Casing Design Methodology for Casing While Drilling

Casing Design

Methodology for Casing

While Drilling Optional Subtitle

Karunakar Charan Nooney


Casing Design Methodology for

Casing While Drilling

Casing Design Methodology for Casing

While Drilling By


in partial fulfilment of the requirements for the degree of

Master of Science

in Applied Earth Sciences

at the Delft University of Technology,

to be defended publicly on Wednesday December 16, 2015 at 04:00 PM.

Supervisor: Prof. Dr. Ir. J.D. Jansen

Thesis committee: Prof. Dr. Ir. J.D. Jansen

Prof. Dr. W.R. Rossen,

Prof. Dr. A.V. Metrikine

E.G.D. Barros

An electronic version of this thesis is available at http://repository.tudelft.nl/.

http://repository.tudelft.nl/

Title : Casing Design Methodology for Casing While Drilling

Author(s) : Karunakar Charan Nooney

Date : December 16, 2015

Professor(s) : Prof. Dr. Ir. Jan-Dirk Jansen

Supervisor(s) : Prof. Dr. Ir. Jan-Dirk Jansen

Postal Address : Section for Petroleum Engineering

Department of Geoscience & Engineering

Delft University of Technology

P.O. Box 5028

The Netherlands

Telephone : (31) 15 2781328 (secretary)

Telefax : (31) 15 2781189

Copyright ©2015 Section for Petroleum Engineering

All rights reserved.

No parts of this publication may be reproduced,

Stored in a retrieval system, or transmitted,

In any form or by any means, electronic,

Mechanical, photocopying, recording, or otherwise,

Without the prior written permission of the

Section for Petroleum Engineering

ii

Abstract In the current plans of Delft Aardwarmte Project (DAP), it is considered to perform the drilling operation by using pipes which remain in the well after drilling thus acting as a casing, the so-called “Casing While Drilling” (CwD) technique. Due to the absence of drill pipe tripping prior to casing the well, this technique results in reduced drilling time compared to conventional drilling. Additionally, potential downhole problems due to drill pipe tripping are precluded. This thesis presents a simulation based approach to selecting casing steel of suitable grade capable of withstanding typical loads encountered while drilling of the well and during its producing life. The developed algorithm is then used in the design of the casing string for the proposed DAP geothermal producer well. The algorithm first considers the effect of uni-axial stresses on casing due to defined burst and collapse pressure loads encountered due to loss of well control while drilling or in the production phase to make a preliminary selection. The effect of axial stress due to buoyed weight of casing and the bending stress due to wellbore curvature is then used to re-evaluate the design against the same collapse and burst loads. This is performed by using a bi-axial approach for the former and the Von-Mises triaxial stress criteria for the latter. A ‘Johancsik’ torque and drag model developed in MATLAB is used to predict drag values during tripping. The bi-axial and Von-Mises stress analysis approach is repeated to include the effect of the computed pull-out drag forces. The associated torque values are used to compute torsional stresses and to identify casing connections of appropriate torque capacity. The final step in the algorithm is to simulate the loads occurring during drilling and calculate the equivalent Von Mises stress values throughout the casing string. Typical drilling loads considered include torque and casing lateral vibration which induce torsional and bending stresses respectively. It was identified that rather than bending stress due to whirling or buckling, torsional stress was more likely to cause casing string failure. This is due to its relatively higher magnitude and the weaker maximum torque capacities of conventional casing connections. Additionally, the MATLAB tools developed for analysing buckling and whirling are used to compute the critical load for inducing sinusoidal buckling as a function of wellbore inclination and the critical rotary speed at surface to induce lateral vibration for varying weight on bit (WOB) respectively. From the generated mode shapes, the bending stress magnitude at each node and therefore the points of maximum stress occurrence for bucking and whirling are also identified.

iii

Acknowledgements

First and foremost, I would like to thank my parents without whom none of this would have been

possible. Their unconditional love and support is the foundation on which I have built my career

thus far. Thanks are also due to my elder brother whose keen insight from having completed a

Master’s degree himself benefited me tremendously in the planning and execution of various

activities throughout my MSc studies.

I am extremely grateful to my thesis supervisor, Professor Jan-Dirk Jansen for accepting me as his

student. I am constantly amazed by how he finds time to fulfil his responsibilities as thesis supervisor

inspite of the numerous demands on his time. Without his understanding and guidance, this project

would never have reached completion.

I would also like to thank Professor W.R Rossen, Professor A.V Metrikine & Eduardo Barros for

consenting to form part of the thesis assessment committee and evaluate this project.

I would be seriously remiss not to acknowledge the moral support of my friends here in Delft, Anand

Sundaresan, Akshey Krishna, Bharadwaj Rangarajan, Jeyakrishna Sridhar & Saashwath Swaminathan.

Thanks for everything guys, I couldn’t have done it without you!

Last but not the least, I would like to thank the management at Cost Engineering Consultancy,

Zwijndrecht for their cooperation in agreeing to defer the starting date of my employment so that I

could complete this thesis.

iv

Contents Abstract ................................................................................................................................................... ii

Acknowledgements ................................................................................................................................ iii

Contents ................................................................................................................................................. iv

1 Introduction .................................................................................................................................... 1

1.1 Casing While Drilling ............................................................................................................... 1

1.1.1 Non-Retrievable BHA ...................................................................................................... 1

1.1.2 Retrievable BHA .............................................................................................................. 2

1.1.3 Liner While Drilling .......................................................................................................... 3

1.1.4 Casing Pipe Connections for CwD ................................................................................... 3

1.2 Thesis Outline .......................................................................................................................... 4

2 Design Algorithm ............................................................................................................................. 5

3 Torque and Drag Analysis ............................................................................................................... 7

3.1 Implementation of Torque and Drag Model ......................................................................... 10

3.2 Model Validation ................................................................................................................... 11

4 Static Deflection ............................................................................................................................ 13

4.1 Derivation of Governing Equation ........................................................................................ 13

4.2 Results ................................................................................................................................... 16

4.2.1 Deflection ...................................................................................................................... 16

4.2.2 Validation of Model with Analytical Solution ............................................................... 16

4.3 Slope & Bending Moment for various Weight-on-Bit Conditions ......................................... 18

5 Buckling Analysis ........................................................................................................................... 19

5.1 Governing Equation .............................................................................................................. 19

5.2 Results ........................................................................................................... 20

6 Natural Frequency of Lateral Vibration for Rotating Casing ......................................................... 22

6.1 Derivation of Governing Equation ........................................................................................ 23

6.2 Results ................................................................................................................................... 24

6.2.1 Comparison with Analytical Solution ............................................................................ 24

6.2.2 Variation of Natural Frequency with Applied Weight on Bit ........................................ 25

7 Application of Developed Concepts to DAP Producer .................................................................. 27

7.1 Initial Well Data ..................................................................................................................... 27

7.2 Stresses Considered .............................................................................................................. 29

7.2.1 Axial Stress .................................................................................................................... 29

7.2.2 Bending Stress ............................................................................................................... 29

7.2.3 Torsional Stress ............................................................................................................. 30

v

7.2.4 Hoop Stress ................................................................................................................... 30

7.2.5 Radial Stress .................................................................................................................. 30

7.2.6 Von Mises Stress ........................................................................................................... 30

7.3 Power Law Fluid Rheology Model ......................................................................................... 31

7.4 Casing Design Load Cases...................................................................................................... 33

7.4.1 Surface Casing ............................................................................................................... 33

7.4.2 Intermediate Casing ...................................................................................................... 35

7.4.3 Production Liner ............................................................................................................ 35

7.5 Casing Selection Based on Uniaxial Loading Criteria ............................................................ 35

7.5.1 Surface Casing ............................................................................................................... 36

7.5.2 Production Casing ......................................................................................................... 36

7.6 Axial Loading ......................................................................................................................... 38

7.6.1 Wellbore Trajectory ...................................................................................................... 38

7.6.2 Surface Casing ............................................................................................................... 38

7.6.3 Intermediate Casing ...................................................................................................... 39

7.6.4 7” Liner .......................................................................................................................... 39

7.6.5 Axial Load due to Well Bore Trajectory ........................................................................ 40

7.7 Combined Loading ................................................................................................................ 40

7.7.1 Collapse with Axial Loading ........................................................................................... 40

7.7.2 Von Mises Analysis for Burst Loading ........................................................................... 42

7.8 Torque & Drag Analysis ......................................................................................................... 42

7.8.1 Axial Loading due to Drag Forces .................................................................................. 43

7.8.2 Torque Analysis ............................................................................................................. 45

7.9 Wellbore Pressure Distribution ............................................................................................. 45

7.10 Drilling Loads ......................................................................................................................... 47

7.10.1 7” Liner – Bending Stress Due to Whirl ......................................................................... 47

7.10.2 9 5/8” Casing – Bending Stress Due to Buckling ........................................................... 49

7.11 Von Mises Analysis of Drilling Loads during 7” Liner Section ............................................... 51

8 Conclusions ................................................................................................................................... 52

8.1 Recommendations ................................................................................................................ 52

Nomenclature ....................................................................................................................................... 53

List of Abbreviations ............................................................................................................................. 54

Bibliography .......................................................................................................................................... 55

Appendix A. Implementation of FDM for Beam Deflection .............................................................. 58

Appendix B. Implementation of FDM for Buckling Analysis ................................................................. 62

Appendix C. Implementation of FDM for Whirling Analysis ............................................................. 64

vi

Appendix D. Supporting Tabular Data ............................................................................................... 66

Appendix E. Torque Analysis & Corresponding Selection of Casing Connection .............................. 73

Appendix F. Fluid Hydraulics – Frictional Pressure Losses ................................................................ 75

vii

List of Figures

Figure 1 Non Retrievable BHA [1] ........................................................................................................... 2

Figure 2 Retrievable BHA. Combination image generated from [2] & [3] .............................................. 2

Figure 3 Retrievable BHA for drilling with Liner [5] ................................................................................ 3

Figure 4 BTC with Torque Shoulder [36] ................................................................................................. 4

Figure 5 Typical Buttress Threaded Connection [10] .............................................................................. 4

Figure 6 Overview of the Casing Design Process .................................................................................... 5

Figure 7 Downhole Forces on Casing [11] ............................................................................................... 7

Figure 8 Force Balance on Drill String Element [13] ............................................................................... 8

Figure 9 Discretization of Drill String into Nodes [7] .............................................................................. 9

Figure 10 Snapshot of EXCEL spread sheet used for accepting Input String Data for T&D Model ....... 10

Figure 11 Sample Output Plots for Surface Hook Load & Cumulative Surface Torque ........................ 10

Figure 12 12 1/4" OH Section Hook Load Measurements for Well South Sangu-4 .............................. 11

Figure 13 8 1/2" OH Section Hook Load Measurements for SS-4 ......................................................... 11

Figure 14 Forces acting in radial direction [19]..................................................................................... 13

Figure 15 Variation of axial load in drill string [19] ............................................................................... 14

Figure 16 Plot of Deflections at Inclination of 10 Degrees ................................................................... 16

Figure 17 Clamped beam with Pinned End on which is exerted a constant lateral load and axial

compressional force. [20] ..................................................................................................................... 17

Figure 18 Verification of Numerical Model ........................................................................................... 18

Figure 19 Variation in Bending Moment for Hold Inclination of 10 Degrees ....................................... 18

Figure 20 Casing initially resting on lower side of wellbore ................................................................. 19

Figure 21 Mode shapes at 0 degrees Inclination .................................................................................. 21

Figure 22 Plot of numerical & analytical critical loads as a function of wellbore inclination ............... 21

Figure 23 BHA Whirl [25] ...................................................................................................................... 22

Figure 24 Section of BHA rotating about axis [19] ................................................................................ 23

Figure 25 Mode shapes for the first natural frequency of Lateral Vibration ........................................ 24

Figure 26 Dependence of natural frequency on the applied Weight on Bit ......................................... 25

Figure 27 Drilling Window for Wellbore Fluid Gradient ....................................................................... 28

Figure 28 Planned Trajectory of Producer ............................................................................................ 28

Figure 29 Graphical representation of Design Loads vs. Rated Strength ............................................. 37

Figure 30 Measurement of Key Wellbore Trajectory Parameters ........................................................ 38

Figure 31 Plot of Design Load vs. Rated Strength for Collapse ............................................................. 41

Figure 32 Plot of Pick Up Drag Forces When Tripping Out of String ..................................................... 42

Figure 33 Design Collapse Load vs. Strength for DAP Producer ........................................................... 44

Figure 34 Increased FOS for Burst Loading Due to Effect of Drag Forces ............................................. 44

Figure 35 Cumulative Torque Observed at Surface for Various Drilled Depths ................................... 45

Figure 36 Flow Path for Drilling Fluid in 7" Liner Drilling Phase............................................................ 46

Figure 37 Fluid Pressure Distribution for 7" Liner Drilling Phase .......................................................... 46

Figure 38 Whirling Mode Shapes .......................................................................................................... 47

Figure 39 Natural Frequency of Lateral Vibration vs. WOB .................................................................. 47

Figure 40 Bending Stress Due to Whirl ................................................................................................. 48

Figure 41 Buckling Mode Shapes and Dependency of Critical Load on WOB ....................................... 49

Figure 42 Bending Stress due to Buckling in 9 5/8" Intermediate CSG ................................................ 50

Figure 43 7" Liner Von-Mises Stress Analysis for Drilling Operation .................................................... 51

Figure 44 Discretization of Drill String [19] ........................................................................................... 58

viii

List of Tables

Table 1 Error Percentages for Simulated Hook Load Results ............................................................... 12

Table 2 Flow Rate for Minimum Annular Velocity [30]......................................................................... 31

Table 3 Factor of Safety [31] ................................................................................................................. 33

Table 4 Production Casing Specifications ............................................................................................. 37

Table 5 Summary of Required Material Properties based on Design Loads......................................... 37

Table 6 Surface Casing Properties ......................................................................................................... 38

Table 7 Intermediate CSG Properties ................................................................................................... 39

Table 8 Liner Hold Section Properties ................................................................................................... 39

Table 9 Build Up Section Properties ..................................................................................................... 39

Table 10 Power Law Input Viscometer Measurements ........................................................................ 46

Table 11 Casing String Design for DAP Producer Geothermal Well ...................................................... 52

Table 12 Von Mises Stress Analysis at Survey Points for Burst Loading Scenario ................................ 66

Table 13 Simulated Pick-Up Drag Values at Survey Points for 7” Liner Drilling .................................... 68

Table 14 Von Mises Analysis at Various Survey Points for 7'' Deviated N80 Liner Section .................. 69

Table 15 Simulated Bending Stress due to Whirling for 7” Liner Stand (30 M) .................................... 70

Table 16 Von Mises Tri Axisal Stress Analysis of 7" Liner for Drilling Conditions at Survey Points ...... 71

Table 17 Bending Stress due to Buckling for 9 5/8" Intermediate CSG Stand (30 metres) .................. 72

Table 18 Torque Analysis at Survey Points for 7" N80 Liner Section .................................................... 73

Table 19 Connection Make-Up Torque Capacities from Manufacturer Catalogue .............................. 74

Table 20 Pressure Loss Computed By Power Law Rheology ................................................................. 75

1

1 Introduction

1.1 Casing While Drilling

The primary motivation for this thesis is the plan of the Delft Aardwarmte Project (DAP) to drill the producer geothermal well by employing the CwD technique. Due to the absence of drill pipe tripping, this technique results in reduced drilling time compared to conventional drilling whilst also precluding numerous downhole problems. The simulation based approach presented in this thesis is designed to select a suitable grade of casing steel for the DAP geothermal producer well but this algorithm can also be extended towards composite materials as well. The reduced weight of composite materials in comparison to steel would allow DAP to use rigs of smaller draw-works capacities without reduction in target depths thereby resulting in significant cost savings. The CwD has the following advantages in comparison to conventional drilling:

Eliminates the need for tripping of drill string prior to casing the well. The primary benefit of

doing so is the reduction in rig operating time. Additionally, potential downhole problems

such as loss of well control, surge and swab pressures when the casing is being run in or hole

collapse due to presence of unstable zones in the wellbore can be avoided.

