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BabsCOMPLETION ESSENTIALSII2007[2]

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COMPLETION ESSENTIALS II
Professor Babs Oyeneyin
b.oyeneyin@rgu.ac.uk
01224-262327
Room C412
1
© The Robert Gordon University 2007
Content Details
SECTION 2
• Completion Functions, Operations & Design
Process
• Completion Architecture & Equipment Selection
• Tubing Specification & Equipment Material
Selection
© The Robert Gordon University 2007
2
Well Completions
• Design and installation of equipment and
treatment cum procedures required to bring a
well to production
− Driven by company objective.
• Decision Areas
− Specification of bottom hole completion technique
− Selection of production conduit
− Assessment of completion string facilities
− Evaluation of well performance
© The Robert Gordon University 2007
3
Well Completion Objectives
• Drill a borehole through reservoir section
• Create the necessary efficient hydraulic connection
between borehole & reservoir
• Install necessary equipment to allow production or
injection
• Provide safe and reliable system for efficient
operation to take place with minimum NPT in line
with company objectives
© The Robert Gordon University 2007
4
Completion Objectives [Cont.]
• Maximise safety of production & Injection system
− Install flow control devices
− Block fluid escape
• Maximise production & injection efficiency
− Maximise well flow potential
•
•
•
•
•
Tubing size
Gas or water shutoff
Leakage control
Reservoir monitoring
Flow assurance
− Optimisation of capital expenditure
− Minimisation of operational expenditure
− Minimise downtime[NPT]
© The Robert Gordon University 2007
SAFE & EFFICIENT PLUMBING JOB!
5
Functional Need of Completion
•
•
•
•
•
•
•
•
Circulation
Isolation & Control
Reservoir monitoring
Reservoir protection during shutoff
Flow, pressure, temperature, etc monitoring
Intervention
Barrier for uncontrolled fluid escape
Tubing stress tolerance
© The Robert Gordon University 2007
6
SUMMARY OF
•
COMPLETION STEPS
Total production rate desired
−
−
AOF?
IPR
•
Need to minimise slugging in tubing = Optimum Tubing Size
•
Define tubing size based on desired production rate, and operating conditions[GLR, Depth,
etc]
•
•
•
•
•
•
•
•
•
−
VLP
−
−
−
Flow Control
Isolation, interventionetc
Monitoring, Artificial lift, etc
Define type of completion [Open Hole, Perforated Completion, Sand Control, etc]
Define Operational Objectives
Process Design
Select Completion Jewels
Stress Analysis
Installation Procedure
Vendor Sourcing
Costing to AFE
AFE = Authorisation for Expenditure
© The Robert Gordon University 2007
7
Example Completion Schematic
CONTROL LINE
FLOW COUPLING
SCSSSV
CAMCO SPM. Valve to be activated by wireline
OTIS
‘XA’
OTIS SSD
XN
LANDING
NIPPLE
OTIS ‘XA’ SSD
95/8in OTIS ‘RDH’ PACKER
BAKER‘FB-1’ PACKER WITH GRAVELPACK
EXTENSION
BAKER ‘H’ LOCATOR & ‘FA-1’ PACKER
BAKER ‘G’ LOCATOR SEAL ASSEMBLY
STRING B
SQUEEZE
PACK
OTIS BLAST JOINT
LOCATOR SEAL ASSEMBLY
BAKER ‘FB-1’ PACKER WITH GRAVELPACK
EXTENSION
OTIS
XN LANDING NIPPLE
WIRE-WRAPPED SCREEN
BAKER ‘H’ LOCATOR & ‘FA-1’ PACKER
BRIDGE PLUG
© The Robert Gordon University 2007
8
Completion Factors
• Well Objectives
− Exploration Well
• Reservoir Fluid Type
− Appraisal Well
• Well Testing for Pressure, rock flow properties
− Development Wells
• Production, Injection or Observation
• Environmental, Geological, Topographical & Legal
−
−
−
−
Onshore vs Offshore [Platform based or Subsea]
Permit
Transport [FPSO Hookup, Subsea tieback]
Environment
• Type of Reservoir
• No. of Pay zones
• Production strategy
− Operating procedure
− Monitoring
− Possibility of Artificial Lift
© The Robert Gordon University 2007
9
Type of Completion
• Interface between reservoir & wellbore
−
−
−
−
Open hole
Slotted Liner
Perforated Liner
Cased hole [Perforated completion]
• Method of production
− Natural or Pumped
• No. of zones
− Single or Multiple
© The Robert Gordon University 2007
10
Open Hole Completion
• For Competent Formation
• Production Casing to top of pay sand
• Open hole barefoot or with slotted
liner or perforated liner
• Best for optimum flow potential
• Low capital cost
• Less completion time
• Large wellbore radius
− Reduced friction pressure
• Poor isolation of gas or water
− Swellable packers?
