Advanced Tubing Design

M ASTER T HESIS
TPG4920 P ETROLEUM T ECHNOLOGY

D EPARTMENT OF G EOSCIENCE AND P ETROLEUM
N ORWEGIAN U NIVERSITY OF S CIENCE AND T ECHNOLOGY
ADVANCED TUBING DESIGN
Author Supervisor
Thanushina T HARMAPALAN Bjørn A STOR B RECHAN
July 4, 2019
Preface
Developing this thesis for the past six months has been an exciting journey, dedicated to
the last step in completing my Master of Science in Petroleum Engineering with a special-
ization in Drilling Technology.
This thesis is carried out during the spring semester of 2019 at the Norwegian University
of Science and Technology at the Department of Geoscience and Petroleum. It was devel-
oped with background from my fall project ”Advanced packer analysis”.
Tubing design is a relevant subject within well design and is considered to be one of the
most important aspects in order to make the well safe for operation. This thesis includes
literature study and analysis of two wells modelled in the sofware WellCatTM .
Trondheim, 2019-07-04
Thanushina Tharmapalan
i
Acknowledgement
I would like to thank and appreciate a number of wonderful individuals, who have been
inspiring and supportive during this journey and making this thesis possible. I owe my
deepest gratitude to my supervisor Bjørn Astor Brechan, for his excellent support and
guidance during the period of developing this thesis. His long experience in the indus-
try has given me a greater understanding of tubing design and good insight on discussion
topics around this. Also, I would like to thank him for the training I got in the use of
WellCatTM in the specialization course before writing my fall project, followed by this
thesis. Lastly, his enthusiasm and motivation have been helpful during all stages of this
project.
My gratitude also goes to my fellow students for the wonderful times we have shared to-
gether the past five years at NTNU. Thank you for the great friendship, and for providing
happy distractions outside the study and being a great support in deliberating over our
problems and findings. These years would never have been the same without you and
thank you for all the memories your presence helped me to create.
Finally, my deep and sincere gratitude to my family for the love and support they have
given me throughout the entire process. Their motivating words have kept me driven to
improve this thesis and to continue at tough points.
ii
Summary
Phases in an oil production involve many physical elements, and one of the major compo-
nents in an oil platform is the well. This thesis details the research and depth analysis of
designing a tubing, which is the production pipe in a well.
When designing a well, the following must be considered:

• Tubing design, FEED (front end engineering design)
• Tubing size, which is one among many basic procedures for determining plateau
production. This includes the size and the life span for the platform which consists
of CPF (Central processing facility)
• Gas lift, protection of the DHSV (downhole safety valve) against scale and other
issues related to well intervention
• Material quality to avoid corrosion and weakening or damage of the production pipe
These are one of the barrier elements in the primary barrier envelope and must therefore
be intact to produce the well safely. Well integrity is a central element for the construction
of the well, especially from the safety and economical aspect. An essential part of well
integrity is designing the tubing and casing to fit the requirements for a well. When de-
signing a well, tubulars will be selected based on the requirements and their exposure to
loads throughout the lifecycle of the well.
All conditions and loads that occur during the operation of a well should be taken care
of when designing the tubing. The tubing should have an acceptable margin for critical
load cases that may affect well conditions. It should withstand burst, collapse, and tension
stresses and be able to bear the weight of completion equipment. In addition, the tubing
should resist corrosive fluids coming from the well. The tubing should help to produce
the fluids from the formation in a safe manner without causing unconscionable operation
problems.
This thesis looks detailed into tubing design and possible factors that may affect the tub-
ing. This is achieved by designing two wells with different wellpaths and analyzing the
difference. The modelling consists of forces from pressures, temperatures and fluids, and
an illustration of how the tubing is exposed for each load case modelled. As packer affect
the tubing in numerous ways, the resulting forces and packer envelope have been evalu-
ated. The final analysis shows how tubing movement is caused by different load effects
and how these are calculated in different softwares.
iii
Sammendrag
Optimal oljeproduksjon krever god tilstrømning av hydrokarboner fra reservoaret til brønnen.
Dette innebærer god brønndesign og en av hovedkomponentene i brønnen er produk-
sjonsrøret. Produksjonsrøret transporterer olje og gass fra reservoaret gjennom brønnen
på en trygg og kostnadseffektiv måte. Denne oppgaven gir en grundig forståelse og anal-
yse av produksjonsrøret i en brønn.
Følgene faktorer er viktig å vurdere ved utforming av en brønn:
• Utkast av produksjonsrøret, som er et av de første elementene som bestemmes i

tidlig fase
• Størrelse på produksjonsrøret som bestemmer underlaget for platå-produksjon, og

som dimensjonerer levetid og størrelse på prosessanlegget
• Gassløft, beskyttelse av nedihullsventilen mot scale og andre behov for intervensjon
• Materialkvalitet for å unngå korrosjon og svekkelse av produksjonsrørene
Disse er et av barriere-elementene i primærbarrieren, og må derfor være intakt for å kunne

produsere i brønnen. En god brønnintegritet innebærer sikre og gode barrierer i en brønn
og er et sentralt element for utformingen av brønnen. Designingen av produksjonsrøret
og foringsrøret er en viktig del av brønnintegritet som må ivaretas for å oppfylle kravene
til en brønn. Rørene bestemmes ut ifra kravene og deres eksponering for belastninger i
brønnens livssyklus.
Når produksjonsrøret skal utformes, bør alle forhold og belastninger som er mulig å oppstå
under drift og vedlikehold tas i betraktning. Røret skal kunne bære vekten av forskjellige
kompletteringsutstyr, samt ha en akseptabel margin for mulige kritiske belastninger som
kan påvirke boreforholdene. Røret må bidra til en sikker og effektiv produksjon, samtidig
motstå mulige korroderende væsker fra reservoaret.
Denne oppgaven utdyper designet av et produksjonsrør og ulike faktorer som kan påvirke
røret. To brønner med forskjellige brønnbaner har blitt modellert og mulige belastninger
i rørdesignene har blitt simulert. Modelleringen består av krefter fra trykk, temperatur
og væsker, og en visualisering av hvordan røret er eksponert for hver last som er mod-
ellert. Produksjonspakningen påvirker produksjonsrøret på mange måter og derfor er re-
sulterende krefter og pakningskonvolutt blitt evaluert. Den endelige analysen viser hvor-
dan rørbevegelse påvirkes av ulike belastningseffekter og hvordan disse beregningene er
utført i forskjellige programvarer.
iv
Contents
Preface i
Acknowledgement ii
Summary iii
Sammendrag iv
Table of Contents vi
List of Tables vii
List of Figures ix
Abbreviations x
1 Introduction 1
1.1 Equipment selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Tubing size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 DHSV - Downhole safety valve . . . . . . . . . . . . . . . . . . 5
1.1.3 Selection of production packer . . . . . . . . . . . . . . . . . . . 6
1.2 Material selection and corrosion considerations . . . . . . . . . . . . . . 8
1.3 Well integrity and tubing as primary barrier envelope . . . . . . . . . . . 8
1.4 Thermal effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 AFE - Annular fluid expansion . . . . . . . . . . . . . . . . . . . . . . . 13
2 Theory - Part I 15
2.1 Acting forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Modelling of forces from formation pressures and temperatures
(load cases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Resulting forces on packer . . . . . . . . . . . . . . . . . . . . . 19
2.1.3 Tubing-to-casing drag . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.4 Different load effects on tubing . . . . . . . . . . . . . . . . . . 24
3 Theory - Part II 29
3.1 Design strength of tubing . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
3.1.1 Selection of tubing grade . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 Combined loads - Triaxial load capacity diagram . . . . . . . . . 36
3.1.3 Packer envelope . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.4 Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Results 45
4.1 Vertical well ”X” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1.1 Packer forces - Vertical well ”X” . . . . . . . . . . . . . . . . . . 47
4.1.2 Packer envelope - Verical well ”X” . . . . . . . . . . . . . . . . . 49
4.1.3 Combined loads - Triaxial load capacity diagram - Vertical well ”X” 51
4.2 Deviated well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Packer forces - Deviated well ”Y” . . . . . . . . . . . . . . . . . 53
4.2.2 Packer envelope - Deviated well ”Y” . . . . . . . . . . . . . . . 55
4.2.3 Combined loads - Triaxial load capacity diagram - Deviated well
”Y” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Tubing movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1 Vertical well - Lubinski’s example . . . . . . . . . . . . . . . . . 57
4.3.2 Deviated well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Discussion 67
5.1 Resulting packer forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Packer envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Tubing design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.4 Tubing movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6 Conclusion 77
7 Further work 79
Nomenclature 81
Bibliography 83
Appendix A 89
Appendix B 93
vi
List of Tables
2.1 Typical parameters for initial condition (IC) and final condition (FC) . . . 17
3.1 Typical tubing grades used in the industry with description of each type,
SPE (2015), Equipment (2008/2009) . . . . . . . . . . . . . . . . . . . . 31
4.1 Casing and tubing design summary for well ”X” from WellCat . . . . . . 46
4.2 Packer data for well ”X” . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Tables showing the simulation made for the tubular designing parameters 48
4.4 Simulation done excel for resulting forces on packer for well ”X” . . . . . 49
4.5 WellCat results for packer loads - well ”X” . . . . . . . . . . . . . . . . 49
4.6 Data for plotting an packer envelope - well ”X” . . . . . . . . . . . . . . 50
4.7 Casing and tubing design summary for well ”Y” from WellCat . . . . . . 53
4.8 Packer data for well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.9 Simulation done excel for resulting forces on packer for well ”Y” . . . . . 54
4.10 WellCat results for packer loads - well ”Y” . . . . . . . . . . . . . . . . 54
4.11 Data for plotting an envelope - well ”Y” . . . . . . . . . . . . . . . . . . 55
4.12 Casing and tubing configuration for the vertical well modelled in WellCat
as Lubinski’s example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.13 Movement table for each effect and total change taken from WellCat . . . 58
4.14 Summary of all tubing movement and the total length change . . . . . . . 64
4.15 Tubing movement summary for the vertical well from WellCat, Matlab
and Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.16 Tubing movement summary for the deviated well from WellCat and Matlab 66
5.1 Simulation done excel for resulting forces on packer for well ”X” . . . . . 68
5.2 Simulation done excel for resulting forces on packer for well ”Y” . . . . . 68
5.3 Tubing movement summary for the vertical well from WellCat, Matlab
and Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Tubing movement summary for the deviated well from WellCat and Matlab 76
7.1 Typical design factors used in the industry . . . . . . . . . . . . . . . . . 89
vii
List of Figures
1.1 Basic illustration of casing and tubing schematic in a well . . . . . . . . . 1

1.2 Deliverability for a high rate gas well with a range of tubing diameters.
The chart shows well flowing bottom hole pressure, Pwf, as a function of
production rate, q, Brechan (2019) . . . . . . . . . . . . . . . . . . . . . 4
1.3 Primary well barrier marked in blue and secondary well barrier envelope
marked in red, NORSOK (2013) . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Tubing is lengthen by temperature increase . . . . . . . . . . . . . . . . 11
1.5 Tubing is shorten by temperature decrease . . . . . . . . . . . . . . . . . 11
1.6 Figure explaining heat transferring mechanism in a well . . . . . . . . . . 12
1.7 Annulus fluid expansion showing the A’ annulus with explanations . . . . 14
2.1 Free motion packer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Limited motion packer . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 No motion packer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Simplified sketch of a packer in a well with tubing and casing . . . . . . . 19
2.5 Simplified sketch of forces acting on the packer . . . . . . . . . . . . . . 20
2.6 A simplified sketch of how forces are transferred from the tubing to the
packer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 A simplified sketch of how forces are transferred from the packer to the
casing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.8 Tubing-to-casing contact forces presented in a deviated well, Bellarby
(2009a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.9 Ballooning → ∆pi > ∆po . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.10 Reverse ballooning → ∆po > ∆pi . . . . . . . . . . . . . . . . . . . . . 25
2.11 Configuration A shows when tubing ID < packer OD and configuration B
shows when tubing ID > packer OD . . . . . . . . . . . . . . . . . . . . 27
3.1 Example of a typical tubing nomenclature . . . . . . . . . . . . . . . . . 30

3.2 Sketch of a tubing with length of tubing, internal and external pressure . . 31
3.3 Figure shows how burst pressure will effect the tubular string . . . . . . . 32
3.4 Figure shows how collapse pressure will effect the tubular string . . . . . 33
3.5 Illustration of an example well with defined variables . . . . . . . . . . . 34
3.6 Illustration shows how axial, radial and tangential stress acts on a tubular
string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7 Figure showing a triaxial load capacity diagram, Bellarby (2009b) . . . . 38
3.8 Example of a packer envelope . . . . . . . . . . . . . . . . . . . . . . . 40
viii
3.9 Buckling in a tubing caused by applied internal pressure . . . . . . . . . 42
3.10 A buckled tubing, where netural point, tension and compression part is
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Well schematic showing the production packer, tubing and casing setting
depth and TOC for well ”X” . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Sketch showing axial force above and below the packer . . . . . . . . . . 47
4.3 Sketch showing pressure above and below the packer . . . . . . . . . . . 48
4.4 Shows a fictitious rating envelope . . . . . . . . . . . . . . . . . . . . . 50
4.5 Packer envelope for well ”X” . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”X” . . . 52
4.7 Well schematic with production packer, tubing and casing setting depth
and TOC for well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.8 Section view of the deviated well ”Y” . . . . . . . . . . . . . . . . . . . 53
4.9 Packer envelope for well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . 56
4.10 Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”Y” . . . 57
4.11 Well schematic of the vertical well . . . . . . . . . . . . . . . . . . . . . 58
4.12 Matlab code output data for the vertical well . . . . . . . . . . . . . . . . 59
4.13 Movement table for the deviated well taken from WellCat . . . . . . . . . 64
4.14 Matlab code output data for the vertical well . . . . . . . . . . . . . . . . 65
5.1 Packer envelope for well ”X” . . . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Packer envelope for well ”Y” . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”X” . . . 71
5.4 Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”X” . . . 72
5.5 Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”Y” . . . 72
5.6 Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”Y” . . . 73
5.7 Steady stage production load detail taken from WellCat - I . . . . . . . . 73
5.8 Steady stage production load detail taken from WellCat - II . . . . . . . . 74
5.9 Steady stage production load detail taken from WellCat for new oil and
water rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.10 Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”Y” . . . 75
7.1 Illustration of stress on a tubular . . . . . . . . . . . . . . . . . . . . . . 90

7.2 Illustration of strain on a tubular . . . . . . . . . . . . . . . . . . . . . . 91
7.3 Typical stress and strain curve for a tubular, Bellarby (2009a) . . . . . . . 92
7.4 Curve showing the behaviour of ductile and brittle material, DrillingFor-
mulas (2016c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
ix
Abbreviations
API American Petroleum Institute

