Stability Analysis of Casings during Plastic Deformation

SPE-170303-MS

Stability Analysis of Casings During Plastic Deformation

Nobuo Morita and Sogo Shiozawa, Waseda University

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Deepwater Drilling and Completions Conference held in Galveston, Texas, USA, 10–11 September 2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Multi-finger caliper logs obtained from the wells in the Gulf of Mexico and in the North Sea showedsignificant casing deformations, while they were still usable without losing integrity. The reason was thatmost of these casings were uniformly deformed without rupture or without kinks. The magnitude ofelongation and compression of these casings were 3 to 5% while the strains at the yield strength were0.3-0.5%. These observations indicate that casing design should include the steel properties beyond theyield strength while the API casing designcriterion is strictly based on the steel properties up to the yieldstrength.

Extension and compression casing tests were conducted from H-40 to V-150 casings up to failure byusing a 5000 kN loading machine. For compression tests, some casings were cemented within a larger pipeto prevent the lateral buckling simulating the in-situ confinement condition. The tests gave the followingresults:

1. Under extension tests, the casings were uniformly deformed after exceeding the yield strength. Theuniform deformation continued while the casing were stretched by 4 to 25% until non-uniformdeformation was induced.

2. The strain up to the peak strength was as large as 25% for H-40 casings while it was as small as4% for P-110 and higher grade of casings.

3. For compression tests, uniform compression continued exceeding the yield point. The uniformdeformation continued up to the peak strength which varied from 3% to 12% from V-150 to H-40casings. Both the cemented casings and short casings induced axisymmetric wrinkles (localbuckling) after uniform deformation.

4. The higher grade casings did not significantly increase the maximum strength after yielding whilelower grade casings increased the strength while being stretched or compressed uniformly afteryielding.

The analyses show that the casing failure observed in the fields can be explained from the casing failuretests beyond the yield points. The casings are uniformly deformed until the maximum load so that theyare usable up to the maximum strength without significant distortion. In the past, casing failures were triedto be mitigated by increasing the casing grade, however, increasing the grade sometimes deteriorated thecasing problems since a higher grade casing could not tolerate the significant stretch or compression once

they exceeded the yield stress. Selecting a proper grade and thickness of casings is the key for mitigatingcasing failure where the data of casing deformation beyond the yield strength are essential information forcasing designing using geomechanical models. This paper analyzed the casing deformation data of severalNorth Sea chalk reservoirs and Gulf of Mexico sandstone reservoirs provided by oil companies anddetermined the usable limit of casing deformation based on the laboratory and field measurements.

IntroductionThe most important casing properties include rated values of casings for axial tension and compression,burst pressure and collapse pressure. Among these casing loads, instabilities induced by large axialextension or compression force are investigated in this work. Fig.1 shows an example of the casing stretchand compression measured along a well in a reservoir of the Gulf of Mexico. The casings werecompressed or extended exceeding the yield stress and minor buckling was observed. Some casingsshowed radially symmetric buckling while other casings showed non-symmetric buckling.

To examine the buckling with more controlled conditions, two types of laboratory compression testswere conducted. One was uniaxial compression test without confining pressure and the other was axialcompression test surrounded by cement simulating a formation. These tests showed that casings slippedalong the cement-casing interface and were uniformly deformed along the axial direction with elastic andplastic deformations. However, if the strain exceeded a critical strain, a local buckling occurred resultingin sine wave wrinkles. No lateral buckling was observed due to the suppression of lateral movement.However, after exceeding the critical plastic strain, a local buckling occurred resulting in wrinkled surface.

To examine the rupture of casing due to extension, extension tests were conducted by using standardspecimens and pipe specimens. After exceeding the critical plastic strain, necks were formed by extension.

Figure 1—Casing joint length change along a well in a reservoir of Gulf of Mexico

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After necking or buckling, casings were ruptured or the deformation became very large so that itbecame an obstacle for various well operations. It was found that if the lateral displacement wassuppressed by cement and formation, a local buckling occurred at the axial strain approximately the sameas the uniaxial compression tests without confining pressure, although the confining stress should affectthe strain to some degree inducing the local buckling.

Empirical method to predict the critical strain and the limit load to induce abuckling for compression without lateral restraintExperimental setupA 5000 kN loading machine shown in Fig. 2 was used for applying the load until a significant bucklingwas observed.