Problematic ‘thief’ zones which absorb drilling fluid completely, thereby causing a loss of

primary well control can be bypassed in this technique due to the “plastering effect” of the

casing. Due to the low annular clearances between casing and borehole wall, the casing

effectively smears the drilling fluid particles into the borehole wall creating a superior filter

cake thereby bypassing these zones.

Low annular volumes enables higher flow velocities which facilitates hole cleaning.

It is not without its disadvantages however and these are:

Low annular clearances lead to higher frictional flow losses which necessitate the use of

higher capacity pumps for same drilled depths in comparison to conventional drilling

In order to execute a CwD operation, the rig hoisting equipment (usually the top drive) has

to be modified to accommodate the casing. Additionally, other special equipment such as

torque rings, modified elevators and tongs have to be employed which result in a further

increase in costs

There are two variations in bottom hole assemblies (BHAs) used for this technique which are applied

based on the well trajectory and target depth requirement.

1.1.1 Non-Retrievable BHA

This technique is used for shallow depth vertical sections in formations with soft to medium

hardness levels only. Typically, the top hole section is drilled using this BHA. No drill collars are used

however stabilizers may be used in regular intervals of one stand. Other cementing equipment such

as float shoe and collar may also be used. Typically, special polycrystalline diamond compact (PDC)

bits which are soft enough to be drilled through by conventional bits used in the next drilling phase

are preferred. The flow path for circulating of drilling fluid is identical to conventional drilling

operations.

2

Figure 1 Non Retrievable BHA [1]

1.1.2 Retrievable BHA

Figure 2 Retrievable BHA. Combination image generated from [2] & [3]

The retrievable BHA as the name suggests can be retrieved by wireline after the section has been

drilled prior to cementing. The primary components are the pilot bit for drilling the initial hole, an

under reamer for subsequently enlarging it, rotary steerable or mud motors, “Measurement While

Drilling” (MWD)/ “Logging While Drilling” (LWD) tools and the drill lock/latch assembly. The DLA is

locked in such a way to prevent relative axial and torsional motion between the BHA and the casing

[4]. Seals used in the DLA as shown in Figure 2 prevent the flow of drilling fluid into the casing and

instead divert into the BHA [4]. Any type of formation can be drilled at any depth without placing

any restrictions on wellbore inclination & depth or formation hardness.

3

1.1.3 Liner While Drilling

In “Liner while Drilling” operations, the drill pipe used to run in the liner includes the liner hanger for

supporting the weight of the liner and the BHA for drilling. Consequently, the circulation path for

drilling fluid is entirely through the inner drill string as a result of which, the entire liner is not

exposed to internal fluid pressure as shown in Figure 3.

Figure 3 Retrievable BHA for drilling with Liner [5]

1.1.4 Casing Pipe Connections for CwD

Typical casing connections are designed for one time use only where the casing connection is made

up at surface and run into the hole. They are not designed for handling torsional and alternating

stresses induced by rotation of the string. Therefore special casing connections have to be designed

with high torque transmission capability. As per [1], [6], [7], [8]& [9] the preferred connections used

are the API Buttress Threaded Coupled (BTC) connections with metal to metal seal. Depending upon

the specific well trajectory, these connections may also provide insufficient torque capacity.

Consequently, special metal torque rings are inserted between casing threads to further increase the

maximum torque capacity by providing a positive torque shoulder which prevents thread crushing

by over-torqueing and acting as a spacer between the two threads.

4

Figure 5 Typical Buttress Threaded Connection [10]

1.2 Thesis Outline

Chapter 2 presents the design algorithm to be followed for the selection of casing steel grade with a

brief discussion of each step in the sequence.

Chapter 3 introduces the torque and drag model starting with a brief discussion of the need for

calculating wellbore torque and drag forces and the subsequent implementation of the ‘Johancsik’

model in this thesis by using a combination of an MS EXCEL spread sheet for accepting input data

and MATLAB for computing actual forces and plotting the results. Steps taken for checking the

accuracy of the model are also presented.

Chapters 4, 5, and 6 are concerned with the theoretical derivation of the governing equations or

Eigen value formulations for buckling and whirling analysis. The starting point is the derivation for

the deflection of the string under the influence of the external load applied at surface. In addition to

the theoretical derivation, the governing equations are solved using the finite difference method in

MATLAB for which the details are contained in Appendix A, Appendix B and Appendix C. Each model

is validated by comparing with analytical solutions from literature.

Chapter 7 focuses on the application of the algorithm and supporting MATLAB tools developed, to

the DAP producer well casing design. The implementation of the previously defined algorithm along

with the analysis of results obtained is described comprehensively. Supporting data for bending

stress due to Buckling & Whirling, Torque, Drag & Von Mises stress obtained from the MATLAB tools

is tabulated in Appendix D & E for reference. Appendix E also presents a simple example of selecting

a suitable buttress casing connection from a manufacturer catalogue on the basis of rated make-up

torque capacity. Implementation of the hydraulic model based on the “Power law” rheology model

for calculating the wellbore pressure distribution is reported. Supporting hydraulic calculations are

summarized in tabular format in Appendix E.

Lastly, in Chapter 8 the conclusions derived from the thesis work are presented and suggestions are

made towards extending specific aspects of this thesis.

Figure 4 BTC with Torque Shoulder [36]

5

2 Design Algorithm

Figure 6 Overview of the Casing Design Process

6

In this section, the overall process of selecting the casing steel for the CwD application is conveyed in

the form of an algorithm displayed in Figure 6 above. The starting point of the algorithm is the

formation strength and fluid pressure gradient data (section 7.1) needed for calculating bottom hole

pressure to maintain hydrostatic balance with formation fluid. The fluid properties of plastic

viscosity, yield point and shear rate are used to calculate the wellbore dynamic fluid pressures on

the basis of the power law rheology model as shown in Appendix F. In the next step, the collapse

and burst loads are estimated for making the preliminary selection of casing on the basis of the

uniaxial loading criteria (section 7.4). The selected grade of casing steel is also verified for axial

loading due to buoyed weight and bending due to wellbore curvature (section 7.6).

As axial loads reduce collapse resistance of the casing string, a combined load analysis for hoop and

axial loads is performed (section 7.7.1) along with a tri-axial stress analysis for the burst scenario

(section 7.7.2). If in each of these cases, the ratio of material yield strength to the equivalent stress is

found to be greater than the design factor of safety, than the design is considered to be effective.

The next step is the simulation of torque and drag forces induced in the casing string when drilling

and tripping out of the wellbore respectively (section 7.8 ). The drag forces are used to compute an

increased axial load for which the combined loading analysis is repeated to ensure that the casing

string does not fail to this increased axial load (section 7.8.1.1). If failure occurs, then the next grade

of casing steel is selected and the process is repeated again starting with the revised torque and drag

analysis.

If however the design does not fail, then the computed torque values (Appendix E ) are used to

calculate the torsional stress. In the final step, torsion together with axial stress due to whirling are

included in the von Mises triaxial stress analysis (section 7.10) to simulate the effect of combined

loads on the casing string during the drilling process. The torque values are also used to select the

casing buttress connection of required torque capacity (Appendix E ). The radial and hoop stress are

determined by the dynamic fluid pressures inside the casing and in the casing open hole annulus and

are obtained from the result of the hydraulic model.

While the buckling and torque & drag analysis assume that the casing string is always in contact with

the wellbore, the whirling analysis considers the casing to be perfectly centered such that the radial

clearance is uniform throughout. These assumptions are needed to overcome the difficulty

associated with assessing the contact points in a realistic scenario where there are many

uncertainties such as wellbore tortuosity, washed-out holes, and varying diameters of casing

centralizers, stabilizers and collars. In short, the nature of the analysis contained in this thesis is

more qualitative in nature rather than quantitative.

7

3 Torque and Drag Analysis

Figure 7 Downhole Forces on Casing [11]

The analysis of torque and drag force encountered by the casing string during the process of tripping

in and out of the wellbore is critical to the design process. It is often the limiting factor in drilling

deviated and extended reach wells as a result of which trajectories are designed to minimize normal

contact forces and consequently the torque and drag as much as feasible. Torque and drag forces

are generally caused by poor downhole conditions such as key-seating, sloughing shales etc. or due

to sliding friction associated with the wellbore trajectory.

Sliding friction acting between the wellbore and the casing string gives rise to an increase in the

tensile force acting along the longitudinal axis of the casing string which is known as drag. Because

friction acts in the opposite direction of string movement, drag causes an increase in the hook load

measured at surface above the free rotating weight of the string during pull out and a reduction in

hook load while running in. The increased axial force component during pull out significantly reduces

the collapse resistance of the casing and the maximum along- hole depth capable of being reached

by a rig with a fixed hook load capacity. The reduction in the axial force when running in can limit the

free movement of the string under its own weight into the hole at higher inclinations and can lead to

buckling if the driller exceeds the critical weight on bit applied at the surface in order to push the

string deeper.

When the casing string is rotating in the wellbore with a weight on bit during drilling, the torque

available at the bit is much less than the external torque applied at surface by the rotary or top

drive. This is due to losses occurring throughout the casing string due to the frictional forces acting

at the point of contact between the wellbore and the casing string creating a resisting moment with

vector direction opposite to that of casing rotation. As torque is directly proportional to the frictional

force, increase in drag forces is usually accompanied by increasing torque loss as well. Consequently,

the limiting factor for rotating the casing while reciprocating (for better conditioning of drilling fluid)

or for drilling deeper and with greater inclination is often the maximum torque deliverable at surface

by the rig and the torque carrying capacity of the casing connections.

8

For designing the casing string, it is therefore necessary to use a torque and drag model which can

simulate the various loads during drilling and tripping operations so that the requisite grade of

casing steel with yield strength greater than design axial and torque loads by a planned factor of

safety can be selected.

As per [12]the most widely used model in the industry is the “soft string” model first developed by

Johancsik et al. [13]. The Johancsik equations were later rewritten in differential form by Sheppard

[14] who also included the effect of buoyancy due to mud pressure in the model.

The Johancsik model assumes that

Torque and drag are caused primarily by sliding friction force with other smaller contributors

neglected

The drill string is in continuos contact with the borehole wall

Normal (side) forces due to pipe bending stiffness are neglected. ie, the drill string is

modelled as a flexible chain or “soft string” model with no bending moments

Figure 8 Force Balance on Drill String Element [13]

Johancsik states that sliding friction force is the product of coefficient of dynamic friction between

drill string and borehole wall and the normal force acting at the point of contact of the two surfaces.

He then calculates the normal force or net side load, by performing a force balance as shown in

Figure 8. Net side load is equated to the normal components of the axial force due to bending of

drillstring in curved (build up or drop off) section of wellbore and gravity force due to its weight.

Johancsik discretizes the drill string into elements of finite length which transmit incremental axial

force and torque to the next section. The analysis starts from the bit and proceeds towards the top.

As shown in Figure 9 at node point i , the axial force transmitted by node point 1i is used as the

input for calculating the normal force acting uniformly on the element 1i iS S and the axial force

1iF . Thus, axial force and torque values are cumulatively summed up to obtain the actual loads.

9

Figure 9 Discretization of Drill String into Nodes [7]

The incremental form of the Johancsik equations for axial force and torque as presented in [7] are:

11

1

( ) cos( )2

ni i

n o i i i i i

i

F F s s w N

, (3.1.1)

1

n

n o i i i

i

r N

, (3.1.2)

where,

iF Axial load at node i , N

w Buoyed specific weight of casing, N

s Distance coordinate along the measured depth of wellbore trajectory, m

Friction coefficient

Inclination angle, radians

Azimuth angles, radians

Torque, Nm

The contact force iN computed from the force balance as used in(3.1.1) and (3.1.2) above is given

by:

2 2

1 1 1 11

1 1

( ) sin sin2 2

i i i i i i i ii i i i i i

i i i i

N s s w F Fs s s s

. (3.1.3)

From(3.1.3), it can be seen that the normal force vanishes for vertical wellbores as inclination

reduces to zero and azimuth remains constant and hence the model returns zero drag and torque

values for vertical sections. This is however untrue in practice because the wellbore cannot be drilled

strictly vertical and will always possess low inclination values upto 3~4 degrees.

10

3.1 Implementation of Torque and Drag Model

The Johansik model is implemented in MATLAB using an excel spread sheet to accept the input

parameters of drill string specifications and the well survey data (Measured Depth, Inclination &

Azimuth). Other input parameters include

Drilling Fluid Density

Friction Factor

WOB for Drilling

TOB in case of downhole motor

Figure 10 Snapshot of EXCEL spread sheet used for accepting Input String Data for T&D Model

The output of the model is the plot of drag and torque forces acting on the casing string at a

particular bit depth. It also computes the plot of hook load measured at surface versus the drilled

depth which is used for estimating the required rig draw works capacity. It is also used for validating

the model by comparing simulated hook loads with real time data obtained from field

measurements.

Figure 11 Sample Output Plots for Surface Hook Load & Cumulative Surface Torque

11

3.2 Model Validation

For the purpose of verifying the accuracy of the torque and drag model, real time hook load

measurement data from offshore well ‘South Sangu-4’ drilled by Santos Ltd. is used to compare

against the simulated hook loads. This data is obtained from MSc thesis report of T.Chakraborty [15].

The author back calculates the friction factor for this well from the real time measurements using

the Halliburton Well Plan simulator. These same friction factors along with drill string specification

and other input parameters are fed into the developed torque and drag model to compare with the

Santos real time hook load data set for an 12 ¼” and 8 ½” open hole sections.

Figure 12 12 1/4" OH Section Hook Load Measurements for Well South Sangu-4

Figure 13 8 1/2" OH Section Hook Load Measurements for SS-4

12

Table 1 Error Percentages for Simulated Hook Load Results

As can be seen from the table above, there is an average error of approx. 8.3% between the

simulation results and real time data. This can possibly be attributed to sophistication of the

WellPlan simulator. Although it is also based on the soft string model [16], it also considers effect of

contact surface area [17] and Hydrodynamic Viscous Drag forces [18]. The latter is induced on the

string when tripping by the drilling fluid in the wellbore. Implementation of the same would require

a more realistic hydraulics model and is beyond the scope of this thesis work.

