional Strain Gτγ ==

elasticity of modulus TorsionalStress Torsional

.........................................(3-22)

Where:

Torsional Stress=J

)2/(*Mt d=τ .....................................................................................................(3-23)

And:

33

Shear Modulus= γτ

==StrainShear StressShear G (Described above)..........................................(3-20)

For accurate shear measurement °= 45@*2 εγ ..................................................................(3-24)

That is reading of the strain with gauges at 45° to center of rotation and in line

with the principal axis.

Mt = torque and J= Polar second moment of area is the measure of an objects

ability to resist torsion which for a drill pipe cross sectional area16

Polar second moment of area for a drill pipe cross sectional area

=32

)(* 44idod ddJ −

=π

(in4) ......................................................................................................................... (3-25)

From these equations, and with correct positioning of the strain gauges, it is

possible to calculate the torsional moments.

Torsional Moment = ⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

dJG

dJMt

2*)(**2*)(* γτ .......................................(3-26)

Where d is the OD of the pipe. (i.e. d/2 = distance from center of cross section to

outer fiber)

3.1.11 Principal Axis

The principal axis describes the axes or planes of maximum and minimum

stress/strain and will always be at right angles to each other. A distinguishing

feature of principal planes is that no shearing stresses or strains act on them.

In a uniaxially loaded bar the normal stress planes fall in the x and y axis where the

x axis is the plane of most stress and the y axis the plane of least stress.

In a biaxial stress environment, for example where a drill string is in or

compression and experiencing torsional stress it is also experiencing a tri-axial

strain state with torsion strain and Poisson’s strain (with compressive forces

16 William F.Riley, loren W.Zachary. ‘Introduction to Mechanics of Materials’, John Wiley and Sons, 1989 ISBN: 0-471-84933-2

34

reducing length and increasing diameter of the string). In this circumstance the

principal axis are aligned to the principal strain/stress axis which are not in the x

and y axis, rather alternate axis in the direction of the torsional forces.

Understanding the orientation of the principal axis and the magnitude of the

maximum and minimum stresses significantly simplify the calculation of the

normal and shear stresses at any point on the object and in any orientation.

3.2 Mohr’s Circles

As stated previously it is important to understand that for all types of loads a

shearing stress at any point on a plane is accompanied by a shearing stress of the

same amount on a perpendicular plane through the same point. Stress

transformation equations are used to determine the normal stress and shearing

stress for different planes through a point in a stressed body. The simplest way of

expressing these multiple principal stresses is to use the Mohr’s circle diagram,

which was developed by Otto Mohr in the late 1800’s and early 1900’s and allows a

pictorial representation of the stress system.

Figure 3-6: Mohr’s circle representation of Normal, Biaxial and Triaxial stress systems.

The Mohr’s circle is constructed by plotting the normal stress σ on the x axis

versus the shear stress τ on the y axis and plotting the maximum and minimum

normal principal stresses on the x axis. (Positive tensile stresses are plotted to the

right of the origin and negative compressive stresses to the left). Shearing stresses

are plotted on the y axis with stresses tending to produce a clockwise rotation of

σ1 σ1

σ

τ

σσ3 = 0

Mohr circle for Biaxial Stress

σ2

σ2

σ

σ1 σ1

σ

τ 2

1max

στ =

σ

σ2 = σ3 = 0

Mohr circle for simple tension

231 σσ −

σ1 σ1

σ

τ

σ1

Mohr circle for Triaxial Stress

σ2

σ2

σ2

σ3

σ3

221 σσ −

232 σσ −

231 σσ −

σ3

35

the stress element plotted above the x Axis and those with counterclockwise

plotted below the x axis. The diameter of the circle represents the difference

between the stresses (e.g. σ1 and σ3). The circle represents the normal and shearing

stresses on one plane through the stress point. The angular position of the radius

to the point gives the orientation of the plane. Examples are shown in figure 3-6

above.

3.3 Strain Gauges

As noted in the previous section stress is a derived quantity and must be computed

from other attributes. Stress can be computed from measurement of strains and

their distribution. Strain gauges are the primary method of measuring the

appropriate strains for a given object. The strain gauge is a device which measures

the deformation of a surface.

There are a number of types of strain gauges including metal wire/foil, carbon

resistive, semiconductor/piezoresistive, and optical gauges. Each type has benefits

and drawbacks dependent on the desired service environment and accuracy

requirement.

Carbon resistance gauges exhibit changes in the carbon resistance with changes in

length of the gauge. Although it demonstrates high strain sensitivity it is

significantly affected by temperature and humidity.

Figure 3-7: Metallic foil gauge17

When a semiconductor (e.g. silicon or germanium) gauge

is deformed it exhibits a piezoresistive effect such that a

voltage difference can be measured which is proportional

to the strain. The benefit of this type of gauge is the

typically increased sensitivity over wire or foil type gauges,

however the drawbacks include potential errors associated

with temperature sensitivity and non linear resistance

response. These errors can prove problematic in bridge

configurations, but can be overcome with accurate computer modeling.

The most common form of strain gauge can be found in the metallic foil gauge

(figure 3-7) which is bonded to the surface of the object being measured. As the

17 www.omega.com

36

surface deforms the gauge stretches or shrinks in a specified plane of movement

and as a result the resistance of the foil also changes, the greater the stretching of

the foil, the higher the resistance and conversely the greater the compression the

lower the resistance becomes.

Gauges are attached to the object in a specific orientation to allow the strain

sensitive pattern to monitor strain in one plane only and be insensitive to strain in

the opposite plane. (i.e. a gauge configured to measure axial strain would be

insensitive to lateral strain, to measure lateral strain, the gauge would need to be

reoriented by rotating 90°)

3.3.1 Gauge Factor

When the gauge is placed in an electrical circuit, the variation of strain can be

directly related to the change in resistance and therefore current flow across the

gauge. In order to measure the strain, it is important to consider the gauges

sensitivity to strain. This sensitivity to strain is expressed as a calculated Gauge

Factor.

εRR

LLRRGF /or

//

(strain)length in change FractionalResistance Electrical Fractional ∆

∆∆

=∆

= ..............................(3-27)

The Gauge Factor reflects the overall sensitivity of the foil/wire, carrier matrix and

associated connections, the greater the GF the more sensitive the gauge. A typical

GF value for the most common devices is 2. Every gauge has a measured GF

which is provided by the manufacturer and used in the calculation of measured

strain. As described earlier semiconductor gauges demonstrate higher sensitivity

which results in greater GF values.

3.3.2 Bonding

The manner in which the gauge is bonded to the object ensures that the strain

being measured is accurately transferred from the object to the strain gauge

foil/wire. The gauges are manufactured in as small a cross-sectional area as

possible whilst maximizing sensitivity and surface area. The wire or foil gauges are

attached to a very thin (0.001 inch) carrier/backing material, typically a plastic such

as polyimide or epoxy, which acts as an electrical insulator and allows installation

of the gauge through cementation to the object being measured.

37

The selection of carrier material and cementation/bonding method is dependent

on the classification of service and includes attributes such as temperature,

pressure and moisture conditions. Table 3-1 provides an indicative list of cement

types and temperature limitations.