BHP Bottomhole pressure
CPF Central processing facility
DF Design factor
DHSV Downhole safety valve
FC Final condition
FEED Front end engineering design
HPHT High pressure high temperature
IC Initial condition
ID Inner diameter
IPR Inflow performance relationship
OD Outer diameter
PVT Pressure, volume, temperature
SF Safety factor
TOC Top of cement
VLP Vertical lift performance relationship
WBS Well barrier schematic
x
Chapter 1
Introduction
Completion design involves some of the most complex engineerings in well construction.
Only a few software tools on the market are able to model tubing design and fewer still
can design HPHT and ultradeep wells. The forces during the production phase comprise
some of the highest in the life cycle of a well. Large temperature variations often result
in thermal expansion, ballooning and annular fluid expansion (AFE). These effects are
proportional to the temperature changes. The resulting stress often set the premises for the
minimum design for the upper completion equipment. The following figure shows a basic
well schematic with all casings and the production tubing which is marked in blue. The
production tubing is placed as the innermost tubular and the production packer is placed
in the annulus, between the production casing and the tubing string.
Figure 1.1: Basic illustration of casing and tubing schematic in a well
1
Chapter 1. Introduction
One critical task for engineers is to carefully decide which type of casing or tubing to
select in order to properly design a completion to meet the objective of each well. As
reservoir properties directly influence equipment in the well, they have to be considered
safe. Reservoir properties can be categorized as rock and fluid properties. In terms of rock
properties, the most essential factors to focus on are permeability, formation temperature,
formation pressure and formation strength. For the fluid properties, the type of reservoir
fluid, H2 S content, PVT of reservoir fluid and CO2 content will be the main elements to
consider, DrillingFormulas (2016d).
The production tubing needs to be strong enough to withstand all production loads and to
be able to do workovers in the later stage of the well. This is mainly because all com-
pletion equipment runs through the tubing string, which again requires the tubing design
to be optimal. The tubing is used to conduit oil, gas or water from the reservoir, in ad-
dition to protect the casing from deposit, wear and corrosion from the reservoir fluids in
the formation. Tubing practice and assumption behind tubing design is further discussed
when design limits are evaluated. Tubing design is essential as it is the foundation of well
integrity which ensures good production of oil in the well.
1.1 Equipment selection

Upper completion in a well should contribute to good well control. The equipment that is
installed in the upper completion of a well will help to carry the flow from the reservoir
to the surface inside the pipes and maintain well control. This ensures unwanted outflow
from the well. Some of the essential equipment in an upper completion is also a part of
the primary barrier in a producing well. These are production tubing, production packer,
downhole safety valve (DHSV) and are further explained in detail in the sections below.
1.1.1 Tubing size

For a well completion process it is essential to determine tubing, production casing and
hole sizes. The first step would be to choose the design of the hole structure and produc-
tion casing. After well completion operations have been planned, the tubing size and the
production mode is decided based on the production casing.
To have a trouble-free and efficient operation of the fluid system; selection of good ma-
terial, type and size of tubing is critical. It is depended on the well operation and fitting
requirements of each well. To select the proper tubing, it is essential to safely consider
right material and optimum tubing size. For the tubing, this particularly means the OD, ID
and wall thickness.
For instant, a small tubing may cause high fluid velocity, which can have negative side ef-
fects like damaged pumps. “In pressure lines, it causes high friction losses and turbulence,
both resulting in high pressure drops and heat generation”, ihservice (2019). Moreover, a
2
high heat generation will result in low efficiency by wasting energy. Contrarily, a too large
tubing may cause an increase in system cost. This explains why an optimum tubing size is
critical at any point.
The procedure for determining tubing size can be explained in simple steps. Step one is to
determine the required flow diameter. This is done by estimating the required flow rate and
type of line in the tubing. In the next step, the tubing OD and wall thickness is determined.
This has to be fulfilled with two conditions, ihservice (2019):
Condition I:
Recommended Design Pressure ≥ Maximum Operating Pressure
Condition II:
Tubing ID ≥ Required Flow Diameter
Tubing performance is the behavior of a producing well in an installed tubing. The flowing
bottom hole pressure (BHP) for a well can be calculated by a vertical flow equation. For a
gas well, Katz has presented the following equation only valid for dry gas, Brechan (2019):
!
sD5 (P2wf − es P2wh )
qg = 200000 (1.1)
Gg TZHf(es − 1)
where,
qg = gas flow rate
D = tubing diameter
Pwf = bottomhole flowing pressure
Pwh = wellhead flowing pressure
Gg = gas gravity
T = average temperature
Z = average gas comparability factor
H = vertical depth
f = friction factor
e = absolute pipe roughness
s = 0,0375Gg H/TZ
There are similar equations for oil and mixed phase (combination of oil and gas) which
are used when determining flow rate for these fluid types.
Tubing diameter can also be determined by using different charts and combining results
from expected flow or production rates in a well. Chart 1.2 shows the well flowing bot-
tom hole pressure, Pwf, on the y-axis and the production rate on the x-axis. Pwf defines
the pressure range between the atmospheric pressure and average reservoir pressure. The
tubing diameter can then be selected depending on the IPR (inflow performance relation-
ship) and VLP (vertical lift performance relationship), also called outflow. IPR describes
3
the flow in the reservoir, while VLP describes the bottom hole pressure as a function of
flow rate. The vertical lift performance depends on factors like the fluid’s PVT properties,
tubing size, well depth and etc, Technology (2017).
The intersection between the VLP and IPR curves, gives the deliverability of the well. It is
called the operating point and expresses the actual production for a given condition. This
will in addition to other factors help find the appropriate tubing size, Technology (2017).
The chart below shows the deliverability of a high rate gas well with different range of
tubing sizes.
Figure 1.2: Deliverability for a high rate gas well with a range of tubing diameters. The chart shows
well flowing bottom hole pressure, Pwf, as a function of production rate, q, Brechan (2019)
Choice of tubing size mainly depends on desired production rate as discussed above. Pro-
duction rate depends on factors like:
• Inflow performance relation
• Pressure drop in tubing
• Pressure drop through the flow line
• Static reservoir pressure
• Pressure drop through the well-head constrictions
• Pressure level in the surface separating facilities
4
When selecting tubing ID, it is essential to look into expected production rate, but also
at completion method and the further needs to conduit fluids from the reservoir. When
designing a well, determination of tubing is one of the first steps to take into account. To
determine the inner diameter of the production tubing it is essential to go deeply into IPR,
VLP, choke performance and horizontal flow performance. These steps will give a well
performance evaluation, which can help finding the right tubing size and flow line, Equip-
ment (2008/2009).
Inflow performance relationships (IPR):

The inflow performance relationship is the “ability of well to produce fluid against various
bottomhole flowing pressures, Pwf”. It also gives the relationship between the flow rate
and the drawdown. Drawdown defines the difference between the average reservoir pres-
sure and flowing bottomhole pressure (PR − Pwf ). The shape of the IPR curve depends on
the drive of the reservoir. The curve “[...] declines with cumulative production and with
formation damage”, Equipment (2008/2009).
Verical lift performance relationship (VLP)/ Outflow:

“Calculation of pressure losses in vertical/deviated wells can be performed from correla-
tions based upon lab mechanistic models”. Pressure gradient curves, also called traverse
curves are determined based on where pressure losses are found, Equipment (2008/2009).
Horizontal flow performance:

As for the vertical flow performance, it is possible to calculate pressure losses in horizontal
pipes. This is done from correlation-based models. The traverse curves are obtained the
same way as for the VLP curves, Equipment (2008/2009).
Choke performance:
During a wells lifetime, different chokes will be installed in the well. For that reason, it is
important to look at the choke performance when selecting tubing size. These chokes are
installed to “1. Control pressure for safety, 2. Allow desired rate, 3. Prevent sand entry to
surface facilities, 4. Control water and gas coning, 5. Prevent press surges downstream”,
Equipment (2008/2009).
1.1.2 DHSV - Downhole safety valve

Down hole safety valve is a “downhole device that isolates wellbore pressure and fluids
in the event of an emergency or catastrophic failure of surface equipment”, Schlumberger
(2019b). It is a valve that is mounted in the upper part of the well in the production tubing.
The valve is kept open by pressure, through a control line. The down hole safety valve
closes if the pressure in the control line falls below a minimum level. This equipment is
part of the primary barrier envelope in a producing well.
The device is a flap valve that is installed to prevent oil or gas from flowing to the surface
when it is closed. “[...] It must be installed at least 50 meters below the seabed. It is nev-
ertheless common to be placed several hundred meters deep in the Norwegian shelf”. The
5
valve is operated using hydraulic control lines, often called a fail-safe-close valve. This
means that if the pressure in the control line falls below the limit value, the flap will close
automatically. The down hole safety valve must be regularly tested for function as long as
the well produces. In addition, it should be tested after well maintenance has been done.
“All testing must be in accordance with the requirements of NORSOK”, Aabø (2017a).
DHSV is usually formed as a flapper valve, but can also be a ball valve. “The valve is open
when the flap is pressed against the tubing wall and closed when the flap is closed against
a seat in the inner diameter of the tubing” .. The flap will close when there is wellstream
coming from below. It is controlled by a hydraulic pressure-controlled piston pushing a
spring together. “If the hydraulic pressure disappears, the spring will push the valve to the
closed position”, Aabø (2017b).
1.1.3 Selection of production packer

To select the right production packer for an optimum well completion design, three major
issues
• Fit, form and functioning of the tool
• Metallurgy
• Elastomeric material and seal design
have to be considered carefully.
All well completion operations need to be developed based on each field with its own re-
quirements. It is essential to identify well integrity and maintenance to have a good well
design. For production packer, it is important to design a fit, form and good functioning
equipment, as it can affect the tubing movement calculation, and consequently influence
completion design.
For completion equipment like production packer, there are many factors which are con-
sidered when determining the metal type. “These include mechanical properties/strength
and corrosion embrittlement, or stress cracking resistance”. It might be uneconomical
and in many cases it is more optimal to select different material for the tubing and acces-
sories like production packer. “For example, material strength derived from cold work may
not be available in the large diameters, which is required for some accessories”, Brechan
Bjørn A. (2017). Environmental data that involves type of well (oil or gas), bottom hole
pressure and temperature, reservoir fluid type, tubing grade, corrosion history is some of
many factors to consider when making material recommendations.
When it comes to elastomeric or plastic materials, it is essential to know the expected

maximum and minimum temperatures at sealing areas since these are the most critical
one. “Inhibition programs and anticipated acid treatment programs should be considered
6
during the completion design stage. Completion fluids can adversely affect seal materi-
als”, Brechan Bjørn A. (2017). After pressures, fluids, temperatures, and chemical data
is known for the particular well, the work with seal applications in the tool design can be
continued.
The understanding of packers and the knowledge of available packer types in the market
helps to select the right production packer. “A packer creates a seal between the tubing
string and the casing string, or in the case of an open hole completion, packers seal against
the formation”, Brechan Bjørn A. (2017). The four major reasons why packers are needed
are:
• To maximize safety and control
• To protect the casing string
• To improve productivity
• To conserve energy
As production packer is placed in the annulus, between the tubing and the casing, it iso-
lates and protects the casing from high pressures and corrosive fluids from the well. This
is important because the casing is cemented in place and can be expensive or difficult to
replace. “The packer may also be plugged, isolating the wellbore from the formation dur-
ing workover operations up the hole”, Brechan Bjørn A. (2017). There are several types
of packers which can be selected by the requirements and needs of each well. This needs
to be investigated before selecting the correct one for the particular well.
To select an optimum packer, an examination of well conditions and capacities of the

operation possibilities are required. It is easier to find correct packer design for the correct
conditions, rather than selecting the packer features, and then fitting the requirements.
The operations that has to be considered when selecting the right production packer, can
be divided into three major categories:
• Production and treating
• Running, setting and tubing space-out
• Retrieving
The production packer should be placed in an area where there is approved cement behind
the casing. The packer is screwed together with the production tubing and must be placed
at the bottom of the upper completion. It should prevent liquid and gas from flowing out-
side the production tubing and anchor the tubing to the casing. It should be set quite far
into the well, ranging from 1500 meters to several thousand meters below the seabed, as it
is placed far down in the production casing.
As discussed above, the positioning of the production packer is very important and there-
fore it should be located in a cemented area. This means that the packer is located far down
in the well, close to the reservoir where formation strength exceeds formation pressure. “If
7
a poor cement bond exists in the interval in which the packer is to be set, the packer’s abil-
ity to serve as a barrier may be compromised should a leak in the casing string occur”, SPE
(2017a). This leads to the cement and the casing in this area to be included in the primary
well barrier envelope.
1.2 Material selection and corrosion considerations

The importance of selecting the right completion equipment and tubing size is equivalent
when considering the material for the equipment. The choice of material are based on en-
vironmental conditions, corrosivity of well fluids, maximum and minimum temperatures
and pressures, safety aspects and cost. The steel quality have to withstand the loads that
come from well fluids, tensile, twisting, change of length and bending forces.
Corrosive environments are critical elements when selecting the material for the tubing.
The tubular string can be damaged by corrosion from both inside and outside. “Acidity
caused by the presence of acid gases (CO2 and H2S) normally increases the corrosion
rate”. It is common to follow the API standard practice grades, and if corrosion becomes
a problem, batch treatments can be used to control or reduce the effect of corrosion. For
steel tubings, corrosion can be a major problem and it will mostly occur where there are
high rate gas condensates containing CO2 . “The CO2 attacks the steel tubing, which cre-
ates an iron carbonate film (corrosion product); it is removed from the wall by erosion
(impingement of well fluids)”, SPE (2017b). This may require frequent batch inhibition to
protect the tubing string.
Metals which are unlike each other and placed close to each other can influence corrosion.
“Plastic internal coating of a tubing string is sometimes used to deter corrosion or ero-
sion in oil and gas wells and may increase tubing life significantly”, SPE (2017b). “Some
practices for corrosion control involve cathodic protection, chemical inhibition, chemical
control (removal of dissolved gases such as hydrogen sulfide, carbon dioxide, and oxygen),
oxygen scavenging, pH adjustment, deposition control (for example, scales) and coatings”,
Schlumberger (2019a). However, when the bottomhole temperature is high, ranging from
400 to 500 o F corrosion control can be extremely difficult.
There is no exact solution or simple resort to control corrosion as it can appear in different
forms depending on the environment. It is therefore important to treat each tubing in a
well individually. To solve a corrosion problem one can attempt to understand the opera-
tion conditions and environmental factors.
1.3 Well integrity and tubing as primary barrier envelope

