InvestigationofMechanicalNumericalSimulationandExpansion ...Liner Hanger Structure of the expansion...

Research ArticleInvestigation ofMechanicalNumerical Simulation andExpansionExperiment of Expandable Liner Hanger in Oil andGas Completion

Yong Chen 1 Guo Ping Xiao1 Wen Jian Zhong2 and Hao Yi2

1School of Mechatronic Engineering Southwest Petroleum University Chengdu 610500 China2Research Institute of Petroleum Engineering SINOPEC Northwest Oilfield Branch Urumqi 830011 China

Correspondence should be addressed to Yong Chen chyswpu163com

Received 5 February 2020 Revised 8 July 2020 Accepted 11 July 2020 Published 27 July 2020

Academic Editor Reza Kolahchi

Copyright copy 2020 Yong Chen et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e expansion experiment of the expansion liner hanger is a one-time failure process so in order to save cost the finite elementtechnology needs to be used to simulate the expansion experiment Obtaining the mechanical parameters of the expansion linerhanger can effectively optimize the size of the expansion liner hanger structure and guide the expansion completion Firstly mainstructure and principle of expandable liner hanger were introduced Secondly mechanical equilibrium equations of the ex-pandable process were established to obtain pressure of the expandable fluid and pressure of the expandable fluid is obtainedirdly finite element (FE) simulation mechanical model of the expansion of the Oslash2445mmtimesOslash1778mm expandable linerhanger was established to analyze the hang mechanism and the change rule of mechanical parameters during the expansion eFE results have shown that radial displacement and residual stress of the inner wall of hanger varied in 5 cycles and the expansionratio of the expandable tube was 74 during the expansion e expansion force did not change stably but gradually increased instages And the hydraulic pressure required for the expandable cone to continuously move down was 18MPa According to thecontact stress generated on five rubber cylinders and the contact stress generated on fivemetal collars the total hang force has beencalculated which exceeds 1000 kN and meets the design requirements Lastly the expansion test results have shown that ex-pansion pressure was 19MPa and the expansion rate was 71 e mechanical analysis results of the expandable liner hangerwere in good agreement with the experiment results in this study which provide important mechanical parameters for wellcompletion with expandable liner hanger

1 Introduction

e liner hanger is an important tool in the oil and gascompletion In the conventional liner hanger system [1ndash6]the liner is placed on the upper casing with the cone and theslip and the liner overlap section has the poor sealingquality e failure of hang and sealing of conventional linerhangers often occurs in the complex down hole conditions indeep wells ultradeep wells horizontal wells multilateralwell etc and seriously affects the well completion

With the progress of the expandable pipe technology theexpandable liner hanger [7ndash15] is developed to help over-come the shortcomings of the conventional liner hangereexpandable liner hanger applies the expansion principle ie

the metal plastic strain characteristics of the expandable pipeand exerts the radial expansion on the expandable hangerwith the mechanical force the hydraulic pressure or bothe expandable body is attached to the outer casing which iscompressed by the residual stress and the liner string ishanged with the friction force e rubber cylinders aregenerally placed on the hanger body to improve the sealingand hang capability e rubber materials are squeezed intothe annulus between the hanger and the upper casing ef-fectively seal the annulus and have an efficient two-waypressure-bearing capacity Compared with the conventionalliner hanger the expandable liner hanger has the followingcharacteristics the packer and the hanger are integrated andthe seal assembly can withstand the high pressure and has

HindawiShock and VibrationVolume 2020 Article ID 9375835 13 pageshttpsdoiorg10115520209375835

the anticorrosion performance e expandable liner hangerhas no pressure-transmitting hole which eliminates thepotential leakage When the liner is blocked the liner hangertool rotates the liner and circulates the killing fluids whichincreases the tripping in depth of the liner and does notcause physical damage on the upper casing Meanwhile theexpandable hanger has no external attachments such as slipsand cones which reduces the annular space occupied by thehangers thereby increasing the available space inside thehanger and liner and improving the inside flow

e expandable liner hangers have been applied inmore than 2000 well-times overseas [16ndash21] which lowerthe potential down hole risk of the conventional linerhanger and the poor sealing quality of the overlappedsection and improves the stability of the liner cementationsystem e Drilling Engineering Research Institute ofCNPC XIBU Drilling Engineering Company Limitedstarted the development of ELH-1 expandable linerhanger in 2011 [18] and completed trial production in-door evaluation etc of the φ245mm timesφ178mm ex-pandable liner hanger prototype In 2014 the expandablehanger developed by SINOPEC Shengli Oilfield DrillingInstitute helped the Jidong Oilfield realize the first side-tracking in φ1778 mm cased-hole and achieve the hang ofφ1397 mm on the φ1778 mm intermediate casing withthe expandable liner hanger [22] In 2015 the DrillingResearch Institute of the CNPC Great Wall DrillingCompany developed a new type metal collar expandableliner hanger which realizes hang and sealing of the linerthrough the metal interference contact after the ex-pandable tube expansion and is characterized by stronghang and sealing performance high temperature resis-tance short overlapped section and large drift diametere sealing pressure difference greater than 40MPa thetemperature resistance higher than 350degC and the hangforce greater than 1000 kN meet the sealing performancerequirements in the heavy oil thermal recovery [23]However these studies did not take an effective method tosystematically discuss and evaluate the mechanicalproperties and suspension capacity of expansion linerhanger e drilling technology in China goes to deepwells and ultradeep wells where the probability of drillingcomplex formations increases and the down hole con-ditions are more complicated which needs the researchand development of expandable liner hangers e ex-pandable liner hanger ensures implementation of Chinarsquostrategy of exploring deep oil and gas resources and en-hances Chinarsquos deep drilling capability

Obtaining the mechanical parameters of the expansionliner hanger can effectively guide the research and devel-opment of expandable liner hangers and expansion com-pletion operation At present physical experiment and finiteelement simulation are the most commonly used methods toobtain mechanical parameters However the physical ex-periment method has a high cost a long cycle and morepersonnel involved With the rapid development of thecomputer hardware and the finite element (FE) theory[24ndash30] the computer simulation is applied in various in-dustries e simulation in the FE software is used as a tool

for pretest verification and posttest optimization whichgreatly reduces the test period and the test cost

