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PREDICTING PIPELINE Duane DeGeer C-FER Technologies Edmonton, Alberta, Canada ABSTRACT Much research has been performed over the past twenty- five years to refine our basic understanding of tubular stability, which includes bifurcation, imperfect systems, factors influencing tubular stability and post-buckling behaviour. Tubular instability resulting from load combinations is not a trivial topic, particularly when inelastic material behaviour occurs. Many influencing factors must be considered when attempting to understand (and predict) the onset of instability. Many existing collapse predictive methods are either simplistic or involve advanced plasticity or finite element methods. Simplistic methods are typically semi-empirical, and contain a degree of uncertainty resulting in conservative collapse predictions. Nonetheless, they are generally considered satisfactory for design purposes. Advanced methods normally involve high-end calculations using specialized software programs that might not be available for general use. Therefore, a relatively easy-to-use method that accurately predicts the actual collapse resistance is, in many cases, the most desirable option. This paper presents a collapse predictive methodology, developed from a variety of research projects performed over the last fifteen years. The prediction method, which can easily be entered into a spreadsheet program, is applicable to most forms of tubular members, including pipelines. Applicable load combinations include external pressure, axial tension and bending. An overview of the parameters influencing collapse resistance is also provided, including manufacturing history, material modelling, and tubular geometry and imperfections. Also presented is a summary of accuracy of the method to predict some test results. The test database largely contains results of collapse tests on tubular members subject to only external pressure, and axial tension with external pressure. The adaptation of the method to include external pressure with bending is summarized, and the accuracy of the prediction method is demonstrated by predicting the results of the Oman- COLLAPSE RESISTANCE J.J. (Roger) Cheng University of Alberta Edmonton, Alberta, Canada India and Blue Stream pipeline collapse test programs, and comparing these predictions with those of other well known methodologies. INTRODUCTION The development of petroleum reserves in high pressure high temperature wells, well completions in Arctic environments and deepwater offshore developments have motivated a significant amount of tubular collapse strength research over the last quarter century. In the oil and gas industry, the efforts of the American Petroleum Institute (API) have resulted in several empirically-based guides and bulletins for designing tubular sections subject to external pressure (API RP 2A 1993; API RP 2T 1997; API Bui 5C3 1994; and API Bui 2U 1987). Others have developed relationships for predicting downhole tubular collapse (Tamano et al. 1982; Pattillo and Huang 1982; and Avakov 1998). Many other similar methods have also been developed to predict the strength of tubular members, including tangent modulus and reduced modulus approaches summarized in Galambos (1998), offshore structural applications (Ellinas et al. 1984), and deepwater pipelines (Langner 1984; API RP 1111 1999; de Winter et al. 1985; Yeh and Kyriakides 1986; and DNV OS-FlOl 2000). All of the above cited prediction methods involve differing techniques to account for the effects of the various materials, geometry and loading conditions that could conceivably be imposed on a tubular member. All appear to be suitable for their intended purpose and applicable within their intended scope of assessment. It has been found, however, that some of the methods accurately predict accompanying experimental results, but do not necessarily accurately predict the test results obtained from other work. Several factors contribute to these inconsistencies, including experimental variations and interpretation of results obtained. It is not the intent of this paper to evaluate the details of each of the above methods, but rather to present a method that has attempted to include most Copyright © 2000 by ASME IPC2000-235 Downloaded From: https://proceedings.asmedigitalcollection.asme.org/ on 04/29/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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Page 1: Predicting Pipeline Collapse Resistance - Proceedings · PDF filePREDICTING PIPELINE Duane DeGeer C-FER Technologies Edmonton, Alberta, Canada ... RP 2A 1993; API RP 2T 1997; API Bui

PREDICTING PIPELINE

Duane DeGeer C-FER Technologies

Edmonton, Alberta, Canada

ABSTRACT Much research has been performed over the past twenty-

five years to refine our basic understanding of tubular stability, which includes bifurcation, imperfect systems, factors influencing tubular stability and post-buckling behaviour. Tubular instability resulting from load combinations is not a trivial topic, particularly when inelastic material behaviour occurs. Many influencing factors must be considered when attempting to understand (and predict) the onset of instability.