Well integrity is defined by NORSOK (2013) Standard D-010 as “application of techni-
cal, operational and organizational solutions to reduce the risk of uncontrolled release of
formation fluids throughout the life cycle of a well”. By maintaining full control of fluid
8
1.3 Well integrity and tubing as primary barrier envelope
within a well at all times, loss of containment to the environment and unintended fluid
movement can be prevented. Well integrity also refers to a policy about commitments and
obligations to safeguard health, safety, environment, assets, and reputation, Juarez (2018),
NORSOK (2013).
“WBS shall be prepared for each well activity and operation”, NORSOK (2013). Bar-
riers in wells should ensure the external environment against leakage of hydrocarbons.
Two separate barriers are divided into primary and secondary barrier. When hydrocarbons
are produced, large amounts of high-pressure hydrocarbons flow out of the reservoir and
up to the production platform or into pipelines. The external environment must be pro-
tected against leaks of these hydrocarbons. It is done by using barriers placed in the well.
The requirements for the barriers and barrier elements are described detailed in NORSOK
standard D-010. The suppliers of the components ensure that the equipment meets the
requirements, and often the equipment is better qualified than the minimum requirement.
Barriers in several different well situations with illustrations shows the primary barriers
and secondary barriers in NORSOK (2013). The figure below shows one example of a
producing well, which is shut-in. The primary barrier envelope is marked in blue, while
the secondary barrier is marked in red in figure 1.3.
Figure 1.3: Primary well barrier marked in blue and secondary well barrier envelope marked in red,
NORSOK (2013)
9
The primary barrier envelope consists of components in the completion string for upper
completion which are the production tubing, DHSV, production packer in addition to the
casing and cement in which the production packer is located. If there is a side pocket with
a valve for a gas lift in the completion, the well should also have an annular safety valve
(ASV). ASV prevents outflow of gas on the outside of the production pipe and is then a part
of the primary barrier. All these components form the wall of the primary barrier envelope.
From the production packer the primary barrier in the production pipe will be continued
for the upper completion. The threads in the production pipes must be gas-tight so that gas
does not leak outside of the production pipe. The production pipe should be able to with-
stand length change due to pressures and temperature variations in the well and be able
to bear weight and the entire completion. Moreover, the tubing should be tested when the
upper completion is installed in the well. In the completion, other components which have
been introduced should be installed with the same requirements for strength and threads
as the production pipe.
1.4 Thermal effect

For a producing well, temperature prediction of production fluids and temperature changes
in surrounding tubing is critical when producing and completing. These can be analyzed
by tubing stress analysis with different load cases, material selection and prediction of the
flow in the tubular string. The tubing string will be subjected to various loads throughout
its lifetime in the well. During operations in the well and production phase, changes in
temperature may occur.
Temperature change causes steel to contract or expand. Contraction of the tubing happens
when cold fluids are injected into the tubing. On the other hand, thermal expansion of
steel happens when hot formations produce fluids. Typically the deeper the formation, the
higher is the temperature of the fluid. Also, the heat capacity of produced fluid influences
the temperature difference, ∆T.
If the tubing is free to move, the length of tubing will either be longer or shorter due to
thermal effects. If the tubing string is anchored, there will be a change in axial force due
to temperature effect. The axial force generated by the change in temperature and can be
described by the following equation:
Ftemp = CT EAs ∆T (1.2)
where,
Ftemp = axial force generated by change in temperature (force in tubing)
CT = thermal expansion coefficient
E = Young’s modulus
As = cross sectional area of tubing = Ao − Ai
∆T = average temperature change from initial condition to final condition
10
1.4 Thermal effect
From equation (1.2) it can be observed that cooling will lead to tension and heating will
lead to compressional force on the tubular string. Equation (1.3) describes the length
change due to thermal effects.
∆Ltemp = CT ∆TL (1.3)
where,
∆Ltemp = length change due to thermal effects
L = length of tubing
Figure 1.4 and 1.5 shows an illustration of length changes due to different thermal loads.
Figure 1.4: Tubing is lengthen by temperature increase
Figure 1.5: Tubing is shorten by temperature decrease
11
There are several heat transfer mechanism which takes place in a producing well. This is
explained by a simple figure:
Figure 1.6: Figure explaining heat transferring mechanism in a well
Conduction is simply described as the transfer of heat through physical contact. “The heat
transfer occurs at a molecular level, when the heat/energy is absorbed by a surface and
causes the molecules of that surface to move more quickly”, Brechan (2017). Conduction
can take place in all phases, such as in liquids, solids, and gases. The heat flow appears
within the body where the heat transfer happens. The empirical law of heat flux, Fourier
(1878) is positive in the direction of energy flow, i.e. going from high to low temperature.
dT
qx = −k (1.4)
dx
where,
qx = the heat flux in x-direction per unit area [Btu/hr ft2]
k = thermal conductivity [Btu/hr ft F]
A =Area of plane the heat moves through [ft2]
dT/dx = temperature gradient [F/ft]
Liquids have higher molecular density, which leads to more molecular interactions. Hence,
liquids are more effective as conductors compared to gasses. Solids have a molecular struc-
12
1.5 AFE - Annular fluid expansion
ture which is organized as a lattice so the waves can be induced by atomic motion.
Convection can be explained as heat or energy transfer by random molecular motion

and/or by mass motion of the fluid. It can happen either forced or natural. “Natural
convection occurs when the drive is e.g. buoyancy or temperature, and forced convection
would be caused by external means as e.g. a pump or a fan”, Brechan (2017). The heat
flux for convection, regardless if the heat transfer is forced or natural can be described
according to Newtons’s law of cooling, Incropera (2007):
qx = hA(TS − T∞ ) (1.5)
where,
h = average heat transfer coefficient [Btu/hr ft F]
TS =Temperature of the surface / body [F]
T∞ = Temperature of the flowing fluid [F]
When fluid goes through a tubular, it causes heat transfer between the fluid and the pipe.
This heat transfer occurs because of the difference of the fluid and geothermal temperature.
Thus, good knowledge about heat transmission which occurs during production, drilling
and injection operations in a well is necessary.
1.5 AFE - Annular fluid expansion
Thermal expansion may change properties of the fluid by either increase the volume or
the pressure of the fluid. This issue is respectively called annular fluid expansion, AFE or
annular pressure build up, APB. AFE can especially be a problem when wells are placed
in deepwater, for subsea wells or when a well is exposed for heat. “In subsea wells, the
casing annulus cannot be accessed once the casing hanger is landed and in this case, the
annulus fluid expansion pressure must be considered during casing design”,Juarez (2015).
When looking at APB, three major factors interact. Firstly, an increase in temperature
causes fluid expansion. This can be seen as the driving force behind the pressure build
up. Secondly, ballooning and reverse ballooning of the casing string may change contain-
ment volume. Lastly, by removing fluid from the annulus, APB may occur. This can, for
example, happen when there is leakage through an open shoe or when bleeding off at the
surface, Bellarby (2009a). When looking at the pressure increas, it will also influence the
axial load profiles, especially in the casing and tubing string for pressure ballooning ef-
fects, Juarez (2015). The factors to take into account when annular fluid expansion occurs
is explained in figure 1.7.
13
Figure 1.7: Annulus fluid expansion showing the A’ annulus with explanations
Annular fluid expansion and annular fluid contraction are phenomena that can have a sig-
nificant influence on the tubing and casing design. For installed equipment in the well,
AFE and AFC will act as an additional load and is caused by temperature variation in the
well. After the well is installed and exposed to initial forces, the well will be exposed to
the given loads. This will eventually give AFE and AFC and may change final conditions.
14
Chapter 2
Theory - Part I
The engineering of upper completion comprises the following main elements and calcula-
tions:
• Acting forces
→ Modelling of forces from formation pressures and temperatures (load cases)
→ Resulting forces on packer
→ Tubing-to-casing drag
→ Different load effects on tubing
• Design strength of tubing
→ Selection of tubing grade
→ Combined loads - Triaxial load capacity diagram
→ Packer envelope
→ Buckling
The following chapters will further go into detail on each element listed above.
2.1 Acting forces

The tubing string will be subjected to various loads throughout its lifetime in the well.
During operations in the well and production phase, changes in temperature and pressure
occur in the tubing and annulus. If the tubing string is free to move, changes in tempera-
ture, density and pressure will cause a change in length. If it is not permitted to move, the
forces will be generated in the tubing. Moreover, these forces will act on the packer and
wellhead to prevent these length changes from occurring, Bellarby (2009a). The produc-
tion packer is exposed to a multitude of forces. “The tubing will transmit axial forces to
the production packer when it is heated and/or pressurised”, Bellarby (2009a).
15
Chapter 2. Theory - Part I
2.1.1 Modelling of forces from formation pressures and temperatures

(load cases)
For tubing design and load calculations, tension and temperature are significant factors
that have to be considered. The packer type, packer load, seal length, and buckling is
likewise essential. Tubing loads are affected by changes in different conditions like in-
ternal fluid density (tubing), surface pressure in tubing, external (annular) fluid density,
surface pressure in annulus and temperature profile. All these conditions are characteris-
tic variables that denote loads in the tubing. The tubing string is run at initial conditions
of pressures, densities and temperatures. The initial condition is the moment at which
annulus is isolated from the perforation. After the initial condition; densities, pressures
and temperatures changes. These changes generate loads on tubing or load combinations.
“Both axial and pressure loads are created by these changes”, Partners (2019).
There are different type of packers which will affect the tubing in different ways. One
is free motion packer. Here will the tubing in the seal bore be able to move freely up or
down. Limited motion packer where tubing in the seal bore can move freely upward only.
While the no motion packer where the tubing in the seal bore is not able to move. Figure
2.1, 2.2 and 2.3 respectively shows an illustration of free motion, limited motion and a no
motion packer.
Figure 2.1: Free motion packer
Figure 2.2: Limited motion packer
16
2.1 Acting forces
Figure 2.3: No motion packer
The following table represent typical values and parameters used to decide initial and final
condition.
Table 2.1: Typical parameters for initial condition (IC) and final condition (FC)
IC FC
Parameter Symbol Typical Design Value Symbol
Density inside(tubing)[ppg] ρi,init Packer fluid density ρi,f
Density out-
ρo,init Packer fluid density ρo,f
side(annulus)[ppg]
Surface pressure in-
psi,init Zero psi,f
side(tubing)[psi]
Surface pressure out-
pso,init Zero pso,f
side(annulus)[psi]
Average temperature [◦ F] tempavg,init Geothermal tempavg,f
It is in rare cases that fluid density in the tubing string differs from the annular density.
Surface pressure is zero most of the time and is the same for the tubing and annulus. An
exception can occur when there are snubbing operations. The average temperature is de-
cided based on the geothermal gradient for the initial condition, while the temperature
profile is used for the final condition.
Initial conditions
Initial condition is one of the most important load cases, as all other loads are calculated
relative to this. It can therefore also be called the base case. A base case that appears to
be incorrect, ensues incorrect output for the other load cases. As a result, it is important to
get the pressures and temperature correct for each load cases applied.
The initial condition is defined when packers have been set and the setting pressures have
been released. When setting on the completion run, the movement of the packer is in-
cluded. “The initial condition should take account of any difference in fluid gradients
between the annulus and tubing fluids”, Bellarby (2009a). The temperature in the initial
17
condition is not always the same as the geothermal gradient, because the circulating op-
erations prior to setting the completion can make a change in temperature. This can for
example be thermal effects which may cause changes in the tubing.
Tubing pressure test

A tubing pressure test is testing the tubing before doing completion setup. “Many compa-
nies stipulate that the tubing pressure test should be 10 percent greater than the maximum
tubing pressure differential during service loads”, Bellarby (2009a). The pressure test is
applied with plugs included or without plugs set in place, before or after the tubing string
has been set or landed with packer included. If the plug is included in a pressure test, the
test will consider effects as if the plug is leaking and the pressure being applied below the
plug.
Annulus pressure test

The main goal of the annulus pressure test is to verify the integrity of the packer or tubing
hanger. It should mainly be tested with the same criteria as a tubing pressure test. This is
to include the scenario of the tubing leak during a service load. The purpose of doing a
pressure test in the A-annulus is to certify the secondary well barrier, NORSOK (2013).
Production
“In general, production-related conditions induce thermal changes in a well and may gen-
erate high-temperature loads with either high or low pressures in the tubing”, Bellarby
(2009a). Temperature is depended on the fluid, flow rate and pressure in the well. Consid-
erations like the highest load case with the highest temperatures, loads with high surface
pressures, high collapse loads and a separate load case made for tubing evacuation have
to be made for production-related conditions. An example of a production load is the pro-
duction early stage in a well, called ”Early Stage Production”. In this particular load case,
the flow rate is high and friction is included in the calculations. Furthermore, tubing is
subjected to thermal loads as production will cause an increase in temperature that comes
from production fluids and warmer surroundings, Bellarby (2009a). This will again heat
up the annulus and cause an annular fluid expansion which is described in the previous
chapter.
Shut-in
During an emergency shutdown situation, shut in the well on command will prevent hy-
drocarbons from flowing from the well. When the well is shut-in, both the pressure and
temperature can be high. The two main shut-in cases are called long-term shut-in and
short-term shut-in. In long-term shut-in, will the well cool down fully until it reaches the
geothermal gradient. This case is normally not required, “[...] as this will have the same
temperature and lower pressure than a tubing pressure test case”, Bellarby (2009a). The
18
2.1 Acting forces
worst-case scenario is when there is high-temperature steady state production followed by

a quick shut-in, as this will lead to high pressures and temperatures.
2.1.2 Resulting forces on packer
Forces on packer
Free body diagram is used to identify all forces that are applied to the tubing, casing or
packer. This is done by drawing simplified figures of the system, and then add the loads
that are acting on the components. Figure 2.4 shows a sketch of the basic geometries of a
production packer set in a well.
Figure 2.4: Simplified sketch of a packer in a well with tubing and casing
where,
IDt = inner diameter tubing
ODt = outer diameter tubing
IDc = inner diameter casing
Figure 2.5 shows the forces acting on the production packer and where these are located:
19
Figure 2.5: Simplified sketch of forces acting on the packer
where,
(a) represent the axial stress above the packer
(b) represent the axial stress below the packer
(c) represent the annular pressure above the packer
(d) represent the annular pressure below the packer
For a static system, Newton’s 3rd law is used. Here the loads are summed and set equal to
zero.
F=p·A (2.1)
X
Fy = 0 (2.2)
where,
F = force
p = pressure
P= area
A
Fy = sum of forces in y-direction
WellCat forces
WellCat analysis and models three packer forces:
1. Tubing-to-packer force
2. Packer-to-casing force
3. Latching/Pinning force
Tubing-to-packer force
Tubing-to-packer force is the total axial force transferred from the tubing and the hydro-
static pressure on the cross section of the tubing. “The tubing-to-packer loads will be
20
2.1 Acting forces
the difference in axial load from immediately above the packer to immediately below the
packer”, Bellarby (2009a).
Tubing-to-packer force can then easily be estimated by the following equation
tubing-to-packer force = axial force below packer − axial force above packer (2.3)
The drawing below shows where the forces are acting:
Figure 2.6: A simplified sketch of how forces are transferred from the tubing to the packer
By using Newton’s third law, tubing-to-packer force is derived:

X
Fy = 0 = pi Ai-t − Fpt − po Ao-t (2.4)
⇐⇒
Fpt = pi Ai-t − po Ao-t (2.5)
where,
pi = hydrostatic pressure acting from below tubing/packer
Ai-t = inner area of tubular = π4 ID2t
Fpt = tubing-to-packer force
po = hydrostatic pressure acting from above packer
Ao-t = outer area of tubular = π4 OD2t
21
Packer-to-casing force
Packer-to-casing force is simply the axial force in addition to the hydrostatic pressure on
the packer bore area and tubing cross section. The packer-to-casing force is simply then:
packer-to-casing force =tubing to packer force+
(pressure above packer − pressure below packer) · (inner diameter casing − outer diameter tubing)
(2.6)
Figure 2.7 shows how the forces are acting:
Figure 2.7: A simplified sketch of how forces are transferred from the packer to the casing
By using Newton’s third law, packer-to-casing force is dervied:

X
Fy = 0 = Fpt + pi Ap − po Ap − Fpc (2.7)
⇐⇒
Fpc = Fpt + pi Ap − po Ap (2.8)
⇐⇒
Fpc = Fpt + Ap (pi − po ) (2.9)
where,
Fpc = packer-to-casing force
Ap = packer bore area= π4 (ID2c − OD2t )
Latching/Pinning force
Latching force, as it is called in WellCat, also known as pinning force is the sum of the
forces acting on the seals and axial load above the packer. Latching forces can be estimated
by the following equation:
latching force = internal pressure · (seal bore ID − tubing ID) (2.10)
22
2.1 Acting forces
On an anchored tubing, the forces will transfer to points in the well like the production
packer or the wellhead. The main problem on the wellhead will be wellhead growth. This
will happen when the tubing is under compression at the tubing hanger. Meanwhile, the
production packer will be subjected to both tension and compression throughout the well
completion part. Therefore it is as mentioned an important element in the primary barrier
envelope and has to be considered carefully.
2.1.3 Tubing-to-casing drag

“Drag opposes tubing movement and transfers axial loads to the casing”, Bellarby (2009a).
Contact force(Fn ) between tubing and casing is caused by three main factors:
1. Forces from buckling
2. Forces due to gravity
3. Forces due to the capstan effect
1. Is caused by the contact force with the casing. The larger the buckling is, the greater
the contact force is.
2. For a deviated well, this force is generated by the tubing weight which acts onto the
casing. While for a horizontal well, all of the buoyed weight will be transferred and cause
this force.
3. This effect is due to tubing passing through doglegs. A contact force will be generated
when the tubing is in tension and results the tubing to be pulled onto the inside of the bend.
The opposite will happen when the tubing is under compressive loads. The following
figure shows all three effects presented in one well in a single load case.
Figure 2.8: Tubing-to-casing contact forces presented in a deviated well, Bellarby (2009a)
23
2.1.4 Different load effects on tubing

There are different load cases that expose the tubing in several ways such as thermal ef-
fect, ballooning, buoyancy, pressure, density, and hanging weight. The thermal effect has
already been discussed in chapter 1, while buckling effect will be discussed in chapter
3. For all load effects explained, Lubinski’s sign conventions are used, Lubinski (1962a).
Compression force will be denoted as positive, tensile force as negative, shorten in length
as negative, and elongate in length as positive.
Ballooning effect
The tubing is exposed to several types of pressures. It will be subjected to both radial and
axial strain. These forces are connected through Poisson’s ratio, 2.11:
Radial strain
µ=− (2.11)
Axial strain
Radial stress can affect the tubing and the result is called ballooning. Ballooning is radial
contraction or swelling which occurs when average pressure changes. If the tubing string
cannot move, stress will be created in the tubing body.
Ballooning
Ballooning occurs when internal pressure is higher than external pressure (∆pi > ∆po ).
This will create a tension force on the packer. Figure 2.9 below shows a simplified sketch
of how the ballooning effect forms the tubing like a balloon and the pressure change inside
the tubing and annulus.
Figure 2.9: Ballooning → ∆pi > ∆po
Reverse ballooning
Reverse ballooning occurs when external pressure is higher than internal pressure(∆po >
∆pi ). This will create a compressive force on the packer. Figure 2.10 shows how reverse
24
2.1 Acting forces
ballooning will affect the tubing and the location of the pressure changes.
Figure 2.10: Reverse ballooning → ∆po > ∆pi
The resulting force due to ballooning or reverse ballooning can be derived as:
Fballooning = −2µ · (Ai ∆pi − Ao ∆po ) (2.12)
where,
Fballooning = axial force from ballooning/ reverse ballooning effect
∆pi = change in average annulus pressure
∆po = change in average tubing pressure
µ = poisson’s ratio
To compute the change in length due to ballooning effect, Hooke’s law needs to be defined
F
σ= (2.13)
A
By combining equation (2.12) and (2.13), the length change due to ballooning or reverse
ballooning can be derived:
2µ
∆Lballooning = − (Ai ∆pi − Ao ∆po ) (2.14)
E(Ao − Ai )
where,
∆Lballooning = length change due to ballooning effect
Piston effect
Archimedes’ principle and buoyancy force
The principle of Archimedes is “when a body is submerged into a fluid, the buoyancy force
equals the weight of the displaced fluid”, Aandoy (2006). Buoyancy is a surface force act-
ing upwards, which is the opposite direction of the gravitational force.“For this reason, it is
25
only pressure acting on the projected vertical area that contributes to buoyancy”, Aandoy
(2011). The calculation for buoyancy exerted in the body is given as:
I
Fb = σdA (2.15)
A
(2.19) shows that the force can be determined by integrating the stress tensor over the
surface of the body which is in contact with the fluid. Using assumptions and deviations
the buoyancy force can then be expressed as:
ρfluid hA = ρfluid V (2.16)
“The submerged weight of a wellbore tubular is obtained by multiplying the weight in air
by a buoyancy factor, β”, Aandoy (2011):
Suspended weight in mud ρmud

β= =1− (2.17)
Weight in air ρpipe
“Temperature effect on the fluid density is often neglected because it is not as pronounced
as pressure effect. However, for HPHT wells, where the temperature gradient is high, it is
important to consider the effect of pressure and temperature on fluid density”.
For different fluids densities, the buoyancy factor is:
ρo r2o − ρi r2i
β =1− (2.18)
ρpipe · (r2o − r2i )
The general expression for the total buoyancy for a composite string consisting of n ele-
ments is then:
Pn
D (ρ r 2 − ρ r 2 )
β =1− Pn k o o k 2 i i k2
k=1
(2.19)
ρpipe k=1 Dk (ro k − ri k )
By using equation (2.19) the buoyancy factor can be computed starting from the bottom
of the string. At any given depth, the axial weight is equal to the pipe weight below
multiplied by the buoyancy factor at that depth, Aandoy (2011). For determining buoyancy
the industry uses either Archimedes’ principle or the piston force method.
Piston force method

The piston force is obtained by setting up a force balance. At each size transition, a force
is obtained equal to the pressure multiplied by the exposed area. This is a one-dimensional
approach. If the stability force is subtracted this method yields the same result as the
Archimedes’ principle, Aandoy (2006).
26
2.1 Acting forces
Piston forces “are loads caused directly by pressure on exposed cross sections of pipe”,
Bellarby (2009a). When having PBR, the pressure inside the PBR will act on the difference
between the seal bore area and the internal area of the tubing. While external pressure will
act on the difference between the seal bore area and the outside area of the tubing.
Two different configurations have been showed below:
Figure 2.11: Configuration A shows when tubing ID < packer OD and configuration B shows when
tubing ID > packer OD
Total force change is defined to be:
∆Fpiston = (Ap − Ai ) · ∆pi − (Ap − Ao ) · ∆po (2.20)
where,
∆Fpiston = change in force
Ap = packer seal bore area = π4 · (ODpac )2
Ai = tubing area = π4 · (IDt )2
∆pi = change in tubing pressure at packer
Ao = tubing area = π4 · (ODt )2
∆po = change in annulus pressure at packer
Total length change derived as:

L · ∆Fpiston
∆Lpiston = − (2.21)
E · As
27
28
Chapter 3
Theory - Part II
3.1 Design strength of tubing

Tubulars in the well must be designed properly to cover all the anticipated load cases
during the wells lifetime. This requires considerations like strength, load, performance,
corrosion, grade, weight and other factors like economic aspect. The most essential prop-
erties of the casing and tubing are burst, collapse, and tensile strength. When designing a
tubular, these properties need to be considered. In reality, pipes in the wellbore are sub-
jected to combined loads. These can be evaluated by triaxial capacity diagrams which will
be described in the sections below.
3.1.1 Selection of tubing grade

All variables that are used to define a tubing is necessary to understand. These variables
are typically nominal OD, metallurgy, size range (length range), weight, connection and
grade, Bellarby (2009b). There are several types and grades of a tubing. The American
Petroleum Institute (API) has several requirements for tubing design. “All tubing should
meet API minimum requirements”, SPE (2015). All API tubings are designed based on
outer diameter(OD)[inch], weight [lbs/ft], grade of steel and wall thickness, Equipment
(2008/2009).
For outer diameter, all tubing strings are standardized on OD following the API specifica-
tion. Hence a 41/2 ” tubing has an OD of 41/2 ”. “API defines tubing as having an OD from
11/20 inch to 41/2 inch”, Bellarby (2009b). All tubulars with an outer diameter greater than
this is defined or categorized as casing. For tubulars, the length range, R, is defined as
joints. Following the API specification, it is only allowed to have two length ranges, but
one can allow three ranges if necessary and practicable for the particular well. “ The API
casing standard allows three ranges namely: Range 1: 16 to 25 feet, Range 2: 25 to 34
feet, Range 3: 34 to 48 feet”, Bellarby (2009b).
29
Chapter 3. Theory - Part II
For weight, it is common to name tubulars with weight per foot[lb/ft]. “Since API stan-
dardizes tubulars on OD, an increase in wall thickness decreases the inside diameter (ID)
and therefore increases the weight”, Bellarby (2009b). As a result, tubulars are specified
in terms of OD and weight of pipe per linear foot.
Another relevant element is the nominal ID. This inner diameter is calculated from outer
diameter and weight per foot. The nominal ID is the parameter which should be used for
strength and flow calculations. In addition, drift ID is important for especially tubings
which are going to produce or do completion. This yields a safe passage of equipment
through the tubing. “The standard for API drift is 0,125” smaller than the nominal ID”,
Bellarby (2009b). Coupling OD is the maximum outer diameter of the tubing connection.
This is used when estimating the clearance required to install the tubing string into the
casing.
Grade expresses the strength of the tubing. The grade of the tubing will partly also de-
fine the metallurgy, although a more detailed definition is needed to provide the full in-
formation of the metal. Figure 3.1 shows an example of a typical fully defined tubing
nomenclature.
Figure 3.1: Example of a typical tubing nomenclature
API lists several types of grades for the tubing. The most common ones are H-40, J-55,N-
80, L-80, C-75, where the letter specify name for various steels and number indicates the
minimum yield strength of the steel in 1000 psi. These are described in detail in table
3.1. “API defines the yield strength as the tensile stress required to produce a specific total
elongation per unit length on a standard test specimen”, SPE (2015).
30
Table 3.1: Typical tubing grades used in the industry with description of each type, SPE (2015),
Equipment (2008/2009)
API
tubing Strength Usage
grade
Not commonly used in tubing sizes because of the
Low strength
H-40 low the yield strength and the cost saving by using
steel
J-55 is minimal.
Commonly used API grade for most wells when
Low strength
J-55 it meets the design criteria. A standard grade to
steel
chose for shallow and low-pressure wells on land.
High strength A relatively old grade with essentially open chem-
N-80
steel ical requirements.
High strength
L-80 A restricted yield-tubing grade
steel
High strength No longer an official API grade and generally not
C-75
steel available or used.
There are other API high strength and non-API strength tubings which are available for
sour service. High grade tubulars can lead to excessive cost, which may not be econom-
ical for a well design. On the other hand, selecting a tubular very close to the anticipated
load might not be safe to operate the well. Thus, good knowledge of tubular grades are
important.
Figure 3.2: Sketch of a tubing with length of tubing, internal and external pressure
Tubing has several loads and mechanical properties. To design a reliable tubular, the actual
31
strength of the pipe under different load conditions has to be found. The most essential
mechanical properties of tubing are burst strength, collapse strength, and tensile strength.
The figure above shows a simple sketch of a tubing were internal pressure is marked as PI
and outer pressure as Po and the length of the tubing specified.
Burst load
Burst is a condition where internal pressure exceeds the pressure loading. It is defined as
Pb , by the following formula:
Pb = PI − PO (3.1)
where,
PO = pressure in tubing-casing annulus/outside tubing
PI = pressure inside tubing
Figure 3.3: Figure shows how burst pressure will effect the tubular string
Burst may occur under well control operations, pumping operations, integrity tests, squeeze
cementing etc, DrillingFormulas (2016a). The minimum burst rating pressure, also called
internal yield pressure can be calculated by equation (3.5), also known as the Barlow equa-
tion, Economides (1998):
" #
2 · Yp · t
Pb = 0, 875 · (3.2)
D
where,
Pb = minimum burst pressure [psi]
Yp = minimum yield strength [psi]
t = nominal wall thickness[inch]
D = nominal OD [inch]
32
The internal yield pressure is where tangential stress of the inner wall of the tubing reaches
the minimum yield strength of the tubular pipe. “The factor of 0.875 appearing in the
equation represents the allowable manufacturing tolerance of –12.5 % on wall thickness
specified in API Bull”, SPE (2016). “A burst failure will not occur until after the stress
exceeds the ultimate tensile strength. Therefore, the use of yield strength criterion as a
measure of burst strength is an inherently conservative assumption”, Economides (1998).
The burst design factor is given as, Bellarby (2009b):

Pb Minimum internal yield pressure
DFburst = = (3.3)
Pi − Po Differential burst pressure
Collapse load
Collapse occurs when external pressure exceeds the internal pressure. It is defined as Pc :
Pc = PO − PI (3.4)
Figure 3.4: Figure shows how collapse pressure will effect the tubular string
Collapse develops in situations when pressure testing the annulus, during cementing op-
erations, well evaluation etc, (DrillingFormulas, 2016b). “Collapse strength is primarily a
function of the material’s yield strength and its slenderness ratio, D/t”. The equation for
yield strength collapse can be estimated by the given formula, Economides (1998):
" #
(D/t) − 1
PYp = 2Yp · (3.5)
(D/t)2
where,
PYp = yield pressure [psi]
33
D/t = slenderness ratio

D = nominal OD [inch]
Collapse pressure equations are computed from experiments from test specimens and the
full detail can be found in API Bulleting 5C3. Collapse design factor is given by, Bellarby
(2009b):
Pc Collapse pressure resistance
DFcollapse = = (3.6)
Po − Pi Differential collapse pressure
Example - Analysing loads on tubing
Figure 3.5: Illustration of an example well with defined variables
Burst load
The burst load is obtained from data for the given tubular string and well schematic shown
in figure 3.5. Burst load at the surface is calculated by using equation (3.1).
Pb1 = PI1 − PO1 = 7000 − 100 = 6900psi (3.7)
Further, burst load at the packer is calculated by taking into account the fluid in the tubing
34
and annulus in addition to the depth:
Pb2 = PI2 − PO2 = (PI1 + ρI L) − (PO1 + ρO L)