2 Structure and Principle of ExpandableLiner Hanger

Structure of the expansion portion of the expansion linerhanger designed in this study mainly includes the ex-pandable cone assembly the rubber cylinder (5 pieces) theexpandable tube the outer casing the mandrel and thepressure relief sleeve as shown in Figure 1emodels of theexpandable cone 5 rubber cylinders the expandable tubeand 10 metal convex collars are shown in Figure 2 eexpandable structure is set as a state before expansion in theouter casing e rubber cylinders are equally spaced on theexpandable tube and are axially separated and positioned bythe metal collar

Working principle of the expansion liner hanger thehigh-pressure fluid enters the internal part of the ex-pandable liner hanger forming a large pressure differenceon both sides of the expandable cone and pushing theexpandable cone to move down As the outer diameter ofthe expandable cone is larger than the inner diameter ofthe hanger body cone radially expands the hanger bodyand thus the plastically deformed hanger body is firmlyattached to the inner wall of the outer casing When thecone moves down to the designed position the pressurerelief sleeve is pushed the pin is sheared the pressurerelief hole is exposed the pressure of the expandable fluidis released and the expansion operation is completed ehang force consists of two parts the first is the frictionforce generated by the rubber cylinder squeezed into theannulus between the hanger and the upper casing due toplastic deformation of the expandable tube and thesecond is the contact force due to contacting deformationbetween the convex metal collar and the outer casingduring the expansion

3 Mechanical Equilibrium Equations of theExpandable Process

According to the research literature of relevant shellstructures [31ndash35] assuming that the expansion cone isexpanded uniformly and is considered as a quasi-staticprocess the force on the expandable cone is shown inFigure 3

e geometric parameters in Figure 3 include the initialinner diameter r0 the initial wall thickness t0 the innerdiameter after expansion r1 and the wall thickness afterexpansion t1 e main parameters of the expandable conein Figure 3(b) include the cone height H and the cone angleα If the hanger body reaches a stable condition during theexpansion the expansion cone is in a state of mechanicalequilibrium the forces include the contact pressure qm

between the expandable cone and the expandable tube andthe friction force f and the expandable force F were appliedto the expandable cone

e lateral area of the expandable cone can be obtainedfrom the geometric relationship in the figure

2 Shock and Vibration

A π r21 minus r20( 1113857

sin α (1)

According to the axial mechanical equilibrium of theexpandable cone we obtain

F qmA sin α + μqmA cos α (2)

e force distribution of the hanger is shown in Figure 4e expandable tube is longitudinally sectioned along its Zaxis for mechanical analysis

According to the mechanical equilibrium equation onthe Z axis we obtain axial principal stress σz

σz r21 minus r20( 1113857(1 + μ cot α)qm

r1 + t1( 11138572

minus r21 (3)

According to the geometric relationship the componentof the friction on the x-axis is established as

Fx(f) r1 + r0( 1113857Hf tan α (4)

According to the mechanical equilibrium in the x-axiswe obtain

σθ r1 + r0( 1113857(1 minus μ tan α)qm

t0 + t1 (5)

Considering that the tensile deformation of the metal isthe Hollomon relationship between the true stress and thetrue strain in the stage of uniform plastic deformation weobtain

σ Kεn (6)

where σ is the true stress K is the hardening coefficient ε isthe true strain and n is the hardening index

As σθ σr and σz are the principal stresses andσθ gt σr gt σz the equivalent stress of the microelement isobtained according to the Mises yield criterion

σθ minus σz 115σeqv (7)

e pressure of the expandable fluid is obtained bycombining formulas (3)ndash(7)

P 115Kεn r1 minus r0( 1113857 t0 + t1( 1113857 2r1 + t1( 1113857t1(1 + μ cot α)

2r1 + t1( 1113857t1(1 minus μ tan α) minus r1 minus r0( 1113857 t0 + t1( 1113857(1 + μ cot α)1113858 1113859r21 (8)

where

0211

Expandable cone

Expandable tube

Rubber cylinder Mandrel

Outer casingPressure relief sleeve

Figure 1 Structure of the expansion portion of the expansion liner hanger

Metal convex collar

Hanger body

1

2

3

4

5

1

23

45

6

7

89

10

Expandable cone

Rubber cylinder

Figure 2 Hanger components of expandable liner hanger

Shock and Vibration 3

qm 115Kεn t0 + t1( 1113857 2r1 + t1( 1113857t1

r1 + r0( 1113857 2r1 + t1( 1113857t1(1 minus μ tan α) minus r1 minus r0( 1113857 t1 + t0( 1113857(1 + μ cot α)1113858 1113859 (9)

4 Numerical Simulation of ExpandableLiner Hanger

41 Finite Element Mechanical Model e expansion de-formation of the expandable liner hanger covers the plasticdeformation of the metal the compression of rubber ma-terials and multiple contacts which are considered as acomplex nonlinear problem and cannot be calculated withtraditional analytical methods e literature research showsthat the research on the expansion mechanism and calcu-lation on parameters of the expandable liner hanger with the

FE software is feasible [36 37] Considering that the outercasing the expandable tube and the expandable cone arecircumferential parts with respect to the central axis theboundary conditions and loads are symmetrical about thecenter axis and in order to save the time of the calculationan axisymmetric model of the expandable liner hanger isestablished e expandable cone is made of a material withhigh rigidity and strength and is regarded as a rigid bodywhen establishing the FE model as shown in Figure 5 In thefinite element model element type of expansion tube rubbercylinder and outer casing is CAX4R e number of

t P r1

α

r0

(a)

Hαl

r0

qm

μqm

F r1

(b)