Many existing collapse predictive methods are either simplistic or involve advanced plasticity or finite element methods. Simplistic methods are typically semi-empirical, and contain a degree of uncertainty resulting in conservative collapse predictions. Nonetheless, they are generally considered satisfactory for design purposes. Advanced methods normally involve high-end calculations using specialized software programs that might not be available for general use. Therefore, a relatively easy-to-use method that accurately predicts the actual collapse resistance is, in many cases, the most desirable option.

This paper presents a collapse predictive methodology, developed from a variety of research projects performed over the last fifteen years. The prediction method, which can easily be entered into a spreadsheet program, is applicable to most forms of tubular members, including pipelines. Applicable load combinations include external pressure, axial tension and bending. An overview of the parameters influencing collapse resistance is also provided, including manufacturing history, material modelling, and tubular geometry and imperfections. Also presented is a summary of accuracy of the method to predict some test results. The test database largely contains results of collapse tests on tubular members subject to only external pressure, and axial tension with external pressure. The adaptation of the method to include external pressure with bending is summarized, and the accuracy of the prediction method is demonstrated by predicting the results of the Oman-

COLLAPSE RESISTANCE

J.J. (Roger) Cheng University of Alberta

Edmonton, Alberta, Canada

India and Blue Stream pipeline collapse test programs, and comparing these predictions with those of other well known methodologies.

INTRODUCTION The development of petroleum reserves in high pressure

high temperature wells, well completions in Arctic environments and deepwater offshore developments have motivated a significant amount of tubular collapse strength research over the last quarter century. In the oil and gas industry, the efforts of the American Petroleum Institute (API) have resulted in several empirically-based guides and bulletins for designing tubular sections subject to external pressure (API RP 2A 1993; API RP 2T 1997; API Bui 5C3 1994; and API Bui 2U 1987). Others have developed relationships for predicting downhole tubular collapse (Tamano et al. 1982; Pattillo and Huang 1982; and Avakov 1998). Many other similar methods have also been developed to predict the strength of tubular members, including tangent modulus and reduced modulus approaches summarized in Galambos (1998), offshore structural applications (Ellinas et al. 1984), and deepwater pipelines (Langner 1984; API RP 1111 1999; de Winter et al. 1985; Yeh and Kyriakides 1986; and DNV OS-FlOl 2000).

All of the above cited prediction methods involve differing techniques to account for the effects of the various materials, geometry and loading conditions that could conceivably be imposed on a tubular member. All appear to be suitable for their intended purpose and applicable within their intended scope of assessment. It has been found, however, that some of the methods accurately predict accompanying experimental results, but do not necessarily accurately predict the test results obtained from other work. Several factors contribute to these inconsistencies, including experimental variations and interpretation of results obtained. It is not the intent of this paper to evaluate the details of each of the above methods, but rather to present a method that has attempted to include most

Copyright © 2000 by ASME

IPC2000-235

Downloaded From: https://proceedings.asmedigitalcollection.asme.org/ on 04/29/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Page 2: Predicting Pipeline Collapse Resistance - Proceedings · PDF filePREDICTING PIPELINE Duane DeGeer C-FER Technologies Edmonton, Alberta, Canada ... RP 2A 1993; API RP 2T 1997; API Bui

factors affecting tubular collapse strength and to compare its predictive accuracy to two other methods. The limitations of the proposed method will also be cited in the following sections. Much of the background work and assessments performed in development of the prediction method have been summarized in DeGeer (1991).

The following sections review the factors known to influence collapse strength, present the prediction method, identify the data sources used to substantiate the prediction method, and provide the predictive results of two notable major collapse test programs recently undertaken.

FACTORS INFLUENCING COLLAPSE RESISTANCE Factors affecting collapse resistance of tubular members

have been summarized below into four categories: geometric factors, material factors, manufacturing processes, and loads and loading sequence.

Geometric Factors The geometry of a tubular member can be defined by its

diameter, wall thickness and variations of these parameters normally regarded as imperfections.

Diameter and wall thickness factors play an integral role in determining the collapse strength of a tubular member. The classical elastic buckling equation, given by Timoshenko and Gere (1961), as

Pe =" 2 E

•[1] d - v / ) L i

identifies external collapse pressure as being dependent on diameter and wall thickness to the third power. Diameter and wall thickness are perhaps the most significant factors influencing collapse strength.

Two factors also commonly considered in determining collapse strength are imperfections in diameter and wall thickness, i.e., ovality and wall thickness eccentricity.