= (7000 + 6, 9 · 0, 052 · 12000) − (100 + 14, 3 · 0, 052 · 12000)
= 2282psi
Collapse load
Collapse load is calculated at the surface, by using equation (3.4)
Pc1 = PO1 − PI1 = 100 − 0 = 100psi (3.8)

At packer, the collapse load is calculated to be:
Pb2 = PO2 − PI2 = (PO1 + ρO L) − (PI1 + ρI L)

= (100 + 14, 3 · 0, 052 · 12000) − (0 + 0)
= 8923psi
By multiplying the safety factor for both burst and collapse for the highest value found
for each load, the maximum load the string can withstand is obtained. The calculation is
shown below:
Max Burst Load = 6900psi · 1, 125(SF) = 7763psi (3.9)
Max Collapse Load = 8923psi · 1, 125(SF) = 10038psi (3.10)
The correct tubing design in tubing tables is found by selecting the lowest grade and weight
of a tubing which has burst and collapse strengths that meet the respective loads. A pos-
sibility is to select a tubing that has lower collapse strength and by that prevent or control
swabbing of the well. The last step is to check the tension load against the tensile strength
of the selected tubing.
Tension load
Tension load is defined as, Equipment (2008/2009):
T = w · L + TP (3.11)
where,
w = weight of tubing [lbs/ft]
L = length of tubing [ft]
TP = tension required to set the packer or to pull the tubing out of the packer
From the given values of max burst load and max collapse load, a possibility is to select
a 23/8 ”, J-55, 4,7lbs/ft tubing from a tubing table. This particular tubing have the given
35
strengths:
Allowable collapse: 8230 psi

Allowable Burst: 8100 psi
Allowable Tension: 71 200 lbs
Calculating the maximum tension load at surface by using equation (3.11), gives:
T = w · L + TP = 4, 7 · 12000 + 10000 = 66400 (3.12)

Then multiplying the safety factor, gives:
Maximum tension load = 66400 · 1, 3(SF) = 86320lbs > Allowable tension (3.13)
From the equation above, it can be observed that the selected tubing will fail and therefore
a stronger tubing must be selected to fit the requirements. The new tubing could be with
the same weight but higher grade, or a tubing with the same grade but heavier weight. If
one go by choosing the same grade but heavier weight, it is necessary to recalculate the
tension load for the heavier tubing. 23/8 ”, N-80, 4,7lbs/ft tubing can for instance, be used
in choosing the first alternative. This gives a maximum tension load of T =104300 lbs
which is applicable for the given well design.
3.1.2 Combined loads - Triaxial load capacity diagram

The previous pipe strength equations are based on a uniaxial stress state. This is a state
where only one of the three principal stresses is nonzero. However, in reality pipe in
the well will always be subjected to combined loads in different conditions, Economides
(1998).
“The fundamental basis of casing design is that if stresses in the pipe wall exceed the yield
strength of the material, a failure condition exists. Hence, the yield strength is a measure
of the maximum allowable stress”. Triaxial stress is a combination of three stresses, axial
stress (σa ), radial stress (σr ) and tangential stress (σθ ). To evaluate pipe strength under
combined loading conditions, the most used is the von Mises criterion. This is a yielding
criterion, that says “[...]if the triaxial stress exceeds the yield strength, a yield failure is
indicated”, Economides (1998). It is as follows:
1
σVME = √ [(σz − σθ )2 + (σθ − σr )2 + (σr − σz )2 ]1/2 ≥ Yp (3.14)
2
where,
σVME = triaxial stress
σz = axial stress
σθ = tangential(hoop) stress
σr = radial stress
Yp = minimum yield stress
36
Axial, radial and tangential stress components can be illustrated in a pipe/cylinder like in
figure 3.6.
Figure 3.6: Illustration shows how axial, radial and tangential stress acts on a tubular string
“The calculated axial stress, σz , at any point along the cross-sectional area should include
the effects of selfweight, buoyancy, pressure loads, bending, shock loads, frictional drag,
point loads, temperature loads, and buckling loads”, Economides (1998). The radial and
the tangential stresses are based on Lamé equations for thick wall cylinders and are re-
spectively as follows:
r2i − r2i r2o /r2 r2 − r2 r2 /r2

σr = 2 2 pi − o 2 i o2 po (3.15)
ro − ri ro − ri
r2i + r2i r2o /r2 r2o + r2i r2o /r2

σθ = pi − po (3.16)
r2o − r2i r2o − r2i
where,
ri = inner wall radius
ro = outer wall radius
r = radius
pi = internal pressure
po = external pressure
It has been developed a method that represents triaxial load capacity of a pipe in a 2D
graph. “The triaxial load capacity diagram is a representation of VME triaxial stress in-
tensity in relation to axial force and either internal or external pressure”, Bellarby (2009b).
The diagram shows the burst region where external pressure equals zero psi as the top half
(plane). The lower half (plane) represents the collapse region where internal pressure is
zero psi. Service loads/combined loads which are to be tested, can be plotted in a triaxial
load capacity diagram. In addition, is specified API load capacity design factor for burst
pressure, collapse pressure and axial tension graphically plotted along with the diagram.
It is then possible to make a direct comparison between the anticipated service loads and
37
the API load capacity and the VME stress intensity design factor. An example of a typical
triaxial load capacity diagram is shown in figure 3.7.
Figure 3.7: Figure showing a triaxial load capacity diagram, Bellarby (2009b)
In the figure, the API operation window marked in blue is the area enclosed to the API ten-
sion and pressure capacity of the particular pipe, adjusted by suitable design factors. “The
biaxial effect of tension on collapse resistance is included”, Bellarby (2009b). The VME
stress curve illustrated in both red and dotted green, defines the stress level in the pipe
represented in terms of internal pressure, external pressure and axial force. By plotting a
service load, the line will show the variation in the stress intensity in the tubing string over
the length of the string. There are four quadrants presented in the figure which represent
different combine loads, and have different effects on tubing design.
1. quadrant: Tension+Burst
The tubing will be subjected to a combined load of burst and tension in the upper right
quadrant seen on the design envelope 3.7. “In this region, reliance on the uniaxial criteria
alone can result in a design that is more conservative than necessary”, Economides (1998).
For loads with high burst pressure and moderate tension, a burst failure will not occur until
after the API burst pressure has been exceeded. Burst failure may take place at a differ-
ential pressure less than the API value when the tension reaches the axial limit. “For high
tension and moderate burst loads, pipe body yield will not occur until a tension greater than
the uniaxial rating is reached”, Economides (1998). It is achievable to reduce cost without
effecting wellbore integrity. This can be achieved by taking advantage of increased burst
load in the presence of tension. It is also possible to allow loads to be within the uniaxial
and triaxial tension limit ratings. However, these decisions should be taken with good care.
38
2. quadrant: Compression+Burst
The second quadrant in the figure represents the area where the tubing is exposed to both
burst and compression. A triaxial analysis is critical in this region as the “reliance on un-
axial criteria alone will not predict several possible failures”, Economides (1998). Burst
failure can occur at a differential pressure less than the API burst pressure when the tubing
is exposed to high burst load and moderate compression. Helical buckling can lead to plas-
tic deformation when there is high compression and moderate burst load. These combined
load cases appear when there is high internal pressure caused by increased casing temper-
ature, as a result of production. High internal pressure can also be a result of situations
like tubing leak or annular pressure build up.“The increased internal pressure also result
on increased buckling”, Economides (1998).
3. quadrant: Compression+Collapse
The tubing is subjected to a combination of compression and collapse load in the lower
left quadrant. Moderate collapse and high compression loads can lead to permanent
corkscrewing resulted from helical buckling. In these cases, it is essential to use triax-
ial criterion. The combination loads in this quadrant typically occurs in wells where there
is a large temperature increase, caused by production. “The combination of a collapse load
that causes reverse ballooning and temperature increase both increase compression in the
uncemented portion of the string”, Economides (1998).
4. quadrant: Tension+Collapse
For the lower right quadrant, “most design engineers use a minimum wall for burst calcu-
lations and nominal dimensions for collapse and axial calculations.”, Economides (1998).
All well designs are recommended to use a triaxial analysis, as this has benefits like cost-
saving aspects and gives better mechanical integrity. In burst design, by taking advantage
of the high burst resistance in tension, money can be saved. For HPHT wells, large tem-
perature effects on the axial load profile is included for combined loads of burst and com-
pression. Buckling severity is evaluated by using the triaxial analysis. This is by knowing
that “permanent corkscrewing occurs when the triaxial stress exceeds the yield strength
of the material”. Apart from all these elements, it has been “acknowledged that the von
Mises criterion is the most accurate method of representing elastic yield behavior, use of
this criterion in tubular design should be accompanied by a few precautions”, SPE (2016).
3.1.3 Packer envelope

The figure below shows a typical illustration of a packer envelope. “The rating envelope
is a graphical representation of the safe operating limits of the packer in combination with
both differential pressure and axial loads”, Fothergill (2002). Therefore packers are not
only designed and used to withstand differential pressure for different downhole temper-
atures, but also needs to be able to keep safe pressure integrity when subjected to various
39
compression and tensile loads. These loads are created by temperature and hydraulic ef-
fects on the tubing string. The packer envelope can also be referred to as the performance
envelope.
Figure 3.8: Example of a packer envelope
The packer envelope is a graph represented by two axis as seen in fig 3.8. On the x-
axis, the negative values represent tension, while the positive x-values represent values
for compression. On the y-axis, the values equal differential pressure on the packer. The
differential pressure from above the packer is shown as negative and below packer as pos-
itive, Fothergill (2002).
The strong blue line is shaped by boundary lines, which is created by the packer tested in
all combined load conditions. The values are plotted on the graph and connected together
by the boundary lines, which will create a ”box shape”. In these conditions, the packer
is tested on its maximum packer ratings. Therefore will any loads of pressure and axial
loads which comes inside the box be considered as safe and inside the tested limits for the
particular packer.
In all cases, the packer envelope assumes that the casing is supported by cement. As dis-
cussed in the earlier sections, it is, therefore, important to assure that it has been done a
good cement job, as well as that the TOC is above the production packer at the setting
depth. The Casing will flex where it is unsupported, which results in a larger effective
casing ID, NORSOK (2013). Referring to figure 1.3 showing the safe barrier envelopes.
If the casing is not cemented, or supported by cement the result will be that the forces
which are acting on the production packer to act radially towards the casing. This will
create a burst load on the casing and this will result in the casing inner diameter to ex-
pand radially. This is the same issue which occurs when ballooning occurs. When casing
expands radially, the production packer has to do the same. The rubber and slips element
40
will extend and move from its optimal positions, which leads to a reduced packer envelope.
The completion can be subjected to many loads, like production, injection, etc. It is es-
sential to do calculations on tubing-movement to determine tubing-to-packer loads and
differential pressures, as this will give an effective usage of the rating envelope. The load
points will be plotted in the performance envelope to see if they fall within the safe zone
of the packer design. If this is not the case, another packer must be considered, or the
operations should be tailed to suit the operating limits of the packer.
3.1.4 Buckling
The tubing will hang straight in a vertical well or lay on the low side of the hole in deviated
wells after it is installed. Thermal or pressure loads may produce compressive loads, and
these loads can make initial conditions unstable if they are too high. A tubing is installed
in within an open hole or a casing and can deform into another stable configuration called
helical or sinusoidal shape. Generally is the helical shape seen in a vertical well and
sinusoidal shape seen in a deviated wellbore. Buckling is per definition referred to the
new equilibrium configuration which happens after the deformation is fell in place. It is
essential to do an accurate analysis of buckling for several reasons, Economides (1998) as:
1. Buckling causes tubing movement
2. Buckling generates bending stresses which are not present in the original configura-
tion.
3. Tubing buckling relieves compressive axial loads when the packer is fixed.
Buckling is a critical scenario to consider when looking at tubing stress analysis. Forces
in the well can give changes in temperature and pressure during production on a tubing,
which may cause compression and lead to buckling post installation. Thus, it is necessary
to calculate buckling length changes and packer forces to evaluate where the neutral sta-
bility point is located on the tubing. When a tubing is buckling, the effective inner area of
the pipe is reduced, which can be a problem for tool passage. A tubing should not deform,
by reason of that tubing have a crucial part in a well design. A deformation can lead to
reduced integrity of the well and further damage the environment around.
There are several reasons to why buckling is an important case when doing tubing stress
analysis, which are, Bellarby (2009a):
1. Potential high bending stresses and therefore low axial (and triaxial) safety factors
as well as bending loads on connections
2. Large tubing-to-casing contact forces which, in the presence of drag, can restrict
axial loads transferring along the tubing.
3. Torque on connections that, in extreme cases, can unscrew them.
4. Shortening of the tubing when buckled – sometimes helpful, usually not.
41
5. Resulting doglegs that can limit through tubing access.
Buckling in a well is associated with the tubing where compression forces have to be pre-
sented to appear. Factors like internal and external pressure are influential, as these can
cause complications. Figure 3.9 shows a small section of a tubing and how the presence
of internal pressure gives a greater sideways force. The outside bend of the tubing has a
greater area and results in a greater sideways force from internal pressure.
Figure 3.9: Buckling in a tubing caused by applied internal pressure
In the figure, the internal pressure inside the bend is acting on both sides of the tubing.
The area of the bend outside is larger than the inside. “The sideways forces resulting from
this pressure will tend to exacerbate the initial bend”, Bellarby (2009a). In other words,
the internal pressure is trying to shift the tubing to the right. While inside of the bend, the
internal pressure is trying to shift the tubing to the left. Consequently, compression and
internal pressure promote buckling, while external pressure and tension reduce the like-
lihood of buckling. It is noticeable that the right-hand force is greater than the left-hand
force by reason of that the areas on the right are larger than those on the left.
The term effective tension (effective buckling force), Feff , define the formula where com-
pression and thermal pressure (pi ) promote buckling, while external pressure (po ) and ten-
sion reducing the possibility of buckling:
Feff = Ftotal + (po Ao − pi Ai ) (3.17)

Ftotal is the total axial load where bending is not included. The effective buckling force is
often referred to as the excess axial force. If Feff is negative, the tubing will behave as if it
is in compression, which will promote helical buckling. It is essential to clearly understand
42
that a tubing which is slightly perturbed will want to buckle. This can not be avoided. “If
the tubing is free to move and only subjected to pressure/area forces, the effective buck-
ling force at packer depth reduces to”, Bellarby (2009b). For a vertical well, “where Feff
is greater than a critical force, buckling will tend not to occur; where Feff is less than this
critical force, buckling will tend to occur”. Buckling can therefore take place where the
entire tubing string is exposed to tension, if the internal pressure is high enough. For a
deviated well, “because Ao and Ai are not equal, there will be no buckling in open-ended
pipe run into the well, unless there is drag or the tubing touches the base of the well”,
Bellarby (2009a).
Sinusoidal and Helical buckling