The test samples were installed between the loading plates as shown in Fig. 2. The deformation wasmeasured with three devices: LVDTs installed in the loading machine, external LVDT displacementmeasurement devices and visual measurement with a video camera. The loading rate was 0.0787inch/minute.

Short and long casings were used for the compression tests as shown in Table 1. The short sampleswere used for measuring the stress strain curves up to the local buckling (wrinkling) and the long sampleswere for measuring the stress strain curves up to the lateral buckling as shown in Fig.3.

Empirical resultsFig.4 shows the stress strain curves measured for only the short casings listed in Table 1. The stress straincurves are similar for each grade of casings regardless of the thickness. Table 2 shows the peak stressesand deformations measured for all the casings. The longer casings started buckling earlier than the shorter

Figure 2—Shimazu 5000 kN loading machine and a test sample installed between loading plates

SPE-170303-MS 3

casings due to the lateral buckling. The strains at the peak stresses became smaller with the grade of thecasings. The stress strain curves of these steels are given in Figs.5 to 7. These curves were used forconstructing the constitutive relation of these steels.

Analyses of limit load of casingsNumerous publications are available to predict the limit load of tubular thin shells. For example, thetypical limit load is predicted by the following equations.

Elastic buckling:

(1)

where E,v�elastic modulus of steel.Based on the plastic deformation theory,

(2)

where Et, Es � tangential and secant Young’s modulus.Based on the incremental plastic theory,

(3)

However, these equations are applicable only if t/D is small or less than 1/30.

Table 1—Casing dimensions used for the compression tests

Grade OD in. ID in. t in. L in.

J-55 3.06 2.24 0.409 9.84

19.68

3.67 2.73 0.468 9.84

19.68

L-80 2.87 1.79 0.539 9.84

19.68

3.67 2.73 0.468 9.84

19.68

P-110 3.06 2.24 0.409 9.84

19.68

Figure 3—J-55 casing for local buckling (left) and J-55 for lateral buckling (right)

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Figure 4—Measured stress strain curves for short casings (note that true stress and true strain are used in this figure)

Table 2—Results of the compression tests (note that the nominal stress and nominal strain are used in this table)

Grade No Diameter/tLength

inchYoung’s modulus

psiYield stress

psiMaximum nominal stress

psiNominal strain atmaximum stress

J-55 1 A 7.48 9.84 2.80�107 70778 123734 �0.1311

2 64910 121916 �0.1184

1 19.68 67612 87568 �0.0482

2 67816 86385 �0.0420

3 64211 85889 �0.0410

1 B 7.83 9.84 65451 122086 �0.1125

2 66610 123324 �0.1094

1 19.68 64520 97073 �0.0634

2 65192 97443 �0.0703

L-80 1 A 5.33 9.84 95905 128998 �0.0466

2 92011 124772 �0.0405

1 19.68 89529 (88085) (�0.0270)

2 90462 (88511)? (�0.0255)

3 85283 (86729)? (�0.0286)

1 B 7.83 9.84 98088 128880 �0.0815

2 95275 127770 �0.0938

1 19.68 96981 106092 �0.0587

2 96822 107214 �0.0646

P-110 1 A 7.48 9.84 125376 154146 �0.0623

2 124057 157934 �0.0750

1 19.68 122120 (122651) (�0.0250)

2 118412 (119560) (�0.0281)

SPE-170303-MS 5

Normally, lateral buckling is common for the tubular goods used for oil and gas production since t/Dis smaller than 1/20. However, if the tubular goods are cemented in a formation, the lateral buckling isprevented. These tubular goods cemented in a formation uniformly expand or shrink with formationdeformation. However, if the stress exceeds a certain limit, they start buckling locally, resulting inwrinkled surface. When tubular strings with a thick wall induce the local buckling, the tangential Young’smodulus becomes close to zero, hence, Eqs.1 to 3 are not applicable.

An alternative method is to use an empirical method to determine the critical plastic strain and the limitload to initiate the buckling.

The critical strain which initiates a local buckling is determined by the following

(4)

It can be explicitly expressed by the following equation since the only term which determines thegeometry is t/D for a local buckling.