Ovality accounts for the out-of-roundness of a pipeline and eccentricity defines the variation in wall thickness around the circumference of a pipeline. Depending on the magnitude of geometric imperfections present, pipeline collapse strength can be reduced by as much as 75%.

Methods of defining ovality for long pipes usually assume that the initial out-of-roundness is similar in form to the assumed buckling mode shape - that of an oval. Although there are some variations, ovality is commonly defined as:

^ _ ^max ^min • [2]

Note that, within the confines of this definition, the effect of ovality on collapsc strength is not independent of the magnitude of other factors. Mimura et al. (1987). Pattillo and Huang (1985). and Madhavan (1988) have all suggested that the

effect of ovality depends on pipeline D/t and the magnitude of axial load present.

Equations that define wall thickness eccentricity usually assume a similar form as that of ovality:

[3]

Pipeline collapse strength is not normally influenced to a large degree by wall thickness eccentricity. For UOE and ERW line pipe, which are manufactured from plate material, practical wall thickness variations are quite small. Collapse of seamless pipe, however, can be influenced by wall thickness eccentricity, as variations in wall thickness are greater.

Material Factors When pipeline collapse occurs in the material elastic range,

material stiffness and Poisson's ratio are the only material parameters to consider, as summarized in Equation [1]. For many pipelines, however, collapse occurs after some material yielding has initiated. In these cases, it is important to properly account for the inelastic behaviour of the material. Several material factors influence inelastic collapse strength, including yield strength, stiffness, anisotropy and the presence of residual stresses.

Three-dimensional constitutive relations can be used to define material behaviour. But for pipelines with a D!t ratio of greater than about 15, one can assume radial stresses in the pipe are negligible (Pattillo and Huang 1982), reducing the problem to a biaxially loaded condition (axial and circumferential). Historical experimental observations have shown that, for tubular members, the von Mises yield criterion provides a better fit to test data than the Tresca yield criterion. The von Mises criterion can be summarized as follows:

[4]

Material response can be modelled using an actual (or assumed) pipe stress-strain curve. To simplify matters one step further, an equation can be used to represent the actual stress-strain curve, such as a modified Ramberg and Osgood (1943) equation, as presented by Workman (1982):

£= — + E

0 . 0 0 5 - -crv

[5]

The actual pipe stress-strain curve can be used to benchmark the Ramberg-Osgood curve fitting procedure to determine <Ty E and n. In this manner, the pipe material response can be characterized by these three parameters. Some prediction methods conservatively use only material yield strength as the limiting material parameter, effectively assuming elastic-perfectly plastic material behaviour. Using the three parameters above provides some generality to material response, accounting for actual material behaviour. Indeed, if

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the material response is elastic-perfectly plastic, one needs to simply use a very high number for the parameter

The above formulations account for biaxially loaded conditions, as well as for material behaviour. As will be discussed below, however, a pipe may exhibit differing material behaviour in the axial and circumferential directions as a result of the pipe manufacture process. Material anisotropy has been accounted for by Yeh and Kyriakides (1986) and Madhavan (1988) by including reduction factors in the von Mises yield function:

o, =

f \ / \

2 I 1

l^e J CxCg +

St l^e J V " y • [6]

where Se is the ratio of the circumferential yield strength to the axial yield strength, and the pipe axial stress-strain curve is taken to represent material behaviour.

Others have accounted for material anisotropy by determining the actual properties in both directions and deriving an effective stress-strain curve that lies between the two curves, depending on the specific biaxial loading conditions.

The effect of residual stresses on tubular collapse has been discussed by numerous authors (Yeh and Kyriakides 1986; Simonen and Shippell 1982; Tokimasa and Tanaka 1986; Mimura et al. 1987; and Mehdizadeh 1975), with all suggesting that the presence of residual stresses tends to reduce collapse strength. However, Bai et al. (1993) report no significant reduction in collapse pressure on thick tubes with residual stresses up to a level of 50% of yield. And there are some instances where residual circumferential stresses may actually increase collapse strength.

Collapse strength gains or losses resulting from residual stresses depend on the specific residual stress distribution, and its magnitude, through the thickness of the pipe. When a pipe is externally pressured, the inner surface experiences the largest magnitude of circumferential compressive stress. If the through-thickness residual stress distribution is linear with compression on the inner surface, this internal compressive residual stress combines with the compressive stress from the application of external pressure, resulting in a higher than expected inner surface compression. Yielding will occur sooner, and subsequently reduce the pipe collapse strength. Alternatively, if the inner surface residual stress were tensile, one would assume a resulting increase in collapse strength.