The neutral point in the tubing is defined as the point where the effective axial load is
zero. This can be interpreted as the boundary where buckling can and cannot occur. Fig-
ure 3.10 shows the neutral point of a buckled tubing. The critical force can be defined for
two types of buckling. One is called sinusoidal buckling and one is called helical buckling.
Figure 3.10: A buckled tubing, where netural point, tension and compression part is shown.
Sinusoidal buckling is often referred to as lateral buckling due to the S shape of the tubing,
post buckling. The equation for the critical force for a vertical well, Fc , is given as:
Fc = 1.94(Elw2 )1/3 (3.18)

where
Fc = critical force [lb]
w = buoyed tubing weight [lb/in]
I = moment of inertia [in4]
43
While in a deviated well, the critical buckling force is given as:

s
4Elwsinθ
Fc = (3.19)
rc
where,
θ = hole angle rc = radial clearance [in]
For helical buckling is the critical force in a vertical well and a deviated well respectively
given as:
Fc = 4.05(Elw2 )1/3 (3.20)

s
4Elwsinθ
Fc = 1.41 ∼ 1.83 (3.21)
rc
“The variation between 1.41 and 1.83 reflects the uncertainty about the point that sinu-
soidal buckling switches to helical buckling”, Bellarby (2009a). “The mathematical ex-
pression showing the relation between mode and axial force in constrained buckling phe-
nomena depends on the type of buckling, i.e. helical and sinusoidal buckling”, Lubinski
(1962a). The mathematical expressions for sinusoidal buckling and helical buckling are
too complicated to be expressed in simple versions. However, the equations expressed
above is the usual way to express both, describing the critical limit for both the buckling
issues.
Problems like drill string failure, stick slip damage, mechanical damage on tubulars or bit
and lockup can be caused by sinusoidal and/or helical buckling. This is a result of “exces-
sive axial compression force on the drill string”, Lubinski (1962a). The industry has been
more aware of bucking issues of pipe, especially as more high deviated wells and longer
horizontal wells are being drilled. As a result, it is important to design the tubing properly
to avoid buckling issues which can damage the well.
44
Chapter 4
Results
Several loads in the well are affected by pressure and temperature difference. In terms of
pressure, it is the packer fluid outside the tubing and the formation fluid inside the tub-
ing. These differences act on the tubing with radial, axial and tangential components. The
effect which gives the most significant change for the tubing, is possibly the increase in
temperature.
Steel and fluid in the annulus are heated up when production in the well starts. With an in-
crease in temperature, both steel and fluid expands. These changes from initial condition,
for initial temperature and pressure, are essential in well design and particularly tubing
design in this thesis. For tubing design analysis the software WellCatTM is used, where
the initial conditions are uploaded. The initial temperature is assumed to be the geother-
mal gradient and the tubing and annulus is assumed to contain packer fluid. The wellhead
pressure is determined on if the initial well design is set onshore or offshore.
In the following section, two wells are introduced where one is constructed to be a ver-
tical well, called ”X” and one horizontal/deviated well called ”Y”. Both wells have the
same TVD, input and production data. The only difference is the wellpath. Both wells
are modeled in WellCatTM to analyze load cases and resulting packer forces on each load
case. Data is used from real example wells.
Design limit plot is created to visualize the integrity of the chosen tubing. Triaxial forces
along the tubing are included for each load case in the design limit plot. API and von
Mises criterion is included in the design limit plot as these are the industry standard. A
presentation of resulting packer forces of each load case and a plot of each load case in a
packer envelope is created to confirm the packer integrity. The final analysis presented is
the tubing movement for one vertical well and deviated well and the comparison of each
effect for these wells.
45
Chapter 4. Results
4.1 Vertical well ”X”

The vertical well constructed in the software WellCat is planned to be a vertical oil pro-
ducer, with a total length of 8218 ftMD, or equivalently 8212 ftTVD. The upper com-
pletion consists of a 2 7/8 ” monobore production tubing. Figure below shows the well
schematic of well ”X”.
Figure 4.1: Well schematic showing the production packer, tubing and casing setting depth and
TOC for well ”X”
The production packer is placed in a 7” casing. It is set at 7850 ftMD as seen in figure 4.1,
sealing off the annulus between the production tubing and the 7” production casing. The
packer is set hydraulically at at an initial set pressure of 5080 psi and a plug depth of 7850
ftMD. TOC is set to be at a 7768 ftMD for the 7” production casing. This is about 50 m
(164 ft) above the production packer, to keep a good well integrity, as production packer is
one of the elements in the primary barrier envelope. Casing and tubing design and setting
depths are shown in table 4.7.
Table 4.1: Casing and tubing design summary for well ”X” from WellCat
Critical loads that the tubing may be exposed to during its lifetime are essential to evaluate.
By simulating all these loads when planning a well, it can be possible to find out if a
complete well design fit the requirements for the expected load cases. If one or several
loads are identified outside a design limit plot or packer envelope, they have to be analyzed
46
again. This may require changes in the tubing design.
4.1.1 Packer forces - Vertical well ”X”

Several loads have been simulated to estimate the resultant packer forces; tubing-to packer
force, latching force and packer-to casing force for well ”X”. The calculations are done in
a comprehensive calculator in excel, made in the master project, Tharmapalan (2019).
Table 4.4 shows the most significant loads and the resultant forces on the packer in well
”X”, simulated in excel. To compute the resultant forces, it is necessary to have input data
for the given well. Table 4.2 shows the axial loads and external pressures above and below
the production packer for each load case. These values are gathered from the simulated
well data in WellCat. Force is calculated in the usual form and to convert to kN, the
equation is multiplied with 100:
FkN = p · Area · 100 (4.1)
Table 4.2: Packer data for well ”X”
In figure 4.2 the axial force above and below the packer in the tubing is shown.
Figure 4.2: Sketch showing axial force above and below the packer
47
Chapter 4. Results
While figure 4.3 shows how the pressure acts both above and below the packer in the
annulus.
Figure 4.3: Sketch showing pressure above and below the packer
The following tables show the input values used based on the determined tubular design
for well ”X”.
Table 4.3: Tables showing the simulation made for the tubular designing parameters
(a) Shows the selected tubular and sealbore diameter

(b) Shows the computed value for area below,
above and annulus
Equations for area below, above and annulus are shown respectively:
Area below = Sealbore ID − Tubing ID (4.2)
Area above = Sealbore ID − Tubing OD (4.3)
Area annulus = Casing ID − Tubing OD (4.4)
The estimated areas will automatically appear if tubular design data are chosen. Table 4.4
shows the resulting packer forces for each load case simulated. The free string weight is
taken into account as it is useful when coordinates for each load case needs to be found.
This is to plot these values into a packer envelope and confirm the packer integrity.
48
Table 4.4: Simulation done excel for resulting forces on packer for well ”X”
The table below shows the results simulated in WellCatTM , which apparently gives the
same values as table 4.4:
Table 4.5: WellCat results for packer loads - well ”X”
4.1.2 Packer envelope - Verical well ”X”

It is possible to plot loads in an actual packer envelope from results found in the section
above. A summary of simulated packer loads for well ”X” is shown in table 4.6. Loads
are calculated based on values in table 4.2 and equation (4.5) is used:
Force = Axial Load Above − Free String Weight (4.5)
When plotting values into the packer envelope, the axial load above is the most impor-
tant one. The reason for this is because one has no control over the axial load below the
packer. The axial load above will be affected by the force above, which include buoyancy
and TVD.
To calculate the differential pressure (∆p), equation (4.6) and values in table 4.2 are used.
∆p = Pressure Above − Pressure Below (4.6)
49
Chapter 4. Results
Data for plotting packer envelope for well ”X” is given in table 4.6. Loads and differential
pressures are normally given in lbs and psi for a real packer envelope. Thus, the values in
the table are converted into these units.
Table 4.6: Data for plotting an packer envelope - well ”X”
To illustrate how loads are plotted into a real packer envelope, a fictitious performance
envelope is made:
Figure 4.4: Shows a fictitious rating envelope
Quadrant 1 represent pressure from below with tension, while quadrant 2 pressure from
above with tension. Quadrant 3 and 4 respectively show pressure from below and above
50
with compression.
Each critical load case imposes a force on the production packer. The performance enve-
lope for well ”X including all critical load cases are shown in figure 4.5. The plot shows
differential pressure and maximum tension or compression for all load cases. It can be
observed that none of the load cases are outside the packer envelope.
Figure 4.5: Packer envelope for well ”X”
4.1.3 Combined loads - Triaxial load capacity diagram - Vertical well

”X”
The triaxial loads for the chosen production tubing design, 2 7/8”, L-80 are presented in
a design limit plot in WellCat. The limiting load case is ”Steady stage production” which
appears right outside the von Mises criterion.
51
Chapter 4. Results
Figure 4.6: Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”X”
4.2 Deviated well ”Y”

Well ”Y” is constructed in WellCat and planned to be a horizontal oil producer, with a total
length of 30000 ftMD. The upper completion consists of a 2 7/8 ” monobore production
tubing, the same as for well ”X”. Figure 4.7 shows the well schematic of well ”Y”.
Figure 4.7: Well schematic with production packer, tubing and casing setting depth and TOC for
well ”Y”
52
The production packer is placed in the 7” casing. It is set at 28500 ftMD to seal off the
annulus between the production tubing and the 7” production casing. The packer is set
hydraulically at an initial set pressure of 5080 psi and a plug depth of 28500 ftMD. TOC
is set to be at 28000 ftMD for the 7” production casing. The following figure 4.8 shows
the wellpath for well ”Y”.
Figure 4.8: Section view of the deviated well ”Y”
The goal of constructing a deviated well is to be able to compare load cases, design lim-
its, packer forces and packer envelope for a tubing upon a vertical well. This is to see
if there are any changes required for the tubing design and find possible challenges and
solutions. Casing and tubing design for the deviated well is summarised in the table below.
Table 4.7: Casing and tubing design summary for well ”Y” from WellCat
4.2.1 Packer forces - Deviated well ”Y”

To find tubing-to packer force, latching force and packer-to casing force for well ”Y” iden-
tical simulations were performed. Table 4.8 shows the most critical loads for the tubing in
well ”Y” with axial loads and pressure above and below the production packer.
53
Chapter 4. Results
Table 4.8: Packer data for well ”Y”
The resultant forces acting on the packer is shown in table 4.9. To find these, the same cal-
culation method for well ”X” is used. Thus, this will not be repeated and only the output
values are shown.
Table 4.9: Simulation done excel for resulting forces on packer for well ”Y”
The table below shows the results simulated in WellCat:
Table 4.10: WellCat results for packer loads - well ”Y”
54
4.2.2 Packer envelope - Deviated well ”Y”
The results found in the section above are used to plot loads in an actual envelope for
well ”Y”. A summary of the packer loads and differential pressure determined in excel
are shown in table 4.11. Loads are calculated based on table 4.8, further equation (4.5) is
used. To compute the differential pressure(∆p), equation (4.6) and values in table 4.8 are
used. The results from the excel simulation are shown in table 4.11.
Table 4.11: Data for plotting an envelope - well ”Y”
Data from the table above are used to plot values into the performance envelope 4.4. The
performance envelope for well ”Y” is shown in figure 4.9. It can be observed that two
loads cases; ”Early stage production” and ”Steady stage production” appear outside the
envelope.
55
Chapter 4. Results
Figure 4.9: Packer envelope for well ”Y”
4.2.3 Combined loads - Triaxial load capacity diagram - Deviated

well ”Y”
The triaxial loads for well ”Y” and the chosen production tubing are presented in a design
limit plot 4.10. The same tubing size and grade used for well ”X” is also used for well
”Y”. However, it can be observed that the limiting load cases for the deviated well are
”Steady stage production”, ”Early stage injection” and ”Steady stage injection” which ap-
pears outside the von Mises criterion and API design limits.
56
4.3 Tubing movement
Figure 4.10: Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”Y”
4.3 Tubing movement

In the following section, tubing movement results are presented. The simulated effects
are thermal, ballooning, piston/hooke’s law and buckling. To see how output changes for
different software tools, one vertical and deviated well is being used. The softwares use
different equations to determine the results. The vertical well data is taken directly from
Lubinski’s example in the paper “Helical Buckling of Tubing Sealed in Packers”, Lubinski
(1962b). While the deviated well is the same well presented in chapter 4, called well ”Y”.
Software tools which are used to compute the results are Matlab, WellCat and Excel. In
Matlab, the simulated code is taken from Remmen (2018) and is made by a former master
student at NTNU. While myself have simulated data in Excel and WellCat to compute the
results for both wells.
4.3.1 Vertical well - Lubinski’s example

The vertical well presented in this section is used from Lubinski’s example. The well data,
tubing, and casing design from the paper are used in Matlab, Excel and WellCat to get the
most exact comparison of the results.
WellCat
The well schematic, casing and tubing design for the vertical well simulated in WellCat
are shown in respectively figure 4.11 and table 4.12.
57
Chapter 4. Results
Figure 4.11: Well schematic of the vertical well
Table 4.12: Casing and tubing configuration for the vertical well modelled in WellCat as Lubinski’s
example
The movement table computed in WellCat is shown below. For vertical wells, WellCat
uses Lubinski’s equations, Lubinski (1962b). The table shows the tubing movement in
length changes for the most critical effects for a tubing.
Table 4.13: Movement table for each effect and total change taken from WellCat
Where results converted from ft to inches are:
• Hook’s law = Piston effect = -67 inch

• Buckling effect = -46 inch
• Ballooning effect = -34 inch
• Thermal effect = -16 inch
58
4.3 Tubing movement
• Total length change = -165 inch

Matlab
The Matlab code runs through the same input values for each tubing movement for the
vertical well and uses Lubinski’s equations, Lubinski (1962b) as WellCat. In the code,
dL1 represents the piston effect, dL2 the buckling effect, dL3 the ballooning effect, while
dL4 shows the thermal effect. The total length change is expressed as dL. The results are
shown in figure 4.12.
Figure 4.12: Matlab code output data for the vertical well
Excel
The excel sheet runs through the same equations, Lubinski (1962b), as the other two soft-
wares for the vertical well. When needed input values are inserted in the sheet, the right
tubing movement for each effect is found. Below, each effect is shown in detail. Tubular
designing parameters, input values for the given well and initial condition and final condi-
tion is shown.
59
Chapter 4. Results
Thermal effect
60
4.3 Tubing movement
Buckling effect
61
Chapter 4. Results
Ballooning effect
62
4.3 Tubing movement
Piston effect
63
Chapter 4. Results
A summary of the total length change is found to be:
Table 4.14: Summary of all tubing movement and the total length change
A table 4.15 is presented where all results from Excel, Matlab and WellCat are gathered
for tubing movement of the vertical well:
Table 4.15: Tubing movement summary for the vertical well from WellCat, Matlab and Excel
Effect WellCat[inch] Matlab[inch] Excel[inch]

Thermal -16 -16,5600 -16,56
Ballooning -34 -34,7946 -34,81
Buckling -46 -46,0954 -46,17
Piston -67 -67,8700 -67,91
Total length
-165 -165,3200 -165,45
change
4.3.2 Deviated well ”Y”