• Limited by lack of selective
production from same wellbore
contact
− May be possible with flow control
devices in intelligent wells
© The Robert Gordon University 2007
11
Open hole Completion Application
• Low Cost & High number of wells
development
• Naturally fractured & competent reservoirs
• High Cost Wells
− Horizontal Well
− Extended Reach Wells
− Multilaterals
© The Robert Gordon University 2007
12
Slotted or Perforated Liner Completion
• Open hole with liner or
screen
− Slotted liner
− Predrilled or perforated
liner
− Screen, etc
•
•
•
•
Uncemented
Liner tieback to casing
Retrievable
Supports wellbore
− Unconsolidated
sands/HW & MLs
Production Tubing
Production Packer
Liner Packer
Slotted Liner
• Poor reservoir
management
© The Robert Gordon University 2007
13
Cased Hole Completion
• Perforated Zone
Production
Casing
− Allows selective or
multiple production
− Co-mingling or no comingling option
− Possibility of zonal
isolation
− Most popular?
− Most efficient? No!
− Depends on
• Perforation Density
[Shots per foot]
• Perforation penetration
• Perforation size
© The Robert Gordon University 2007
Cement
Perforation
Production
Liner
14
Perforated Completion Application
•
•
•
•
•
Heterogeneous reservoirs
Water or Gas management
Selective completion
High intervention cost areas
High operating cost
© The Robert Gordon University 2007
15
Natural vs Pumped Production
• Natural Production
− Best. Based on reservoir
energy
− Less facilities &
complexity
− Optimisation by
• Pumped Production
• Artificial Lift with Gas or
Pump
• minimising resistance to
flow
• Optimise production
• Reservoir treatment
© The Robert Gordon University 2007
16
Number of Zones
• Single Zone
− One pay zone
• Multiple Zones
Multiple pay sections
Selective or simultaneous production
Produce through multiple string [No co-mingling]
Several zone producing to a single string[Comingling]
− Multilateral proction
−
−
−
−
• Multiple zones into a single bore
© The Robert Gordon University 2007
17
Single Zone Completion
• Tubingless Casing Flow
−
−
−
−
Simple and low cost,
High Rate Wells
No longer in use
Disadvantages
• High Fluid Slippage and
Friction Loss
• Casing Contact/Corrosion
• Casing Burst at Wellhead
• Tubing Flow with
Annular Isolation
− Most Popular
− Use of Isolation Packer
− Max. Well Security
• Casing & Tubing Flow
− Better Well Control
− Circulation Capability
© The Robert Gordon University 2007
18
Single Zone Completion
Casing
Production
© The Robert Gordon University 2007
Casing & Tubing
Production
Tubing production with
packer Isolation
19
STRATIGRAPHIC COLUMN[Multiple Pay]
© The Robert Gordon University 2007
20
Multiple Completion
• > One Pay Section.