Figure 5—Stress strain curves of J-55 steel constructed from Fig.4

Figure 6—Stress strain curves of L-80 steel constructed from Fig.4

6 SPE-170303-MS

(5)

The ratio t/D is less than 0.15 for standard casings. Hence, the equation can be approximated bylinearizing the above equation:

(6)

If t/D ¡ 0, the critical strain inducing a buckling also approaches to zero, hence, another approxi-mation of Eq.6 is given by,

(7)

Eq.6 or Eq.7 is expressed in Fig.8 where the elastic buckling is induced only if t/D is very large.Fig.9 plots the strain at the peak stress for short casings. The strains at the peak stresses become smaller

for higher grade casings. To determine the equations for the maximum strength and the strain beforeinducing a local buckling, two plots are shown in Figs.10 and 11.

The test results gave the following coefficients for each grade of casing.For J-55,

Figure 7—Stress strain curves of P-110 steel constructed from Fig.4

Figure 8—Plastic and elastic critical buckling strain (elastic buckling occurs only for large D/t >>250)

SPE-170303-MS 7

(8)

For L-80,

(9)

For P-110,

(10)

The fitted curves for the maximum strain and maximum stress initiating the local buckling are givenas follows.

(11)

(12)

where �y (kpsi) is the actual yield strength for each casing.

Summary for the uniaxial compression tests

1. The short casings deform uniformly up to the peak stress when a local buckling starts appearing.2. The ratio of peak stress and yield strength are lower as the grade of the casings becomes higher.3. The maximum strain with uniform deformation is larger for a casing of a lower grade4. The long casings induce lateral buckling, where this phenomenon may not occur for the casings

installed in oil fields due to the lateral support from the formation.

Figure 9—Maximum strength and strain of the casings initiating a local buckling

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Critical strain initiating a localwrinkle for axial compression with lateral restraint

Experimental setupWithout lateral restraint, casings start buckling with a lower stress than the stress given by Eq.12. Table2 shows that all the casings with 19.685 inches in length induced lateral buckling so that the maximumstrengths were reduced more than the maximum strengths of the test samples with 9.84 inches in length.

Although the radial stress loaded from the formation is not significant compared with the axial stressinduced by the reservoir compaction, it is essential to conduct casing compression tests with formationsupport. The following tests were performed.

1. A casing with 19.685 inches in length was cemented with a large casing. This condition was themost extreme case where a casing was confined within a strong formation with cement betweenthe casing and formation. Note that the function of the external casing was a strong confinementsimulating a strong formation.

2. The internal casing was pushed by two hard cylindrical rods. A 5000 kN machine was used to loadon the casings.

3. The compressive deformation of the casing was measured by a video camera and the LVDTs.4. After testing, the changes of ID and length were measured.

Fig.12 shows the experimental set up and Fig.13 is the schematic view. A 5000 kN loading machinewas used to push the upper and lower cylindrical rods to compress the casings. Fig.12 also shows the crosssectional view after this experiment. The upper cylindrical rod was pushed down along the annular cementring within the confining casing simulating a hard formation. When the upper cylindrical rod was removedafter testing, the casing deformation was visible as shown in Fig.14a. The upper and lower rods slid alongthe cement inner surface to compress the casing.

Three casings were tested as shown in Table 3. These casings have the same dimensions as the casingstested for uniaxial compression without confinement. Figs.14a to 16c show the test results. All the testsshowed large axial stresses and the stresses monotonically increased. However, if the axial deformationexceeded a certain limit, a local buckling was induced. The strain which induced the local buckling was

Figure 10—(D&/t) vs. Yield stress Figure 11—(D/t)x (Max strength) vs. Yield stress

SPE-170303-MS 9

slightly smaller than those which were observed for casing compression tests without confinement. Thestrain to induce the local buckling was also smaller if the casing grade became higher.

Critical strain and stress initiating necking with axial extension

Experimental setupExtension tests were performed using the standard specimen and tubular samples for H-40, J-55, K-55,L-80, P-110, Q-125 and V-150. Table 4 shows the API specification of the test specimens.