The deviated well presented in this section is well ”Y”. Matlab and WellCat is used to
simulate the results. The same well data, casing, and tubing configuration is used to get
the most exact comparison of the results.
WellCat
For deviated wells, WellCat uses Lubinski’s equations, Lubinski (1962b) for thermal, bal-
looning and piston effect (Hooke’s law). While for buckling effect a combination of Lubin-
ski’s and Mitchell’s, Mitchell (1999) equation are used. The resulting tubing movements
are shown in the following table.
Figure 4.13: Movement table for the deviated well taken from WellCat
Where the effects in inches are:
64
4.3 Tubing movement
• Hook’s law = Piston effect = -243,12 inch
• Buckling effect = -255,36 inch
• Ballooning effect = -118,44 inch
• Thermal effect = 148,8 inch
• Total length change = -468,12 inch
Matlab
The Matlab code in Remmen (2018) includes Aadnøy (2002), Mitchell (1999) and Lu-
binski (1962b) equations for buckling effect in deviated wells while the other effects are
based on Lubinski and Aadnøy’s equations. The results are presented in figure 4.14.
Figure 4.14: Matlab code output data for the vertical well
where,
dL1 = Piston effect
dL2 = Buckling effect
dL3 = Ballooning effect
dL4 = Thermal effect
dL = Total length change
The summary from both the softwares are shown in the table below:
65
Chapter 4. Results
Table 4.16: Tubing movement summary for the deviated well from WellCat and Matlab
Effect WellCat[inch] Matlab[inch]

Thermal 148,8 184,2921
Ballooning -118,44 -149,4521
Buckling -255,36 -143,6378
Piston -243,12 -327,2056
Total length
-468,12 -436,0034
change
66
Chapter 5
Discussion
5.1 Resulting packer forces
Forces acting on the packer depend both on type and setting method. These forces can
either cause compression or tension one the packer. When designing a packer it is essen-
tial to qualifying a possible rating envelope. By looking at the resulting forces acting on
the packer, it is possible to identify the distributed forces on the packer for each load case.
There are different load cases modeled for each well as described in chapter 4. It is fun-
damental to analyze the right load case and to define them correctly. The comprehensive
calculator used for estimating resulting packer forces matched the results in WellCat.
As discussed in the section about well integrity, the primary barrier envelope includes the
production packer. Since the cement around the casing where the packer is located is in-
cluded in this barrier, it is obvious to look at the height of the cement. The height has
to be selected to give good support for the pressure applied at the casing shoe, including
for the production packer. Pressure and temperature variation after cementing can cause
movement in the casing and leakage of well fluids. In addition, these effects may result in
poor cement bonding, which can create small pathways through the cement. Moreover, a
worn casing may be a problem by not giving enough support to the production packer. It
is therefore important to verify the cement job and casing used in the well.
In this thesis, resulting packer forces are developed for each well and a stepwise calculation
has been given to a better understanding. The resulting forces for the vertical well and
deviated well is respectively given as:
67
Chapter 5. Discussion
Table 5.1: Simulation done excel for resulting forces on packer for well ”X”
Table 5.2: Simulation done excel for resulting forces on packer for well ”Y”
5.2 Packer envelope

It is possible to evaluate a packer’s design by looking at a performance envelope. A packer
envelope produces a representation of a predictable safe zone for the packer by under-
standing the interaction of different loading conditions. The packer envelope is created
by testing the packer in different conditions. The most important conditions to test the
packer for is combined loading, pressure reversal, API casing tolerance, temperature, and
fluid environment. Eventually, a packer testing will typically be done at 25◦ C, but must
be adjusted for higher temperatures. Testing of combined loads is necessary for evaluating
68
5.2 Packer envelope
pressure differential with applied tensile and compressive loads. Each packer should also
be subjected to pressure reversals. It is expected that it withstands pressure differential
from below and above, and then below the packer. The API casing tolerance is to build
a safety factor into the rating envelope. Here will various casing ID for any given casing
weight be seen. The packer element system should be qualified and include verification of
the seal. This can be done on maximum and minimum setting temperature. An effective
cooldown temperature should also be verified through the test.
It is essential to evaluate all the possible loads that the well may be exposed to during the
lifetime of the well. By simulating the most important loads when planning the well, it
can be observed if the design will fit the requirements for the tested load cases. For the
analyzed wells ”X” and ”Y”, it is possible to see if the critical loads fit the created rating
envelope 4.4 for the packer. For well ”X” it is clear from the created rating envelope 5.1
that none of the load cases are outside the envelope:
Figure 5.1: Packer envelope for well ”X”
For well ”Y” it can be observed from the packer envelope 5.2, that “Steady stage produc-
tion” and “Early stage production” are load cases which appear outside the envelope. To
avoid that these load cases are outside the envelope, it can rather be used another packer
with a bigger rating envelope or changes can be made in the software like WellCat for
inputs values. This can be further investigated in more detail.
69
Figure 5.2: Packer envelope for well ”Y”
It is imperative to consider the load cases carefully since these are production loads which
can create changes in conditions for the packer and the tubing. Early stages in a produc-
tion consist of high flow rate. Since the fluids is produced from warmer surroundings, the
tubing will be subjected to high thermal loads. This again will increase the temperature in
annulus where the production packer is set. This will result in AFE as discussed in chapter
2. Careful consideration has to be done to get the loads “Steady stage production” and
“Early stage production” to fit a given packer envelope and select the right packer that can
withstand these effects and temperature changes.
5.3 Tubing design

Critical loads have been evaluated to determine an optimum tubing design. The tubing
string will directly be subjected to different conditions in the well including loads from
when testing the well during production, installation and killing the well. Combination
loads from burst and collapse including axial loads can be critical for the tubing. This can
cause tubing movement which causes length changes and buckling which is discussed in
the next section. Moreover, it also causes axial forces in the well.
For each load cases simulated for well ”X” and ”Y”, design limit plots have been made
which includes the triaxial forces along the tubing. As for the industry standard, the limit-
ing criterion which is given by API standards and von Mises are also included in the plots.
The simulated results is from the software WellCat and all the critical load cases are shown
70
5.3 Tubing design
in the design limit plot.
The design limit plot 5.3 shows that for well ”X” the most critical load case, which is the
case that appears outside the von Mises ellipse, is the “Steady stage production”.
Figure 5.3: Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”X”
As discussed in section “Design strength of tubing” a higher graded tubing string can be
chosen to fit the requirement for a well if needed. In this case, a new simulation with a
higher grade tubing was done in WellCat. The chosen grade was P-105, and the result is
shown in figure 5.4.
71
Figure 5.4: Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”X”
After selecting a higher grade for the tubing, all load cases appears inside the design limit
plot, for both the API and the von Mises criterion, which coincides with the theory.
In design limit plot for well ”Y”, the critical load cases are ”Steady stage production”,
”Early stage injection”, ”Steady stage injection” and ”Early stage production”. These load
case must be inside the triaxial load capacity diagram as they are important production
load cases for the tubing.
Figure 5.5: Design Limit Plot for the 2 7/8, L-80 Production Tubing - Well ”Y”
72
5.3 Tubing design
The same method is used to improve the plot by changing the grade of the tubing to P-105.
The result is shown below:
Figure 5.6: Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”Y”
Figure 5.6 shows that the load cases ”Early stage injection”, ”Steady stage injection” and
”Early stage production” is now inside the design limit plot. However, ”Steady stage
production” still appears outside the triaxial capacity diagram. Trying to fix this, it is
essential to take a detailed look into the load case in Wellcat:
Figure 5.7: Steady stage production load detail taken from WellCat - I
73
Figure 5.8: Steady stage production load detail taken from WellCat - II
After repeated attempts of trying and failing, finally the change in oil rate from 9686 bbl/D
and water rate from 1572 bbl/D to respectively 8000 bbl/D and 1000 bbl/D appears to give
an optimal result. The new input values are shown in figure 5.9.
Figure 5.9: Steady stage production load detail taken from WellCat for new oil and water rates
The new design limit plot with a higher tubing grade and reduced oil and water production
rates is given in figure 5.10.
74
5.4 Tubing movement
Figure 5.10: Design Limit Plot for the 2 7/8, P-105 Production Tubing - Well ”Y”
The result shows that all the critical load cases are inside the capacity diagram, which is
one of the main goals to achieve a safe tubing design.
The results for both wells ”X” and ”Y” shows that a higher graded tubing may help to fit the
requirements for the well. Further, the desired plot can be accomplished by changing input
data. However, the economical part for when designing a well is as much as important, so
changing the grade might not necessarily be the optimal solution. Therefore, the tubing
design should be scrutinized, so alternative solutions that give cheaper results may be
considered.
5.4 Tubing movement

In this thesis, tubing movement is measured based on length changes from the following
effects:
• Thermal
• Ballooning
• Buckling
• Hooke’s law / Piston effect
The physical length changes due to thermal, ballooning and buckling effects is transferred
through the material, while piston effect is described by the materials ability to strain.
75
For the vertical well simulated for tubing movement; Matlab, Excel and WellCat calcula-
tions are shown in the ”Results” section. A tubing movement summary of the results was
given by the table 5.3:
Table 5.3: Tubing movement summary for the vertical well from WellCat, Matlab and Excel
Effect WellCat[inch] Matlab[inch] Excel[inch]

Thermal -16 -16,5600 -16,56
Ballooning -34 -34,7946 -34,81
Buckling -46 -46,0954 -46,17
Piston -67 -67,8700 -67,91
Total length
-165 -165,3200 -165,45
change
The results from the three simulators show the same result for each tubing movement effect
for the vertical well. This can be interpreted that the simulators have the correct calcula-
tion method and equations to simulate load effects on a vertical well.
For the deviated well simulated for tubing movement; Matlab and WellCat calculations
are shown in the ”Results” section. A tubing movement summary of the results is shown
in the following table:
Table 5.4: Tubing movement summary for the deviated well from WellCat and Matlab
Effect WellCat[inch] Matlab[inch]

Thermal 148,8 184,2921
Ballooning -118,44 -149,4521
Buckling -255,36 -143,6378
Piston -243,12 -327,2056
Total length
-468,12 -436,0034
change
The results from WellCat and Matlab differ from each other. The biggest difference is
especially seen for the buckling effect. WellCat uses Lubinski’s equation when calculating
thermal, ballooning and piston effects. While for the buckling effect it uses Lubinski’s and
Mitchell’s model for deviated wells. The Matlab code runs through Lubinski and Aadnøy’s
equation for thermal, ballooning and piston effect. In addition, it uses Mitchell’s equation
when calculating the buckling effect for deviated wells.
The simulation of the horizontal well gives a more complex result than for the vertical well
as both softwares are based on different theories. The output of buckling effect in WellCat
can be interpreted as a conservative analysis for the deviated well. The Matlab code is an
improved model for buckling effect and includes the latest theory and is therefore more
trustworthy.
76
Chapter 6
Conclusion
• Resulting packer forces for the wells ”X” and ”Y” have been computed using a com-
prehensive calculator. The results correspond with the simulated data in WellCatTM .
• Packer envelope is an important development, which represents a predictable safe

operating zone for a production packer. The area outside the performance envelope
is beyond the calculated safe operating zone. The results show that for well ”X”,
all the load cases are inside the packer envelope in the safe operating zone. While
for well ”Y”, two load cases appeared outside the fictitious performance envelope.
This can be interpreted as that the selected packer for well ”X” will withstand all
critical load cases. Whereas for well ”Y”, the selected packer will not withstand
these load cases. To keep the load cases inside the envelope, another packer with a
bigger rating envelope should be considered for well ”Y”.
• Defining initial conditions accurately is important when load cases are simulated in
WellCat. This is because all other load cases are based on this load case. If the base
case is incorrect, it will affect the output for the other simulated cases. In this thesis,
the main factors that are dependent on correct initial conditions, are length changes
in the well, load cases and tubing-to-packer forces which are given by the change
from the initial condition.
• Well integrity is an essential aspect for safety and regularity in production. A funda-
mental part of well integrity is the primary and secondary barrier envelope. In this
thesis, production tubing is discussed in detail, including elements of the production
packer. The production tubing should be able to bear the weight of the entire com-
pletion and withstand length changes due to pressure and temperature variations in
the well. In the completion, other components that have been installed will have
the same requirements for strength as the production pipe. The production packer
separates the barrier envelopes and enables continuous monitoring of the barriers,
which prevents unwanted leakage from the reservoir environment.
77
Chapter 6. Conclusion
• This thesis aimed to identify potential critical load cases that may affect the tubing
when producing. By analyzing design limit plots for both wells ”X” and ”Y”, the
results indicate that some of the load cases appeared outside the plot for both wells.
For well ”X” changing to a higher tubing grade, made the load cases appear inside
the triaxial capacity diagram. While for well ”Y”, a higher graded tubing and a
lower production rate was required to have a safe operating zone.
• If tubing movement is allowed, potential elongation or shortening effects gives

length changes in the tubing. The length changes for thermal, piston and ballooning
effect were found to be the same for the vertical well and all the three softwares
tested on. While for the deviated well, the effects gave slightly different outputs in
WellCat and Matlab, but not big enough to a further enquiry.
• Compressive forces and imperfections in the geometry affect the likelihood of buck-
ling. WellCat is found to perform conservative buckling analysis for deviated wells.
As a result, buckling effects were computed by an improved model from Remmen
(2018) with the latest theory. This model is modified to be applicable for all well
designs and was used to estimate the right buckling effect for the deviated well.
78
Chapter 7
Further work
• To create a more economical tubing design and protecting the integrity of the well,
further work can include improvement of the design limits plot. This can be im-
provements based on industry practice.
• In this thesis, tubing design was developed for a vertical and a deviated well. Ad-
ditional work can include applying models and investigation of the difference in
packer loads, load cases and length changes caused by temperature effects, in addi-
tion, a more detail look on annular fluid expansion.
• A further study of buckling effect can be conducted to get a broader overview of

tubing behaviour in deviated wells.
• More depth analysis of how the different effects on tubing and production packer
react to different load case scenarios can be useful to find. This will give a better
understanding of how the forces are distributed, and why the different load cases go
outside a packer envelope and design limit plot. By investigating the critical load
cases it will make it easier to choose correct tubing and packer design.
• The WellCat software tool has some other functional limitations that should be cor-
rected or improved. This can further be discussed in details.
• Investigation of the tubing condition from installation to further operations. This

can help understanding factors like tubing grade, wear, and corrosion from the in-
stallation process.
79
Chapter 7. Further work
80
Nomenclature
e = Absolute pipe roughness
A = Area
A = Area of plane the heat moves through
Z = Average gas comparability factor
h = Average heat transfer coefficient
PR = Average reservoir pressure
T = Average temperature
tempavg,f = Average temperature, final condition
tempavg,init = Average temperature, initial condition
σz = Axial stress
Pwf = Bottomhole flowing pressure
Fb = Buoyancy force
w = Buoyed tubing weight
DFburst = Burst design factor
CO2 = Carbon dioxide
DFcollapse = Collapse design factor
Pc = Collapse pressure resistance
Fc = Critical force
As = Cross sectional area
ρi,f = Density inside, final condition
ρi,init = Density inside, initial condition
ρo,f = Density outside, final condition
ρo,init = Density outside, initial condition
∆p = Differential pressure
Feff = Effective buckling force
po = External pressure
∆po = External pressure change
F◦ = Fahrenheit
ρfluid = Fluid density
F = Force
FkN = Force in kN
∆Fpiston = Force change generated by piston force
Fballooning = Force due to ballooning
Ftemp = Force generated by temperature
f = Friction factor
qg = Gas flow rate
Gg = Gas gravity
qx = Heat flux in x-direction per unit area
h = Height
H2 S = Hydrogen sulphide
81
Chapter 7. Further work
Ai = Inner area of tubular