Well South Sangu 4 12 ¼’’ OH 8 ½’’ OH

Friction Factor, 0.35 0.45

Maximum POOH Error

6.87 % 11.11%

Maximum RIH Error 8.18% 7%

13

4 Static Deflection

4.1 Derivation of Governing Equation

The static deflection analysis begins with the derivation of the governing differential equation for the

lateral displacement of the casing string by considering a section of the casing of length ‘dz’ shown

below. The z axis is chosen as the longitudinal axis of the borehole with the origin at the bit. The

analysis will be carried out for one ‘single’ of casing pipe of standard length.

Figure 14 Forces acting in radial direction [19]

Let the radial component of the buoyant weight of steel per unit length be defined as:

sinyw A gh . (4.1.1)

Similarly, the longitudinal component of buoyant weight of steel per unit length is:

coszw A gh . (4.1.2)

Additionally, let

m = Density of drilling fluid, 3/kg m

= Density of tubular, 3/kg m

1 mh

, buoyancy factor

N = axial force acting through the casing

0F = applied weight on bit

y = lateral deflection in the y-z plane

ys =shear force in the drill string in the y-z plane

= Inclination from the vertical

14

The axial load varies linearly throughout the casing string as shown in Figure 15. At the drill bit, the

load is compressive in nature owing to the weight of the overlying portion of the string slacked off by

the driller in order to exert the weight on bit. This is why drill collars possess a greater internal

cross-section to reduce the likelihood of buckling. Towards the top, the drill pipes are in tension due

to the weight of the string underneath. The point at which the tensile and compressive forces negate

each other thereby reducing the axial force to zero is known as the ‘Neutral point’ indicated by the

point '

0l . In general, the drill string is designed in such a way that the neutral point falls within the

BHA. The applied weight on bit is used to determine the position of the neutral point by using the

relation:

0 0cosF A gh l . (4.1.3)

Thus the axial load is given by the relation:

0 ZN F w z . (4.1.4)

Figure 15 Variation of axial load in drill string [19]

From [20], we know that the angle of deflection of the beam with respect to the longitudinal axis:

,dy

dz (4.1.5)

and the shear force:

3

3y

d yS EI

dz . (4.1.6)

From Figure 14, we can form the equilibrium equation of forces in the radial direction as:

sin )(sin ) 0y

y y y

ds dNs dz w dz s N N dz d

dz dz . (4.1.7)

For small deflections,

sin( )d d . (4.1.8)

Substituting (4.1.8) in(4.1.7), we get:

15

0y

y

ds dN ddz w dz dz N dz

dz dz dz

. (4.1.9)

Substituting(4.1.4),(4.1.5) & (4.1.6) in(4.1.9), and dividing throughout by z :

4 2

004 2

( )( ) 0z

y z

d F w zd y dy d yEI w F w z

dz dz dz dz

, (4.1.10)

4 2

04 2( )z z y

d y d y dyEI F w z w w

dz dz dz . (4.1.11)

Substituting (4.1.3) in(4.1.11), and dividing throughout by MA C to account for the drilling fluid

contained within the casing string, we finally obtain:

4 2

04 2

cos sin( )

M M M

EI d y gh d y dy ghl z

A C dz C dz dz C

. (4.1.12)

Equation (4.1.12) is the static equilibrium equation for forces acting on a section of the casing string

in the y-z plane. A similar method can be applied to obtain the equilibrium equation for the x-z plane

which is similar to (4.1.11) except for the presence of the lateral gravity componentyw . The two

equations can be combined using polar coordinates to obtain the complete deflection equation in

the wellbore. Equation (4.1.12) can be expressed in a dimensionless form as follows:

2

0 4

m

EI

A C L

, (4.1.13)

0t , (4.1.14)

z

wL

, (4.1.15)

'

y wy w

L , (4.1.16)

00

' ll

L . (4.1.17)

Making use of these terms, the following dimensionless equation is obtained:

4 ' 2 ' '

'

04 2 2 2

0 0

m m

d y ghcos d y dy ghsinl w

dw L C dw dw L C

. (4.1.18)

16

Equation (4.1.18) can be rewritten in the form of a series of a series of algebraic equations by using

the finite difference method [19] and solved at various node points throughout the drill string in

order to find the nodal displacements as shown in Appendix A.

4.2 Results

4.2.1 Deflection

Figure 16 Plot of Deflections at Inclination of 10 Degrees

As a test case, deflection of a drill collar with outer and inner diameters 7.5 inches (190.5 mm) and

2.81 inches (71.37 mm) respectively at an inclination of 10 degrees to the vertical was plotted in

Figure 16 and as expected, with increasing weight on bit, the observed deflection is found to

increase.

4.2.2 Validation of Model with Analytical Solution

The analytical solution considered here is of a beam which is clamped on one end and pinned on the

other end. It is subjected to an axial compressive force and a constant lateral force (gravity).

17

Figure 17 Clamped beam with Pinned End on which is exerted a constant lateral load and axial compressional force. [20]

As per [20], the analytical expression for deflection in this situation is given by:

24

4 2

2cos sin 1 ( )164 cos 8 sin

bx

uxu ql x l x Mql kx xl

EIu u EIu P kl l

. (4.2.1)

where,

X = Deflection, m

P = Longitudinal compressive force, N

l = Length of beam, m

q , Buoyed uniform lateral load,N

m

2 2

kl l Pu

EI

bM , Bending moment =2 ( )

8 ( )

ql u

u

, Nm

( )u Trigonometric factor representing influence of P on X 3

3(tan )u u

u

.

( )u Trigonometric factor representing influence of P on deflection angle at the beam ends

=3 1 1

2 2 tan 2u u u

.

Numerical values of the functions ( )u and ( )u for varying u are tabulated in [20].

The numerical deflection for the test drill collar was then computed with an inclination of 90 degrees

on the well trajectory. Both curves were then plotted on the same graph as shown in Figure 18.

18

Figure 18 Verification of Numerical Model

From Figure 18, it can be seen that the results of the numerical model are in close agreement with

the analytical solution for deflection.

4.3 Slope & Bending Moment for various Weight-on-Bit Conditions

As per [20], bending moment of a beam is 2

2

d yEI

dw which is then computed at each node point for

the drill collar test case in section 4.2 using the Finite Difference method. The result is plotted for

the test drill collar case in Figure 19. We see that as the Weight on Bit increases, the Bending

Moment also increases.

Figure 19 Variation in Bending Moment for Hold Inclination of 10 Degrees

19

5 Buckling Analysis

5.1 Governing Equation

When the weight on bit causes the axial load to increase beyond a certain critical value, the drill

string becomes unstable and buckles transversely to come in contact with the wellbore. When

drilling inclined holes, the drill string in spite of resting on the lower side of the borehole will first

buckle into a sinusoidal shape. Upon further increase of the weight on bit, the drill string will

eventually transition into a helical shape when the axial load approaches the second critical load.

Determining the limiting value of the allowable weight on bit is an important part of the well design

process due to the numerous disadvantages associated with buckling such as failure of down hole

tools, BHA being subjected to fluctuating fatigue loads and the reduced drilling progress.

Figure 20 Casing initially resting on lower side of wellbore

In the following analysis, the tendency for drill strings to buckle in inclined well bores will be studied

by determining the critical load for sinusoidal buckling when the string is in contact with the

borehole wall. This is done by using the finite difference method to discretize the governing

differential equation and reshape it into an Eigen value problem. The governing differential equation

is derived in [21]by combining the equations for deflection in the y-z (4.1.12)& the x-z plane using

complex coordinates to form a fourth order non-linear differential equation with variable

coefficients. This equation is linearized by a Jacobian transformation [21]to obtain the equation for

the deflection in the y-z plane as:

4 2

04 2( ) 0

y

z z

wd y d y dyEI F w z w y

dz dz dz c . (5.1.1)

where sinWellbore Ca gc D D , radial clearance between casing and wellbore wall in m .

In equation(5.1.1), the first term on the left hand side corresponds to the flexural rigidity of the

tubular. The second term on the left represents the effect of the uniformly varying axial load along

the longitudinal axis of the casing on the lateral deflection. The third term quantifies the gravity

effect on the casing string which is the buoyed weight per uniform length. Finally, the fourth term

represents a restoring force. From Figure 20, it can be seen that the natural tendency of the casing is

to rest on the lower side of the wellbore. When the casing is displaced laterally or sideways from this

20

position during buckling, the resistance of the wellbore wall to this motion induces a restoring force

in the casing proportional to the magnitude of its displacement from the equilibrium position.

The radial clearance term c , can be dimensionalized as:

sin'

2

Wellbore Ca gD Dc

L

, (5.1.2)

where L = length of casing section between drill bit and stabilizer, m .

The same procedure used to obtain the dimensionless form of the governing equation for static

deflection in section 4.1 is repeated here to obtain the scaled governing equation for the stability

analysis in the y-z plane. By substituting the dimensionless parameters (4.1.13) to (4.1.17) &

equations (4.1.1),(4.1.2), and (5.1.2) in (5.1.1), we obtain

4 ' 2 ' '

'

4 2 2

'

'2

0 0

0 0m m

d y ghcos d y dy ghsinl w y

dw L C dw dw L C c

. (5.1.3)

The homogenous linear differential equation (5.1.3) is discretized using the finite difference method

with similar clamped & pinned boundary conditions described in Appendix A and then rearranged

into an eigen value problem as:

A y B y , (5.1.4)

0A B y . (5.1.5)

Where = weight on bit multiplier for determining critical load.

The Eigen value problem defined in (5.1.5) is solved by implementing the finite difference technique

in Appendix B.

5.2 Results

The following curves were plotted for the previously defined drill collar test case using MATLAB to

represent the buckling of the casing string in the wellbore. The deflection is scaled to the annular

clearance between the drill collar outer diameter and wellbore diameter specified by the chosen bit

diameter. In Figure 21, the eigen vector solution of equation (5.1.5) is plotted as the buckled mode

shape of the casing string in a vertical wellbore. The numerically computed solution is then

compared with the standard analytic formula for the critical load to induce sinusoidal buckling in

inclined or vertical wellbores as presented in [22]:

2crit

EI AghsinF

r

. (5.2.1)

21

Figure 21 Mode shapes at 0 degrees Inclination

Figure 22 Plot of numerical & analytical critical loads as a function of wellbore inclination

From Figure 22, we see that the numerical solution computed corresponds reasonably to the

analytical solution for increasing weight on bit and angle of inclination. It is also observed that the

critical load increases at a much faster rate at lower wellbore inclinations.

22

6 Natural Frequency of Lateral Vibration for Rotating Casing

In order to gain an insight into the dynamic loading conditions of the BHA, the lateral or bending

vibrations will be studied in this section with the aim of determining the natural frequencies and

their dependence on the applied weight on bit. Historically, of the three different vibration modes,

lateral vibrations were the last to be studied, as they typically went undetected at the surface owing

to their relatively higher frequency which caused them to attenuate much faster. They have been

identified as the leading cause of drill string failure by [23]. They can be caused by amongst other

things, improperly balanced, bent or off-centre BHA components [24]. Interaction of the drill bit with

the formation or of the drill string with the wellbore may also lead to lateral vibrations.

Lateral vibrations are a complex phenomenon, an important subset of which is the forward

synchronous whirl. When the instantaneous centre of rotation of the BHA is eccentric or away from

its centre of gravity, a whirling motion occurs and when the BHA rotates about its instantaneous

centre in the same direction as its revolution around the borehole axis due to the torque applied by

the rotary table, it is known as forward synchronous whirl. By performing an Eigen value analysis of

the natural frequency of lateral vibration, the critical rotary speed at which forward synchronous

whirl will occur can be theoretically determined and can then be used by the driller as a rough guide

on which rotary speed range for drilling ahead without causing resonant vibrations.

Figure 23 BHA Whirl [25]

Another significant subcategory is the backward whirl which occurs when the directions of rotation

of the BHA about its instantaneous centre and the rotary table are different. One of the causes of

backward whirl as described by [26] and [23]is the friction between the stabilizers and the wellbore

which can induce the backward whirl of the entire BHA.

23

6.1 Derivation of Governing Equation

Figure 24 Section of BHA rotating about axis [19]

For determining the governing differential equation of lateral vibration for a rotating BHA, the

inertia force must be defined so that it can be included in the subsequent force balance equation as:

2

2

2( sin )i M

d yF A C b t

dt . (6.1.1)

Where iF = inertia force

= rotary speed

b = offset of the centre of gravity of the section from the geometric centre along the Y-axis

'

1 mM

s

MC

M , added mass coefficient to account for drilling fluid contained per unit length

of BHA

Recalling the previously defined equation (4.1.11) for the static force equilibrium in the Y-Z plane,

the aspect of rotation of the BHA is included in it by substituting the inertia force thereby obtaining:

4 2 2

2

04 2 2( ) ( ) sinz z M y M

d y d y dy d yEI F w z w A C w A C b t

dz dz dz dt . (6.1.2)

This is the governing equation for lateral vibration from which the resonant frequencies are to be

determined. To execute the Eigen value analysis, the excitation force on the RHS in equation (6.1.2)

is considered to be zero. It is also assumed that the lateral force due to gravity yw will not influence

the natural frequency and hence can be ignored. Therefore, equation (6.1.2) reduces to:

24

4 2 2

04 2 2( ) ( ) 0z z M

d y d y dy d yEI F w z w A C

dz dz dz dt . (6.1.3)

Let standard harmonic function described below be the solution to (6.1.3)

i ty y z e , (6.1.4)

2..

i ty e . (6.1.5)

Substituting (6.1.4)&(6.1.5) in(6.1.3), and dividing throughout byMA C :

4 2

2

04 2

cos( ) 0

M M

EI d y gh d y dyl z y

A C dz C dz dz

. (6.1.6)

Equation (6.1.6) is now the equation to be discretized and solved in similar fashion to previous

examples as an Eigen problem in the form of:

A y B y , (6.1.7)

0A B y . (6.1.8)

Where is the Eigen value which when multiplied with the rotary speed is yields the natural

frequency. Implementation of Finite Difference method to solve this Eigen value problem is detailed

in Appendix C.

6.2 Results

6.2.1 Comparison with Analytical Solution

Figure 25 Mode shapes for the first natural frequency of Lateral Vibration

25

Using MATLAB, the Eigen value statement was solved for the example drill collar of outer and inner

diameters 7.5 inches (190.5 mm) and 2.81 inches (71.37 mm) respectively rotating at a speed of 10

RPM with no applied weight on bit at 0 degrees inclination from the vertical. The mode shapes

shown in Figure 25 above are plotted for a normalized deflection where the maximum deflection

value of 1 corresponds to the maximum annular clearance between the drill collar outer diameter

and the borehole diameter defined by the specified bit diameter. The computed natural frequency

was found to be 0.73 Hz (43.67 RPM). To confirm the accuracy of the tool, the solution was

compared with the analytical solution for the bending natural frequency of a beam with similar

boundary conditions of simply supported or pinned at one end and clamped or fixed at the other

end [27] given by:

2

43.9267 0.71

EIHz

AL

(6.2.1)

From the above, it is confirmed that the tool developed is in close agreement with the analytical

solution. The reason for the computed natural frequency being higher than its analytical counterpart

is because although the weight on bit is zero, the linearly varying tension (equal to the weight of the

buoyant drill string beneath that point) throughout the drill string increases the resistance to

bending and hence results in a higher natural frequency.