Mimura et al. (1987) and Tokimasa and Tanaka (1986) have investigated the effect of residual stresses on casing collapse performance and have come up with an "optimum" residual stress - one that produces the greatest collapse resistance. This would occur when the entire thickness of the casing wall yields at the same instance. Their formula is given as:

ae.oP =

a

P

1 -kA

7/3 + 2 k2+kA •{1}

The optimal residual stress pattern would thus be a tensile stress on the inner surface of between 5% and 15% of the material proportional limit, and a compressive stress of the same value on the outer surface.

In terms of actual reductions in collapse strength, test and analytical results have shown that residual stress, as much as 50% compression on the inner surface of a pipe, reduces collapse resistance by 5% to 10%. Others have noted that this reduction may be as great as 40% (Mehdizadeh 1975).

Manufacturing Processes It has been found that the collapse strength of a pipeline

can be significantly affected by its manufacturing process. Typical larger diameter pipes are manufactured by a process known as UOE, where a long plate is formed into a circular shape, longitudinally welded, then radially plastically expanded (cold expanded) to achieve a uniform diameter. Kyriakides and Corona (1991) and Shoemaker (1984) provide good summaries of the effects this process has on reducing pipe circumferential compressive material strength. Williams and Elsea (1977) also provide a good summary of this reduction, which can be attributed to the Bauschinger effect. Basically, the cold expansion of the pipe reduces the pipe yield strength in hoop compression.

Williams and Elsea (1977) also discuss the beneficial effects of strain aging and thermal aging in recovering hoop compressive strength. This strength recovery has also been experimentally demonstrated in collapse tests performed for the proposed Oman-India pipeline (Stark and McKeehan 1995). Thermal aging investigative work on the Blue Stream prototype pipeline material has also been performed.

In some instances, pipe manufactured by the ERW process may be cold expanded, as well. In these cases, it can be expected that a similar reduction in circumferential yield strength would result. In other instances, however, ERW pipe may not be cold expanded. Reductions in circumferential compressive yield strength for non-cold expended ERW pipe have been observed to be in the order of only around 5%. DNV OS-FlOl (2000) uses a yield strength reduction factor of 0.93 and 0.85 to account for the UOE and UO (non-cold expanded pipe) manufacturing effects, respectively.

Also, for non-cold expanded pipe, residual stresses tend to be higher (as high as 50% of yield) than pipe that has been cold expanded. The cold expansion process tends to reduce pipe residual stresses.

Loads and Loading Sequence The effect of axial tension on collapse is relatively well

established and has been reported by many in the past. The effect of an axial tensile load can be considered in the von Mises yield stress formulation, effectively reducing the circumferential compressive yield strength. Depending on the magnitude of axial tension, this load can significantly reduce collapse strength. Figure 1 illustrates a typical axial tension-external pressure interaction diagram.

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Page 4: Predicting Pipeline Collapse Resistance - Proceedings · PDF filePREDICTING PIPELINE Duane DeGeer C-FER Technologies Edmonton, Alberta, Canada ... RP 2A 1993; API RP 2T 1997; API Bui

1 0.9 0.8 0.7

> 0.6

a 0.4 0.3 0.2 0.1

0

Figure 1 Effect of axial tension on collapse.

Interestingly, in one series of tests, pipe collapse has been demonstrated to be independent of initial axial tensile deformations. These tests were performed to assess the effect on an initial tensile strain on pipe collapse. As reported in DeGeer (1991), experimental results have shown that, even when the initial axial strain is as high as 4%, collapse strength is not reduced. Under a constant axial tensile deformation, the application of external pressure contributes Poisson tensile strains in the axial direction. The axial load required to maintain the fixed magnitude of axial deformation decreases and the material stiffness becomes elastic due to this axial tensile unloading. As the external pressure is applied, the effective stress imposed on the pipe material increases at a much slower rate due to the axial tensile unloading. The pressure causing collapse is thus much higher than initially anticipated.

The results of this one set of tests have quite a significant impact on the collapse strength of pipe systems that undergo large secondary loads, like thermal stresses and soil deformations. In some unique situations, a designer may be able to take advantage of this "apparent" increase in capacity.