Ai-t = Inner area of tubular
ID = Inner diameter
IDc = Inner diameter casing
IDt = Inner diameter tubing
ri = Inner wall radius
pi = Internal pressure
∆pi = Internal pressure change
pi = Internal pressure of tubular
L = Length
∆Lballooning = Length change due to ballooning
∆Lpiston = Length change due to piston
∆Ltemp = Length change due to temperature
L = Length of tubing
Pb = Minimum burst pressure
Yp = Minimum yield strength
Yp = Minimum yield stress
I = Moment of inertia
ρmud = Mud density
D = Nominal OD
t = Nominal wall thickness
Ao = Outer area of tubular
Ao-t = Outer area of tubular
OD = Outer diameter
ODt = Outer diameter tubing
po = Outer pressure of tubular
ro = Outer wall radius
Ap = Packer bore area
Fpc = Packer-to-Casing Force
ρpipe = Pipe density
µ = Poisson’s ratio
p = Pressure
σr = Radial stress
r = Radius
D/t = Slenderness ratio
σ = Stress
psi,f = Surface pressure inside, final condition
psi,init = Surface pressure inside, initial condition
pso,f = Surface pressure outside, final condition
pso,init = Surface pressure outside, initial condition
82
σθ = Tangential(hoop) stress
TP = Tension required to set the packer
∆T = Temperature change
dT/dx = Temperature gradient
T∞ = Temperature of the flowing fluid
TS = Temperature of the surface
k = Thermal conductivity
CT = Thermal expansion coefficient
Ftotal = Total axial load
σVME = Triaxial stress
D = Tubing diameter
Fpt = Tubing-to-Packer Force
H = Vertical depth
w = Weight of tubing
Pwh = Wellhead flowing pressure
PYp = Yield pressure
E = Young’s modulus
83
84
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URL https://stier.ndla.no/nb/learningpaths/35/step/332
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tion of Buoyancy in Wells. SPE, Baker Oil Tools, pp. 15–17.
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URL http://www.drillingformulas.com/
burst-internal-yield-pressure-property-of-tubular/
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York, Wiley.
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tubing sealed in packers. SPE.
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TRANSACTIONS. SPE, pp. 1–16.
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87
88
Appendix A
Tubing Stress Analysis
A.1. Design factor
Tubing strings should be designed properly to cover all anticipated load cases during the
lifecycle of the well. To select the appropriate tubing with the correct weight and grade,
the concept about design factor in tubular design is essential to understand.
Design factor describes the design intensity to ensure that the tubular will have addition
load to cover all load cases. The design factor can be expressed by the following formula,
Bellarby (2009a):
Pipe Rating
Design Factor(DF) =
Expected Load
A design factor of 1 is what a tubular can withstand before it starts to yield. Tensile loads,
burst loads, collapse loads, triaxial loads, drilling loads, production loads, axial loads,
running and cementing loads and service loads are all examples of anticipated load cases.
Each company have their own standard when it comes to design factor and to meet the
required well. The following table shows general design factors used in the industry:
Table 7.1: Typical design factors used in the industry
Failure
Design Facor
Mode
Burst 1.1 - 1.25
Collapse 1.0 - 1.1
Axial 1.3 - 1.6
Triaxial 1.2 - 1.3
A.2 Safety Factor

Safety factor can be described in the similar way as the design factor. The difference is
that safety factor can be more than or equal to the design factor. The minimal safety factor
will be equal to the design factor. The relationship between the safety factor and design
factor can therefore be explained by the equation below, Bellarby (2009a):
Pipe Rating
Design Factor(DF) = Safety Factor (SF)min ≤ Safety Factor (SF)
Expected Load
89
A.3 Material properties
When looking at the safety aspect of a well it is essential to understand the mechanical
properties of the tubulars. If a failure occurs during a completion operation, it can cause
catastrophic problems. This can be major losses like production from the well, damage
on the equipment and also safety of personal. The following section will describe basic
mechanical properties which are fundamental to understand when designing a tubular.
Stress
Stress, σ is force applied per unit area, Bellarby (2009a):

Force
σ=
Area
Figure 7.1: Illustration of stress on a tubular
where,
σ = stress of material
Strain
A tubular can be subjected to loads that makes the tubular long. This load is referred to as
tensile load and the elongation it makes is called ”strain”, ε. Strain can be expressed as,
Bellarby (2009a):
∆L
ε=
L
where,
ε = strain of material
90
L = length of tubular
∆L = length change of the tubular
Figure 7.2: Illustration of strain on a tubular
Elasticity
Tubulars are made of steel, and steel is a ductile material which can have elastic behaviour.
Elasticity is a property of the material which allows the material to return to its original
shape when the load is released. Stress and strain can be described by an equation where
the material is under elastic limit, Bellarby (2009a):
σ =E·ε
where,
E = young’s modulus (Modulus of elasticity)
For steel, young’s modulus of elasticity is about 30·106 psi. When a material is exposed
to a force, strain and stress can be plotted in a stress-strain curve like in figure 7.3. It is
essential to understand the meaning of the given points in the stress-strain plot.
91
Figure 7.3: Typical stress and strain curve for a tubular, Bellarby (2009a)
From the figure above, the elastic region can be defined from the origio till the yield point.
While the plastic region is described from the yield point til the end of the curve, which
can be defined as the failure point where the material will be parted.
If the material is within the elastic region, it will go back to its original shape when the
force is released. Under the plastic region, the material will be plastically deformed and
the stress and strain is under Hooke’s law.
The proportional limit point illustrates where stress is a proportional limit to strain. The
elastic limit point is where stress and strain have a linear relationship. While the yield
point is the maximum stress the material can withstand before it is plastically deformed.
After this point, the material will not be able to come back to its original shape. The ul-
timate tensile stress describes the point where the material can withstand the maximum
stress and is the top point of the stress-strain curve.
Poisson’s Ratio
When axial and radial strain is present, the material is under tension. When both these
strains are in the elastic region, they will be proportional to each other. This relationships
is called poisson’s ratio, µ, Bellarby (2009a):
radial strain ∆t/t

µ=− =
axial strain ∆L/L
Ductile and brittle material
Ductile material is a material type which has a large degree of plastic deformation before
fracturing the component. Carbon steel is an example of a ductile material. Brittle material
has on the other hand low degree of plastic deformation.An example of a brittle material is
grass. This means that after yield strength is exceeded the brittle material will break apart
92
easily, while the ductile material will elongate first before it gets parted.
Figure 7.4: Curve showing the behaviour of ductile and brittle material, DrillingFormulas (2016c)
Appendix B
Different load effects on tubing and production packer
B.1. Thermal effect
Example calculation
The following example will demonstrate the method of calculating tubing length change
caused by change in temperature:
Well data for a vertical well which allows the tubing move:
• Packer setting depth: 10 000 ft = 120 000 inch
• CT : 6.9·10−6 (1/F)
Data at the initial condition:
• Surface temperature: 60F
• Bottomhole temperature: 150F
Data at the final condition:
• Surface temperature: 90F
93
• Bottomhole temperature: 150F
(a) Initial condition (b) Finial condition
This problem can be solved by calculating the average temperature at both the initial and
final condition:
60 + 150
Average temperature at the initial condition = = 105F (7.1)
2
90 + 150
Average temperature at the final condition = = 120F (7.2)
2
The next step is to determine the temperature change in total, ∆T:
∆T = 120 − 105 = 15F (7.3)
Finally, the change in length can be estimated by using equation (1.3) and inserting the
numbers found:
94
∆Ltemp = 6, 9 · 10−6 · 120000 · 15 = 12, 42inch (7.4)
→ The result shows a positive value, which means that an increase in temperature leads to
an increase in the length of the tubing string, with 12.42 inches.
Excel calculation
B.2 Ballooning effect

Example calculation
This effect can easily be illustrated by an example. Well data for a vertical well, where
tubing and seal bore is free to move.
• Packer setting depth: 10 000 ft = 120 000 inch
• Tubing: 4,5”
• ID of tubing: 3,862”
• Packer seal bore OD: 5,0”
• Weight per length of tubing: 17,7 lb/ft
• Young’s modulus(E): 30·106
• Poisson’s ratio(µ): 0,3
95
Data for initial condition:
• Fluid in tubing: 10,0 ppg
• Fluid in annulus: 10,0 ppg
• Tubing pressure: 0 psi
• Annulus pressure: 0 psi
Data for final condition:
• Fluid in tubing: 8,0 ppg
• Fluid in annulus: 10,0 ppg
• Tubing pressure: 1500 psi
• Annulus pressure: 0 psi
(a) Initial condition (b) Finial condition
A stepwise calculation is shown to determine the change in length due to ballooning.
1. The first step would be to calculate the cross sectional areas:

π
Ai = · 3, 8622 = 11.497in2 (7.5)
4
96
π
Ao = · 4, 52 = 15, 904in2 (7.6)
4
2. The second step is to determine average pressure at initial condition:
po at surface = 0psi
pi at surface = 0psi
po at packer = po at surface + Hydrostatic p in annulus

= 0 + (0, 052 · 10 · 10000) = 5200psi
pi at packer = pi at surface + Hydrostatic p in tubing

= 0 + (0, 052 · 10 · 10000) = 5200psi
(0 + 5200)
po at initial condition = = 2600psi (7.7)
2
(0 + 5200)
pi at initial condition = = 2600psi (7.8)
2
3. The third step is to estimate the average pressure at the final condition:
po at packer = po at surface + Hydrostatic p in annulus

= 0 + (0, 052 · 10 · 10000) = 5200psi
pi at packer = pi at surface + Hydrostatic p in tubing

= 1500 + (0, 052 · 8 · 10000) = 5660psi
(0 + 5200)
po average at initial condition = = 2600psi (7.9)
2
(1500 + 5660)
pi average at initial condition = = 3580psi (7.10)
2
97
Finally the pressure change, ∆p is estimated:
∆po = 2600 − 2600 = 0psi (7.11)
where ∆po shows the change in average annulus pressure and ∆pi shows the change
in average tubing pressure:
∆pi = 3580 − 2600 = 980psi (7.12)
The final step is to use (2.14) and insert the numbers estimated.
→ The result for the length change due to ballooning is a decrease of length by 6,14 inches:
2 · 0, 3 · 120000
∆Lballooning = − · (11.497 · 980 − 15, 904 · 0) (7.13)
30 · 106 · (15, 904 − 11.497)
= −6, 14inch (7.14)
98
Excel calculation
B.3 Piston effect

Example calculation
To illustrate this with one example, the exact welldata and calculations are taken from the
previous examples. Since most of the calculations are done in the other examples, the
remaining is to estimate the packer seal bore area, which is:
π 2
Ap = · 5 = 19, 635in2 (7.15)
4
Cross sectional area of tubing:
As = A0 − Ai = 15, 904 − 11, 497 = 4, 407in2 (7.16)
99
Change in annulus pressure at packer:
∆po = 5200 − 5200 = 0psi (7.17)
Change in tubing pressure at packer
∆pi = 5660 − 5200 = 460psi (7.18)
Finally the force change, ∆Fpiston is estimated using equation (2.20)
∆Fpiston = (19, 635 − 11, 497) · 460 − (19, 635 − 15, 904) · 0 = 3744lbs (7.19)
→ This describes a compression force, as the it is a positive value.
In the same way, the length change can be estimated by using equation (2.21):
12000 · 03744
∆Lpiston = − = −3, 4inch (7.20)
30 · 106 · 4, 407
→ Which means tubing is shorter length by 3.4 inch.
100
Excel calculation
101
B.4 Buckling effect
Excel calculation
102
B.5 Matlab Code for all load effects
Inputs
103
104
Length Changes for packers permitting free motion
105

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What is the thesis about?

What is the thesis about?

What are the main considerations when designing a well?

What are the main considerations when designing a well?

M ASTER T HESIS

TPG4920 P ETROLEUM T ECHNOLOGY

ADVANCED TUBING DESIGN

When designing a well, the following must be considered:

Følgene faktorer er viktig å vurdere ved utforming av en brønn:

• Utkast av produksjonsrøret, som er et av de første elementene som bestemmes i

• Størrelse på produksjonsrøret som bestemmer underlaget for platå-produksjon, og

• Gassløft, beskyttelse av nedihullsventilen mot scale og andre behov for intervensjon

• Materialkvalitet for å unngå korrosjon og svekkelse av produksjonsrørene

Disse er et av barriere-elementene i primærbarrieren, og må derfor være intakt for å kunne

List of Tables vii

7.1 Typical design factors used in the industry . . . . . . . . . . . . . . . . . 89

1.1 Basic illustration of casing and tubing schematic in a well . . . . . . . . . 1

2.1 Free motion packer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Example of a typical tubing nomenclature . . . . . . . . . . . . . . . . . 30

5.1 Packer envelope for well ”X” . . . . . . . . . . . . . . . . . . . . . . . . 69

7.1 Illustration of stress on a tubular . . . . . . . . . . . . . . . . . . . . . . 90

API American Petroleum Institute

Figure 1.1: Basic illustration of casing and tubing schematic in a well

1.1 Equipment selection

1.1.1 Tubing size

Recommended Design Pressure ≥ Maximum Operating Pressure

• Inflow performance relation

• Pressure drop in tubing

• Pressure drop through the flow line

• Static reservoir pressure

• Pressure drop through the well-head constrictions

• Pressure level in the surface separating facilities

Inflow performance relationships (IPR):

Verical lift performance relationship (VLP)/ Outflow:

Horizontal flow performance:

1.1.2 DHSV - Downhole safety valve

1.1.3 Selection of production packer

• Fit, form and functioning of the tool

• Elastomeric material and seal design

have to be considered carefully.

When it comes to elastomeric or plastic materials, it is essential to know the expected

To select an optimum packer, an examination of well conditions and capacities of the

1.2 Material selection and corrosion considerations

1.3 Well integrity and tubing as primary barrier envelope

1.4 Thermal effect

∆Ltemp = CT ∆TL (1.3)

Figure 1.4: Tubing is lengthen by temperature increase

Figure 1.5: Tubing is shorten by temperature decrease

Figure 1.6: Figure explaining heat transferring mechanism in a well

Convection can be explained as heat or energy transfer by random molecular motion

1.5 AFE - Annular fluid expansion

2.1 Acting forces

2.1.1 Modelling of forces from formation pressures and temperatures

Figure 2.1: Free motion packer

Figure 2.2: Limited motion packer

Figure 2.3: No motion packer

Tubing pressure test

Annulus pressure test

worst-case scenario is when there is high-temperature steady state production followed by