Figure 3 Mechanical equilibrium model of expansion inside the hanger

Z

Y

Xf

qm

t1r1

r0 t0

σZ

σr

σ θ

Figure 4 Distribution of forces applied to the expandable tube


expansion tube grids is 1450 the number of rubber cylindergrids is 3256 and the number of outer casing grids is 1600eboundary conditions and loads are set as follows the ex-pansion tube and outer casing are fixed axially and thedownward velocity of 05ms is applied to the expansion cone

42 Geometric Parameters and Material Parameters of theModel e size of hanger is φ2445mmtimesφ1778mm theouter diameter φ204mm the inner diameter φ179mm therubber cylinder length 300mm the rubber cylinder wallthickness 36mm the expandable cone outer diameterφ190mm the length of expandable plastic deformation part2300mm and the outer casing diameter φ2445mm Somematerial parameters of the components are shown in Ta-bles 1 and 2

e rubber cylinder is made of modified nitrile rubbere MooneyndashRivlin model is used to describe the super-elasticity of the rubber cylinder with Mooney constants C01and C10 and the incompressibility ratio D1

e relationship among the elastic modulus E and theshear modulus G and the rubber material constant isexpressed as follows [37]

G 2 C10 + C01( 1113857

E 6 C10 + C01( 1113857(10)

5 Finite Element Calculation Result

e expansion rate of the hanger body the expansion forcepushing the expandable cone to move downward and thehang force aremainmechanical parameters in the study of theexpandable liner hanger [38ndash51] e visualization module inFE software is used to obtain parameters such as the contactstress between the rubber cylinder and the outer casing thecounter force of the expandable cone and the radial ex-pansion displacement of the expandable tube and indirectlycalculate the minimum hydraulic thrust the hang force etc

51 Expansion Rate of the LinerHanger Body e expansionrate of the liner hanger is an index determining the plasticdeformation of the material of the expandable tube and the

available space inside the hanger and the casing It refers tothe ratio of the difference between the diameter after ex-pansion and the diameter before expansion to the diameterbefore expansion e formula is written as follows

δ D1 minus D

D (11)

where D1 is the diameter after expansion of the expandabletube and D is the diameter before expansion of the ex-pandable tube

e radial displacement cloud diagram of the expand-able liner hanger after expansion is shown in Figure 6 andthe maximum radial displacement of the hanger body is757mm As the model is axisymmetric the expansion valueof the expandable body is 1514mm e size of the hangertube is 204mm and according to formula (11) the ex-pansion rate is 74

Figure 7 shows the relation between the radial dis-placement of the expandable tube inner wall and the axialpath of the expandable tube e five rubber cylinders areaxially equally spaced by the metal convex collar on theexpandable tube (Figure 2) which causes five cyclic dis-placement variation during the expansion

52 Calculation of Expansion Pressure e expansion forceis the axial driving force applied to the expandable coneduring the expansion operation It is the basic parameter forthe expansion deformation of the hanger body and is also theraw data for the design of the expansion structure eexpansion force is mainly composed of two parts one isovercoming the friction of the contact surfaces and anotheris internal energy consuming the internal unevendeformation

e expansion force is the basis for selecting the groundpressure equipment e expansion force directly deter-mines whether the pressure equipment can continuouslymove the expandable cone downward to push the ex-pandable tube to expand and deform With the post-processing in FE software the expansion force of theexpandable cone along the axial path is obtained when theexpandable cone moves downward (Figure 8) During theexpansion the expansion force does not vary uniformly butgradually increases in stages

FF

Expansion cone

Expansion tube

Casing

Rubber cylinder

Figure 5 e FE model of expandable liner hanger

Table 1 Metal material parameters

Structurename

Density(kgm3)

Youngrsquosmodulus(MPa)

Poissonrsquosratio

Yieldstrength(MPa)

Expandablebody 7800 207000 0264 530

Outercasing 7850 207000 028 860

Table 2 Nitrile rubber parameters

C10 (MPa) C01 (MPa) D1

184 049 00214


Taking the maximum value 352 kN of axial counter forceFmax in Figure 8 as the basis for calculating maximal ex-pansion pressure Pmax where Se is the area of pressureaction

Pmax Fmax

Se

(12)

e hydraulic pressure for continuous downwardmovement of the expandable cone is 18MPa So the groundpressure equipment is required to provide the hydraulicpressure 18MPa to expand the expandable liner hanger epressure capacity of Chinarsquos field operation ground pipemeets the requirements for pressurization

53 Analysis of Equivalent Stress During the expansion thehanger body is subjected to mechanical internal compres-sion force which causes a large plastic deformation Figure 9shows the equivalent stress generated on the hanger bodyduring the expansion e maximum equivalent stressreaches 530MPa which exceeds the yield strength of thehanger body As the body is deformed the hanger is closelyattached to the inner wall of the outer casing by compressingthe rubber cylinder after the expansion Figure 10 shows theresidual stress generated on the inner wall of the hanger

body after the expansionemetal convex collars placed onthe outer wall of the hanger body at equal intervals cause thecyclic variation in residual stress axially

54CalculationofHangForce e hang force is a parametercharacterizing the mechanical properties of the expandablehanger e hang force consists of two parts the first is thefriction force generated on the rubber cylinders squeezedinto the annulus between the hanger and the upper casingdue to plastic deformation of the expandable pipe and thesecond is the hang force generated by the metal convexcollars which contact the outer casing and are embedded inthe inner wall of the outer casing during the expansion eformula for the hang force is as follows

FT FR + FM (13)

where FT is the total hang forceFR is the hang forcegenerated by the rubber cylinder and FM is the hang forcegenerated by metal convex collars

Outer casing

Rubber cylinderExpandable cone

Axial path ofexpandable

tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01

Figure 6 Radial displacement cloud diagram of the expandable liner hanger after expansion

219118261095 14607303650

Axial path of expandable tube inner wall (mm)

012345678

Expa

nsio

n di

spla

cem

ent (

mm

)

Figure 7 Relation between the radial displacement of the ex-pandable tube inner wall and the axial path of the expandable tube

2400800 1200 200016004000Axial displacement of expandable cone (mm)

0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)