Table 3-1: Example bonding adhesives based on temperature ranges

3.3.3 Temperature

Due to the concept of thermal coefficient of expansion, every gauge will be

affected by changes in temperature, over and above the effects of strain. The GF

will change as a function of the difference between the thermal coefficient of

expansion for the gauge and the thermal coefficient of expansion for the material

being monitored. Understanding this concept is important to ensure accuracy of

measurement and selection of appropriate gauge alloys to match the coefficients of

thermal expansion as closely as possible. Temperature compensation can also be

addressed in the configuration of the Wheatstone bridge circuit described later in

this document.

In recognition of the temperature effects, manufacturers provide a plot of the GF

variation in relation to temperature, which enables a look up of the GF dependent

on the actual measured temperature. The actual GF can be defined as:

Temperature adjusted Gauge Factor =100

GF)%(1 ∆+= GFGFA ..................................(3-28)

<100°C (212°F) <250°C (480°F) <350°C (662°F)

<800°C (662°F)

Cynocrolate/ Cynoacrelate adhesives

Two part solid epoxy Two part solids epoxy (high resistance)

Two part epoxy phenolic adhesive

Two part epoxy phenolic adhesive

Polyimide based adhesive

Ceramic Cement

38

3.3.4 The Wheatstone bridge

The Wheatstone bridge circuit is a universally accepted method of accurately

measuring the resistance change associated by applicable resistive strain gauges.

The gauges themselves generate extremely small values in micro strain terms (ε x

10-6) and therefore the associated resistance change is also extremely small. To

compensate for this the gauges are organized in a Wheatstone bridge configuration

which consists of 4 (four) resistive arms (one or multiple of which would contain

the strain gauge(s)) with an input of excitation voltage applied across the bridge.

Figure 3-8 Wheatstone bridge circuit

Figure 3-8 depicts a basic ¼ Wheatstone

bridge configuration). The output voltage of

the ¼ bridge indicates the resistance change

and therefore the measured strain and can

be defined by the following equation:

Bridge output voltage = ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+=

21

2

3

3*RR

RRR

RVVg

EXo (3-29)

Where Rg is a single strain gauge and R1 , R2 and R3 are known values. In order to

accurately measure the strain value the bridge must be balanced in the unstrained

state, i.e. when the value of R1 / R2 = R3 / Rg the output voltage must equal zero,

thereafter any change in resistance in the strain gauge will reflect a change in the

output voltage. In its simplest configuration the bridge would be balanced by

adjusting the value of R2 in the unstrained state. Changes in Rg in the strained state

would create a voltage measurement, adjusting the value of R2 to balance the

bridge in the strained state would indicate the change of resistance in gauges as Rg.

Alternately, when ignoring non linearity errors, the strain can be calculated by

rearranging the equation ε

gg RRGF

/ ∆

= to determine the change in resistance as:

Bridge resistance change = ε**R g GFR =∆ ...........................................................................(3-30)

39

and therefore the strain as:

Measured Strain =GF

Rg

*Rg

∆=ε .........................................................................................................(3-31)

A simplified method of measuring the strain is to calibrate a meter to measure Vo

as a function of the strain (in micro strain units).

3.3.5 Unbalanced bridges

The increasing utilization of computer modeling techniques remove the need to

balance the bridge and allows considerable flexibility in the configuration of

bridges with multiple gauges in one or ultimately all of the resistive arms and

measure strain in an unbalanced bridge configuration. By rewriting the

fundamental bridge equation, the relationship of the excitation voltage to the

output voltage can be determined:

Voltage Ratio = ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+=

21

2

3

3

RRR

RRR

VV

gEX

o .............................................................................(3-32)

This ratio is consistent for both the strained and unstrained state, therefore the

difference in strained versus unstrained voltage ratio can be written as

Voltage Ratio = unstrained strained ⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

EX

o

EX

oR V

VVVV ...............................................(3-33)

Also, given that in the strained condition the resistance of the gauge is gR∆+gR

and that ε

gg RRGF

/ ∆

= , the following equation can be derived to reflect the

actual strain measurement in a ¼ bridge configuration:

¼ Bridge Strain = )21(

4

R

R

VGFV+

−=ε .........................(3-34) (Ignoring lead wire resistance)

Given the above equation, and the relationship of VR, equations can be derived for

half and full bridge configurations.

40

Half bridge configuration

Half bridges are configured to have active strain gauges in two resistive arms of the

Wheatstone bridge. This can serve to double the output sensitivity in certain

configurations by recognizing that the strains are opposite but equal, and as such

creates a combined voltage difference. An example would be measurement of both

compressive and tensile strain on a beam where one gauge is in tension

( gR∆+gR ) and the other compression ( gR∆−gR ).

Axial or bending strain calculations for half bridges are :( ignoring errors)

For axial strain:

½ bridge axial strain = [ ])1(2)1(4

−−+−

=νν

εR

R

VGFV

...........................................................(3-35)

where ν is Poisson’s ratio.

For bending strain:

½ bridge bending strain = GF

VR2−=ε ............................................................................................(3-36)

Full bridge configuration

Full bridges are configured with active gauges in each of the resistive arms; the

sensitivity of the circuit would differ based on the configuration and orientation of

the gauges.

Axial or bending strain calculations for full bridges are :( ignoring errors)

For axial strain:

Full bridge axial strain = [ ])1()1(2

−−+−

=νν

εR

R

VGFV

...........................................................(3-37)

where ν is Poisson’s ratio.

For bending strain:

41

Full bridge bending strain = GFVR−

=ε ...........................................................................................(3-38)

For bending strain, (with the Poisson arrangement for the temperature

compensated dummy gauge on the same tensile surface):

Full bridge bending strain (Poisson) )1(*

2+

−=

νε

GFVR ........................................................(3-39)

Given the basic understanding of bridge configurations it can be seen that there

are numerous configurations of ¼, ½ and full bridges that can be utilized to

measure axial, bending and torsional/shear strain. Figures 3-9, 3-10 & 3-11 show

the orientation of each gauge, associated circuit diagram and the attributes of each

of the ¼, ½, and full bridge configurations covering all three strain states.