In assessing the effect of load path dependency on pipes subject to axial tension and external pressure, the experimental results and analyses by Madhavan (1988) suggest pipe collapse is not significantly load path-dependent for tubes with lower ovalities. That is, the final collapse pressure is independent of whether tension is applied before pressure (T—>P), or pressure then tension (P—>7). This appears to be true for lower values of tension, but when the tension stress is greater than approximately 50% of the yield stress, the P-*T load path tends to give lower collapse pressures. This load path dependency under high axial tension is supported by Bai et al. (1993), who suggest the same load path dependency for tension stresses above 60% of yield. Also noted in Bai et al. is that the dependency is less for higher values of D/t.

The effect of bending on collapse pressure has been addressed by many in the past. Work by Ju and Kyriakides (1990), de Winter et al. (1985), and Langner (1984) has all demonstrated the reduction in collapse pressure due to the application of bending. Also shown in the above references, was the dependency of collapse on load path. The load path of pressure application followed by increasing bending (/>-ȣ) has been shown to result in lower collapse pressures, and the load path dependency appears to be greater for pipes with lower D/t ratio. Figure 2 illustrates these effects.

1.00

0.80

0.60 Q.

OL 0.40

0.20

0.00 0 10 20 30

Scr̂ Ey

Figure 2 Pressure-strain load path dependencies.

PREDICTION METHOD For the load combinations of external pressure and axial

tension, the prediction method considers only the load path of initial axially imposed tension load, followed by increasing external pressure to collapse. For the case of external pressure and bending, the method accounts for the more conservative loading path of initially applying external pressure, followed by increasing bending until collapse. The method does not consider a failure mode associated with local buckling due to bending (axial compressive instability); it only accounts for instability of the cross section due to high circumferential compressive stresses.

The primary advantages of the method are considered to be the ability to input a complete stress-strain curve via a Ramberg-Osgood equation, the ability to input two stress-strain curves (one axial and one circumferential) for the case of external pressure and bending, its ability to account for the decreased influence of initial ovality for members undergoing plastic collapse, and the ability to predict the bending capacity of a tubular member under external pressure and axial tension using just one methodology.

The method has been developed from the culmination of various previous methods, as described in the next sections.

0 0.25 0.5 0.75 1 <rx/cy

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External Pressure with or without Axial Tension

/ v = 4 P J [8]

where:

a = 1-0 .2— £ V 0.005

[ i - x ] . •[9]

Pc =71 2 E

E, =

?7 =

_L n

E + (Jy

a V 0.005 -E

V V""1)' - l

r i - v 2 " 1 y

e r £ s + 3 £ , i [ l - v 2 J 4 £

£ = S £

<re = ^ a j - ( 7 e a x + a 2x

pD On =-

2/

£ = — + E

o\ 0.005 ^

E

V Y

A • /

^ _ ^max ^min ^max ^min

^ m̂ax m̂in

.[10]

.[11]

.[12]

•[13]

.[14]

.[15]

• [16]

.[17]

•[18]

• [19]

The inputs for the analysis are the geometric parameters D, t, A and X; the material parameters crv, £ and n; and the axial tensile stress <TX. The effect of axial compressive stress is not considered in the prediction, as its effect on collapse has been shown as minimal, even for axial compressive stresses nearing 50% of yield (Ellinas et al. 1984; Stark and McKeehan 1995).

The effective stress-strain curve is to be modelled beforehand, and should account for the circumferential compressive properties, as well as the axial tensile properties if axial tension is very high. A Ramberg-Osgood fit to the stress-strain curve will determine the parameters cr„ £ and n. In the absence of an actual stress-strain curve, it is, in most cases, conservative to use the specified minimum yield stress (SMYS). Instances where this may not be conservative are when the

Bauschinger effect from the manufacturing process reduces the circumferential yield strength to less than the SMYS.

At present, the method is restricted to allowing only one effective stress-strain curve for axial tension and external pressure, and material anisotropy is thus addressed at the stress-strain modelling stage, prior to collapse calculations. The method, as presented, allows for the rational manipulation of the effective stress-strain curve to properly account for the differing material properties in the two directions. The method does not account for the effects of residual stresses, as there is evidence that its effect may be small for UOE pipe with a relatively low D/t (Bai et al. 1993). However, the effect of residual stresses can be accounted for by modifying the stress-strain curve prior to its input into the prediction method.