Figure 8 Expandable force generated on the expansion coneduring the expansion


541 Hang Force Generated by the Rubber Cylinder econtact stress between the inner wall of each rubber cylinderand the expandable tube and that between the outer wall ofeach rubber cylinder and the outer casing are calculated by FEnumerical simulation e rubber cylinder is made ofhyperelastic material and it is elongated and deformed axiallyafter radial compression and deformatione axial extensionpart of the rubber cylinder goes beyond the metal collar edeformed rubber cylinder is divided into two parts the firstpart is the contact region with the inner wall of the casing andanother is the noncontact region (shown in Figures 11ndash15)e data points along the axial path a-b are averaged to obtainthe average contact stress value on the rubber cylinder wall(Figures 11ndash15) e hang force of a single rubber cylinder iscalculated with the friction on the inner and outer walls

As the rubber cylinder has a relatively small thicknessthe effective contact area between the inner and outer wallsof rubber cylinder is considered to be uniform before andafter compression and the inner wall is considered as theeffective contact area

FiR 2fR times Ao times σiR (14)

where FiR is the hang force of the i rubber cylinder fR is thefriction coefficient between the rubber cylinder and the innerand outer tube walls fR 015 in this paper [30] AO is theeffective contact area between the rubber cylinder and theinner and outer tube walls mm2 and σiR is the averagecontact stress of the inner and outer walls of the i rubbercylinder MPa

e hang force generated on each rubber cylinder iscalculated according to the FE analysis and formula (14) asshown in Figure 16 e hang force gradually increases fromthe rubber cylinder 1 to the rubber cylinder 5 and the totalhang force of five rubber cylinders is FR 1112 kN

542 Hang Force Generated by Metal Convex Collar Inaddition to the compression deformation of the rubbercylinder the radial expansion deformation of metal convexcollar and the contact with the inner wall of outer casing

S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)

+5328e + 02+4884e + 02+4440e + 02+3996e + 02+3552e + 02+3108e + 02+2664e + 02+2220e + 02+1776e + 02+1332e + 02+8881e + 01+4441e + 01+1126e ndash 02

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


Figure 9 Cloud diagram of equivalent stress generated on the hanger body during the expansion

0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)

2000 220016001400 1800400 1000800600200 12000Hanger body length (mm)

Figure 10 Residual stresses generated on the inner wall of the hanger body after expansion


Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)

0 50 100 150Along axial path A-B on the outer wall

of rubber cylinder 1 (mm)

200 250 300

y = ndash1E ndash 08X4 + 7E ndash 06X3 ndash00014X2 + 00826X + 10759

(b)

Figure 11 Contact stress variation in the rubber cylinder 1 and the average contact stress along the axial path on the outer wall of the rubbercylinder during the expansion

Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300

y = ndash2E ndash 08X4 + 9E ndash 06X3

ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)



result in the hang force Similarly the hang force on themetal convex collar is calculated with the method of cal-culating the hang force on the rubber cylinders

In order to fix five rubber cylinders with equal intervalsfive sets (10) of metal convex collars are processed on thehanger body As the metal collar has the small size a re-gional mesh refinement (Figure 17) shows the metal convexcollar grid and deformation diagram e contact stressvalue is extracted and averaged along the axial contact pathc-d between the metal convex collar and the casing (Fig-ure 18) e average contact stress generated on the metalcollars ① ③ ⑤ ⑦ and ⑨ has a low value and thatgenerated on the metal collars ② ④ ⑥ ⑧ and ⑩ has ahigh value

e contact axial deformation length of the convex collaris 18mm the average diameter after deformation is

207mm and the hang force of each metal convex collar iscalculated with the formula as follows

Fim fm times Amσim (15)

where fm is the friction coefficient between the metal collarand the casing fm 025 [31] Am is the effective contact areabetween the metal collar and the casing wall mm2 σim is theaverage contact stress between the metal collar and the casingwall MPa shown in Figure 18 and Fim is the hang forcegenerated on the metal convex collar kN shown in Figure 19

Fm 111394410

i1Fim 597 kN (16)

According to formulas (13)ndash(16) the total hang force of theexpandable liner hanger is F 1112 kN+597 kN 11717 kN

Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

y = ndash2E ndash 08X4 + 9E ndash 06X3 ndash00019X2 + 01328X + 10116C

onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)

4 52 31Rubber cylinder number

Figure 16 Hang force generated by each rubber cylinder

(a)

Convex collar

(b)

CndashD

(c)

Figure 17 Metal convex collar grid and contact deformation diagram (a) metal convex collar 3D diagram (b) metal convex collar grid (c)metal convex collar deformation diagram

020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)

1054 8 96 7321Metal convex collar number

Figure 18 Average contact stress on each metal collar

02468

101214

Han

g fo

rce (

kN)

93 4 5 7 82 6 101Metal convex collar number

Figure 19 Hang force generated on each metal collar


6 Expansion Test

After assembling the processed parts of the expansion linerhanger shown in Figure 20 support it with the experimentaldismounting frame and keep it in a horizontal position(shown in Figure 21)e dimension parameters of key partsare as follows the outside diameter of the expansion cone is190mm the inside diameter is 143mm and the length is121mm e outer diameter of the liner hanger body is204mm the inner diameter is 179mm and the expandedlength is 4500mm Conduct a low-pressure test (3MPa) for5 minutes to ensure that the sealing performance of eachsealing component is sufficient After the low-pressure testprepare for the expansion test

61 Test Step

(1) Use a pressure pump to slowly build the pressurethrough low displacement

(2) Boosting the pressure to 19MPa the expansion conebegins to move forward and the hanger body beginsto expand and seal

(3) e expansion cone is moved to the position of thepressure relief sleeve e pressure relief sleeve ispushed the pin is sheared the pressure relief hole isexposed the pressure drops and the expansionoperation is completed

62 Test Results

(1) e expansion pressure in the test was 19MPa andthe expansion pressure obtained by finite elementanalysis was 18MPa with the expansion pressureerror of 53

(2) By measuring the diameter of the hanger body afterexpansion and before expansion the expansion rateis 71 By comparing the results of finite elementanalysis the expansion rate error is 4