• Co-Mingling from Various Zones
• segregated Flow but Multiple Depletion
• Alternate Zone Completion
• Multilateral Completion
© The Robert Gordon University 2007
21
Dual Single String + Annular Flow
DUAL ZONE , ANNULAR FLOW
© The Robert Gordon University 2007
DUAL ZONE , CROSS-OVER FLOW
22
Multiple Completion
DUAL STRING
© The Robert Gordon University 2007
SINGLE STRING,
SELECTIVE
PRODUCER
TRIPLE
COMPLETION
23
Completion String Facilities
• FUNCTIONS
− Control of anticipated flowing pressure and hydraulic
pressure
− isolation of Annulus
− Wellbore Fluid and Remote Control
− isolation of tubing
− Circulation between Annulus and Tubing
− Tubing Detachment
− Controlled Fluid Injection
− Suspension of Monitoring Equipment(BHP Gauge,
Thermometers, etc)
© The Robert Gordon University 2007
24
COMPLETION DESIGN PROCESS
© The Robert Gordon University 2007
25
Design Process
Initial Design
Completion
Technique
Well Productivity
or Injectivity
Production Conduit or
Artificial lift
Completion String Facilities
Cost
Casing String
Design
Completion Architecture
[Conceptual Design]
Intervention
Strategy
Risk assessment
Performance Optimisation
Equipment
Specification &
Selection
© The Robert Gordon University 2007
Final Design
Installation & Integrity Testing
Tubing Stress
Analysis
26
Initial Design
• Type of Completion
− Open Hole or Perforated
• Tubing Size
− Nodal Analysis
• Artificial lift requirements
• Production or Injection Target
© The Robert Gordon University 2007
27
Design Process [Coint.]
• Prelim Equipment Selection
Riusk Assessment
Cost
Casing Design
Equipment features
Suitable Well Architecture
Well
Intervention/Maintenance
− Workover strategies
− Re-Entry Options, etc
−
−
−
−
−
−
© The Robert Gordon University 2007
• Well Performance
Optimisation
− Production optimisation @
minimum energy
− Response to reservoir
pressure, GLR, etc
− Optimum rate
− Maximum recovery
28
Final Design
•
•
•
•
•
•
•
Final specification
Final verification
Tubing stress analysis
Erosion checks
Condition monitoring options
Installation procedures
Tendering- Equipment, services
− Costing
− Organisation tasks
• Asset Team
− 2nd , 3rd party review
− Independent review?
• Flexibility
− New ideas, new techniques or equipment
− Field peculiarity
• Design against failure
− Injury, death, pollution [Spillage]
Formalised Approach
© The Robert Gordon University 2007
Quality Assurance
29
COMPLETION ARCHITECTURE
© The Robert Gordon University 2007
30
Completion Components
Two Sections
C O M P L E T IO N
U pp er
•
Upper Completion
•
Lower Completion
CO M PO NENT
F U N C T IO N
T u b in g h a n g e r
S u sp e n d th e strin g /c o m p o n e n ts
S a f ety sy ste m s
C o n ta in p ro d u c tio n flu id s
Packer
Iso la te / c o n ta in flu id s
T u b in g
T ra n sp o rt/c o n ta inm e n t of fluid s
A rtificia l lift sy ste m s
A id /e n h a n c e p ro d u c tio n
D a ta a c q u isitio n
sy ste m
W ell/re se rv o ir m a n a g em e n t
S lid in g sle ev e s
W ell c irc u la tio n / saf e ty
P e rf o ra tin g
E sta b lish c om m u n ic a tio n b e tw e e n
w e llb o re a n d re se rv oir
S a n d c o n tro l
S to p /c o n trol so lid s p ro d u c tio n
F ra c tu rin g
E n h a n c e p ro d u c tio n
Iso la tio n sy ste m s
R e se rv oir iso la tio n / sa f e ty
Low er
© The Robert Gordon University 2007
31
Upper Completion
Methods & Equipment used above reservoir to
surface
• Functions
− Effective lifting of produced fluids to surface
− Fluid containment for safety
− Minimise energy losses from production or injection
© The Robert Gordon University 2007
32
Lower Completion
• Interface between reservoir & wellbore