Figure 3-9: Axial strain configurations

R4

R3

R4

R3

R4

R3

R1

R2

Comments:

• Basic ¼ bridge configuration• Simple strain measurement• No temperature compensation• Sensitive to bending strain• Lowest relative sensitivity (0.5 mV/V @ 1000µε)

Comments:

• ½ bridge configuration• Amplified strain measurement• Temperature compensation with dummy gauge positioned transverse to

applied strain• Sensitive to bending strain• Improved relative sensitivity (0.65 mV/V @ 1000µε)

Comments:

• ½ bridge configuration• Further amplified strain measurement with 2 identical gauges on

opposite sides.• No temperature compensation as both subject to the same temperature

error.• Compensates for bending strain• Improved relative sensitivity (1.0 mV/V @ 1000µε)

Comments:

• Full bridge configuration• Further amplified strain measurement with 4 gauges (2 measurement, 2

dummy)• Temperature compensation with dummy gauges positioned transverse

to applied strain• Compensates for bending strain• Improved relative sensitivity (1.3 mV/V @ 1000µε)

Axial Strain Gauge and associated bridge configurations

FA

R4

FA

FA

FA

FA

FA

FA

FA

42

Figure 3-10: Bending Strain configurations

Comments:

• Basic ¼ bridge configuration• Simple strain measurement• No temperature compensation• Sensitive to axial strain• Lowest relative sensitivity (0.5 mV/V @ 1000µε)

Comments:

• ½ bridge configuration• Amplified strain measurement• Temperature compensation with dummy gauge positioned in same

plane but opposite side (in compression compressive• Compensates for axial strain• Improved relative sensitivity (1.0 mV/V @ 1000µε)

Comments:

• Full bridge configuration• Further amplified strain measurement with 4 identical gauges on (2 on

opposite sides).• Temperature compensation • Compensates for axial strain• Improved relative sensitivity (2.0 mV/V @ 1000µε)

Bending Strain Gauge and associated bridge configurations

R4

FV

FV

FV

R4

R3

R4

R2

R1R3

Figure 3-11: Torsional/Shear strain configurations.

Comments:

• Basic ½ bridge configuration, gauges positioned at 45° from centerline to measure principal strains

• Simple strain measurement• Temperature compensation• Compensates for Axial and bending strain as both are equal • Lowest relative sensitivity (1.0 mV/V @ 1000µε)

Comments:

• Full bridge configuration, gauges positioned at 45° from centerline to measure principal strains

• Amplified strain measurement• Temperature Compensation• Compensates for Axial and bending strain as both are equal • Improved relative sensitivity (2.0 mV/V @ 1000µε)

Torsional Strain Gauge and associated bridge configurationsMT

MT

R4

MT

MT

R3

R4 R3

R1R2

43

C h a p t e r 4

4.0 APPLICATION TO DOWNHOLE MEASUREMENT

4.1 WOB/TOB/BOB measurement devices.

As mentioned previously, significant progress has been made over the years in

measurement of down hole vibration, direction control and pressure through

direct application of sensors within MWD subs in the BHA. The deployment of

down hole tools which directly measure WOB/TOB and BOB has been a

relatively recent occurrence. Some tools only measure WOB/TOB whilst others

also measure BOB. Reliability at the temperatures and pressures experienced in

today’s wells add complexity and require careful engineering to ensure that the

measurements are within a relatively reasonable margin of error necessary to add

value to the drilling process.

Research reveals that the techniques required to deliver down hole

WOB/TOB/BOB measurement have been well known for decades in the

industry, all based on the theories described within chapters 2 and 3 of this thesis.

For clarity, within the collar where the strain gauges are installed:

• WOB is the measurement of axial compressive and tension load

applied to the collar

• TOB is the measurement of torsional strain applied to the collar

• BOB is the measurement of bending strain applied to the collar

There are numerous patents and SPE/IADC papers and patents written on the

specific application of strain gauges and associated Wheatstone bridge

configurations, many of which are more than 20 years old.

Three specific patents were studied in detail in the preparation of this thesis and

are summarized below in order to demonstrate the common application methods.

The specific patents are referenced by the last name of the first author within the

thesis, and include:

44

• Anderson18: US Patent # 3,827,294 - Aug 6, 1974; Wellbore force

measuring apparatus; Ronald A Anderson, Houston Tx – Assignee:

Schlumberger Technology Corporation, New York, N.Y.

• Das19: US Patent # 5,386,724 - Feb 7, 1995; Load Cells for Sensing

Weight and Torque on a Drill Bit While Drilling a Well Bore; Pralay K.

Das; Haoshi Song, Sugarland Tx – Assignee: Schlumberger Technology

Corp, Houston TX.

• Woloson20: US Patent # 6,216,533 - Apr 17, 2001; Apparatus For

Measuring Down hole Drilling Efficiency Parameters; Scott E. Woloson,

Dale A Jones, Houston, TX - Assignee: Dresser Industries Inc, Dallas TX

All of the patents describe various methods of configuring strain gauges within a

down hole drilling sub and coupling through Wheatstone bridge circuits to

generate a measurable voltage. The output of the circuits is processed, captured

and relayed though electrical connection to the MWD sub and thereafter to the

surface through the existing MWD mud pulse telemetry system.

It is not the intent of this thesis to analyze these patents in detail, however the key

elements of their application are described to demonstrate the contrast in approach

and further describe the application of the associated measurement and error

correction methods.

4.1.1 Anderson (patent No. 3,827,294)

The Anderson patent is the oldest of the three and is interesting to reference as an

early application of gauges to the drilling sub.

The application includes a pair of force-measuring sleeves or loops which are

attached to the collar with specifically placed strain gauges to allow the sleeves to

be exposed to the same torsional and axial (longitudinal) forces as the sub. The

18 US Patent # 3,827,294 - Aug 6, 1974; Wellbore force measuring apparatus; Ronald A Anderson, Houston

Tx – Assignee: Schlumberger Technology Corporation, New York, N.Y.

19 US Patent # 5,386,724 - Feb 7, 1995; Load Cells for Sensing Weight and Torque on a Drill Bit While Drilling a Well Bore; Pralay K. Das; Haoshi Song, Sugarland Tx – Assignee: Schlumberger Technology Corp, Houston TX.

20 US Patent # 6,216,533 - Apr 17, 2001; Apparatus For Measuring Down hole Drilling Efficiency Parameters; Scott E. Woloson, Dale A Jones, Houston, TX - Assignee: Dresser Industries Inc, Dallas TX

45

loop has two donut like rings located 180° opposite to each other, which are

connected with strips or bars of metal between them to form the loop.

Gauges are placed on the strips between the donuts on the sides of the loop bars

which allows measurement of tension and compression of the loop when the sub

is exposed to torsional strain, and therefore the TOB.

Gauges are also placed in the inner wall of the donut rings at 4 locations starting at

12 o’clock and then positioned equidistantly at 3 o’clock, 6 o’clock and 9 0’clock

positions. These gauges measure the axial strain on the loop and sub, and therefore

the WOB.

Figure 4-1: Diagram showing layout of force measuring sleeve/loop.

The strain gauges are connected into two separate Wheatstone bridge circuits one

for TOB measurement and the other for WOB. The TOB bridges are configured

with two gauges in each arm each measuring the same either compressive or

tensile strain. The theory described in chapter 3 is applied here to provide an

amplification of the strain signal by coupling multiple gauges within all four arms

of the bridge to maximize sensitivity.

Differential pressure errors are in part offset through a relatively elaborate pressure

equalized chamber configuration which encapsulates the deformable loop and

WOB Strain Gauges (Inside donut rings) TOB Strain Gauges

(On bars between donut rings)

Loop mounted within Sub wall

Device under strain (On bars and donut rings)

Loop encapsulated in Pressure sealed

chamber (Not Shown)

46

maintains the environment at a relatively constant pressure. This mechanism also

serves to isolate the measurement mechanism from the drilling fluid.