Figure 20 Expansion cone assembly

Experimental dismounting frame

Expansion liner hanger

Figure 21 Expansion liner hanger supported with the experimental dismounting frame and kept it in a horizontal position

Rubber cylinder

Outer casing

Hanger body

Figure 22 Rubber cylinder is completely squeezed between the hanger body and the outer casing


(3) After expansion the rubber cylinder is completelysqueezed between the hanger body and the outercasing so as to realize sealing and suspension asshown in Figure 22

7 Conclusion

In this paper a FE simulation mechanical model of theOslash2445mmtimesOslash1778m expandable liner hanger is estab-lished e conclusions are as follows

(1) When the hanger body is expanded its radial dis-placement and the residual stress of the inner wallvary in 5 cycles due to that the five rubber cylindersare axially equally spaced by the metal convex collaron the expandable tube and the expansion ratio ofthe expandable tube is 74

(2) e variation in the expansion force is indirectlycalculated with the axial reaction force applied to anexpandable cone e expansion force does not varyuniformly but gradually increases in stages ehydraulic pressure required for pushing the ex-pandable cone to move down is 18MPa

(3) According to the contact stress generated on fiverubber cylinders and the contact stress generated onten metal collars the total hang force has beencalculated which exceeds 1000 kN and meets thedesign requirements

(4) e FE mechanical analysis results of the expandableliner hanger were in good agreement with the ex-periment results in this study which provide im-portant mechanical parameters for well completionwith expandable liner hanger

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors are grateful to the support from the NationalNatural Science Foundation of China (no 51574198)

References

[1] K HMa DW Zhu L R Ma et al ldquoAdvances in liner hangertechniques in deep wells outside Chinardquo Petroleum DrillingTechniques vol 33 no 5 pp 52ndash55 2005

[2] L R Ma Z H Guo X D Jiang et al ldquoDesign and applicationof a new packer liner-hangerrdquo Petroleum Drilling Techniquesvol 34 no 5 pp 54ndash56 2006

[3] K H Ma ldquoA consideration on the development of linerhanger technologies in Chinardquo Oil Drilling amp ProductionTechnology vol 30 no 6 pp 108ndash112 2008

[4] Y S Chen ldquoDevelopment and application of a new double-slip HPHT liner hangerrdquo Natural Gas Industry vol 30 no 8pp 48ndash50 2010

[5] C L Ruan L Y Feng J F Zhang et al ldquoDevelopment andapplication of liner hanger embedded with slipsrdquo ChinaPetroleum Machinery vol 40 no 08 pp 15ndash18 2012

[6] J H Cao and B Cao ldquoAnalysis on application and benefit oftechnology of drilling liner hangerrdquo Journal of Tianjin Vo-cational Institutes vol 15 no 11 pp 60ndash64 2013

[7] K Dupal ldquoExpandable tubular technology a year of drillingcase historiesrdquo JPT Journal of Petroleum Technology vol 53no 5 pp 32ndash34+77 2002

[8] Z H Guo L R Ma H M Zhu et al ldquoNew development ofoverseas expandable liner hangerrdquo Drilling Petroleum Tech-niques vol 36 no 5 pp 66ndash69 2008

[9] M Tang Z Z Teng X T Ning et al Research and Ap-plication of Expandable Liner Hanger Oil Drilling ampPro-duction Technology Society of Petroleum Engineers vol 31no 6 London UK 2009

[10] H Q Yao L Y Ren Z H Guo et al ldquoExpansionmaterial andexpansion approach of expandable liner hangerrdquo DrillingPetroleum Techniques vol 38 no 1 pp 72ndash76 2010

[11] D W Zhu ldquoDevelopment of overseas novel drilling toolrdquoSino-Global Energy vol 16 no 4 pp 41ndash46 2011

[12] F Liu X C Luo R X Wang et al ldquoForce analysis of ex-pandable tube for expandable linerrdquo Hanger Oil FieldEquipment vol 41 no 1 pp 30ndash32 2012

[13] G S Liu Y P Huang B Jia et al ldquoApplication of expandableliner hangerrdquo Petrochemical Industry Technology no 7 2017

[14] X G Bao ldquoApplication and effect of expandable liner hangerin exploratory wellrdquo Petrochemical Industry Technologyvol 25 no 6 2018

[15] T Walvekar and A T Jackson ldquoExpandable technologyimproves reliability of conventional liner hanger systemsrdquo inProceedings of the IADCSPE Drilling Conference Miami FLUSA February 2006

[16] J W Williford and P E Smith ldquoExpandable liner hangerresolves sealing problems and improves integrity in linercompletion scenariosrdquo in Proceedings of the Production andOperations Symposium Oklahoma OK USA March 2007

[17] A T Jackson B Watson L K Moran et al ldquoDevelopment ofan expandable liner hanger with increased annular flow areardquoin Proceedings of the SPE Annual Technical Conference andExhibition Denver CO USA September 2008

[18] C M Montanez S L Jensen D A De Clute-Melancon et alldquoExpandable liner hanger drill-in capability provides reliablesolution for north sea case historyrdquo in Proceedings of the SPEOffshore Europe Oil and Gas Conference and ExhibitionAberdeen UK September 2009

[19] S Huang Q Chen W Han et al ldquoSuccessful application ofexpandable liner hanger in ht sidetracking well completion acase study in liaohe oilfield Chinardquo in Proceedings of the SPEIATMI Asia Pacific Oil amp Gas Conference and ExhibitionJakarta Indonesia October 2017

[20] S Y Cui Y T Shao Y Wang et al ldquoResearch on expandableliner hangerrdquo Exploration Engineering (Rock amp Soil Drillingand Tunneling) vol 46 no 02 pp 65ndash70 2019

[21] M Lobo A Singhal C Lang et al ldquoA case study of usingexpandable liner hangers advanced cementation techniques forERDwells in Indiardquo in Proceedings of the SPE Annual TechnicalConference and Exhibition Houston TX USA 2015