6.2.2 Variation of Natural Frequency with Applied Weight on Bit

Figure 26 Dependence of natural frequency on the applied Weight on Bit

From Figure 26, It can be seen that as the applied weight on bit increases, the natural frequency

reduces. This phenomenon will appear intuitive after examining the terms of the Eigen value

26

statement for the governing equation (6.1.6) and comparing it with the analytical expression for

buckling under excitation [28]reproduced below:

2

0 0G Gk m k v (6.2.2)

k - Stiffness which corresponds to the flexural rigidity 4

4

d yEI

dz

GOk - Geometric stiffness term capturing the effect of axial loading. The minus sign indicates

compressive load which is consistent with the typical load distribution in the BHA. This term

corresponds with (2

0 2)z z

d y dyF w z w

dz dz

2 - Natural frequency corresponding to rotary speed 2

Thus it can be clearly seen from(6.2.2), when increases as shown in Figure 26, the natural

frequency 2 decreases until eventually it reduces to zero. The corresponding weight on bit is the

buckling load and hence a further check on the accuracy of the buckling result computed earlier in

section 5.2 is obtained because of the agreement in the computed buckling load of 306 kN in both

cases for similar input conditions of wellbore inclination (vertical), tubular material properties and

dimensions.

GOk

27

7 Application of Developed Concepts to DAP Producer

The concepts discussed thus far can now be applied towards selecting the appropriate steel grade

for the DAP geothermal producer well. This will be done by following the previously proposed

algorithm for casing string design.

7.1 Initial Well Data

The following assumptions are made regarding the initial well data:

o Overburden gradient = 6.89 /kPa m

o Entire well is drilled with same mud weight

o Surface temperature = 25 C

o Assume ideal gas behaviour for Methane

Formation fluid density is taken to be 144 3/kg m which is obtained from the study of total

dissolved solids observed in the water samples contained in the report of IF technologies

Netherlands

This means that in any forthcoming calculations,

(1000 144) 9.81 11.223 /mud gradient g kPa m . (7.1.1)

To maintain sufficient overbalance, the gradient of the drilling fluid is taken as 12 /kPa m

It was not possible to obtain any data pertaining to the formation fracture gradient from the

DAP. Therefore the Hubbert and Willis equation [29] for wellbore injection pressure

required to initiate fracture propagation was used as an approximation of the formation

strength gradient as follows:

1 2(1 )

3

1{1 (2 0.49614)}

3

0.66409 /

15.022 / .

PF

D

psi ft

kPa m

(7.1.2)

Where,

F Fracture Gradient in psi/ft.

P

D Pore pressure gradient in psi/ft.

Note that this formula assumes the overburden gradient to be 1 psi/ft. which is a reasonable

assumption in the absence of specific data as per Hubert and Willis

The producer has a planned TVD of 2300m. Using the geothermal gradient, the bottom hole

temperature is found to be:

28

0.03 ( ) 8.21

(0.03 2200) 8.21

77.21 .

T d TVD

C

(7.1.3)

This is below the boiling point of water so the occurrence of steam as a potential well bore

influx can be ruled out. The only gaseous influx which can occur is typically Methane [9] with

or without H2S in small quantities. The design for burst will then be carried out considering

the case of methane influx into the casing.

Figure 28 Planned Trajectory of Producer

Figure 27 Drilling Window for Wellbore Fluid Gradient

29

7.2 Stresses Considered

The following section consists of a brief recap of some basic mechanical engineering concepts

pertaining to stress. . During the drilling process, the tubular used will be subjected to any or all of

the following stresses simultaneously. The fundamental formulas used to calculate these stresses

are obtained from [7].

7.2.1 Axial Stress

The axial stress at any point on a tubular is the tension caused by the gravity component of the

buoyed weight of the section below it, exerting a loading force vertically downwards.

2 2

1 2

4,

( )

F

D D

(7.2.1)

where,

1D Outer Diameter, m

2D Inner Diameter, m

7.2.2 Bending Stress

Bending stress in the tubular acts along its longitudinal axis and can be caused when the tubular

undergoes bending due to curvature of the wellbore trajectory, tubular buckling and due to lateral

vibration. For the former, it is calculated using the formula:

,b

rE

R (7.2.2)

where,

b Bending Stress, Pa

E Young’s Modulus of Elasticity, Pa

r Radius of tubular, m

R Well bore radius of curvature, m

Bending stresses due to whirling and buckling are calculated as the product of the flexural rigidity

with the second order derivative of the nodal displacements obtained from simulation results as will

be discussed in sections 7.10.1 and 7.10.2 respectively.

30

7.2.3 Torsional Stress

The maximum torsional stress is induced in casing or drill pipe due to the torque or twisting force

applied at the surface by the top drive or rotary table system as:

12

,T

rT

J (7.2.3)

where,

T Torsional Stress, Pa

T Applied Torque, Nm

J Polar Moment of Inertia, 4m

7.2.4 Hoop Stress

Hoop stress acts in the circumferential direction of the tubular and is caused by a difference in

internal and external pressures. This form of stress becomes especially relevant in well control

situations such as collapse and burst loading and is given by the formula:

2 2 2 2 2 2 2 2

2 2 2 2

( / ) ( / ),i i o o i o

h i o

o i o i

r r r r r r r rp p

r r r r

(7.2.4)

where,

h Hoop Stress, Pa

,i or Internal or external radius, m

,i op Internal or external Pressure, Pa

7.2.5 Radial Stress

Radial stress is also caused by internal & external pressure differences but acts orthogonal to the

hoop stress. It is calculated as:

2 2 2 2 2 2 2 2

2 2 2 2

( / ) ( / ).i i o o i o

r i o

o i o i

r r r r r r r rp p

r r r r

(7.2.5)

7.2.6 Von Mises Stress

The Von Mises stress is a theoretical construct which allows for the conversion of a triaxial stress

state into an equivalent uniaxial value for comparing with a material’s uniaxial yielding criterion. The

various stress components calculated in the preceding section are combined to obtain the resultant

Von Mises stress equivalent as follows:

2 2 2 26.

2

r h a r h a t

VM

(7.2.6)

31

7.3 Power Law Fluid Rheology Model

In order to determine the circulating fluid pressures in the wellbore, the pressure drop due to

frictional losses needs to be estimated. The frictional pressure drop when added to the hydrostatic

pressure at a particular depth gives a simple estimation of the flowing wellbore pressures. This

pressure drop is a function of the fluid viscosity. Most drilling fluids are typically Non-Newtonian and

therefore, fluid viscosity cannot be determined by usual means. Consequently, various fluid rheology

models were developed to calculate fluid viscosity. The power law is one such rheology model for

Non-Newtonian fluids which relates the shear stress to the shear rate as follows:

,nK (7.3.1)

where,

Shear stress, Pa

Shear rate, 1s

K Consistency index, nPaS

n Flow behaviour index

Given the laboratory measurements of the drilling fluid shear rate, the values of constants K and n

in equation (7.3.1) can be determined as:

600

300

3.32log ,n

(7.3.2)

6005.11( ),

1022nK

(7.3.3)

where,

XXX Measurement of shear rate made in a fluid viscometer at XXX rpm, 1s

The minimum fluid flow velocity required for lifting of cuttings in the annulus is determined from

Table 2 by looking for flow rate corresponding to the annulus hole size.

Table 2 Flow Rate for Minimum Annular Velocity [30]

For a given fluid velocity, the effective viscosity of the fluid in the wellbore under ideal conditions

can then be determined in field units as:

196 3 1

100 ,4

n n

e

V nK

D n

(7.3.4)

32

where

e Effective viscosity, cP

V Flow velocity, m

s

D o iD D for annular flow, .m

iD for pipe flow, .m

The frictional pressure losses are dependent on the friction factor between fluid flow and the

wellbore. The friction factor is in turn affected by the nature of the flow, i.e. laminar or turbulent.

This is quantified by the Reynolds number as:

Re ,

VDN

(7.3.5)

where,

Fluid density,3

.kg

m

The friction factor is then calculated for laminar flow as:

Re

16,f

N (7.3.6)

Additionally, the friction factor for turbulent flow is:

1

20.75 1.2

1 4 4log Re ,

n

n nf

(7.3.7)

where,

f Friction factor

Finally, the frictional pressure drop can be calculated as follows:

22

.dp f V

dz D

(7.3.8)

where,

z

Wellbore longitudinal axis, m

dp

dz Frictional pressure drop, .

Pa

m

33

7.4 Casing Design Load Cases

The operational pressures which can be expected in the worst case scenarios are first computed for

the different casing sections in order to select casing steel grades of suitable yield strength. These

pressures are then multiplied with specifc safety factors to arrive at the design loads against which

the casing must be rated.

Table 3 Factor of Safety [31]

7.4.1 Surface Casing

The analysis of design load is first carried out for the 13 3/8” surface casing with planned shoe at

350M as shown in Figure 27.

7.4.1.1 Collapse Scenario

External pressure is due to the column of mud outside the casing which is present when the

casing was run

Internal pressure is taken as complete evacuation due to fluid loss when drilling subsequent

section

Collapse pressure at casing shoe located at 350m depth:

12000 350

4200 .

mud gradient Depth

kPa

(7.4.1)

Corresponding design load including the factor of safety(FOS) for collapse:

. .

1.2 4200

5040 .

F O S Collapse Load

kPa

kPa

(7.4.2)

34

7.4.1.2 Burst Scenario

In the event of a poor cement job, the fluid in the spaces where cement is absent or has

channelled has density similar to fresh water. Therefore external pressure is calculated as

per fresh water gradient of 9.81kPa/m

Internal pressure is due to Gas influx. At the casing shoe, the influx pressure is given by the

hydrostatic pressure equivalent of the formation strength at that point:

( . ) 15022 350 5257.7 .Fracture Grad Depth kPa (7.4.3)

The external pressure at casing shoe is:

9.810 350 3433.5 .kPa (7.4.4)

Burst pressure at casing shoe is calculated as the difference between external and internal

pressure which is 1824.2kPa

Corresponding design load including the FOS for burst at shoe is given as:

. . 1.8 1824.2 3284 .F O S Burst Load kPa (7.4.5)

Temperature at the casing shoe is calculated by linearly interpolating between previously

calculated bottom hole temperature of 77.2 C and surface temperature of 25 C:

(77.21 25)

25 [ 350] 33 .2300

T C

(7.4.6)

The average temperature is:

(25 33)

273.15 302.15 .2

K

(7.4.7)

By using ideal gas law with appropriate compressibility factor for methane, internal pressure

at surface is calculated as:

2 1( )

2 1

9.81 16(0 350)

3 1 847.8 302.15

3

5257.7 10

5143.98 10 .

avg

gM h h

ZRTP Pe

e

Pa

(7.4.8)

Where

,M Molecular mass of gas = 16 g/mole for Methane

,Z Compressibility factor = 1

,R Ideal gas constant = 847.8 gm/(Mol.Kelvin )for Methane

Since there is no external pressure due to fresh water gradient at surface, the burst pressure

is the internal pressure itself

35

Corresponding design load including the FOS for burst at surface is given as:

. . 1.8 5143.98 9259 .F O S Burst Load kPa (7.4.9)

Tabulating the results of computed design loads for surface casing,

Design Collapse (kPa) Design Burst(kPa)

Surface 0 9259

Shoe(300M) 5040 3284

7.4.2 Intermediate Casing

The intermediate casing comprises of the 9 5/8” liner casing for which the loads encountered will be

computed in a similar manner. Repeating the procedure followed previously, the results of the

design load computation are summarized as:


Surface 0 18128

Shoe(700M) 10080 6567

7.4.3 Production Liner

For the production liner, the worst case loading scenario for burst loading is defined as entire casing

filled with a column of gas during production. Consequently, it is not necessary to consider the

formation strength in this condition and the formation fluid pressure will be sufficient as stated in

[7].

As the liner will be tied back to the intermediate casing, the intermediate casing will also be exposed

to the production loads. Consequently, the burst pressure will be computed up to surface to

compare with the previously computed design loads for the intermediate casing. The higher of the

two loads will then be chosen as the effective design load for the intermediate casing.


Surface 0 40640

Shoe(2200M) 33120 5850

Clearly, the burst gradient of the liner plotted upto surface is higher and so the gradient of the

production liner will be adopted for the intermediate casing as well.

7.5 Casing Selection Based on Uniaxial Loading Criteria

Typical choice of steels from the API-5CT standards for use in Geothermal wells as per [9] are K55,

H40, J55, C75 & L80 which are chosen for relatively low tensile strength which reduces the tendency

for hydrogen embrittlement. Subsequent selections will therefore use these recommendations as a

starting point.

36


7.5.1.1 Collapse Loading

As per [32], the yield strength of 13 3/8” diameter K55 surface casing casing,83.8 10pY N

This yield strength is de-rated by a factor of 0.955 because of exposure to temperature of

production fluid up to80 C degrees as a conservative estimate as per [6]

Thermally de-rated yield strength is then:

6 60.955 3.8 10 3.63 10 .pY N N (7.5.1)

On the basis of calculated D/t ratio for this steel, theAPI-5C3 Transition Collapse [32] formula was to

be applicable as follows:

6

2 2

[ ]/

3.63 10 1.989[ 0.0360]35.02

(0.3397 0.3204 )4

7.54 .

T p

FP Y G

D t

MPa

(7.5.2)

WhereTP Rated Collapse Pressure

7.5.1.2 Burst Loading

Applying the API-5C3 [32] formula for calculating the minimum internal yield pressure or burst

strength:

6

2 2

20.875[ ]

2 3.63 100.875[ ]

(0.3397 0.3204 )35.024

18.1 .

PY tp

D

MPa

(7.5.3)

The selected material is thus found to withstand the expected design loads

7.5.2 Production Casing

7.5.2.1 Collapse Loading

In the DAP proposal, the production casing comprises of the intermediate casing run upto 700m TVD

and the liner hung off from the intermediate casing shoe upto the TD. By following a similar

procedure to the preceding section, the results are tabulated below.

37

Table 4 Production Casing Specifications

Casing 9 5/8” Intermediate 7” Liner

Material 53.5 ppf, L80 29 ppf, N80

Applicable Collapse Formula Plastic Plastic

Thermally Derated Yield Strength, pY 65.28 10 N 62.874 10 N

Derated Collapse Rating, TP 42.91MPa 46.66MPa

7.5.2.2 Burst Loading

For 9 5/8”, 53.5ppf, L80 grade steel:2

0.875[ ] 52.13 .PY tp MPa

D (7.5.4)

For 7”, 29ppf N80 grade steel:2

0.875[ ] 55.28 .PY tp MPa

D (7.5.5)

Tabulating the results, we obtain:

Table 5 Summary of Required Material Properties based on Design Loads

O.D(Inches) GRADE Density(PPF) Derated Yield

(106 N)

Collapse (106MPa)

Burst(Mpa) (106MPa)

Surface 13 3/8 K55 54.5 3.63 7.5 18

Intermediate 9 5/8 L80 53.5 5.28 43 52

Liner 7 N80 29 2.87 47 55

Figure 29 Graphical representation of Design Loads vs. Rated Strength

38

7.6 Axial Loading

7.6.1 Wellbore Trajectory

Figure 30 Measurement of Key Wellbore Trajectory Parameters

The well trajectory shown in Figure 27 must be converted into survey data points containing

Measured Depth, Inclination & Azimuth in order to be usable for the developed Torque & Drag

model. This is done by using trigonometric relations to calculate the position of key points in the

trajectory such as the Kick-off point etc. as shown in Figure 30. From Figure 30, the radius of

curvature, r for the build-up section is calculated as 443.3Metres and the maximum wellbore

inclination to the vertical, is found to be 43 or 0.75 radians. Consequently, arc length BC is:

332.7r m . (7.6.1)

The total measured depth is then found to be: 700 332.68 1649.56 2683m .