As with all the patents described here, the gauges are connected via wired

connections channeled within the walls of the sub to the MWD sub for

subsequent transmission to the surface through the available telemetry system.

4.1.2 Das (patent No. 5,386,724)

The Das patent introduces the use of two radial pockets positioned 180° opposite

each other around the drill collar and sealed from the drilling fluid with caps.

These radial pockets allow measurement of the necessary strains through

placement of the gauges within a ring configuration load cell.

Figure 4-2: Layout showing load cell insert configuration of DAS patent.

The load cells comprise of radial inserts, (similar to an automotive brake disk with

a central hub and gauges positioned on the face of the disc), onto which the gauges

(numbered W1 to W4 and T1 to T4) are attached around the circumference

starting at 0° (W1 @12 o’clock) then 90°(W2), 180°(W3) and 270°(W4) for the

WOB gauges and 45°(T1), 135°(T2), 225°(T3) and 315°(T4) for the TOB gauges.

0°

45°

90°

135°

180°

225°

270°

315°

WOB 1

WOB 2

WOB 3

WOB 4

TOB 4

TOB 1

TOB 2

TOB 3

Plan view showing orientation of gauges

Side view showing insert positioned inside pocket with gauges on face of ring

Pocket in sub wallInsert with load cell

attached

47

This approach allows for independent measurement of the separate WOB and

TOB strains i.e. minimizing interference from the other strain type.

Figure 4-3: Example of radial pocket and strain gauge insert configuration.

During the stressed condition the ring load cells within the radial pockets change

shape from round to oval, the extent of this change places compressive and tensile

strains on differing gauges.

Figure 4-4: Effect on gauges during pure axial compressive load (WOB Measurement)

For example in the pure axial compression state (figure 4-4) the radial pocket is

compressed causing the load cell to narrow between the 0° and 180° gauges and

Section of drilling sub/pipe.

Typical pocket/radial insert in side wall, 2 or more located at opposite sides of sub or at regular intervals around circumference of sub.

Example of separate insert with strain gauges attached and configured as load cell (e.g. Das patent)

WOB 1 - Tension

WOB 2 - compression

WOB 3 - Tension

WOB 4 - Compression

TOB 4 – No effect

TOB 1 – No effect

TOB 2 – No effect TOB 3 – No effect

48

widen between the 90° and 270° positions which places the gauges in the 0° and

180° positions (W1 & W3) in tension and the other two gauges in compression.

Correspondingly the pure axial strain has no effect on the TOB gauges in the 45°,

135°, 215° and 315° positions.

Figure 4-5: Effect on gauges during pure axial tension load (WOB Measurement)

Figure 4-5 shows the similar effects on pure axial tension load on the cell where

the tension and compression loads are reversed in comparison with the pure axial

compression state described in figure 4-4.

In the pure torsion state (figure 4-6), the oval shape is slanted, placing compressive

strain on the TOB gauges at 45° and 215° positions and tension on the TOB

gauges at the 135° and 315° positions, but with no effect on the WOB gauges at

0°, 90°, 180° and 270° positions. This is achieved by offsetting the corresponding

tensile and compressive strains within the full bridge circuits through placement in

opposite arms of the bridge as described in chapter 4.

WOB 1 - Compression

WOB 2 - Tension

WOB 3 - Compression

WOB 4 - Tension

TOB 4 – No effect

TOB 1 – No effect

TOB 2 – No effect

TOB 3 – No effect

49

Figure 4-6: Effects on gauges of pure torsional load (TOB measurement)

Errors associated with the temperature gradients experienced by the load cells are

considered and also compensated through placement of respective strain gauges

within the full bridge configuration. It achieves this by balancing the measured

strains through formation of a full Wheatstone bridge circuit which couples 2 the

gauges reading tension strain from one load cell (e.g. 0° and 180° positions) to the

gauges reading compressive strain (e.g. 90° and 270° positions) of the other load

cell on the opposite side of the collar, and similarly for the TOB bridge

configuration.

It should be noted that in this application the gauges are attached to the load cell,

not directly to the collar and therefore the material selection mentioned above

applies only to the load cell insert.

Fluctuations in pressure differentials are compensated by placing an additional

gauge adjacent to the WOB gauges in each of the positions 0° (P1) then 90°(P2),

180°(P3) and 270°(P4) and orienting them in a manner that measures the

differential pressure only. The output of the pressure measuring bridge is coupled

with the WOB output to cancel the effect of differential pressure.

One benefit of this design is the relative simplicity of maintenance through the

load cell configuration and ease of replacement.

WOB 1 – No effect

WOB 2 – No effect

WOB 3 – No effect

WOB 4 – No Effect

TOB 4 – TensionTOB 1 – Compression

TOB 2 – Tension TOB 3 – Compression

50

4.1.3 Woloson (patent No. 6,216,533 B1)

The Woloson patent is the most recent reviewed here and describes a more

complete Drilling Efficiency Sensor sub which measures WOB/TOB/BOB,

differential pressure/temperature and triaxial vibration.

Figure 4-7: Summary definition of Woloson ‘Drilling Efficiency Sensor’ apparatus.

Applied forces to the drill collar cause the load cell rings to deform from a circular geometry into an oval geometry causing the WOB, TOB & BOB measurements to change proportionally

10a

64

68

7274

1260

62 10c

668

Load cells thermally insulated from borehole fluid

Independent load cells located in each of 4 radial chambers 90° apart.(10a-10d)

Drill Collar

Quartz pressure transducers ported through two independent fluid communication ports 60 and 62 to the annulus and internal bore fluid respectively which enables pressure differential measurement

Three temperature detectors (RTD’s) located in line with each load cell & positioned at drill collar inner & outer diameters and at load cells to measure temp. gradient across drill collar wall.

Triaxial vibration sensors/ DDS (Drilling Dynamics Sensor) and magnetometer array measure acceleration forces and allow identification and tracking of low side of hole while rotating.

Bending moment is determined regardless of rotation through application of 4 Wheatstone

bridges located 90° apart around the drill collar.

Borehole fluid

Drill String

Side wall readout

Woloson Patent Summary

Figure 4-7 describes the key elements of the apparatus which utilizes ring

configuration load cells within four sealed atmospheric chambers positioned at 90°

intervals around the drill collar (10a-10d) rather than two. The configuration of the

gauge rings also provides a method for adjusting the sensitivity by increasing or

decreasing the wall thickness of the ring which the gauges are bonded to.

The configuration with four independent bridges allows for the determination of

bending moment of the drill string and therefore BOB regardless of the state of

rotation (rotating or stationary), in addition to corrected TOB and WOB

measurements. The combined Drilling Dynamics Sensors (DDS), with

accelerometers and magnetometer array, enables determination of the direction of

the BOB in relation to the low side of the hole

51

Pressure differential is directly measured by measuring the internal and annulus

pressures and applied correction of the respective bridge outputs.

Temperature is measured with Resistance Temperature Detectors (RTD’s) located

at 3 specific points within the load cell chamber to determine the temperature

gradient across the collar wall and therefore provide more accurate correction for

temperature.