• Functions
− Long term integrity of wellbore
− Full access to reservoir
•
•
•
•
Monitoring
Surveillance
Management
Performance improvement
− Address specific requirements
• Sand Control
• Selective production, etc
© The Robert Gordon University 2007
33
Completion Component Sequence
XMAS REE
Flow Control & Isolation
WELLHEAD
Tubing & Casing Suspension
S.S.S.V
SIDE POCKET MANDREL
SLIDING SIDE DOOR [SSD]
SEAL ASSEMBLY
Safe isolation downhole
Circulation or Fluid Injection
Circulation
Accommodate Tubing Stress
PACKER
Annular Isolation
NIPPLE
Tubing Isolation
PERFORATED JOINT
Alternate Entry for flow
NIPPLE
Landing Gauges
W.E.G
Wireline Re-Entry
© The Robert Gordon University 2007
34
Completion Schematic
CONTROL LINE
FLOW COUPLING
SCSSSV
CAMCO SPM. Valve to be activated by wireline
OTIS
‘XA’
OTIS SSD
XN
LANDING
NIPPLE
OTIS ‘XA’ SSD
95/8in OTIS ‘RDH’ PACKER
BAKER‘FB-1’ PACKER WITH GRAVELPACK
EXTENSION
BAKER ‘H’ LOCATOR & ‘FA-1’ PACKER
BAKER ‘G’ LOCATOR SEAL ASSEMBLY
STRING B
SQUEEZE
PACK
OTIS BLAST JOINT
LOCATOR SEAL ASSEMBLY
BAKER ‘FB-1’ PACKER WITH GRAVELPACK
EXTENSION
OTIS
XN LANDING NIPPLE
WIRE-WRAPPED SCREEN
BAKER ‘H’ LOCATOR & ‘FA-1’ PACKER
BRIDGE PLUG
© The Robert Gordon University 2007
35
Facilities Functions
• PRESSURE AND FLOW
CONTROL
• CIRCULATION CAPABILITY
− Xmas Tree- For pressure
containment within production
casing, tubing wellhead,
surface valve closing system
•
− Packer Isolation
− Tubing Selection - Stable
Production
• ANNULAR ISOLATION
− Packers
− Prevents Pressure Exertion on
•
Wellhead
© The Robert Gordon University 2007
− Well Control capability
•
•
•
•
Sliding Side Door(SSD)
Sliding Sleeve
Side Pocket Mandrel
Ported Nipple
TUBING ISOLATION
− SEAL ASSEMBLY
− Supplement to SSSV
• Used when SSSV is to be removed
• Lands and locks in a wireline nipple
inside tubing string.
. DOWNHOLE ISOLATION OF
PRODUCTION TUBING
− Subsurface safety valve
36
Facilities [Cont.]
• DOWNHOLE TUBING DETACHMENT
− removable locator device which seals with rest of
tubing left in well.
• DOWNHOLE HANGER SYSTEM Suspends tubing beneath
well Head
• POLISHED BORE RECEPTACLE(PBR) - TUBING
STRESS COMPONENTS
• WIRELINE NIPPLE - LANDING NIPPLE System for holding pressure and Temperature
Gauges, etc
© The Robert Gordon University 2007
37
Completion
String
Components –
XMAS TREE
© The Robert Gordon University 2007
38
Xmas Tree
• Combination of Valves pressure control
systems located at Wellhead
• Interface control barrier between
Reservoir/Well & Topside facilities
• Controller of Production/Injection
• Permit Well kill prior to workover
• Permit deployment of intervention strings
© The Robert Gordon University 2007
39
Types of Xmas Tree
Surface vs Subsea
Surface
• Conventional Flanged
Trees
− Land
− Offshore wells
• Solid Block Trees
−
−
−
−
−
Offshore Application
HPHT
High rate wells
Reduces potential leaks
For turbulent conditions =
Y configuration
Subsea
• Conventional Dual bore
trees
− 2 vertical bores for tubing
access and annulus
• Horizontal/Spool trees
• Inclined Trees [New]
− Housed within wellhead
• Horizontal /Spool Trees
© The Robert Gordon University 2007
40
Trees Schematic
© The Robert Gordon University 2007
41
Wellhead
Functions
− Transfers
casing/completion
loads to ground or
platform
− Provides seal system
and valve to control
tubing & annular
access
© The Robert Gordon University 2007
• Selection Factors
− Loads
− Requirements for
annular injection
− Exposure to nasty
annular fluid
− Annular pressure
monitoring
42
Subsurface Safety Valves
• Installed below wellhead to prevent uncontrolled flow
in emergency situation [Prevent Blowout!]