Figure 12—Experimental set up and casing after testing – hard loading piston pushed into cemented casing

Figure 13—Compression test surrounded by cement simulating a tight formation

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Two types of test specimens were used, one for tubular shape and the other for standard shape as shownin Fig.17. Table 5 shows the size and type of specimens where c-*** indicates the standard specimen andp-*** indicates the pipe specimen. Figs.18 and 19 compare the stress strain curves for the two types ofspecimen. Comparing with the results of the two types of specimen, it was found that they gave the samestress strain results up to the maximum stress where the cross-sectional area began to decrease in alocalized region. After a neck was formed as the specimen elongated further, the stress strain curves varieddepending on the cross-sectional area of the specimens. The specimens were uniformly deformed up tothe ultimate strength. It means that casings were usable up to the ultimate strength even if they exceededthe yield strength. Since the deformation and the stress strain curves of both the standard and pipe

Figure 14a—Deformed casing J-55-1 with cement confinement (top and bottom views)

Table 3—Three casing samples used for confining tests

Grade Length in. OD in. ID in. t in. D/t

J-55-1 19.685 3.075 2.205 0.435 7.07

J-55-2 19.685 3.684 2.713 0.485 7.60

L-80-1 19.685 2.882 1.744 0.568 5.07

Figure 14b—Casing deformations J-55-1 (blue: cemented casing, red: short casing without confinement, green: a long casing without confinement)

SPE-170303-MS 11

specimens were identical up to the ultimate strength, only the stress strain curves up to the maximumstress were plotted in figures. Fig.20 shows the specimen after testing.

Figure 14c—ID change measured after test J-55-1

Figure 15a—Deformed casing J-55-2 with cement confinement (top and bottom views).

Figure 15b—Casing deformations J-55-2 (blue: cemented casing, red: short casing without confinement, green: a long casing without confinement)

12 SPE-170303-MS

Fig.21 and Table 6 show all the results of the extension tests. The results show:

A. H-40 to L-80 grade casings showed a constant yield stress right after yielding. The stress startedincreasing after the flat stress strain curves.

Figure 15c—ID change measured after test J-55-2

Figure 16a—Deformed casing L-80-1 with cement confinement (top and bottom views)

Figure 16b—Casing deformations L-80-1 (blue: cemented casing, red: short casing without confinement, green: a long casing without confinement)

SPE-170303-MS 13

B. The ratio of the ultimate strength to the yield strength decreased with grade.C. The strains at the ultimate strength were also significantly reduced with grade.

Analysis of the experimental results

Stress-strain curves The stress strain curves look different for compression and extension loadings. Themain reason is that the nominal stress is used where it is defined by the load divided by the specimen areawhere the area changes. The nominal strain is defined by the length change divided by the original length.The true stress and strains are defined as follows:

Figure 16c—ID change measured after test L-80-1

Table 4—API specification of the test specimens

API grade

Yield strength[psi]/[MPa]Tensile strength

[psi]/[MPa]Max

Elongation(%)Minimum Maximum

H-40 40000/276 80000/552 60000/414 30

J-55 55000/379 80000/552 75000/517 24

K-55 55000/379 80000/552 95000/655 20

L-80 80000/552 95000/655 95000/655 20

P-110 110000/758 140000/965 125000/862 15

Q-125 125000/862 150000/1034 135000/931 14

V-150 150000/1034 180000/1241 160000/1103 14

Figure 17—Standard and tubular specimens for extension tests

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(13)

(14)

Table 5—Size and type of specimens

GradeJIS

specification

Casing size

Width(inch)

Marker distance(inch)

Grade &specimen type

OD(inch)

ID(inch)

T(inch)

H-40 14B 2.36 1.89 0.236 0.492 1.969 c-H-40-A1

c-H-40-A2

14B 3.50 2.91 0.300 0.492 2.362 c-H-40-B1

c-H-40-B2

J-55 14C 2.756 2.244 0.256 7.874 p-J-55-2

p-J-55-3

14B 2.756 2.244 0.256 0.492 1.969 c-J-55-1

c-J-55-2

K-55 14B 4.216 3.374 0.421 0.787 3.346 c-K-55-1

L-80 14C2.244 1.795 0.224 7.874 p-L-80-1

p-L-80-2

p-L-80-3

14B 2.756 2.244 0.256 0.492 1.969 c-L-80-1

c-L-80-2

P-110 14B 4.512 3.610 0.452 0.787 3.346 c-P-110-1

c-P-110-2

Q-125 14B 4.535 3.630 0.452 0.787 3.346 c-Q-125-1

c-Q-125-2

V-150 14B 10.625 9.020 0.803 1.575 6.693 c-V-150-1

c-V-150-2

Figure 18—Comparison of stress strain curves for the pipe and the standard specimens (J-55)