[22] Y R He and H B Zhu ldquoExpansion sand screen developmentand field testrdquo Petroleum Drilling Techniques vol 39 no 03pp 106ndash109 2011


[23] R Yang L Luo C L Shen et al ldquoApplication of the ex-pandable liner hanger in horizontal wells of zhetybai oil fieldin Kazakhstanrdquo Xinjiang Oil amp Gas vol 10 no 4 pp 87ndash892014

[24] Y Chen X Peng H Yu et al ldquoMechanical performanceexperiments on rock and cement casing residual stressevaluation in the thermal recovery well based on thermal-structure couplingrdquo Energy Exploration amp Exploitationvol 35 no 5 pp 591ndash608 2017

[25] Y Chen T Liang X Peng et al ldquoCalculation and analysis ofthe first interface micro-gaps of the thermal productionwellsrdquo Advances in Mechanical Engineering vol 9 no 2pp 1ndash14 2017

[26] Q Bai Q Liu D J Li et al ldquoFinite element analysis andexperimental study of copper suspension system for ex-pandable tubularrdquo Journal of Plasticity Engineering vol 25no 1 pp 92ndash99 2018

[27] Z A Cai and C F Li ldquoFinite element analysis of the ex-pansion of the twinning induced plasticity steel solid ex-pandable tuberdquo Chinese Journal of Engineering Design vol 20no 3 pp 236ndash242 2013

[28] E Liu W Li H Cai and S Peng ldquoFormation mechanism oftrailing oil in product oil pipelinerdquo Processes vol 7 no 1 p 72019

[29] S Peng Q Chen C Zheng and E Liu ldquoAnalysis of particledeposition in a new-type rectifying plate system during shalegas extractionrdquo Energy Science amp Engineering vol 8 no 3pp 702ndash717 2020

[30] Z Su E Liu Y Xu P Xie C Shang and Q Zhu ldquoFlow fieldand noise characteristics of manifold in natural gas trans-portation stationrdquo Oil amp Gas Science and Technology-RevueDrsquoIFP Energies Nouvelles vol 74 p 70 2019

[31] J J Chen D J Li Q Bai et al ldquoCalculation model of ex-pansion force based on strain hardening behavior of ex-pandable tubularrdquo Transaction of Materials and HeatTreatment vol 38 no 8 pp 151ndash158 2017

[32] S Asghar M N Naeem M Hussain et al ldquoPrediction andassessment of nonlocal natural frequencies of DWCNTs vi-bration analysisrdquo Computers and Concrete vol 25 no 2pp 133ndash144 2020

[33] M Taj M Arfan M Hussain et al ldquoNon-local orthotropicelastic shell model for vibration analysis of protein micro-tubulesrdquo Computers and Concrete vol 25 no 3 pp 245ndash2532020

[34] M Hussain M N Naeem A Tounsi and M Taj ldquoNonlocaleffect on the vibration of armchair and zigzag SWCNTs withbending rigidityrdquo Advances in Nano Research vol 7 no 6pp 431ndash442 2019

[35] B Karami M Janghorban and A Tounsi ldquoOn pre-stressedfunctionally graded anisotropic nanoshell in magnetic fieldrdquoJournal of the Brazil Ian Society of Mechanical Sciences andEngineering vol 41 no 11 pp 494ndash511 2019

[36] P Liu X H Xie W J Tong et al ldquoFinite element analysis andcalculation of outer rubber module of expansion tuberdquo OilField Equipment vol 46 no 1 pp 17ndash21 2017

[37] C F Li Z G Peng Y Q Wang et al Nonlinear Finite El-ement Analysis and Application Examples of ExpandableTubular China Petrochemical Press Beijing China 2012

[38] G M Qin D S He L P Zhang et al ldquoAnalysis on defor-mation force of solid expandable tubular based on ANSYSLS-DYNArdquo Oil Field Equipment vol 38 no 8 pp 9ndash11 2009

[39] Q B Wang K Gao L Jiang et al ldquoNumerical simulation ofsolid expandable tubular based on ABAQUSrdquo Oil FieldEquipment vol 45 no 2 pp 54ndash57 2016

[40] T Li F P Li L X Zhang et al ldquoSimulative study of drivingforce for solid expandable tubularrdquo Oil Field Equipmentvol 42 no 2 pp 39ndash42 2013

[41] B Yue K C Man D Walters et al Tension and ExpansionAnalysis of Pipe-In-Pipe Risers Part B Finite Element Mod-eling International Society of Offshore and Polar EngineersAnchorage Alaska 2017

[42] E R Malta and C d A Martins ldquoFinite element analysis offlexible pipes under compression influence of the frictioncoefficientrdquo in Proceeedings of the 35th ASME InternationalConference on Ocean Offshore and Arctic Engineering BusanSouth Korea December 2016

[43] R Provasi F G Toni and C de A Martins ldquoA frictionalcontact element for flexible pipe modeling with finite macroelementsrdquo Journal of Offshore Mechanics and Arctic Engi-neering-Transactions of the ASME vol 140 no 5 Article ID061601 2018

[44] X L Yang ldquoExperimental study of hanging force of solidexpandable tubular based on metal sealrdquo Oil Field Equipmentvol 44 no 8 2015

[45] L Gu F Han M Liu et al ldquoResearch on improving the loadcapacity of expandable liner hangerrdquo Petroleum DrillingTechniques vol 44 no 4 2014

[46] J Zhang and J Xie ldquoEffect of reservoirrsquos permeability andporosity on the performance of cellular development modelfor enhanced geothermal systemrdquo Renewable Energy vol 148pp 824ndash838 2020

[47] J Zhang H Zhang and L Zhang ldquoBuckling response analysisof buried steel pipe under multiple explosive loadingsrdquoJournal of Pipeline Systems Engineering and Practice vol 11no 2 Article ID 040200 2020

[48] H Patel S Salehi R Ahmed and C Teodoriu ldquoReview ofelastomer seal assemblies in oil amp gas wells performanceevaluation failure mechanisms and gaps in industry stan-dardsrdquo Journal of Petroleum Science and Engineering vol 179pp 1046ndash1062 2019