Lastly, the Dog Leg Severity (DLS) is calculated to be:43

30 3.88 per 30332.68

m


Once the wellbore survey data is obtained, the various axial load properties of the different casing

grades selected are tabulated below:

Table 6 Surface Casing Properties

Unit Weight 795 N/M

Density 8099.18 Kg/m3

Buoyancy Factor 0.8489

Buoyed Unit Weight 674.93 N

Axial Load at Top of Hold Section (TVD-1000m) 2.362 X 105 N

F.O.S 1.8

Design Axial Load 4.24 X 105 N

Yield Strength 36.3 X 105 N

39

7.6.3 Intermediate Casing

Table 7 Intermediate CSG Properties

Unit Weight 781 N/M



Buoyed Unit Weight 660.57N

Axial Load at Top Joint 4.62 X 105 N

F.O.S 1.8


Yield Strength 52.8 X 105 N

7.6.4 7” Liner

7.6.4.1 Hold Section at 43 Deg. Inclination

For section CD in Figure 30,

Table 8 Liner Hold Section Properties

Unit Weight 423 N/M



Buoyed Unit Weight 357.66 N

Buoyed & Inclined Weight 261.57 N

Axial Load at Top of Hold Section (TVD-1000m) 4.32 X 105 N

F.O.S 1.8


7.6.4.2 Build Up Section Table 9 Build Up Section Properties

Measured Depth[m]

Inclination [deg]

Inclination [rad]

Buoyed & Inclined Weight

700 0 0 1.07E+04

730 3.88 0.06771877 1.07E+04

760 7.76 0.13543755 1.06E+04

790 11.64 0.20315632 1.04E+04

820 15.52 0.2708751 1.02E+04

850 19.4 0.33859387 9.99E+03

880 23.28 0.40631265 9.71E+03

910 27.16 0.47403142 9.38E+03

940 31.04 0.5417502 9.00E+03

970 34.92 0.60946897 8.59E+03

1000 38.8 0.67718775 8.65E+03

1032 43 0.75049158

1.08X 105N

40

7.6.5 Axial Load due to Well Bore Trajectory

Axial load due to well bore trajectory arises from the bending stress acting along the longitudinal

axis of the casing string in the wellbore due to the curvature of the wellbore trajectory. Bending

stress is computed as per (7.2.2) for which the variables are:

E Young’s Modulus of Elasticity = 112.052 10 Pa

r Outer radius of liner at which maximum bending occurs = 0.0889m

R Well bore radius of curvature = 443.295m

11 60.08892.052 10 41.15 10 .

443.295b Pa

(7.6.2)

Axial Load due to Bending:

6

5

(7" 80)

41.15 10 0.005445

2.24 10 .

b Area N

N

(7.6.3)

The total axial load at the uppermost joint of 7” liner is then given by summing the unit inclined

buoyed weights in the build-up and hold sections with the axial load due to bending:

5 5 5

5

=4.32 X 10 1.08X 10 2.24 10

7.64 10 .N

(7.6.4)

Multiply axial load computed in (7.6.4) with the FOS of 1.8 gives design axial load of 61.375 10 N

In comparison to the thermally de-rated yield strength 62.87 10 N , the design is found to be within

the rated limit.

7.7 Combined Loading

7.7.1 Collapse with Axial Loading

To determine reduced collapse strength for 7” liner casing, we substitute the maximum axial load

obtained at the topmost joint of the 7” casing string in(7.6.4) in the Reduced Von-Mises 2D collapse

with axial loading formula defined as:

21 0.75( ) 0.75( ) .a apa p

p p

S SY Y

Y Y

(7.7.1)

Where,

aS Axial Load, Pa

pY Yield Strength

41

5 52 6

6 6

6

7.64 10 7.64 101 0.75( ) 0.75( ) 2.87 10

2.87 10 2.87 10

2.48 10 .

paY

Pa

(7.7.2)

Using the reduced yield strength due to axial loadpaY , for the Plastic collapse formula [32], the rated

collapse load for the 7” N80 liner was found to be:

6 3.0712.48 10 [ .0667] 1955 36.07 .

17.5TP MPa (7.7.3)

Similarly, for the top joint of the 9 5/8” intermediate L80 casing string which forms the top section of

the production casing, the procedure above is repeated to obtain:

Maximum axial load at surface due to combined effect of 7” and 9 5/8” combination string:

5 57.64 4.62 10 N 12.26 10 N, (7.7.4)

This gives the reduced yield strength and rated collapse load of:

5 5

2 6 6

6 6

12.26 10 12.26 101 0.75( ) 0.75( ) 5.28 10 4.68 10 ,

5.28 10 5.28 10paY Pa

(7.7.5)

6 3.0714.68 10 [ .0667] 1955 36.51 .

17.5TP MPa (7.7.6)

Figure 31 Plot of Design Load vs. Rated Strength for Collapse

42

7.7.2 Von Mises Analysis for Burst Loading

For the tri-axial Von Mises stress analysis, the critical point where failure is likely to occur is the inner

diameter. Therefore, the Bending stress calculations are repeated for the inner diameter as follows

for the 7” N80 liner casing using the same data as above:

11 60.078552.052 10 36.36 10 .

443.295b Pa

(7.7.7)

Axial load due to bending is now:

6

5

(7" 80)

36.36 10 0.005445

1.98 10 .

b Area N

N

(7.7.8)

Consequently, total axial load at the topmost joint of the 7” liner will be:

5 5 5 5=4.32 X 10 1.08X 10 1.98 10 7.38 10 .N (7.7.9)

The results of the triaxial stress analysis computed at the survey points which are at 30metres

interval from each other are recorded in Appendix D ,Table 12.

7.8 Torque & Drag Analysis

Figure 32 Plot of Pick Up Drag Forces When Tripping Out of String

43

Maximum axial loading including the effects of pick up drag forces is now 58.72 10 N which is

obviously higher than the previous maximum calculated at the same position including only the

effects of buoyant forces and well bore inclination previously. The increased friction observed in

build-up section is due to implicit relationship between string axial tension and the normal force as

can be seen in(3.1.3). This analysis was carried out with friction factor for Delft sand of 0.46

corresponding to the maximum observed dynamic friction value for steel in contact with dry sand

obtained from the experimental investigation performed in [33]. Analysis carried out only for 7” N80

liner section as the 9 5/8” and 13 3/8” sections are vertical sections and would therefore not

experience any normal (side) force component. Tabulated drag values are published in Appendix D,

Table 13.

7.8.1 Axial Loading due to Drag Forces

Total Axial load at the uppermost joint of 7” liner will now include the effects of drag in addition to

the axial stress caused by bending of the liner in the build-up section. Therefore the design

calculation for the liner casing subjected to axial loading alone will be:

5 5=(8.72 2.24)X 10 10.96 10 .N (7.8.1)

This gives a design axial load using FOS 1.8 of 61.972 10 .N Therefore the design is found to be

within the rated limit when comparing against thermally de-rated yield strength value obtained from

Table 5, i.e. 62.87 10 .N Additionally, the combined loading scenarios for collapse and burst are

now repeated to include the effect of the increased axial loading due to drag forces as follows:

7.8.1.1 Collapse with Axial Loads Including Drag Forces

To determine reduced collapse strength for 7” liner casing, we substitute the new maximum axial

load obtained at the topmost joint of the 7” casing string including the effect of drag forces in

equation (7.7.1) to obtain:

5 5

2 6 6

6 6

10.96 10 10.96 101 0.75( ) 0.75( ) 2.87 10 2.34 10 .

2.87 10 2.87 10paY Pa

(7.8.2)

Using the reduced yield strength due to axial loadpaY , from the API Plastic collapse formula [32], the

rated collapse load for the 7” N80 liner was found to be:

6 3.0712.34 10 [ .0667] 1955 33.27 .

17.5TP MPa (7.8.3)

This is only just above the design collapse load observed in section 7.4.3 and Figure 29 so depending

upon the company specific policy of the operator, it may be decided to consider the next grade of

casing for the liner to remove any chance of failure due to collapse loading. Similarly, for the top

joint of the 9 5/8” intermediate L80 casing string which forms the top section of the production

casing, the procedure above is repeated to obtain the maximum axial load at surface due to

combined effect of 7” and 9 5/8” combination string:

44

5 510.96 4.62 10 N 15.58 10 N. (7.8.4)

De-rated collapse strength due to axial loading is then:

5 5

2 6 6

6 6

15.58 10 12.26 101 0.75( ) 0.75( ) 5.28 10 4.45 10 .

5.28 10 5.28 10paY Pa

(7.8.5)

This gives reduced collapse strength of:

6 3.0714.45 10 [ .0667] 1955 34.05 .

17.5TP MPa (7.8.6)

Figure 33 Design Collapse Load vs. Strength for DAP Producer

7.8.1.2 Von Mises Analysis for Burst Loading Including Effect of Drag Forces

Figure 34 Increased FOS for Burst Loading Due to Effect of Drag Forces

45

As expected, when the Von Mises analysis is repeated at the survey points including the effect of

drag forces, the FOS is observed to increase as shown in Figure 34 due to the supporting effect of the

axial loading on the collapse strength of the casing pipe. Tabulated Von Mises stress analysis values

at survey points are published in Appendix D, Table 14.

7.8.2 Torque Analysis

Figure 35 Cumulative Torque Observed at Surface for Various Drilled Depths

As can be seen from Figure 35, the maximum surface torque required to overcome the cumulative

torque losses while drilling the inclined section of the well is of the order of approx. 21 kN. Due to

constant wellbore inclination after 1000m TVD, the torque increases linearly whereas it increases at

relatively higher rate in the build-up section. The simulated torque and corresponding torsional

stress at survey points are tabulated in Appendix E for reference. As previously stated, the torque

analysis is integral for selecting casing buttress connections with suitable torque capacity required

for drilling operations. Sample manufacturer catalogue presenting connections with improved

torque capacity is also present in Appendix E. Computed torsional loads which used as input

parameters for simulating the combined Von-Mises stresses in the liner section during the process of

drilling the inclined section are also tabulated.

7.9 Wellbore Pressure Distribution

Based on drift diameter of 9 5/8” L80 intermediate casing, the bit size used for drilling next open

hole section was chosen to be 8 ½ “. The following assumptions were then made for implementing

the power law rheology model to calculate pressure distribution of drilling fluid in wellbore during

drilling:

46

From [30], the discharge for obtaining minimum annular velocity required for lifting the

cuttings is3

0.017m

s

Typical viscometer readings required as input for power law model obtained from [34] and

shown in Table 10

Pressure drop across the bit for 8 ½” PDC is typically approx. 5MPa [34]

Table 10 Power Law Input Viscometer Measurements

Viscometer Reading Shear Rate

RPM (1/Sec)

3 5.11

100 170.3

300 511

600 1022

0

5

10

15

20

25

30

35

40

0 1000 2000 3000 4000 5000

Flu

id P

ress

ure

[M

Pa]

Distance from Stand Pipe [M]

Wellbore Fluid Pressure Distribution

Wellbore Hydrostatic

Circulating WellborePressure

Figure 37 Fluid Pressure Distribution for 7" Liner Drilling Phase

Figure 36 Flow Path for Drilling Fluid in 7" Liner Drilling Phase

47

As shown in Figure 36, The drilling fluid from the mud pumps flows into the wellbore first through

the 5” drill pipe used to hang the liner from the surface from the liner hanger and then through the

retrievable BHA necessary for drilling inclined sections. Consequently, the interior of the 7” Liner is

not exposed to fluid pressures at all. Only the external surface is in contact with fluid flow in the

annulus between open hole and Intermediate casing. The frictional pressure losses due to fluid flow

as calculated by the power law model are tabulated in Appendix F. The total wellbore pressure at

any depth as shown in Figure 37 is than obtained by summing the hydrostatic pressure at that point

with the annular pressure losses as previously stated.

7.10 Drilling Loads

7.10.1 7” Liner – Bending Stress Due to Whirl

Figure 38 Whirling Mode Shapes

Figure 39 Natural Frequency of Lateral Vibration vs. WOB

48

During Drilling, the casing string is likely to be deflected laterally when the rotary speed applied at

surface by the rotary table approaches the critical value as predicted by the MATLAB tool developed

in chapter 6. Using the material properties of N80 Liner casing, the range of rotary speed values for a

particular WOB which cause resonance or whirling can be seen in Figure 39. This tool may be used as

a quick estimate for determining the RPM range to drill at so that the alternating bending stresses

associated with whirling which can cause string failure due to fatigue can be avoided.

For drilling the deviated sections, the retrievable BHA needs to be used as discussed in Chapter 1.

Consequently, the casing stand (30metres) is modelled with the fixed or clamped boundary

condition at both ends. This is because the loads from the retrievable BHA are transferred onto the

lowermost stand of the liner casing at the bottom through internal stabilizers and through the Drill-

Lock assembly at the top of the stand (section 1.1.2). For simplicity, it is assumed that the weight on

bit transfers directly to the bottom of the liner stand. The corresponding mode shapes for this

boundary condition are shown in Figure 38. From these mode shapes, the corresponding bending

stress is calculated and tabulated results for bending stress across one liner stand are published in

Appendix D, Table 15. Bending stress is also plotted in Figure 40 from which it can be observed that

the critical points occur at 1.4metres from both end points. As expected, a maximum bending stress

of 15MPa is experienced at the midpoint of the casing stand which equates to approximately 10%

of the total axial load at the topmost joint of the 7” liner. Knowledge of where maximum bending

stresses are likely to occur can be applied to the design of casing pipe with composite materials

which can then be selectively strengthened at the appropriate points. The advantage of doing so is

that overall pipe weight can be reduced and cost of hiring drilling rigs can also be brought down as

the hook load capacities needed for drilling to the target depth will be comparatively lesser.

Figure 40 Bending Stress Due to Whirl

49

7.10.2 9 5/8” Casing – Bending Stress Due to Buckling

Figure 41 Buckling Mode Shapes and Dependency of Critical Load on WOB

It is advisable to investigate the magnitude of the axial stress induced by buckling of casing in static

conditions to ensure that the selected casing steel grade will not fail under buckling. As an example,

the driller will sometimes apply WOBs that exceed the critical load threshold in order to clear a

downhole block. However for identical boundary conditions as seen from Figure 21 & Figure 25, the

mode shapes and hence the bending stresses induced are the same. In the case of the 9 5/8”

Intermediate casing which is being used in drilling the completely vertical top section of the

wellbore, the drillable non-retrievable BHA specified is used. This can be modelled using a different

end condition of “pinned or hinged” at the bit. Although the magnitude of maximum bending stress

occurring will be determined by the casing-wellbore annular clearance, the location of the points of

maximum bending stress may be different and it is therefore of interest in order to specify additional

strengthening points when using composite materials for the casing. The results obtained from the

MATLAB buckling analysis tool developed in chapter 5 for the 9 5/8” intermediate casing with the

“pinned at bit” and “fixed at stabilizer” boundary end condition are shown in Figure 41. Also of

interest is the plot of critical frequency as a function of the wellbore inclination which provides a

limit on the maximum WOB which should be used by the driller in normal conditions.