The approach for calculating the collapse pressure is summarized in the flow chart shown in Figure 3. The process for calculating pc is iterative, initiating with an estimate of the collapse pressure, performing the calculations and arriving at a calculated collapse pressure. The correct collapse pressure has been determined when the initial estimate is close to the calculated pressure, within a given tolerance, and subsequently multiplied by the imperfection parameter.

Figure 3 Prediction calculation process.

The method uses the plasticity factor, rj, and Poisson's ratio equations as reported in Gerard (1962). The formula for the imperfection parameter, a, can be found in Miller (1981), but has been modified to account for wall thickness eccentricity and the varying effect of initial ovality. The ovality term has been modified in recognition that its effect decreases as material inelastic behaviour progresses.

External Pressure with Bending Perhaps more relevant to the issue of deepwater pipeline

collapse is the combined loading of external pressure with bending. In many cases, this loading combination represents

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the most critical combination for pipeline collapse and occurs during initial pipeline installation.

The prediction given by de Winter et al. (1985) for pipelines subject to bending and external pressure has been shown to provide a good basis for predicting the critical maximum bending strain for a pipe under external pressure. The formula is:

-,1.5

ODtfi 1-0.75 \2

Pi

4 R' -S _P_ PV

- 0.75 / \ 2

P_ Py

V

•[20]

This formula is intended to predict the critical axial bending strain initiating circumferential compressive instability while under constant external pressure and increasing bending, and not in cases where, while under pressure, the pipeline buckles longitudinally due to high bending (axial compressive instability).

Modifications to this equation have been performed to improve its predictive accuracy. These modifications have been derived on the basis that, while the critical curvature a pipeline with isotropic, elastic-perfectly plastic material behaviour is relatively easy to obtain, the actual material properties of a pipeline rarely exhibit such material behaviour. The yield pressure term, py, has, therefore, been replaced with the collapse pressure term, pcr, which allows for the use of actual pipeline stress-strain behaviour.

Also, the material properties in the axial direction may vary significantly from those in the circumferential compressive direction. Using the pipeline axial material properties in the calculation of pcr will provide a good prediction for load combinations involving moderate levels of initially-applied external pressure. In these cases, effective material behaviour is largely influenced by the axial bending loads, as axial strains will be much larger than those in circumferential compression. However, in cases where the initially-applied external pressure is very close to the collapse pressure, a very small amount of bending will initiate collapse. In these cases, circumferential compressive loads largely influence material response, and the axial compressive stress-strain curve is appropriate for use.

This implies that py (or the newly substituted pcr) in Equation [20] will vary, depending on which load dominates effective material behaviour. A modification to the value to pcr, depending on the value of the initially-applied external pressure, has thus been derived to account for this effect. The following has been developed:

infi-(,>//>„, r " 0 7 ] Per' = Perl nPcrl ~ Pcr\ )e V ' I21 ] The resulting modified equation is thus:

ODt43 1 - 0 . 7 5

1.5

AR' 1 + V3 V f V o , / A \

The approach for predicting collapse due to external pressure and bending is to initially calculate pcrl and pcr2 using circumferential compressive and axial stress-strain curves, respectively, as input into the basic collapse prediction Equations [8] to [19]. pcr- and £„ are then calculated using Equations [21] and [22],

COMPARISON TO TEST RESULTS The development of the prediction method required

satisfactory validity from a database of experimental results. For the load combination of axial load and external pressure, the test results used for validation are publicly available, and include those reported in the following references:

• Edwards and Miller (1939) • Stuiver and Tomalin (1959) . Tamano etal. (1982) • Madhavan (1988) • DeGeer (1991) • Luft et al. (2000) The inclusion of bending in the prediction method has only

recently been added, with limited validation to experimental results obtained independently from the public domain. Results from the Oman India and Blue Stream collapse test programs have been used. Specific results for the Oman India testing are reported, but due to the proprietary nature of the Blue Stream results, only the accuracy of the prediction method has been reported. • •