• Remote Controlled
− Tubing retrievable
− Wireline Retrievable
− Surface Controlled (SCSSSV)
• Closed and held open by external pressure @ surface
• Pressure controlled most popular
• Electric, electromagnetic & acoustic versions
• Direct Controlled
− Designed to be opened at preset differential pressure, flow or
well pressure
− Subsurface controlled (SSCSSSV)
− Less reliable than surface controlled
© The Robert Gordon University 2007
43
Subsurface Safety Valves
• CATEGORIES
− According to Closure
Mechanism
− Wireline or tubing
Retrievable
− Non-equalising or self
Equalising Concentric
or Rod Piston
• Single Control Line
or Dual Balanced
Line
© The Robert Gordon University 2007
TUBING RETRIEVABLE
WIRELINE RETRIEVABLE
44
Subsurface Safety Valves
FLAPPER TYPE
© The Robert Gordon University 2007
BALL TYPE
45
Joints & Couplings
• FLOW COUPLING - FC
− These are short sections of thick-walled pipes used to
withstand any erosion caused by turbulent flow through
different tubing sizes
− FC below & above landing nipple useful close to SSSV
• BLAST JOINTS
− Couplings designed to withstand external erosion
− Usually positioned either side of a Sliding Sleeve situated
at perforated production zones or lateral joints in
Multilateral completions.
• PUP JOINTS
− Short tubing joints that give flexibility in attaining a
desired tubing length such as spacing out completion
© The Robert Gordon University 2007
46
Landing Nipples
• Short tubular sections with an internally machined
profile that provide location points for various flow
control devices and gauges in the production string
• When holding pressure monitoring systems they
are called Gauge mandrels
• Applications include:
− Plugging tubing for pressure testing
− setting hydraulic set packers
− Zonal isolation
− installation of downhole chokes
− Landing off BHP recorders
© The Robert Gordon University 2007
47
Landing Nipples
No-Go
Nipples
© The
Robert Gordon University 2007
Non-Selective
Selective
Wireline
Operated
48
Side Pocket Mandrels(SPM)
− These are joints having
offcentre pockets with ports
in the wellbore annulus.
− Applications include:
• As Gas Lift Madrels
− As Chemical Injection Valves
− Circulation Devices for kill
fluids
− Usually activated by annular
pressure
© The Robert Gordon University 2007
49
Sliding Sleeves or SSD
• System that allows
− Communication between
tubing and the annulus for
well kill operation
− Circulation for tubing or
annulus
− Selective zone
© The Robert Gordon University 2007
50
Polished Bore Receptacle/Expansion Joint Seal
• PBR - Useful where
large tubing movement
is anticipated.
• ELTSR – Inverted PBR.
− Run with permanent
packers
© The Robert Gordon University 2007
51
Anchor Seal Nipple
• Anchoring & sealing device
− Connects retrievable tubing string to upper bore
of production packer
− Provides sealing barrier at tubing bottom
− Facilitates workover of damaged tubing
− Provides tubing anchor to minimize movement
− Assists well killing operation by providing +ve
safety barrier.