SPE-170303-MS 15

The relation of the true strain and nominal strain is,

(15)

(16)

Figs.22 to 24 show the true stress strain curves. The short compression samples gave approximately thesame stress strain curves as the extension samples for J-55 and P-110. The short compression samplesgave similar stress strain curves to those for extension samples for L-80. This showed that while thespecimens were deformed uniformly, the stress strain curves were approximately the same for extensionand compression loadings. The long compression specimens with 19.68 inches in length started bucklinglaterally soon after yielding was initiated, hence, the load on samples declined with deformation. Theseresults show that the stress strain curves are the same for compression and extension until plastic bucklingoccurs. The constitutive relations can be obtained by adjusting the unknown coefficients with the stressstrain curves shown from Figs.22 to 24.

Figure 19—Comparison of stress strain curves for the pipe and the standard specimens (L-80)

Figure 20—Specimens after testing

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Ultimate strength and deformationBefore a neck is formed, casings are uniformly deformed. The ultimate strength is the stress forming aneck. Since casings can be used if the deformation is uniform, the ultimate strength and the strain at theultimate strength need to be determined for casing designing.

Fig.25 plots the ratio of ultimate true strength vs. yield stress for both compression and extension tests.The true strength is used in this plot. Fig.25 indicates that the local buckling for compression occurs withthe same tensile stress which induces a local necking. This phenomena occurs since the tested casingshave relatively a thick wall where casing buckling is induced locally due to the irregular materialdeformation after a critical strain. It does not occur for thin casings which start buckling with plastic,transition and elastic collapses. Fig.26 shows the strains at the ultimate strength for both compression andextension tests. These figures show that both the local buckling induced by compression and the neckinginduced by tension occur with the same magnitudes of deformation and stress. Figs.27 and 28 are plottedto find the equations to fit the empirical data. The fitted curves are given by

(17)

Figure 21—Stress strain curves up to the maximum stress for the standard specimens

SPE-170303-MS 17

Table 6—Test results (c-*** indicates standard specimen and p-*** indicates pipe specimen)

Grade and type Yield Stress(psi)Maximum

strength(psi)Strain at maxstrength (%)

Max strength /Yield strength

c-H-40-A1 45400 86400 14.3 1.90

c-H-40-A2 53500 91500 11.8 1.70

c-H-40-B1 39100 67800 26.3 1.73

c-H-40-B2 40400 65700 25.5 1.62

p-J-55-2 68600 96800 12.5 1.41

p-J-55-3 68700 96900 13.0 1.41

c-J-55-1 65500 95700 12.9 1.46

p-J-55-2 66500 95400 12.8 1.43

c-J-55-1 65500 95700 12.9 1.46

c-J-55-2 66500 95400 12.8 1.43

c-K-55-1 61200 93500 10.8 1.53

p-L-80-1 86200 95700 8.6 1.11

p-L-80-2 84500 95400 8.27 1.13

p-L-80-3 86400 96500 7.99 1.12

c-L-80-1 85000 97300 8.62 1.14

c-L-80-2 84300 96700 8.57 1.15

c-P-110-1 124400 132900 3.84 1.07

c-P-110-2 126300 133600 3.90 1.06

c-Q-125-1 134500 143600 4.74 1.07

c-Q-125-2 135100 143700 4.69 1.06

c-V-150-1 162900 169100 5.60 1.04

c-V-150-2 164200 170200 4.90 1.04

Figure 22—Comparison of extension and compression stress strain curves for J-55. (B for samples with larger thickness for compression tests, andJ-55-AL and BL are long samples).

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Figure 23—Comparison of extension and compression stress strain curves for L-80. (B for samples with larger thickness for compression tests, andL-80-AL and BL are long samples).

Figure 24—Comparison of extension and compression stress strain curves for P-110. (AL and BL are long samples for compression tests).

SPE-170303-MS 19

(18)

(stress unit:kpsi)

Minimum elongation of a casingAPI specification includes minimum elongation of specimen. It is defined by the elongation of 2 in.specimen. Normally, a casing set in a field induces at most one neck within one joint. Hence, the minimumelongation measured with a specimen must be corrected to the field elongation when it is applied to a realcasing.

The ultimate strain at casing rupture depends on the cross sectional area according to Barba’s law(Unwin 1903). The equation is given by the following form.