In general the Woloson apparatus provides a more complete and accurate method

of measuring WOB/TOB/BOB than the other two methods described here and is

a progression of understanding and application within the industry.

4.1.4 Temperature and pressure compensation

Recognition is given to the issues associated with differential pressure and

temperatures on the drilling sub and therefore strain gauges. The differentials are

associated with the difference between the fluid temperature and pressure within

the inner bore of the drill collar and the annulus between the collar and wellbore as

the drilling mud exits the string and flows back up through the annulus. The

pressure differential will typically be further extenuated by the mud pulse telemetry

pressure fluctuations. Differential pressure, for example, causes elongation and

circumferential expansion of drill collar which introduces errors in the

measurement of axial strain and therefore the WOB measurement. Where the

fluctuations in pressure are relatively minor, the WOB bridges can be re balanced

to a datum by lifting off bottom and resetting to zero. In today’s more complex

drilling environments this is not typically an option with significant and constant

variations in differential pressure.

Temperature fluctuations effect the strain gauge sensitivity as described in chapter

3 and can be typically offset through appropriate placement of the gauges within

the bridge circuit.

The material selection for the drilling sub or inserts is also chosen carefully to

ensure a relatively low young’s modulus of elasticity to increase sensitivity, and

relatively high coefficient of thermal expansion/conductivity as to diminish

temperature transients more rapidly. The material selection, typically a high

strength alloy such as beryllium copper, or nickel chromium alloys, serves to

52

minimize residual stress and thermal transients and therefore measurement drift

associated with these attributes.

4.1.5 Calibration and Accuracy parameters

The previous chapters and the specific application of the technology to a down

hole environment in this chapter, have discussed a lot of potential errors which can

be introduced into the WOB/TOB/BOB measurement including those associated

with pressure and temperature fluctuations/differentials. In general these errors

continue to be recognized and addressed with specific correction methods as the

technology matures.

The challenge becomes one of accuracy and the associated calibration tolerances

required to make the tool useful without incurring too high a cost for relative

differences in real-time WOB/TOB/BOB measurements during drilling is the

important aspect being addressed here, and as such the accuracy of the

measurements needs to strike a balance with practical implementation.

The accuracy of the measurements required by the industry varies from 2-3% in

early implementations to up to 20% in less sensitive designs. The challenge to

understand is one of practicality. If the tool is designed to be too accurate, it is

likely that it will require regular maintenance and calibration, which typically

required transport of the tool to a repair and calibration center remote from the

well site.

Calibration methods utilized compare the actual performance and measurements

made in simulated environments and determine the expected output from the

gauges and bridges at given WOB/TOB/BOB loads and at anticipated

temperature and pressure environments.

The following devices are example of what can be used to perform calibration but

are often dependent on the specific design of the device:

• Oldham Coupling Adapter and breakout unit for torque

• Modified jar tester for WOB

• Bending Stand for BOB

• Oven to test temperature effects

53

• Precision pressure testers to test pressure gauge accuracy

Information derived from the calibration tests are recorded and downloaded into

the memory of the tool to allow the actual measurement to be compared with the

calibration or offset values and stored for transmission to the surface or memory

storage if required.

The output of the respective bridges is processed on the WTB sub directly against

the software algorithms, with only the desired output measurements being

transmitted to the surface. This approach is driven by a number of factors but

primarily due to the need to minimize the amount of data transmitted to the

surface.

54

C h a p t e r 5

5.0 THE IMPACT OF ADVANCED TELEMETRY ON DRILLING EFFICIENCY

All down hole MWD/LWD and certain activated tools require a mechanism to

transfer the data to and from the down hole equipment. Sensor data traveling to

the surface is displayed and analyzed appropriately to assess trends, identify

problems and optimize intervention tasks appropriately.

To date significant progress has been made in real-time data capture devices, the

constraint however continues to be around the limited bandwidth available to

transmit the data efficiently to the surface. Figure 5.1 demonstrates an example of

the real-time monitoring and analysis capability provided today. In this case a mud

motor configuration is being monitored with the drilling dynamics attributes

(predicted limits and actual), formation lithology data, RPM, ROP, measured

vibration, critical speeds, WOB, and motor output torque etc. This display

indicates traditional data in the absence of a down hole WTB sub.

Figure 5-1: Example real-time data analysis application.21

21 Courtesy of Halliburton – Sperry Drilling Services © All rights reserved

55

5.1 Traditional Down-hole telemetry methods

5.1.1 Mud Pulse Telemetry

Mud Pulse Telemetry is the most common method for transmitting data used in

drilling today and operates by sending pressure pulses in the drilling mud to and

from the rig floor. The actual pulses can be sent as positive pulses, negative pulses

or continuous sinusoidal waves and can be received and interpreted as a binary

sequence of data. This method is generally reliable but slow with only 10-12

bits/sec transmission rate in ideal conditions and can only function in the presence

of drilling mud, which is almost always the case during traditional drilling

operations, but not in certain under balanced conditions where gases or foam

fluids are utilized.

5.1.2 Acoustic Telemetry

Acoustic telemetry systems utilize acoustic energy to transmit signals through the

wall of the drill pipe to the surface. Acoustic systems have typically been utilized

within non-drilling activities such as drill stem testing, cementing services etc.

where transmission rates of 40-50 bits per second can be achieved in a relatively

noiseless environment. Limited progress has been made to utilize acoustic

telemetry in rotating conditions, due to the relatively high acoustic noise

environment during drilling operations, the achievable data rates are typically

around 20 bits per second which has not as yet proven commercial viability.

5.1.3 Electromagnetic Telemetry

Electromagnetic telemetry transmits data through low-frequency electromagnetic

waves which propagate through the subsurface formations from the drill string

and are received by surface antennas. The successful implementation of

electromagnetic telemetry requires understanding of the formation types and

associated resistivities along with a robust antenna location at the surface.

These attributes lead to limitations dependent on the well depth and formation

types. EM technology can deliver rates of between 50 and 100 bits per second in

land applications where there are relatively shallow resistive formations which

allow the surface antenna to more easily detect the signal. In an offshore

environment this becomes a lot more complex with typically deeper wells, less

56

resistive formations and the requirement to transmit the signal through sea water

from the antenna located on the sea floor. The combination of these factors

degrades the performance and prevents EM from delivering data rates much

above mud pulse rates. EM telemetry is however an important attribute of

successful under balanced drilling applications where traditional mud circulation

systems are not applicable. EM telemetry also has merits in a “Short-Hop”

configuration where the signal is transmitted short distances between subs in the

BHA where the signal quality can be maintained more easily.

5.2 Intelligent/Wired Pipe

Wired pipe has recently emerged as a viable technology within the industry and

allows a stepped change performance in the available bandwidth down hole with

achievable data transmission rates up to 2 megabits/second which reflects up to

100,000 to 200,000 times the bandwidth currently available, without any

dependencies on mud circulation or formation types. The system is effectively a

down hole wired network which is equivalent to a traditional Ethernet Local Area

Network and allows any compliant devices to use the network to transmit data to

and from the surface.