50

From Figure 42, the point of maximum bending stress observed is observed at approximately

10metres from the bit or at the beginning of the 2nd single of the casing stand which is not the case

in the mode shapes observed for the “Pinned at both ends” boundary condition examined so far.

Bending stress is also significantly high and only slightly lesser at the stabilizer placed at the ending

of the casing stand (30 metres from bit). The magnitude of this additional bending stress (1.74 MPa)

tabulated in Appendix D is clearly not significant to alter the casing selection. Note that the value of

bending stress is determined by the annular clearance which generally tends to be low when drilling

with casing. This observation corresponds with the low values of bending stress encountered in [1]

when drilling the vertical hole section with the non-retrievable BHA.

Figure 42 Bending Stress due to Buckling in 9 5/8" Intermediate CSG

51

7.11 Von Mises Analysis of Drilling Loads during 7” Liner Section

Figure 43 7" Liner Von-Mises Stress Analysis for Drilling Operation

The final test of the selected design is to verify the resultant Von Mises stress due to triaxial loading

and compare it with the yield stress throughout the casing string for the 7” Liner section for typical

drilling conditions. The hoop and radial stresses are calculated based on the fluid pressure gradient

computed [section 7.9]. The axial stress includes the effect of buoyed string weight, bending stress

due to wellbore curvature in the build-up section [section 7.6.5] and bending stress due to whirling

[section 7.10.1]. Since the string is rotating in the wellbore, there will be no drag forces. However,

induced torsional stress [section 7.8.2] is included in the analysis. A graphical representation of the

result is shown in Figure 43 where the resultant von Mises stress is clearly lower than the yield stress

by a FOS ranging between 2 & 2.3, thereby validating the design for drilling the final section.

Tabulated values of the stress analysis at survey points are also include in Appendix D Table 16 for

reference. It is observed that the maximum torsional stress is 38% of the total axial stress which

indicates the importance of the torque analysis and the selection of appropriate casing connection

with enhanced torque capacity in order to prevent design failure.

700.00

900.00

1100.00

1300.00

1500.00

1700.00

1900.00

2100.00

2300.00

0.00 100.00 200.00 300.00 400.00 500.00 600.00

TVD

[M]

Stress [MPa]

Liner Stress Distribution at TVD

Axial[Mpa] Torsional[Mpa] Radial[Mpa]

Hoop[Mpa] Von Mises[Mpa] Yield [Mpa]

52

8 Conclusions An algorithm was developed to select the required API steel grade of casing pipe for use in

the “Casing While Drilling” technique which evaluates the effect of conventional casing Burst

& Collapse pressure loads and Drilling loads i.e. Torque, Drag, Buckling and Whirling.

Supporting tools were developed in MATLAB to calculate the Drilling loads.

The algorithm was applied towards the DAP producer Geothermal Well with the following

recommendations being made:

Table 11 Casing String Design for DAP Producer Geothermal Well

The effect of induced bending stresses due to buckling and whirling of the Casing String was

not found to be significant due to the relatively small annular clearances available.

Maximum Bending Stress due to whirling was calculated to be 10.6% of the axial stress.

For a casing stand of 30m length, the maximum bending stress due to whirling when

modelled with the boundary conditions of “fixed” or “clamped” at both ends was observed

at the midpoint and at a distance of 1 m from both ends. Similar points of maximum stress

due to buckling with the boundary conditions “clamped” at the stabilizer and “pinned or

hinged” at the bit were located at 10.5 metres from the bit (close to casing joint between 1st

& 2nd single) and at the stabilizer.

The critical rotary RPM as a function of the WOB for inducing whirling of the casing was

calculated by the developed MATLAB tool to help the driller avoid string failure due to

fatigue loads caused by alternating bending stresses. The critical weight on bit for inducing

sinusoidal buckling of casing string was also determined for varying wellbore inclination from

the vertical axis

The effect of torque on casing string was found to be significant with a maximum torsional

stress calculated as 38% of the total axial stress which is close to four times the bending

stress due to whirling. Buttress threaded connections with torque rings to boost the make-

up torque capacity must be used to avoid string failure

8.1 Recommendations The hydraulic model used to model the wellbore pressure distribution during drilling has to

be expanded to more realistically simulate fluid pressure losses and to include effects such

as surge and swab pressure loads

The torque and drag model must be altered to include hydrodynamic effects of viscous drag

and the effect of bending stiffness of the casing

The boundary conditions used to simulate drilling with the retrievable BHA can be expanded

to more accurately represent downhole conditions

The algorithm used in the thesis can be adapted to include the analysis of composite

materials for the CwD application.

Casing Shoe TVD (m)

Outer

Diameter

(Inches)

Grade

Nominal

Weight

(daN/m)

Surface 350 13 3/8" K55 79.5

Intermediate 700 9 5/8" L80 78.1

Liner 2200 7" N80 42.3

53

Nomenclature

A Cross sectional area of casing, 2m

⁄ , Added mass coefficient

Radial clearance in wellbore, m

E Young’s Modulus of Elasticity, Pa

0F Applied weight on bit, N

g Acceleration due to gravity, 2

m

s

Buoyancy factor

i Area Moment of Inertia, 4m

l Length of segment of interest between bit and first stabilizer, m

Dimensionless effective length of compression

Mass of volume of mud displaced by solid cylinder of same outer diameter (per

metre), Kg

Mass of steel per m , /Kg m

Number of segments into which casing is divided into

yS Shear stress, Pa

w Dimensionless distance along Z axis

Angle subtended by deflected beam with respect to its longitudinal axis

Inclination from vertical, radians

Density of Mud, 3

kg

m

Density of Steel, 3

kg

m

Dimensionless time

Dimensionless angular velocity

54

List of Abbreviations

BHA Bottom Hole Assembly

CwD Casing while Drilling

DAP Delft Aardwarmte Project

FOS Factor of Safety

LWD Logging while Drilling

MWD Measurement while Drilling

PDC Polycrystalline Diamond Compact

WOB Weight on Bit

55

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[3] Schlumberger, "Using Casing to Drill Directional Wells," Oil Field Review, pp. 44-61, 2005.

[4] Hendry Shen, "Feasibility Study on Combining Casing with Drilling with Explandable Casing ,"

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[5] Abubakar Mohammed, Chika Judith Okeke, and Ikebudu Abolle-Okoyeagu, "Current Trends and

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[6] British Gas, "Well Engineering and Production Operations Management System ," BG, Casing

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[8] M.Enamul Hossain, Fundamentals of Sustainable Drilling Engineering.: Scrivener-Wiley.

[9] Geoelec, "Report on Geothermal Drilling," European Union, 2013.

[10] Xie Jueren and Gang Tao, "Analysis of Casing Connections Subjected to Thermal Cycle Loading,"

in SIMULIA Customer Conference , Alberta, 2010.

[11] B. Bennetzen, J. Fuller, and E. Isevcan. Schlumberger. [Online].

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[12] Robert F. Mitchell and Robello Samuel, "How Good is the Torque & Drag Model?," SPE Drilling

Engineering, pp. 62-72, March 2009.

[13] C. A. Johancsik, D. B. Friesen, and Rapier Dawson, "Torque and Drag in Directional Wells-

Prediction and Measurement," Journal of Petroleum Technology, pp. 987-992, June 1984.

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SPE Drilling Engineering, pp. 344-351, Decemeber 1987.

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NTNU, Msc Thesis 2012.

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well casinG," in SPE Middle East Oil Show, Manama, 1987.

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Directional Wellbore Friction," Modern applied science, pp. 2-22, 2010.

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of Technology, Cambridge, MSc Thesis, 1983.

[20] Gere Timoshenko, Theory of Elastic Stability.: Mc-Graw Hill, 1985.

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During Drilling for Oil & Gas," TU Delft, Delft, MSc Thesis 1991.

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[24] Kim Vandiver and Rong-Juin Shyu, "Case Studies of the Bending Vibration and whirling Motion

of Drill Collars," SPE Drilling Engineering, 1990.

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Technology, Cambridge, PhD Thesis 1989.

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Manual.

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[32] American Petroleum Institute, "Bulletin on Formulas and Calculations for Casing, Tubing, Drill

Pipe, and Line Pipe Properties ," API, 1994.

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http://www.powershow.com/view4/5b3668-

M2M4N/PETE_411_Well_Drilling_powerpoint_ppt_presentation

[35] TESCO Corp., "Casing & Tubing Torque Tables for API Buttress with TESCO MLT™ Rings," TESCO

Corp., Field Make-Up Handbook https://www.scribd.com/doc/87734864/API-Thread-Torque-

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57

Perspective," The Shock and Vibration Digest, vol. 35, no. 2, pp. 85-103, March 2003.

58

Appendix A. Implementation of FDM for Beam Deflection

Figure 44 Discretization of Drill String [19]

To simplify the implementation of FDM, the constant terms of equation(4.1.18) are grouped into the

following coefficients:

1 2

0 m

ghcosa

L C

, (A.1)

2 2

0 m

ghsina

L C

. (A.2)

The equation to be discretized now reads:

4 ' 2 ' '

'

1 0 24 2

d y d y dya l w a

dw dw dw

. (A.3)

The length of the BHA being investigated here is the first casing single of standard length, 10 metres.

It is bounded by the bit on one end and the first stabilizer on the other end. This single is considered

to be divided into N segments of length 1

Neach or 1N node points. The Taylor series is then used

to approximate the differential terms in equation (4.1.18) into their algebraic equivalent by using the

central difference method as follows:

4 '

4

( 2) ( 1) ( 1) ( 2)4( 4 6 4 )j j j j j

d yN y y y y y

dw , (A.4)

'

2

( 1) ( 1)2

2

( 2 )j j j

d yN y y y

dw , (A.5)

'

1 12

j j

dy Ny y

dw . (A.6)

59

The term w in equation (A.3) represents the longitudinal distance along the casing single from the

origin at the bit. To facilitate the discretization process, it is represented by the formula:

j

wN

. (A.7)

Where the value of j varies from 0 at the bit to N at the stabilizer as depicted in Figure 44. By

examining the terms carefully in(A.4),(A.5)&(A.6), it can be seen that extra points which fall outside

the casing single will be required at the end points of the Bit and the first stabilizer. Imaginary points

can be taken which will be related to known points within the domain of the casing single by making

use of the boundary conditions at the bit and the stabilizer. Since the casing single is essentially a

beam element, the stabilizer owing to the fact that it restricts movement in all directions is modelled

as a clamped end. The dimensionless boundary conditions are:

' 0y L , (A.8)

'

0dy

Ldw

. (A.9)

Substituting (A.6) & (A.8) in the boundary condition defined by (A.9), we can obtain the imaginary

point at the stabilizer as:

1 1

02 j j

N

y y

, (A.10)

1 1N Ny y . (A.11)

The bit however is chosen to be a pinned end. Therefore the boundary conditions are:

00

Zy

, (A.12)

2 '

( 0)

2 0

Zd y

dw

. (A.13)

Making use of (A.5) by substituting in (A.13), boundary condition simplifies to:

141y a y , (A.14)

Where

4 1a . (A.15)

Now that the boundary conditions have been defined and applied to determine the imaginary

points, the next step is to substitute the finite difference approximations defined in(A.4) (A.5),&

(A.6) and also the relation (A.7) in the governing differential equation(A.3) to obtain:

60

4 4 2 4 2

2 1 1 1 1 1 1 1

4 2 411 1 1 1 2 2

14 6 2 2

2

42

j j

j j

y N y N a l N a j N y N a l N a jN

a Ny N a l N a jN y N a

.(A.16)

Equation (A.16) is the discretized general equation applicable for node points 3 3j N which

can be further simplified by grouping constant coefficients as shown below:

4

1C N , (A.17)

4 2 12 1 1

( )4

2

a NC N a l N , (A.18)

4 2

3 1 16 2C N a l N , (A.19)

4 2 14 1 1

( )4

2

a NC N a l N . (A.20)

Thereby obtaining

2 1 2 1 1 1 1 2 11 3 4 22j j j jy y c a N y a jN y a jN y c ac j c c . (A.21)

Similarly, making use of the relations defined in (A.11) &(A.14), the finite difference formulation at

the node points 1,2, 2& 3j N N are evaluated as:

At 1j ,

1 3 4 1 2 4 11 23 1[ ] [[ 2 ] ] y C a C a y C a N ay CN . (A.22)

At 2j ,

1 2 1 2 3 1 3 4 1 1 24[ 42 ] [ ] [ ]4 ] [y C a N y C a N y C a N y C a . (A.23)

At 2j N ,

4 1 3 2 1 2 3 1

1 4 1 2

( 2) ] [ 2 ( 2)]

[

[

( 1) ]

N N N

N

y C y C N a N y C a N N

y C N a N a

. (A.24)

At 1J N ,

3 1 2 2 1 1 3 1 1 2[ ( 1) ] 2 ( 1)[ ]N N Ny C y C N a N y C a N N C a . (A.25)

Finally, the 1N equations can be arranged in the form of matrices according to the expression

[ ] [ ]A y B . (A.26)

This can then be solved by using standard functions in MATLAB. The diagonal matrix A containing

the constant coefficients is:

61

3 4 1 4 1 1

2 1 3 1 4 1 1

1 2 1 3 1 1 1

1 1

1 2 1 1 1 1

1 1

1 2 1 3 1 4 1

1 2

1

4

3

1 3

4

1

1

2 0 0 0 0 0

4 0 0 0 0

3 6 3 0 0 0

0 0 0

0 0 0

0 0 0

0 0 0 0

0 0 0 0

2 4

2

( 2) 2 ( 2

0

) ( 1)

( 1) 2 (

C a C a C a N C

C a N C a N C a N C

C C a N C a N a N C

C C

C C a N ja N a N C

C C

C C N a N C a N N C N a N

N

C

C C N a N C a

j C C j

N N

A

11) C

(A.27)

Y Is a vector containing the displacements at each node:

'

1

'

2

'

'

2

'

1

j

N

N

y

y

yy

y

y

, (A.28)

And lastly, [ ]B is given by:

2

2

2

[ ]

a

Ba

a

. (A.29)

62

Appendix B. Implementation of FDM for Buckling Analysis

The matrix A defined in (5.1.5) is similar to the earlier coefficient matrix defined earlier in

Appendix A except for the parameter denoting the weight on bit which is contained in the B

matrix. Recalling equation(5.1.3):

4 ' 2 ' ' 2 '

'

4 2 2 2 2 2

0 0

'

'

0

0 m m m

ghcos ld y ghcos d y dy ghsin d yw y

dw L C dw dw L C L C dwc

. (B.1)

Substituting finite difference approximations(A.4) to (A.6) and the terms (A.1) & (A.2) in (B.1), we

obtain the general equation for nodes3 3j N as:

4 4 4 22 1 1 1 '

4 411 1 2

2 2' ' '

0 0

2

1 1 1 1 1 0

14 6 2

2

42

2

j j j

j j

j j j

ay N y N a j N y N a jN

c

a Ny N a jN y N

y a l N y a l N y a l N

. (B.2)

Equation (B.2) can be simplified by making use of:

, (B.3)

4

51( )

42

a NC N , (B.4)

4 26 '

6c

C Na

, (B.5)

4

71( )

42

a NC N , (B.6)

' 2

18 0aC l N , (B.7)

' 2

1 09 2a lC N . (B.8)

Thus obtaining:

2 1 2 1 3 1 1 4 1 2

1

1 1

5 6 51

2j j j j j

j j j

y y C a N y C a jN y C aC j C

C

jN y

y y Cy C

. (B.9)

4

1C N

63

Equation (B.9) is the general equation which is discretized at all 1N node points to obtain a set of

1N linear equations which can be solved in MATLAB by using standard Eigen functions. MATLAB

returns two matrices as the output of the Eigen value analysis. The first is a diagonal matrix

containing the Eigen values or the critical loads. The lowest Eigen value thus observed is the first

critical load to induce sinusoidal buckling. The second matrix contains the Eigen vectors or the mode

shapes in each column. The first mode shape corresponding to the lowest critical load is found in the

first column and so on.