(19)

where Ao and Lo are the cross-sectional area and length of the two reference points of the specimen.This equation shows that the overall elongation of two reference points of a specimen Lo� is the sum ofuniform elongation �Lo and the neck elongation . Fig.30 shows the neck elongation vs. the square

root of the specimen cross sectional area. The slope � is equal to 0.4685 according to the figure. Hence,assuming one neck appears within one casing joint, the overall casing strain is given by the followingequation.

(20)

Considering the casings ranging from OD 4.5 inches and ID 4.09 inches to OD 20 inches and ID 18.73inches, the value of is at most 0.0192. Hence, the strain induced by a neck for each casing is at

Figure 25—Ratio of ultimate true strength vs. yield stress for both compression and extension tests

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Figure 26—Strain at the ultimate strength for both compression and extension tests

Figure 27—Ratio of maximum true strength vs. yield stress for extension tests

SPE-170303-MS 21

Figure 29—Comparison of elongation of a specimen and a casing

Figure 28—Strain at the ultimate strength for extension tests

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most 0.009. Table 7 shows expected elongation at tensile rupture for 27~30 ft casings assuming one neckappears per casing. As the table shows, the elongation due to one neck is negligibly small comparing withthe uniform elongation. Eq.21 is used to estimate the limit elongation.

(21)

(stress unit: kpsi)

Summary of the uniaxial extension tests

1. The casings deform uniformly up to the peak stress where a neck starts appearing.2. The ratio of peak stress and yield strength becomes lower as the grade of the casings becomes

higher.3. The maximum strain with uniform deformation is larger for a casing of a lower grade4. The stress strains are similar between compression and extension tests if true stress and strains are

used.5. If one neck appears within one casing joint, the elongation tolerated by one casing is less than one

half of the API minimum elongation.

Figure 30—Plot of neck elongation vs. SQRT(specimen area)

Table 7—Expected elongation at tensile rupture for 27~30 ft casing assuming one neck per one joint.

Grade H-40 H-55 K-55 L-80 P-110 Q-125 V-150

API minimum elongation % 30 24 20 20 15 14 14

Uniform elongation per one casing % 18.65 12.90 10.80 8.57 3.84 4.69 4.90

Total elongation per one casing % 19.95 13.80 11.70 9.47 4.74 5.59 5.80

SPE-170303-MS 23

Field ApplicationsNormally, a vertical borehole is very stable. Since it is very stable, we wonder whether a high grade casingis needed to prevent casing collapse or local sine-shape buckling. The following is an example fieldproblem for a highly compacting reservoir.

The reservoir conditions are given as follows:

Depth �10000 ft, reservoir thickness�200 ft, a vertical wellVertical stress gradient �v/depth�0.9 psi/ftHorizontal stress gradient �h/depth�0.84 psi/ftInitial pore pressure �6000 psi, depletion�2900 psiFormation�817 psi UCS sandstone (the stress strain curves are shown in Fig.31)Casing L-80, OD�6-5/8, ID�5.675 in.

Casing is set at the initial condition. Casings installed in a field are deformed with lateral restraint dueto the cementation to the formation. Fig.32 shows typical stresses around a casing after reservoirdepletion.

Fig.32 shows the stress in x direction after 2900 psi depletion. It is equivalent to the radial stress inx-coordinate and the tangential in y-coordinate. The radial compression stress increases from zero to thereservoir horizontal stress while the tangential compressive stress becomes high in the casing, low in thecement and reduces in the formation as the location departs from the rigid casing. Fig.32 also shows theaxial stress around a casing. The axial compressive stress in the casing is very high and exceeds the yieldstress. The axial stress in the cement is not high since the casing is set with the cement when the reservoirpressure is 6000 psi. Fig.32 shows that although the casing yields due to the high axial stress, the casingcollapse problem should not be induced since the horizontal confining stress is small.

Fig.33 shows the stress state and the plastic strain around a casing after 2900 psi reservoir pressuredepletion. The small plastic strain indicates that the casing starts yielding when the depletion becomes2900 psi. The confining radial stress loaded through the cement is still small although the cement andformation prevent lateral buckling.

Figs.34 and 35 show the stress state and the plastic strain around a casing after 5000 psi reservoirpressure depletion. The plastic strain is still small. It indicates that the casing is still usable after the

Figure 31—A set of stress strain curve for a sandstone with 817 psi UCS

24 SPE-170303-MS

depletion becomes 5000 psi according to the experimental results in this work. The confining radial stressloaded through the cement is still small although the cement and formation prevent lateral buckling.