The system was originally conceived by a company called Novatek Engineering

which received partial funding from the US Department of Energy. Novatek

formed a joint venture with Grant Prideco in 2000 in order to leverage the

collective experience of drilling collar manufacture and intellipipe technology to

deliver the IntelliServ™ Network commercial system.

Figure 5-2: Configuration of IntelliServ™ Network wired pipe22

22 Grant Prideco IntelliServ™ - www.intellipipe.com

High-Speed Data Cable

Non- Contact Line Couplers

Non- Contact Line Coupler

Double Shouldered Tool Joint

High-Speed Data Cable

57

The fundamental element of the system is the wired pipe which is comprised of

traditional drill pipe in standard sizes that has a high-speed data cable embedded in

the inner wall of the pipe and connected to inductive coupling rings at each end, as

shown in figure 5-2.

The non-contact couplings at each end of the pipe provide the method of data

transmission without the need for a direct connection. This significantly simplifies

the implementation of the system at the rigsite with the crew making up the pipe in

the traditional manner, with minimal training to ensure proper handling, torque

and make up procedures.

Three other key elements of the system are necessary to complete the IntelliServ™

Network and include the:

1. Interface Sub – to allow connectivity to the MWD sub and subsequent

measurement/down hole devices in the BHA,

2. Booster subs – which are inserted in the string every 2000ft or so to boost

or amplify the signal and are configured to allow additional monitoring

sensors along the drill string,

3. Top Drive Swivel – This is specifically designed to allow connectivity to

and from the control and analysis computers on the rig site.

The system provides connectivity to any compliant down hole tool or device

which provides continuity of the high-speed link from the surface to the interface

sub.

5.3 Implications on drilling dynamics, MWD and LWD

The obvious primary benefit of this system relates to the vast increase in

bandwidth available to the driller to send and transmit data. Traditional MWD and

LWD systems have to significantly compress or periodically sample the captured

data to minimize data transmission rates and capture the higher resolution data in

memory devices for recovery and analysis when brought to surface. These existing

systems therefore provide an indicative sense of what is actually going on down

hole at lower resolution or at intervals of sampling. The wired drill pipe network

58

allows transmission of a real-time data signal which transmits the full resolution of

the data being captured by the sensors almost instantaneously.

There are many significant advantages to this increase in bandwidth including:

• High resolution (almost wireline quality) logs in real-time allowing accurate

formation evaluation, correlation and geosteering as appropriate.

• More accurate management of the drilling envelope and associated pore

pressure and ECD values. This is not only at the BHA but also in the

annulus at intervals along the pipe where the booster subs allow additional

sensor monitoring.

• Ability to manage under balanced or managed pressure drilling where mud

pulse telemetry is not functional or not reliable due to lack of or

fluctuation of mud weights.

• Improved identification of well control issues and associated management

with real-time data availability which is not typically available or accurate

with traditional methods

• Increased control of down hole devices such as steerable systems and

reamers.

• Delivery of stepped change monitoring of the drilling dynamics and forces

affecting the BHA which enable rapid and accurate mitigating action to

optimize drilling processes.

Figure 5-3: Example of Drilling Dynamics monitoring and analysis in wired pipe configuration

59

Figure 5-3 shows an example23of improved drilling dynamics analysis using

IntelliServ™ Network data where high drill string friction caused cocking and

firing of the drilling jar. Real-time analysis of this data quickly identified the

problem and the associated increase of WOB followed by the fluctuation after the

jar fired on picking up the bit, which would be the standard procedure where

WOB increase without ROP increase was experienced. The rapid identification of

the cause to the unplanned event minimized the time taken to pinpoint other

possible causes or to make other unnecessary changes drilling parameters to

further investigate the causes.

The commercial viability of the IntelliServ™ Network is still in its early days, with

only a handful of live rig implementations to date. The real key to success will lay

in the reliability of the connections, in particular the coupling sensitivity to damage

due to incorrect pipe handling or attention to make-up torque ratings. Given that

the drill string is typically an attribute of the drilling rig configuration and provided

by the rig contractor, reliability will be a high priority in selection of the system,

since the rig contractor will typically not carry a duplicate traditional string as a

backup.

23 Grant Prideco IntelliServ™ - www.intellipipe.com/intelliservDocs/

60

C h a p t e r 6

6.0 FINDINGS AND DISCUSSION

6.1 Description of Findings

As has discussed in this thesis, the industry will continue to face increasingly

complex drilling environments such as extended reach and highly deviated wells,

higher pressure/temperature and deep water environments, and continuously

challenging precise well placement/collision avoidance in mature producing fields.

Coupled with this will be the issue of lack of availability of qualified and proficient

personnel able to support these environments.

This will further increase dependency on real-time technologies, rapid data analysis,

engineering remote from the rig-site and automation of the drilling and production

processes in order to economically access and develop more reserves.

Today’s estimated non-productive time (NPT) associated with drilling

environment exceeds $20 billion per annum24, the issue of drilling efficiency and

identification/management of the associated drilling dysfunctions will continue to

be a high priority to operators and service companies in order to contain and

reduce these significant costs going forward.

In particular the industry recognizes the significant challenges presented to drillers

in monitoring BHA performance in these increasingly complex environments.

6.1.1 The benefits

This thesis demonstrates how it is possible to measure down hole

WOB/TOB/BOB forces on the BHA more accurately than current surface

measurement techniques and in so doing significantly improve the overall

efficiency of the drilling process.

The benefits to this approach include the ability to:

24 Lehman Brothers survey 2006.

61

• Provide the driller the tools and information to more readily identify and

mitigate the conditions associated with the various drilling dysfunctions (i.e.

more readily identify and manage the dysfunctions identified in chapter 2, table 2-1 in

section 2.2.5 )

• Enable the driller to more readily recognize when the founder point is

reached during drilling and what parameters can be adjusted while drilling

to extend performance (described in chapter 2 – section 2.4.6 )

• Optimize drilling ROP and associated equipment performance by

understanding when performance limits are reached for a given operating

environment (e.g. through application of real time down hole WTB data and rig

constraints within the MSE and related drilling efficiency models described within

chapter 2)

• Provide improved understanding of the drill-string and BHA performance

in the drilling of highly deviated and extended reach horizontal wells. (e.g.

the use of BOB measurement to monitor/identify local doglegs not readily identified by

traditional measurement techniques)

• Provide data to improve the design of BHA configurations and associated

down hole components including stabilizers, reamers, bits etc. (e.g. the

enhancement of torque/WOB models through better correlation of bit and reamer cutting

performance within the predicted rock strength described in Chapter 2 – Section 2.4.3 )

• Improve the accuracy of current simulators and models to allow enhanced

prediction of the drilling activities. (e.g. the modeled attributes within chapter 2,

figures 2-10 and 2-11)

6.1.2 The physics

The basic physics of stress and strain theory demonstrate how simple strain gauges

can deliver the required force measurements.

Metal foil strain gauges and Wheatstone bridge configurations demonstrate that

robust and relatively cheap technology is available today to effectively deliver down

hole WOB/TOB/BOB measurement.