The matrix A defined in(5.1.5) is thus given by:

6 1 7

5 6 7

6 7

6 7

5 6 7

5

4 1 1 1

1 1 1 1

1 5 1 1 1 1

1 1

1 5 1 1 1 1

1 1

1 1 1 1

1 1 6 1

1

2 0 0 0 0 0

4 0 0 0 0

3 6 3 0 0 0

0 0 0

0 0 0

0 0 0

0 0 0 0

0 0 0 0 0

2 4

2

( 2) 2 ( 2) ( 1)

( 1) 2 (

C a C a C a N C

C a N C a N C a N C

C C a N C a N a N C

C C

C C a N ja N a N C

C C

C C N a N C a N N C N a N

N

C

C C N a N C a

j C C j

N N

A

11) C

(B.10)

And the diagonal matrix matrix B is given by:

9 8

8 9 8

8 9 8

8 9

0 0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 0

C C

C C C

B

C C C

C C

. (B.11)

64

Appendix C. Implementation of FDM for Whirling Analysis

The implementation of the finite difference method for identifying natural frequencies is essentially

the same as that described previously in Appendix A & Appendix B. Here, the following terms can be

defined to simplify equation(6.1.6):

1

M

EIa

A C , (C.1)

2

cos

M

gha

C

. (C.2)

Resulting in:

4 2

2

1 2 04 2( ) 0

d y d y dya a l z y

dz dz dz

. (C.3)

Let

LN

LH

N , (C.4)

where L = length of casing single

N =Number of segments the BHA single is divided into

Then the discretized general equation based on (C.3) is obtained by substituting the finite difference

approximations (A.4) to (A.6) yielding:

2 0 2 01 1 2 2 1 22 14 4 2 4 2

22 01 2 2 11 24 2 4

2 2( ) ( 4 ) (6 )

2

( 4 ) ( )2

j j j

LN LN LN LN LN LN LN LN

j j j

LN LN LN LN LN

a l a la a a j a a a jy y y

H H H H H H H H

a la a a j ay y y

H H H H H

. (C.5)

The constant coefficients in (C.5) are grouped together as:

11 4

LN

aC

H , (C.6)

2 0 2 01 2 1 24 4 2 4 2

4 42 2LN LN LN LN LN LN

a l a la a a aC

H H H H H H , (C.7)

2 013 4 2

26

LN LN

a laC

H H , (C.8)

2 01 24 4 2

42LN LN LN

a la aC

H H H . (C.9)

65

Equations (C.6) to (C.9)are then substituted in (C.5) to yield the following general equation:

22 2 21 2 2 1 3 4 1 1 2

2( ) ( ) ( ) ( ) ( )j j j j j j

LN LN LN

a j a j a jC y C y C y C y C y y

H H H . (C.10)

Thus, A from(6.1.8) is given by:

3 4 1 4 1

2 3 4 1

1 2 3 1

1 1

1 1

1 1

1 2 3 4

1 2 3

2 2

2 2 2

2 2 24

2 2 2

2

1

2 0 0 0 0 0

4 0 0 0 0

0 0 0

2 2

2

( 2) 2 ( 2) ( 2)

( 1)

0 0 0

0 0 0

0 0 0

0 0 0 0

0 0 0 0 0

LN LN

LN LN LN

LN LN LN

LN LN LN

LN

a aC a C C C

a a aC C C C

a a aC C C C

C C

C C

C C

a N a N

H H

H H H

j j jC

a NC C C C

a NC C C

H H H

H H H

H

A

23 1

2 ( 1)

LN

a N

HC C

(C.11)

The same boundary conditions as described in Appendix A are used to fill in the first and last two

rows of the matrix. Similarly, B is a diagonal matrix of same dimensions as :

2

2

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

B

. (C.12)

A

66

Appendix D. Supporting Tabular Data

TVD Axial Stress Radial Stress Hoop Stress Von Mises Stress FOS

[M] [Mpa] [Mpa] [Mpa] [Mpa]

0.00 99.84 -40.64 339.62 333.03 1.58

30.00 97.86 -40.72 335.10 329.19 1.60

60.00 95.89 -40.80 330.58 325.34 1.62

90.00 93.91 -40.88 326.06 321.49 1.64

120.00 91.94 -40.96 321.55 317.64 1.66

150.00 89.96 -41.04 317.03 313.79 1.68

180.00 87.99 -41.12 312.51 309.94 1.70

210.00 86.02 -41.20 307.99 306.10 1.72

240.00 84.04 -41.28 303.47 302.25 1.74

270.00 82.07 -41.35 298.96 298.40 1.76

300.00 80.09 -41.43 294.44 294.55 1.79

330.00 78.12 -41.51 289.92 290.71 1.81

350.00 76.80 -41.57 286.91 288.14 1.83

360.00 76.14 -41.59 285.40 286.86 1.83

390.00 74.17 -41.67 280.88 283.01 1.86

420.00 72.19 -41.75 276.37 279.17 1.88

450.00 70.22 -41.83 271.85 275.32 1.91

480.00 68.24 -41.91 267.33 271.48 1.94

510.00 66.27 -41.99 262.81 267.63 1.97

540.00 64.29 -42.07 258.30 263.79 1.99

570.00 62.32 -42.15 253.78 259.94 2.02

600.00 60.35 -42.23 249.26 256.10 2.05

630.00 58.37 -42.31 244.74 252.26 2.09

660.00 56.40 -42.39 240.22 248.41 2.12

690.00 54.42 -42.47 235.71 244.57 2.15

700.00 135.46 -42.49 227.21 237.51 2.22

727.27 133.49 -42.57 223.20 234.18 2.25

754.55 131.53 -42.64 219.20 230.84 2.28

781.82 129.59 -42.71 215.19 227.52 2.32

809.09 127.67 -42.78 211.19 224.20 2.35

836.36 125.79 -42.85 207.18 220.89 2.39

863.64 123.96 -42.93 203.18 217.59 2.42

890.91 122.18 -43.00 199.17 214.31 2.46

918.18 120.45 -43.07 195.17 211.04 2.50

945.45 118.80 -43.14 191.16 207.80 2.54

972.73 117.22 -43.21 187.16 204.57 2.58

1000.00 115.64 -43.29 183.15 201.36 2.62

1021.94 114.19 -43.34 179.93 198.73 2.65

1043.88 112.75 -43.40 176.71 196.12 2.69

1065.82 111.31 -43.46 173.48 193.50 2.72

1087.76 109.87 -43.52 170.26 190.89 2.76

1109.70 108.43 -43.58 167.04 188.28 2.80

1131.64 106.99 -43.64 163.82 185.68 2.84

1153.58 105.55 -43.69 160.59 183.08 2.88

1175.52 104.11 -43.75 157.37 180.49 2.92

1197.47 102.66 -43.81 154.15 177.90 2.96

1219.41 101.22 -43.87 150.93 175.31 3.01

1241.35 99.78 -43.93 147.71 172.73 3.05

1263.29 98.34 -43.98 144.48 170.16 3.10

1285.23 96.90 -44.04 141.26 167.59 3.15

1307.17 95.46 -44.10 138.04 165.02 3.19

1329.11 94.02 -44.16 134.82 162.46 3.24

1351.05 92.58 -44.22 131.60 159.91 3.30

1372.99 91.13 -44.27 128.37 157.37 3.35

1394.93 89.69 -44.33 125.15 154.83 3.40

1416.87 88.25 -44.39 121.93 152.30 3.46

1438.81 86.81 -44.45 118.71 149.78 3.52

1460.75 85.37 -44.51 115.48 147.26 3.58

1482.69 83.93 -44.56 112.26 144.75 3.64

1504.63 82.49 -44.62 109.04 142.26 3.71

1526.57 81.05 -44.68 105.82 139.77 3.77

1548.52 79.60 -44.74 102.60 137.29 3.84

Table 12 Von Mises Stress Analysis at Survey Points for Burst Loading Scenario

67

1570.46 78.16 -44.80 99.37 134.82 3.91

1592.40 76.72 -44.85 96.15 132.37 3.98

1614.34 75.28 -44.91 92.93 129.92 4.06

1636.28 73.84 -44.97 89.71 127.49 4.13

1658.22 72.40 -45.03 86.48 125.07 4.21

1680.16 70.96 -45.09 83.26 122.66 4.30

1702.10 69.51 -45.15 80.04 120.27 4.38

1724.04 68.07 -45.20 76.82 117.89 4.47

1745.98 66.63 -45.26 73.60 115.53 4.56

1767.92 65.19 -45.32 70.37 113.19 4.66

1789.86 63.75 -45.38 67.15 110.87 4.75

1811.80 62.31 -45.44 63.93 108.56 4.86

1833.74 60.87 -45.49 60.71 106.28 4.96

1855.68 59.43 -45.55 57.49 104.02 5.07

1877.62 57.98 -45.61 54.26 101.78 5.18

1899.57 56.54 -45.67 51.04 99.57 5.29

1921.51 55.10 -45.73 47.82 97.39 5.41

1943.45 53.66 -45.78 44.60 95.24 5.53

1965.39 52.22 -45.84 41.37 93.11 5.66

1987.33 50.78 -45.90 38.15 91.02 5.79

2009.27 49.34 -45.96 34.93 88.97 5.92

2031.21 47.90 -46.02 31.71 86.96 6.06

2053.15 46.45 -46.07 28.49 84.98 6.20

2075.09 45.01 -46.13 25.26 83.05 6.35

2097.03 43.57 -46.19 22.04 81.17 6.49

2118.97 42.13 -46.25 18.82 79.34 6.64

2140.91 40.69 -46.31 15.60 77.56 6.80

2162.85 39.25 -46.36 12.38 75.84 6.95

2184.79 37.81 -46.42 9.15 74.18 7.11

2200.00 0.00 0.00

68

Table 13 Simulated Pick-Up Drag Values at Survey Points for 7” Liner Drilling

700 8.72 1722 3.64

730 8.38 1752 3.53

760 8.08 1782 3.42

790 7.79 1812 3.30

820 7.53 1842 3.19

850 7.28 1872 3.08

880 7.06 1902 2.97

910 6.85 1932 2.85

940 6.67 1962 2.74

970 6.51 1992 2.63

1000 6.35 2022 2.52

1032 6.23 2052 2.40

1062 6.12 2082 2.29

1092 6.00 2112 2.18

1122 5.89 2142 2.07

1152 5.78 2172 1.95

1182 5.67 2202 1.84

1212 5.55 2232 1.73

1242 5.44 2262 1.62

1272 5.33 2292 1.50

1302 5.22 2322 1.39

1332 5.10 2352 1.28

1362 4.99 2382 1.17

1392 4.88 2412 1.05

1422 4.77 2442 0.94

1452 4.65 2472 0.83

1482 4.54 2502 0.72

1512 4.43 2532 0.60

1542 4.32 2562 0.49

1572 4.20 2592 0.38

1602 4.09 2622 0.27

1632 3.98 2652 0.15

1662 3.87 2680.037 0.05

1692 3.75 2681.561 0.02

Measured

Depth (m)

Axial Pick-Up

Load ( x 10^5 N)

Measured

Depth (m)

Axial Pick-Up

Load ( x 10^5

69

Table 14 Von Mises Analysis at Various Survey Points for 7'' Deviated N80 Liner Section

TVD FOS TVD FOS

[M] [M]

700.00 196.43 255.70 2.06 1482.69 105.31 153.47 3.43

727.27 190.36 250.96 2.10 1504.63 103.24 150.85 3.49

754.55 184.67 246.39 2.14 1526.57 101.17 148.23 3.56

781.82 179.50 242.04 2.18 1548.52 99.11 145.62 3.62

809.09 174.65 237.81 2.22 1570.46 97.04 143.02 3.69

836.36 170.15 233.73 2.26 1592.40 94.97 140.42 3.75

863.64 166.01 229.78 2.29 1614.34 92.91 137.83 3.82

890.91 162.22 225.97 2.33 1636.28 90.84 135.25 3.90

918.18 158.87 222.32 2.37 1658.22 88.77 132.67 3.97

945.45 155.88 218.81 2.41 1680.16 86.71 130.11 4.05

972.73 152.93 215.31 2.45 1702.10 84.64 127.55 4.13

1000.00 150.77 212.11 2.49 1724.04 82.57 125.00 4.22

1021.94 148.71 209.42 2.52 1745.98 80.51 122.46 4.30

1043.88 146.64 206.72 2.55 1767.92 78.44 119.93 4.40

1065.82 144.57 204.03 2.58 1789.86 76.37 117.41 4.49

1087.76 142.51 201.34 2.62 1811.80 74.31 114.91 4.59

1109.70 140.44 198.66 2.65 1833.74 72.24 112.41 4.69

1131.64 138.37 195.97 2.69 1855.68 70.17 109.93 4.79

1153.58 136.31 193.29 2.73 1877.62 68.11 107.47 4.90

1175.52 134.24 190.61 2.77 1899.57 66.04 105.02 5.02

1197.47 132.17 187.94 2.80 1921.51 63.97 102.58 5.14

1219.41 130.11 185.26 2.85 1943.45 61.91 100.16 5.26

1241.35 128.04 182.59 2.89 1965.39 59.84 97.77 5.39

1263.29 125.97 179.93 2.93 1987.33 57.77 95.39 5.53

1285.23 123.91 177.26 2.97 2009.27 55.71 93.03 5.67

1307.17 121.84 174.60 3.02 2031.21 53.64 90.70 5.81

1329.11 119.77 171.95 3.07 2053.15 51.57 88.40 5.96

1351.05 117.71 169.29 3.11 2075.09 49.51 86.12 6.12

1372.99 115.64 166.65 3.16 2097.03 47.44 83.87 6.29

1394.93 113.57 164.00 3.21 2118.97 45.37 81.65 6.46

1416.87 111.51 161.36 3.27 2140.91 43.31 79.47 6.63

1438.81 109.44 158.72 3.32 2162.85 41.24 77.32 6.82

1460.75 107.37 156.09 3.38 2184.79 39.17 75.22 7.01

Von Mises

Stress [Mpa]

Axial Stress Including

Drag Forces [Mpa]

Axial Stress Including

Drag Forces [Mpa]