© The Robert Gordon University 2007
52
Packers
• TYPES
− Based on Retrievability
• PERMANENT PACKERS
• RETRIEVABLE PACKERS
− Based on Setting Mechanism
•
•
•
•
Mechanical Setting - Tubing Rotation
Compression or Tension Setting
Hydraulic setting
Electrical - Special Adaptor/Settiong Tool
− Based on Packer Bore
• Single, Dual and Triple Bores
© The Robert Gordon University 2007
53
Packer Classifications
• SEAL WITHOUT TUBING MOVEMENT
− External Rubber Seal element
• SEAL WITH TUBING MOVEMENT
− Locator Seal assembly
− Extra Long tubular Seal receptacle - ELTSR
− Travel Joint - Inverted ELTSR
− PBR- Polished Bore Receptacle
© The Robert Gordon University 2007
54
Packer
© The Robert Gordon University 2007
55
Tubing Specification & Equipment Selection
© The Robert Gordon University 2007
56
Tubular Nomenclature
•
Nominal Size = Outside Diameter,
OD
−
−
−
•
Tubings : 11/20’’ to 4-1/2’’
Casings : 4-1/2’’ +
Different IDs depending on strength
& Wall thickness
Length Range®
−
Tubings
−
Casings
• R1 = 20-24ft
• R2 = 28 – 32ft
API Spec.
• R3 = 32-48ft - Mill
• R1 = 16-25ft
• R2 = 25-34ft
• R3 = 32-48ft
© The Robert Gordon University 2007
•
•
•
WT/ft
−
−
Dictates mechanical strength
Nominal ID depends on OD & WT/ft!
−
Max. size of equipment to pass thru
tubular
Drift ID
Coupling OD
−
−
•
Maximum OD of tubing
Applied when estimating clearances
to install tubing
GRADES
−
−
−
−
Single or Double letter prefix
XT155 = Xtra tough 155kpsi strength
material
API Class: N80 = 80Kpsi Yield
Not Ultimate strength
57
Tubular Design Factors
• Adopted to ensure tubing is selected and used in
manner to prevent premature failure
• DF based on:
− Service loads
− Allowance for unexpected events
− Effect of packer setting, temperature, buckling, corrosion
• Design Loads
−
−
−
−
Burst
Collapse
Axial
Triaxial – Axial, Radial, Tangential
© The Robert Gordon University 2007
58
Mechanical Design
• Four failure modes:
− Parting of tubing under axial load
• [Bending, overpull, dogleg friction]
• DF = 1.1
− Bursting due to internal pressure
• Corrosion & erosion effects
• [DF = 1.1]
− Collapse under external pressure
• DF = 1.0
− Combined stress[Triaxial] exceeding yield of tubing
• DF = 1.1
© The Robert Gordon University 2007
59
Tubular Design Factors
RatedAxial Tension
Axial =
Actual
Axial
Calculated Burst Rating
Burst =
[ Internal Pr essure − Ext . Pr essure ]
Calc . Collapse Pr essure
Collapse =
[ External Pr essure − Int . Pr essure ]
Material API Yield
Triaxial =
Triaxial Stress
© The Robert Gordon University 2007
60
Tubing Design Considerations
• Maximum & Optimum flow rate
•
•
•
•
•
•
•
− Size determination
Maximum surface pressure [Flowing & Shut-in]
Corrosion potential over life of string
Erosion potential
Well intervention effects E.g Stimulation
Necessary Tensile stress
Burst & Collapse Loading
Forces
− Determine Wt. & Grade of tubing material
• Tubing movement
− Tubing components
© The Robert Gordon University 2007
61
Mechanical Loads on Tubing Strings
• Changing forces = Changing
in movement/Length
• Key Factors contributing:
−
−
−
−
−
Weight
Pressure
Fluid Friction
Ballooning
Temperature
• Loads excluded from axial
stress:
− Ballooning & Temperature
© The Robert Gordon University 2007
62
FWT = W ' TVD
Tubing Forces
• Axial Forces = Sum of
forces for free system +
Forces induced by
resistance to length
change
• W’ = WT/FT
• W = Weight
© The Robert Gordon University 2007
FWT = W '*TVD
N = W sin A
63
∆L =
LF
E ( Ao − Ai )
Tubing Movement
• Piston Effect = Changes in
length caused by the pressure
forces acting on the tubing
∆L = Tubing extension
• L= Measured Length of
Tubing
• F= Force due to plug, etc.