[49] A Zhong DMoeller and SMaddux ldquoDevelopment of a highhang weight expandable liner hanger for deepwater appli-cationsrdquo in Proceedings of the Offshore Technology ConferenceHouston TX USA May 2017

[50] H Patel and S Salehi ldquoInvestigation of elastomer seal en-ergization implications for conventional and expandablehanger assemblyrdquo Energies vol 12 no 4 p 763 2019

[51] S A Al-Hiddabi T Pervez S Z Qamar and etal ldquoAnalyticalmodel of elastomer seal performance in oil wellsrdquo AppliedMathematical Modelling vol 39 pp 236ndash2848 2015


the anticorrosion performance e expandable liner hangerhas no pressure-transmitting hole which eliminates thepotential leakage When the liner is blocked the liner hangertool rotates the liner and circulates the killing fluids whichincreases the tripping in depth of the liner and does notcause physical damage on the upper casing Meanwhile theexpandable hanger has no external attachments such as slipsand cones which reduces the annular space occupied by thehangers thereby increasing the available space inside thehanger and liner and improving the inside flow

e expandable liner hangers have been applied inmore than 2000 well-times overseas [16ndash21] which lowerthe potential down hole risk of the conventional linerhanger and the poor sealing quality of the overlappedsection and improves the stability of the liner cementationsystem e Drilling Engineering Research Institute ofCNPC XIBU Drilling Engineering Company Limitedstarted the development of ELH-1 expandable linerhanger in 2011 [18] and completed trial production in-door evaluation etc of the φ245mm timesφ178mm ex-pandable liner hanger prototype In 2014 the expandablehanger developed by SINOPEC Shengli Oilfield DrillingInstitute helped the Jidong Oilfield realize the first side-tracking in φ1778 mm cased-hole and achieve the hang ofφ1397 mm on the φ1778 mm intermediate casing withthe expandable liner hanger [22] In 2015 the DrillingResearch Institute of the CNPC Great Wall DrillingCompany developed a new type metal collar expandableliner hanger which realizes hang and sealing of the linerthrough the metal interference contact after the ex-pandable tube expansion and is characterized by stronghang and sealing performance high temperature resis-tance short overlapped section and large drift diametere sealing pressure difference greater than 40MPa thetemperature resistance higher than 350degC and the hangforce greater than 1000 kN meet the sealing performancerequirements in the heavy oil thermal recovery [23]However these studies did not take an effective method tosystematically discuss and evaluate the mechanicalproperties and suspension capacity of expansion linerhanger e drilling technology in China goes to deepwells and ultradeep wells where the probability of drillingcomplex formations increases and the down hole con-ditions are more complicated which needs the researchand development of expandable liner hangers e ex-pandable liner hanger ensures implementation of Chinarsquostrategy of exploring deep oil and gas resources and en-hances Chinarsquos deep drilling capability

Obtaining the mechanical parameters of the expansionliner hanger can effectively guide the research and devel-opment of expandable liner hangers and expansion com-pletion operation At present physical experiment and finiteelement simulation are the most commonly used methods toobtain mechanical parameters However the physical ex-periment method has a high cost a long cycle and morepersonnel involved With the rapid development of thecomputer hardware and the finite element (FE) theory[24ndash30] the computer simulation is applied in various in-dustries e simulation in the FE software is used as a tool

for pretest verification and posttest optimization whichgreatly reduces the test period and the test cost

2 Structure and Principle of ExpandableLiner Hanger

Structure of the expansion portion of the expansion linerhanger designed in this study mainly includes the ex-pandable cone assembly the rubber cylinder (5 pieces) theexpandable tube the outer casing the mandrel and thepressure relief sleeve as shown in Figure 1emodels of theexpandable cone 5 rubber cylinders the expandable tubeand 10 metal convex collars are shown in Figure 2 eexpandable structure is set as a state before expansion in theouter casing e rubber cylinders are equally spaced on theexpandable tube and are axially separated and positioned bythe metal collar

Working principle of the expansion liner hanger thehigh-pressure fluid enters the internal part of the ex-pandable liner hanger forming a large pressure differenceon both sides of the expandable cone and pushing theexpandable cone to move down As the outer diameter ofthe expandable cone is larger than the inner diameter ofthe hanger body cone radially expands the hanger bodyand thus the plastically deformed hanger body is firmlyattached to the inner wall of the outer casing When thecone moves down to the designed position the pressurerelief sleeve is pushed the pin is sheared the pressurerelief hole is exposed the pressure of the expandable fluidis released and the expansion operation is completed ehang force consists of two parts the first is the frictionforce generated by the rubber cylinder squeezed into theannulus between the hanger and the upper casing due toplastic deformation of the expandable tube and thesecond is the contact force due to contacting deformationbetween the convex metal collar and the outer casingduring the expansion

3 Mechanical Equilibrium Equations of theExpandable Process

According to the research literature of relevant shellstructures [31ndash35] assuming that the expansion cone isexpanded uniformly and is considered as a quasi-staticprocess the force on the expandable cone is shown inFigure 3

e geometric parameters in Figure 3 include the initialinner diameter r0 the initial wall thickness t0 the innerdiameter after expansion r1 and the wall thickness afterexpansion t1 e main parameters of the expandable conein Figure 3(b) include the cone height H and the cone angleα If the hanger body reaches a stable condition during theexpansion the expansion cone is in a state of mechanicalequilibrium the forces include the contact pressure qm

between the expandable cone and the expandable tube andthe friction force f and the expandable force F were appliedto the expandable cone

e lateral area of the expandable cone can be obtainedfrom the geometric relationship in the figure


A π r21 minus r20( 1113857

sin α (1)






r1 + t1( 11138572

minus r21 (3)


Fx(f) r1 + r0( 1113857Hf tan α (4)



t0 + t1 (5)