Advances in the methods since the early WTB patents have primarily been made in

the areas of differential pressure and temperature compensation either through the

placement and configuration of the gauges themselves, or direct measurement of

62

the pressures and temperatures necessary to calculate and compensate for the

differentials.

6.1.3 The remaining challenges

One challenge still left to overcome, is related to the relative cost to not only

manufacture but maintain and calibrate these measurement subs. Efforts to deliver

tools with accuracy at 5% or below require considerable field calibration with tools

which are not currently common place. Initially operators are comfortable with

tools with +/- 10 to 20% accuracy because the relative changes in measured force

are more accurate than the surface measurements currently being taken. Going

forward developments of down hole measurement tools must enhance accuracy

and maintain tighter tolerances to enable improvements in data accuracy and

latterly efforts in automation.

A second challenge revolves around the constraints of traditional mud pulse or

EM telemetry systems which limit availability of bandwidth for the transmission of

new data sources such as that generated by the down hole WTB measurements.

The advent of wired pipe configurations, such as the IntelliServ™ Network will

deliver a stepped change in the drilling world due to enhanced visibility of the

formations and identification of drilling dynamics issues in true real-time.

6.1.4 The future potential

As down hole WTB measurement becomes common place and improvements in

accuracy continuously evolve, drilling simulations models such as the MSE model,

torque and drag models and others, will refine the predicted versus actual drilling

performance and as such allow for further development of rules based, signature

analysis or neural network techniques. This in turn will lead to advances in rig floor

and down hole automation which will reduce errors and NPT and free up

resources to develop more reserves.

The potential to deliver game changing drilling performance is not lost on the

industry, developments will continue to provide competitive advantage to

operators and service companies alike who can harness the potential and maintain

a profitable commercial return. Without a sufficient commercial return,

technologies such as these will continue to be seen as a nice to have or impossible

63

reality. For the industry to benefit investments and incentives need to be offered

and realized and commercial viability secured.

6.2 Thesis

As wired pipe begins to break down today’s paradigm of available “raw” real-time

data to the surface, the industry will need to grasp the challenging issue of deciding

whether to drive the technology to surface analysis and interaction due to high

bandwidth data availability, or increasing down hole tool automation with more

and more complex down hole systems providing the intelligence to automatically

drill and adapt based on high quality sensor data.

6.2.1 Closed Loop Automation

In the authors opinion, the next generation will be one where true drilling

automation will be achieved through “closed loop” down hole data processing,

analysis and action will be taken within the BHA electronics and computers

directly, without intervention from the surface. The system will be pre-

programmed, based on accurate subsurface and drilling simulation models, along

with the drilling plan, and will automatically adjust drilling parameters (initially by

adjusting surface drilling functions from down hole instructions) and trajectories

based on real time geological interpretation updates and comparisons to predicted

models.

The development of wired pipe coupled with methods of down hole power

generation will provide the requirements to allow increased down hole processing

and interpretation.

Complexity and reliability will be issues that must be overcome to maximize the

mean time between failure (MTBF) of these sensitive BHA components, and in

the ideal world allow drilling of complete hole sections, (i.e. casing point to casing

point sections), with one optimized BHA.

6.2.2 Importance of WOB/TOB/BOB

Down hole WTB measurement is a key missing element in realizing this vision,

because the data trends and associated modeling techniques are not currently

robust enough to base an automated system on. As the down hole drilling sensor

64

sub technology develops to encompass WTB in conjunction with other critical

vibration, temperature and pressure measurements, the industry will begin to refine

predictions and deliver common place automation techniques to minimize the

onset of drilling dysfunctions. Early real-time detection of the predicted trends

associated with each dysfunction will enable the driller to take early corrective

action to minimize escalation of the issue and therefore minimize the potential to

induce coupling and catastrophic drill string integrity failures.

6.2.3 Modeling accuracy

The statement often made is that a computer or model can only realize the value

that has already been experienced or learned by the initial human interaction. To

date this statement is largely true, hence the requirement to drive increased down

hole measurement and data transmission techniques to enable accurate modeling

to evolve. The onset of Artificial Intelligence and Neural Network techniques may

well accelerate the opportunity to develop automated down hole drilling systems,

these however also require some element of trended data to base their learning on.

Once sufficient modeling exists, and automated systems evolve, there will be a

reduction in the need for bandwidth to the surface and an increased focus of

sensor accuracy, robust electronics and reliability of down hole systems to allow

rapid and efficient drilling to depths of 30-50,000 ft or more, in extreme

temperatures and pressures.

6.2.4 Overcoming paradigms

Some of the potential barriers to realizing this vision will also relate to the costs to

develop the technology and sustained market demand to justify multi-year R&D

projects. In addition, paradigms will need to be broken in terms of traditional

human intervention from the driller, with a period of time where the driller will

transition from hands-on intervention, to hands-off monitoring whilst trust is

developed in the automation process.

All these capabilities are achievable in the future, the opportunity exists today to

embed direct down hole WTB measurement to enable the next breakthrough

towards that vision and build confidence and accuracy of the evolving modeling

and analysis techniques.

65

LIST OF EQUATIONS

Specific Energy = )(in area sectional crossBit

(lbf) ForceBit Total)( 2=psiEs (2-1) ............... 14

ROPOutput EnergyInput )( ≈psiMSE (2-2) ....................................................................... 14

Specific Energy = ROPA

TNA

WOBEsbitbit *

***120 π+= (2-3) .................................... 14

Also Specific Energy Es = ⎟⎟⎠

⎞⎜⎜⎝

⎛+

ROPDN

AWOB

bitbit *33.131 µ (2-4) .......................... 15

Coefficient of Friction =WOBD

Torque

bit *36=µ (2-5) .......................................... 15

36*WOBD

Torque bitµ= (2-6) .............................................................................. 15

EsEs

EFFMmin= (2-7)........................................................................................... 15

100*Es

EFFMσ

= (2-8) ........................................................................................ 15

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ROPATRPM

AWOBpsiMSE

BITBIT ****120*35.0)( π (2-9)................................ 16

tEAWL

tWROP

S ∆∆

=∆∆

=*

* (2-10)............................................................................ 18

Strain = εLL∆

= (3-1)........................................................................................... 27

Poisson Ratio =LLDD

axial

trans

//

straindirection alLongitudinstraindirection Transverse

∆∆

−=−=−=εεν (3-2) 27

Shearing Strain = Tan length original

nDeformatio φγ == (3-3) ...................................... 28

Normal Stress =AnFor

AreaForcelar Perpendicu

=σ (3-4)................................... 29

66

Shear Stress =Aττ For

AreaForce Parallel

= (3-5) .................................................... 29

Hooke’s Law: εσ *E= or εσ

=E (3-6)............................................................ 30

Shear Modulus =γτ

==StrainShear StressShear G (3-7) ................................................... 30

Shear Modulus =)2(1

Eν+

=G (3-8).................................................................... 30

Bending Strain =E

BB

σε ==Elasticity of ModulusStress Bending (3-9) ............................ 31

Sectional Modulus =(e)Gravity ofCenter of Distance(I) Inertia ofMoment lGeometrica