• E = Young’s Modulus
• Ao= External area
• Ai= Internal area
© The Robert Gordon University 2007
∆L =
LF
E ( Ao − Ai )
64
Tubing Movement
• Temperature Effect
• CT = Coeff. Of Thermal
Expansion, 1/oF
• DT = Temperature Change,
oF
• L = Tubing Length, Ft
• If Tubing is Free,
− Faxial = 0
• For Anchored tubing
− Faxial = FTemp
∆ L TEM P = C T ∆ T L
n
FTEMP = − ∑ CTi Ei ∆Ti ( Aoi − Aii )
i =1
• For Combination Completion
• i = individual components
© The Robert Gordon University 2007
65
Buoyancy Effect
• FB = Buoyancy Effect
• FB = - p* [Ao – Ai]
© The Robert Gordon University 2007
66
Ballooning Effect
• Radial expansion or contraction
caused by pressure change
• Result = Length Change!
• Computation is essential for each
section with same OD & wall
thickness
© The Robert Gordon University 2007
67
Poisson Effect
µ = Poisson ration
∆p = Change in
pressure compared to
base case
• Lp = Length to packer
• For combination
system, add cumulative
lengths to packer point
• For Anchored Tubing
− 2µLP
(∆pi Ai − ∆po Ao )
∆LBAL =
E( Ao − Ai )
FBAL = 2µ( Ai∆pi − Ao∆po )
− Faxia = FBAL
© The Robert Gordon University 2007
68
Fluid Friction
• Friction by fluids moving inside
the tubing and the associated
friction between the fluid and
the tubing wall
• Fluid Flowing Down =
Lengthening of tubing
• Fluid Flowing up = Shortening
of Tubing
• Frictional Pressure Force = FFR
F FR
•
Change in Length, DLFR
∆ L FR
© The Robert Gordon University 2007
− ∆p
=
Ai L
∆L
⎤
⎡⎛ − ∆p⎞ 2
⎢ ⎜⎝ ∆ L ⎟⎠ L p A i ⎥
⎥
= ⎢
⎢ 2 E (Ao − Ai )⎥
⎥⎦
⎢⎣
69
RADIAL & TANGENTIAL STRESSES
• Radial Stresses
pi Ai − po Ao ( pi − po ) Ai Ao
σr =
−
( Ao − Ai ) A
( Ao − Ai )
• Tangential Stresses
pi Ai − poAo ( pi − po ) Ai Ao
σt =
+
( Ao − Ai ) ( Ao − Ai ) A
For inner radius, A = Ai & σr = - pi
For outer radius, A = Ao & σr = -po
σ t ,i
σ t ,o
© The Robert Gordon University 2007
pi ( Ai + Ao ) − 2 p o Ao
=
Ao − Ai
2 pi Ai − p o ( Ai + Ao )
=
Ao − Ai
70
Helical Buckling Effect
• Excess Axial Force
• -ve Effective Force =
Helical Buckling
• Neutral Point = Depth
at which FEFF = 0
moving up from packer
© The Robert Gordon University 2007
71
Helical Effect
•
Effective Force
FEFF = FTOTAL + ( po Ao − pi Ai )
F EFF = A p ( p o − p i )
•
If free to move
•
Ap = Packer ID
•
•
•
•
•
n = Neutral Point
Gio = Fluid Gradient [in or annulus]
W’ = WT/FT
C = Radial clearance b/w casing and tubing
E = Youngs Modulus
© The Robert Gordon University 2007
•
Elongation or Compression?
n =
•
For free tubing and n within string
∆ LHB =
•
F EFF
W '+ G i A i − G o A o
− C 2 FE F F 2
8 E I (W ' + G i A i − G o A o )
For n >Lp
− C 2 F EFF 2
L
⎡L ⎛
∆ L HB =
−
2
⎜
8 EI (W ' + G i A i − G o A o ) ⎢⎣ n ⎝
n
I =
[
OD 4 − ID 4 ]
64
π
72
⎞⎤
⎟⎥
⎠⎦
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