σ Kεn (6)







where

0211

Expandable cone

Expandable tube




Metal convex collar

Hanger body

1

2

3

4

5

1

23

45

6

7

89

10

Expandable cone

Rubber cylinder



qm 115Kεn t0 + t1( 1113857 2r1 + t1( 1113857t1





t P r1

α

r0

(a)

Hαl

r0

qm

μqm

F r1

(b)


Z

Y

Xf

qm

t1r1

r0 t0

σZ

σr

σ θ







G 2 C10 + C01( 1113857

E 6 C10 + C01( 1113857(10)





δ D1 minus D

D (11)






FF

Expansion cone

Expansion tube

Casing

Rubber cylinder



Structurename

Density(kgm3)


Poissonrsquosratio

Yieldstrength(MPa)


Outercasing 7850 207000 028 860



184 049 00214



Pmax Fmax

Se

(12)





FT FR + FM (13)


Outer casing



tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01


219118261095 14607303650


012345678

Expa

nsio

n di

spla

cem

ent (

mm

)



0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)









S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References






















































A π r21 minus r20( 1113857

sin α (1)






r1 + t1( 11138572

minus r21 (3)


Fx(f) r1 + r0( 1113857Hf tan α (4)



t0 + t1 (5)


σ Kεn (6)







where

0211

Expandable cone

Expandable tube




Metal convex collar

Hanger body

1

2

3

4

5

1

23

45

6

7

89

10

Expandable cone

Rubber cylinder



qm 115Kεn t0 + t1( 1113857 2r1 + t1( 1113857t1





t P r1

α

r0

(a)

Hαl

r0

qm

μqm

F r1

(b)


Z

Y

Xf

qm

t1r1

r0 t0

σZ

σr

σ θ







G 2 C10 + C01( 1113857

E 6 C10 + C01( 1113857(10)





δ D1 minus D

D (11)






FF

Expansion cone

Expansion tube

Casing

Rubber cylinder



Structurename

Density(kgm3)


Poissonrsquosratio

Yieldstrength(MPa)


Outercasing 7850 207000 028 860



184 049 00214



Pmax Fmax

Se

(12)





FT FR + FM (13)


Outer casing



tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01


219118261095 14607303650


012345678

Expa

nsio

n di

spla

cem

ent (

mm

)



0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)









S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References






















































qm 115Kεn t0 + t1( 1113857 2r1 + t1( 1113857t1





t P r1

α

r0

(a)

Hαl

r0

qm

μqm

F r1

(b)


Z

Y

Xf

qm

t1r1

r0 t0

σZ

σr

σ θ







G 2 C10 + C01( 1113857

E 6 C10 + C01( 1113857(10)





δ D1 minus D

D (11)






FF

Expansion cone

Expansion tube

Casing

Rubber cylinder



Structurename

Density(kgm3)


Poissonrsquosratio

Yieldstrength(MPa)


Outercasing 7850 207000 028 860



184 049 00214



Pmax Fmax

Se

(12)





FT FR + FM (13)


Outer casing



tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01


219118261095 14607303650


012345678

Expa

nsio

n di

spla

cem

ent (

mm

)



0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)









S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References


























































G 2 C10 + C01( 1113857

E 6 C10 + C01( 1113857(10)





δ D1 minus D

D (11)






FF

Expansion cone

Expansion tube

Casing

Rubber cylinder



Structurename

Density(kgm3)


Poissonrsquosratio

Yieldstrength(MPa)


Outercasing 7850 207000 028 860



184 049 00214



Pmax Fmax

Se

(12)





FT FR + FM (13)


Outer casing



tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01


219118261095 14607303650


012345678

Expa

nsio

n di

spla

cem

ent (

mm

)



0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)









S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References























































Pmax Fmax

Se

(12)





FT FR + FM (13)


Outer casing



tube inner wall

Hanger body

U U1 (mm)+7569e + 00

+6861e + 00

+6153e + 00

+5445e + 00

+4737e + 00

+4030e + 00

+3322e + 00

+2614e + 00

+1906e + 00

+1198e + 00

+4903e ndash 01

ndash2176e ndash 01

ndash9254e ndash 01


219118261095 14607303650


012345678

Expa

nsio

n di

spla

cem

ent (

mm

)



0

50

100

150

200

250

300

350

400

Axi

al co

unte

rforc

e of e

xpan

dabl

e con

e (kN

)









S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References




























































S Mises MPa(Avg 75)

+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00+0000e + 00

S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)


S Mises MPa(Avg 75)



0

100

200

300

400

500

600

Resid

ual stress o

f hanger

body in

ner w

all (MPa

)




Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References






















































Contactregion

Noncontactregion

B

A

(a)

16141210

86420

Con

tact

stre

ss (M

Pa)



200 250 300


(b)


Contactregion

Noncontactregion

B

A

(a)

Con

tact

stre

ss (M

Pa)



200 250 300


ndash 00016X2 + 0097X + 10684

201816141210

86420

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300

Con

tact

stre

ss (M

Pa)


ndash 00024X2 + 01562X + 96215

15

10

5

0

(b)









Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References




























































Fm 111394410

i1Fim 597 kN (16)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


ndash 00027X2 + 01817X + 91858Con

tact

stre

ss (M

Pa)

15

20

0

10

5

(b)


Contactregion

Noncontactregion

B

A

(a)



200 250 300


onta

ct st

ress

(MPa

)

02

101214161820

468

(b)



210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References






















































210

215

220

225

230

Han

g fo

rce (

kN)



(a)

Convex collar

(b)

CndashD

(c)


020406080

100120140160180

Ave

rage

cont

act s

tres

s (M

Pa)



02468

101214

Han

g fo

rce (

kN)




6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References






















































6 Expansion Test


61 Test Step




62 Test Results







Rubber cylinder

Outer casing

Hanger body




7 Conclusion






Data Availability




Acknowledgments


References























































7 Conclusion






Data Availability




Acknowledgments


References






















































InvestigationofMechanicalNumericalSimulationandExpansion ...Liner Hanger Structure of the expansion...

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Transcript of InvestigationofMechanicalNumericalSimulationandExpansion ...Liner Hanger Structure of the expansion...