=Z (in3) (3-10). 31

Drill String section: String

StringString

ODIDOD

ODIZ

*32)(*2 44 −

== π (in3) (3-11) ............ 31

Bending Stress =Z

M BB ==

modulus SectionalMoment Bendingσ (3-12) ............................. 31

Bending Moment = lFM B *= (3-13) ................................................................ 31

Bending Stress =Z

lFB

*=σ (3-14)...................................................................... 31

Bending Forces =lZEF B **ε= (3-15) ........................................................... 31

Axial Strain =E

AA

σε ==Elasticity of Modulus

Stress Axial (3-16)............................... 32

Axial Stress =AFA

A ==Area Sectional Cross

Force Axialσ (3-17) ................................ 32

Axial Force = AEF AAxial **ε= (3-18)............................................................... 32

Shear Strain = Gτγ ==

StressShear of ModulusStressShear (3-19).............................. 32

Shear Modulus= GLA

FLLLAF

∆=

∆===

//

StrainShear StressShear

γτ (3-20)................... 32

Second Moment of Area= 64

)(* 44idod ddI −

=π (in4) (3-21)............................. 32

67

Torsional Strain Gτγ ==

elasticity of modulus TorsionalStress Torsional (3-22)............. 32

Torsional Stress=J

)2/(*Mt d=τ (3-23)............................................................ 32

For accurate shear measurement °= 45@*2 εγ (3-24)................................. 33

Polar second moment of area for a drill pipe cross sectional area

=32

)(* 44idod ddJ −

=π (in4) (3-25).... 33

Torsional Moment = ⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

dJG

dJMt

2*)(**2*)(* γτ (3-26)........... 33

εRR

LLRRGF /or

//

(strain)length in change FractionalResistance Electrical Fractional ∆

∆∆

=∆

= (3-27) .... 36

Temperature adjusted Gauge Factor =100

GF)%(1 ∆+= GFGFA (3-28) ....... 37

Bridge output voltage = ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+=

21

2

3

3*RR

RRR

RVVg

EXo (3-29)................... 38

Bridge resistance change = ε**R g GFR =∆ (3-30)........................................ 38

Measured Strain =GF

Rg

*Rg

∆=ε (3-31) ............................................................... 39

Voltage Ratio = ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+=

21

2

3

3

RRR

RRR

VV

gEX

o (3-32)......................................... 39

Voltage Ratio = unstrained strained ⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

EX

o

EX

oR V

VVVV (3-33).................. 39

¼ Bridge Strain = )21(

4

R

R

VGFV+

−=ε (3-34) (Ignoring lead wire resistance) 39

½ bridge axial strain = [ ])1(2)1(4

−−+−

=νν

εR

R

VGFV (3-35)........................... 40

½ bridge bending strain = GF

VR2−=ε (3-36) ..................................................... 40

Full bridge axial strain = [ ])1()1(2

−−+−

=νν

εR

R

VGFV (3-37) ........................... 40

68

Full bridge bending strain = GFVR−

=ε (3-38) .................................................... 41

Full bridge bending strain (Poisson) )1(*

2+

−=

νε

GFVR (3-39)......................... 41

69

REFERENCES & BIBLIOGRAPHY

Specific references are identified within the body of the text and are identified below along with additional references: • Perry C.C , Lissner, H.R , ‘The Strain Gauge Primer’ second edition,

McGraw-Hill Book Company 1962 ISBN: 07-049461-4

• Economides M J, et al, 'Petroleum Well Construction', John Wiley and Sons, 1998 ISBN: 0-471-96938-9

• William F.Riley, loren W.Zachary. ‘Introduction to Mechanics of Materials’, John Wiley and Sons, 1989 ISBN: 0-471-84933-2

• OMEGA Engineering, Inc. ‘The Pressure Strain and Force Handbook. Volume 29’, 1995

• Teale, R.: “The Concept of Specific Energy in Rock Drilling”, Intl. J. Rock Mech. Mining Sci. (1965) 2, 57-73

• SPE 49206 - Down hole Diagnosis of Drilling Dynamics Data Provides New Level Drilling Process Control to Driller. G. Heisig, SPE Baker Hughes INTEQ, J Sancho, Elf Exploration Production and J.D.Macpherson, SPE, Baker Hughes INTEQ

• SPE 24584 - Quantifying Common Drilling Problems With Mechanical Specific Energy and a Bit-Specific Coefficient of Sliding Friction. R.C. Pessier, Hughes Tool Co., and M.J. Fear, BP Exploration

• IPTC 10607 - Maximizing ROP with Real-Time Analysis of Digital Data and MSE. F.E.Dupriest, SPE, Exxon Mobil, and J.W. Witt, SPE, and S.M. Remmert, SPE, Rasgas Co. Ltd.

• AADE-05-NTCE-66 - A Real-Time Implementation of MSE. William L. Koederitz, M/D Totco, a Varco Company, Jeff Weis, Orion Drilling Company

• IADC/SPE 74520 - Real-Time Specific Energy Monitoring Reveals Drilling Inefficiency and Enhances the Understanding of When to Pull Worn PDC Bits. Robert J. Waughman, SPE Woodside Energy Ltd., John V. Kenner, SPE, Hughes Christensen/Baker Hughes and Ross A. Moore, SPE, Hughes Christensen/Baker Hughes

• SPE/IADC 92194 - Maximizing Drill Rates with Real-Time Surveillance of Mechanical Specific Energy Fred E. Dupriest, SPE, ExxonMobil and William L. Koederitz, SPE, M/D Totco, a Varco Company

• SPE 102210 - Comprehensive Drill Rate Management Process to Maximize Rate of Penetration. F.E.Dupriest, Exxon Mobil Development Co.

70

• SPE/IADC 98931 - Gage Design - Effects of Gage Pad Length, Geometry and Active (Side Cutting) on PDC Bit Stability, Steerability, and Borehole Quality in Rotary Steerable Drilling Applications. G.Mensa-Wilmot, SPE, and B. James, Smith Bits; L.Aggarwal and H.Van Luu, Schlumberger; and F.Rueda, BP

• Drill off test - Proposed by A.Lubinski – January 1958 edition of “The Petroleum Engineer” – Proposal for future tests.

• Robert Gordon University course notes – PgDip/MS Oil & Gas Engineering

• US Patent # 3,827,294 - Aug 6, 1974; Wellbore force measuring apparatus; Ronald A Anderson, Houston Tx – Assignee: Schlumberger Technology Corporation, New York, N.Y.

• US Patent # 5,386,724 - Feb 7, 1995; Load Cells for Sensing Weight and Torque on a Drill Bit While Drilling a Well Bore; Pralay K. Das; Haoshi Song, Sugarland Tx – Assignee: Schlumberger Technology Corp, Houston TX.

• US Patent # 6,216,533 - Apr 17, 2001; Apparatus For Measuring Down hole Drilling Efficiency Parameters; Scott E. Woloson, Dale A Jones, Houston, TX - Assignee: Dresser Industries Inc, Dallas TX

• Grant Prideco IntelliServ™ - http://www.intellipipe.com/intelliservDocs/

• Halliburton Drilling Optimization – http://www.halliburton.com