This field example shows the following results.

1. A casing can stand far beyond the yield stress if the yielding is induced due to a high axial stress.The deformation is not excessive due to the strain hardening effect of the casing.

2. A L-80 casing is used for this field example. However, the casing can be down-graded furthersince the confining stress for a vertical well is relatively small.

3. However, the thickness must be maintained so that D/t � 10~12 to prevent axial local buckling.

Figure 32—Left figure: effective stress �x in x direction around a vertical casing with �h � �H after 2900 psi depletion. Right figure: effective stress�z around a vertical casing with �h � �H and 2900 psi depletion after installing the casing

Figure 33—Left: around a L-80 casing after 2900 psi depletion. Right: small plastic strain around a L-80 casing after 2900 psi depletion

SPE-170303-MS 25

Figure 35— around a L-80 casing after 5000 psi depletion and plastic strain around a L-80 casing after 5000 psi depletion

Figure 34—�z around a L-80 casing after 5000 psi depletion and �z around a L-80 casing after 5000 psi depletion

26 SPE-170303-MS

Conclusions

1. Under extension tests, the casings were uniformly deformed after exceeding the yield strength. Theuniform deformation continued while the casings were stretched by 4 to 25% until non-uniformdeformation was induced.

2. The strain up to the peak strength was as large as 25% for H-40 casings while it was as small as4% for P-110 and higher grade casings.

3. For compression tests, uniform compression continued exceeding the yield point. The uniformdeformation continued up to the peak strength which varied from 3% to 12% from V-150 to H-40casings. Both the cemented casings and short casings induced axisymmetric wrinkles (localbuckling) after uniform deformation.

4. A field example shows that a casing can stand far beyond the yield stress if the lateral confiningpressure is not large.

5. The higher grade casings did not significantly increase the maximum strength after yielding whilelower grade casings increased the strength while being stretched or compressed uniformly afteryielding. Hence, if the formation compaction or stretch is the cause of casing failure, reducing thecasing grade with a heavy duty casing (D/t�10) may solve the problem.

Nomenclatures

ao, a1 � polynomial coefficientsAo �original areaAafterdeformation �area after deformation

OD,ID,t,L � casing outer diameter, internal diameter, thickness and lengthE, � � elastic moduliEt, Es � tangential and secant Young’s modulusF �force

�deviatric stress

l, L, Lo � length(variable), casing length after deformation, initial casing lengthpout, pin �external and internal pressure on casing�, � �coefficients of neck strain�v, �H, �h �insitu stresses (vertical, maximum horizontal and minimum horizontal stresses)�x, �y, �z �insitu stresses (in the Cartesian coordinate))

�critical stress based on elastic limit, plastic deformation, and incremental plastictheory

�y �yield strength (kpsi)�true, �true �true stress and strain�, �critical �strain, critical strain

�critical strain (nominal strain)

�radial, �nominal �radial and nominal strains

ReferencesAllen, D.R. 1984. Development in Precision Casing Joint and Radioactive Measurements for Com-

paction Monitoring. SPE2684-PA.Adam, T. B. Jr., 1991. APPLIED DRILLING ENGNEERING. SPE EXTBOOK SERIES VOL 2.Furui, K., Fuh, G. and Morita, N. 2011. Casing and Screen Failure Analysis in Highly Compacting

Sandstone Fields. SPE146231.

SPE-170303-MS 27

Yasui, N. and Inoue, K. 1993. Plastic Analysis of the Post-Buckling Behavior of Axially CompressedCircular Tubes Journal of Structure Engineering No. 446.

Jinnai, Y., Kawakami, T. and Morita N. 2012. Failure Analysis and Mitigations of Casings Installedwithin Cap Rocks around Compacting Reservoir, July 2012, Journal of Japanese Petroleum Technology,pp 194–205.

Unwin, W.C. 1903. Tensile Tests of Mild Steel and the Relation of Elongation to the Size of the TestBar, Proc. Inst. Of Civil Engineers, 1903.

Morita, N. 2014. Elastic-Plastic Behavior and Limit Load Analysis of Casings, presented at theIADC/SPE Asia Pacific Drilling Technology Conference and Exhibition held in Bangkok, Thailand,25–27 August 2014.

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