Von Mises

Stress [Mpa]

70

Table 15 Simulated Bending Stress due to Whirling for 7” Liner Stand (30 M)

0 13.92 9.2 -5.20 18.4 -11.90

0.2 14.06 9.4 -5.86 18.6 -11.41

0.4 14.17 9.6 -6.50 18.8 -10.90

0.6 14.25 9.8 -7.14 19 -10.37

0.8 14.30 10 -7.77 19.2 -9.82

1 14.32 10.2 -8.38 19.4 -9.26

1.2 14.31 10.4 -8.97 19.6 -8.67

1.4 14.26 10.6 -9.55 19.8 -8.08

1.6 14.19 10.8 -10.12 20 -7.46

1.8 14.08 11 -10.66 20.2 -6.84

2 13.94 11.2 -11.18 20.4 -6.20

2.2 13.77 11.4 -11.69 20.6 -5.56

2.4 13.57 11.6 -12.17 20.8 -4.90

2.6 13.35 11.8 -12.63 21 -4.24

2.8 13.09 12 -13.06 21.2 -3.57

3 12.80 12.2 -13.47 21.4 -2.90

3.2 12.49 12.4 -13.85 21.6 -2.22

3.4 12.14 12.6 -14.21 21.8 -1.54

3.6 11.78 12.8 -14.55 22 -0.86

3.8 11.38 13 -14.85 22.2 -0.18

4 10.96 13.2 -15.13 22.4 0.49

4.2 10.52 13.4 -15.37 22.6 1.17

4.4 10.05 13.6 -15.59 22.8 1.84

4.6 9.56 13.8 -15.78 23 2.50

4.8 9.04 14 -15.94 23.2 3.16

5 8.51 14.2 -16.07 23.4 3.80

5.2 7.96 14.4 -16.17 23.6 4.44

5.4 7.39 14.6 -16.23 23.8 5.07

5.6 6.80 14.8 -16.27 24 5.68

5.8 6.20 15 -16.28 24.2 6.28

6 5.58 15.2 -16.25 24.4 6.87

6.2 4.95 15.4 -16.20 24.6 7.44

6.4 4.31 15.6 -16.11 24.8 7.99

6.6 3.65 15.8 -15.99 25 8.52

6.8 2.99 16 -15.85 25.2 9.04

7 2.32 16.2 -15.67 25.4 9.53

7.2 1.64 16.4 -15.46 25.6 10.01

7.4 0.96 16.6 -15.23 25.8 10.46

7.6 0.27 16.8 -14.96 26 10.89

7.8 -0.42 17 -14.67 26.2 11.29

8 -1.11 17.2 -14.35 26.4 11.67

8.2 -1.80 17.4 -14.01 26.6 12.02

8.4 -2.49 17.6 -13.63 26.8 12.35

8.6 -3.17 17.8 -13.24 27 12.65

8.8 -3.85 18 -12.81 27.2 12.93

9 -4.53 18.2 -12.37 27.4 13.17

Distance

From Bit(M)

Bending Stress

(MPa)

Distance

From Bit(M)

Bending Stress

(MPa)

Distance

From Bit(M)

Bending Stress

(MPa)

71

Table 16 Von Mises Tri Axisal Stress Analysis of 7" Liner for Drilling Conditions at Survey Points

TVD Axial Torsional Radial Hoop Von Mises FOS TVD Axial Torsional Radial Hoop Von Mises FOS

[Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa] [Mpa]

700.00 151.74 57.59 -8.55 -69.42 221.59 2.38 1724.04 84.35 18.76 -22.99 -186.69 238.64 2.21

727.27 149.77 57.07 -8.93 -72.54 221.59 2.38 1745.98 82.91 17.93 -23.30 -189.21 239.57 2.20

754.55 147.81 56.47 -9.32 -75.66 221.55 2.38 1767.92 81.47 17.09 -23.61 -191.72 240.51 2.19

781.82 145.87 55.79 -9.70 -78.79 221.50 2.38 1789.86 80.03 16.25 -23.92 -194.23 241.47 2.18

809.09 143.95 54.91 -10.09 -81.91 221.35 2.38 1811.80 78.59 15.42 -24.23 -196.74 242.45 2.17

836.36 142.07 53.95 -10.47 -85.03 221.22 2.38 1833.74 77.15 14.58 -24.54 -199.26 243.46 2.17

863.64 140.24 52.47 -10.86 -88.16 220.78 2.39 1855.68 75.71 13.75 -24.85 -201.77 244.48 2.16

890.91 138.46 51.10 -11.24 -91.28 220.53 2.39 1877.62 74.26 12.91 -25.16 -204.28 245.52 2.15

918.18 136.73 49.82 -11.63 -94.40 220.43 2.39 1899.57 72.82 12.07 -25.47 -206.80 246.58 2.14

945.45 135.08 48.54 -12.01 -97.53 220.45 2.39 1921.51 71.38 11.24 -25.78 -209.31 247.66 2.13

972.73 133.50 47.37 -12.40 -100.65 220.64 2.39 1943.45 69.94 10.40 -26.09 -211.82 248.75 2.12

1000.00 131.92 46.36 -12.78 -103.77 220.98 2.39 1965.39 68.50 9.57 -26.39 -214.33 249.87 2.11

1021.94 130.47 45.52 -13.09 -106.29 221.12 2.38 1987.33 67.06 8.73 -26.70 -216.85 251.00 2.10

1043.88 129.03 44.68 -13.40 -108.80 221.28 2.38 2009.27 65.62 7.89 -27.01 -219.36 252.15 2.09

1065.82 127.59 43.85 -13.71 -111.31 221.48 2.38 2031.21 64.18 7.06 -27.32 -221.87 253.32 2.08

1087.76 126.15 43.01 -14.02 -113.83 221.69 2.38 2053.15 62.73 6.22 -27.63 -224.38 254.51 2.07

1109.70 124.71 42.18 -14.33 -116.34 221.94 2.38 2075.09 61.29 5.38 -27.94 -226.90 255.71 2.06

1131.64 123.27 41.34 -14.64 -118.85 222.21 2.37 2097.03 59.85 4.55 -28.25 -229.41 256.93 2.05

1153.58 121.83 40.50 -14.95 -121.36 222.50 2.37 2118.97 58.41 3.71 -28.56 -231.92 258.16 2.04

1175.52 120.39 39.67 -15.26 -123.88 222.82 2.37 2140.91 56.97 2.88 -28.87 -234.44 259.41 2.03

1197.47 118.94 38.83 -15.56 -126.39 223.17 2.36 2162.85 55.53 2.04 -29.18 -236.95 260.68 2.02

1219.41 117.50 37.99 -15.87 -128.90 223.54 2.36 2184.79 54.09 1.20 -29.49 -239.46 261.97 2.01

1241.35 116.06 37.16 -16.18 -131.41 223.94 2.35

1263.29 114.62 36.32 -16.49 -133.93 224.36 2.35

1285.23 113.18 35.49 -16.80 -136.44 224.80 2.34

1307.17 111.74 34.65 -17.11 -138.95 225.27 2.34

1329.11 110.30 33.81 -17.42 -141.47 225.77 2.33

1351.05 108.86 32.98 -17.73 -143.98 226.29 2.33

1372.99 107.41 32.14 -18.04 -146.49 226.83 2.32

1394.93 105.97 31.31 -18.35 -149.00 227.40 2.32

1416.87 104.53 30.47 -18.66 -151.52 227.99 2.31

1438.81 103.09 29.63 -18.97 -154.03 228.60 2.31

1460.75 101.65 28.80 -19.28 -156.54 229.24 2.30

1482.69 100.21 27.96 -19.59 -159.05 229.90 2.29

1504.63 98.77 27.12 -19.90 -161.57 230.59 2.29

1526.57 97.33 26.29 -20.21 -164.08 231.29 2.28

1548.52 95.88 25.45 -20.52 -166.59 232.02 2.27

1570.46 94.44 24.62 -20.83 -169.10 232.77 2.26

1592.40 93.00 23.78 -21.13 -171.62 233.55 2.26

1614.34 91.56 22.94 -21.44 -174.13 234.34 2.25

1636.28 90.12 22.11 -21.75 -176.64 235.16 2.24

1658.22 88.68 21.27 -22.06 -179.16 236.00 2.23

1680.16 87.24 20.44 -22.37 -181.67 236.86 2.23

1702.10 85.79 19.60 -22.68 -184.18 237.74 2.22

72

Table 17 Bending Stress due to Buckling for 9 5/8" Intermediate CSG Stand (30 metres)

0 0.00 9.2 1.72 18.4 0.64

0.2 0.05 9.4 1.73 18.6 0.59

0.4 0.11 9.6 1.73 18.8 0.54

0.6 0.16 9.8 1.74 19 0.49

0.8 0.21 10 1.74 19.2 0.44

1 0.27 10.2 1.74 19.4 0.39

1.2 0.32 10.4 1.74 19.6 0.34

1.4 0.37 10.6 1.74 19.8 0.29

1.6 0.42 10.8 1.74 20 0.24

1.8 0.47 11 1.74 20.2 0.19

2 0.52 11.2 1.73 20.4 0.14

2.2 0.57 11.4 1.72 20.6 0.09

2.4 0.62 11.6 1.72 20.8 0.03

2.6 0.67 11.8 1.71 21 -0.02

2.8 0.72 12 1.69 21.2 -0.07

3 0.77 12.2 1.68 21.4 -0.12

3.2 0.82 12.4 1.67 21.6 -0.17

3.4 0.86 12.6 1.65 21.8 -0.22

3.6 0.91 12.8 1.63 22 -0.27

3.8 0.95 13 1.61 22.2 -0.32

4 1.00 13.2 1.59 22.4 -0.37

4.2 1.04 13.4 1.57 22.6 -0.42

4.4 1.08 13.6 1.55 22.8 -0.47

4.6 1.12 13.8 1.52 23 -0.52

4.8 1.16 14 1.50 23.2 -0.57

5 1.20 14.2 1.47 23.4 -0.62

5.2 1.24 14.4 1.44 23.6 -0.67

5.4 1.28 14.6 1.41 23.8 -0.71

5.6 1.31 14.8 1.38 24 -0.76

5.8 1.35 15 1.35 24.2 -0.81

6 1.38 15.2 1.31 24.4 -0.85

6.2 1.41 15.4 1.28 24.6 -0.90

6.4 1.44 15.6 1.24 24.8 -0.94

6.6 1.47 15.8 1.20 27.6 -1.45

6.8 1.50 16 1.17 27.8 -1.47

7 1.52 16.2 1.13 28 -1.50

7.2 1.55 16.4 1.09 28.2 -1.52

7.4 1.57 16.6 1.05 28.4 -1.55

7.6 1.59 16.8 1.00 28.6 -1.57

7.8 1.61 17 0.96 28.8 -1.59

8 1.63 17.2 0.92 29 -1.61

8.2 1.65 17.4 0.87 29.2 -1.63

8.4 1.67 17.6 0.83 29.4 -1.65

8.6 1.68 17.8 0.78 29.6 -1.66

8.8 1.70 18 0.73 29.8 -1.68

9 1.71 18.2 0.69 30 -1.69

Distance

From Bit(M)

Bending Stress

(MPa)

Distance

From Bit(M)

Bending Stress

(MPa)

Distance

From Bit(M)

Bending Stress

(MPa)

73

Appendix E. Torque Analysis & Corresponding Selection of Casing Connection

700 20681.34 57.59 1722 9741.37 27.12

730 20496.58 57.07 1752 9441.07 26.29

760 20281.32 56.47 1782 9140.78 25.45

790 20036.12 55.79 1812 8840.49 24.62

820 19721.17 54.91 1842 8540.20 23.78

850 19376.83 53.95 1872 8239.91 22.94

880 18843.58 52.47 1902 7939.61 22.11

910 18352.02 51.10 1932 7639.32 21.27

940 17892.89 49.82 1962 7339.03 20.44

970 17432.07 48.54 1992 7038.74 19.60

1000 17011.98 47.37 2022 6738.45 18.76

1032 16648.08 46.36 2052 6438.16 17.93

1062 16347.79 45.52 2082 6137.86 17.09

1092 16047.49 44.68 2112 5837.57 16.25

1122 15747.20 43.85 2142 5537.28 15.42

1152 15446.91 43.01 2172 5236.99 14.58

1182 15146.62 42.18 2202 4936.70 13.75

1212 14846.33 41.34 2232 4636.41 12.91

1242 14546.03 40.50 2262 4336.11 12.07

1272 14245.74 39.67 2292 4035.82 11.24

1302 13945.45 38.83 2322 3735.53 10.40

1332 13645.16 37.99 2352 3435.24 9.57

1362 13344.87 37.16 2382 3134.95 8.73

1392 13044.58 36.32 2412 2834.65 7.89

1422 12744.28 35.49 2442 2534.36 7.06

1452 12443.99 34.65 2472 2234.07 6.22

1482 12143.70 33.81 2502 1933.78 5.38

1512 11843.41 32.98 2532 1633.49 4.55

1542 11543.12 32.14 2562 1333.20 3.71

1572 11242.82 31.31 2592 1032.90 2.88

1602 10942.53 30.47 2622 732.61 2.04

1632 10642.24 29.63 2652 432.32 1.20

1662 10341.95 28.80 2682 0.00 0.00

1692 10041.66 27.96

Torsional Stress

[Mpa]

Measured

Depth[m]

Torque

[Nm]

Torsional Stress

[Mpa]

Measured

Depth[m]

Torque

[Nm]

Table 18 Torque Analysis at Survey Points for 7" N80 Liner Section

74

Table 19 Connection Make-Up Torque Capacities from Manufacturer Catalogue

Data presented in Table 19 is obtained from Tesco Corp. manufacturer catalogue [35]. As previously

stated, the torque capacities of typical buttress connections used for casing in geothermal wells is

insufficient to withstand high torque loads during drilling and even while rotating the casing string

when running in to clear blockages. Thus special torque rings have been designed and tested by

manufacturers to increase the make-up torque capacities of buttress connections substantially .The

ideal connection based on the outer diameter of the liner (177.80mm) and the inner diameter

(157.07mm) of the same grade (N-80) as the pipe body for the 7” Liner casing string is highlighted in

the table above. With the addition of the torque rings, the maximum rated make up torque for this

connection will clearly contain the maximum simulated torque of approx.20,000 Nm from Table 18

and is thus the recommended choice.

75

Appendix F. Fluid Hydraulics – Frictional Pressure Losses

Table 20 Pressure Loss Computed By Power Law Rheology

Standard Properties

Discharge (gal/min) 270.00

Density (lbs/gal) 10.15

Flow Behaviour Index 0.54

Fluid Consistency Index,K 6.34

7" Liner- OH Annular Loss

Average Bulk Velocity (ft/s) 4.64

Effective Viscosity(Cp) 51.93

Reynolds Number 1269.42

Friction Factor 0.02

Friction Pressure Gradient (psi/ft) 0.10

Pressure Drop (psi) 507.19

In SI Units,(Mpa) 3.50

5" DP-9 5/8" CSG Annular Loss








5" DP-Internal Pressure Loss




Reynolds No. Turbulent Flow

Constant, A0.08

Reynolds No. Turbulent Flow

Constant, B0.27





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Casing Design Methodology for Casing While Drilling

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