External Pressure with or without Axial Tension The database of test results includes over 250 data points of

tubular members under external pressure only, and external pressure with tension. Specimens include line pipe, casing, small diameter tubes and coiled tubing. Figure 4 illustrates the predictive results in relation to the ratio of the axial tensile stress to the yield stress, c j ay. As displayed in this manner, the results demonstrate the increasingly high scatter as <jJ ay

exceeds 0.5. There are several reasons for the inaccuracy in this range. Some of the authors of the test results have reported errors due to a frictional restraint effect when axial loads are high. At incipient collapse, the axial deformations become large, and the seal surface on the specimen end cap chamber may extend onto the specimen, increasing axial frictional forces. Also, for larger diameter specimens, the rate of specimen axial elongation may exceed the capacity of the pump used to maintain axial load. This, of course, depends on the pump used, but maintaining a constant axial load is critical in obtaining reliable data. Even a small reduction in axial load

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will delay collapse, as the elastic axial unloading tends to maintain specimen stability. This was demonstrated in the constant axial strain tests reported in DeGeer (1991).

? -| 1.8 -1.6 -

•o © 1.4 -o 1.2 , T3 0) 1 a 53 0.8 J </> 0) H 0.6 -

0.4 -0.2 -

0

Dctapoints =251 OD/trcnge= 10-30 4rcnge = 0-2% X rcnge=0-4%

o,rcnge=67-900 MPa E rcrge = 72-221 GPa a,/c»ronge=0-0.94

Test/Predmscn = 1.02 Test/Predasv =18.0%

0.2 0.4 0.6 a*/cy

0.8

Figure 4 Pressure-tension predictive results.

Of course, there are also inherent limitations in the use of only one stress-strain curve to model both circumferential compression and axial tension in the prediction method itself. This is one area in which the method could be improved.

To illustrate the influence of OD/t, ovality and axial stress on collapse strength, Figure 5 plots the predictive variation in collapse strength for these parameters.

0 0 .2 0 .4 0 .6 0 .8 Oxfoy

Figure 5 Effect of OD/t, A and ox on collapse.

External Pressure with Bending The prediction method summarized above for bending and

external pressure has been used to predict the critical bending strain causing collapse of pipes proposed for the Oman-India and Blue Stream pipelines. Note that, as the results of the Blue Stream pipeline collapse test program are not yet publicly available, specific results have been removed. The results of

the external pressure only collapse tests f rom these test programs have also been included in this section.

The Oman-India full-scale pipeline collapse test program, which was performed at C-FER Technologies in Edmonton, Canada, was used as the primary data set. The specimens were 660mmOD, 41mmWT, grade X60 UOE linepipe.

8000

7000

«» 6000 a

| 5000 <D £ 4000

3000

2000

1000

i -

— — Presented Method AP11111 (1999)

. . - - - - DNV OS-FlOl (2000) o Oman India Test Data

— — Presented Method AP11111 (1999)

. . - - - - DNV OS-FlOl (2000) o Oman India Test Data

— — Presented Method AP11111 (1999)

. . - - - - DNV OS-FlOl (2000) o Oman India Test Data

0 0.5 1 1.5 2 Max. Bending Strain (%)

Figure 6 Oman-India pipeline predictive results.

Figure 6 presents the predictive results. The collapse equations found in API RP 1111 (1999) and DNV OS-FlOl (2000) have also been included for comparison. Predictive results in this figure are based on average material properties f rom the complete data set. For the API and DNV equations, the actual average yield stress was used rather than the SMYS. Also, because actual yield stress values were used, the DNV fabrication factor, afah, was assumed equal to unity. The following summarizes the predictive results:

Oman-India Test Data Predictions -Test/Predicted Ratios

Collapse Pressure -Bend

Oman-India Test Data Predictions -Test/Predicted Ratios mean cov mean cov Presented Method 1.01 * 0.82 22.1% AP11111 (1999) 0.96 1.11 11.2% DNV OS-F1Q1 (2000) 0.90 0.75 23.1%

* - only two data points were used

Similar results were obtained for the Blue Stream pipeline collapse test program, also performed at the C-FER Facility. The following table summarizes the predictive accuracy obtained for the Blue Stream tests (610mmOD, 32mmWT, grade X65 UOE linepipe):

Blue Stream Test Data Predictions -Test/Predicted Ratios

Collapse Pressure -Bend

Blue Stream Test Data Predictions -Test/Predicted Ratios mean cov mean cov Presented Method 1.00 3.3% 1.17 13.6% AP11111 (1999) 0.92 3.3% 1.19 14.9% DNV OS-F1Q1 (2000) 0.79 3.3% 0.76 14.2%

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The prediction results indicate that, while the collapse predictions are accurate, there is some variation in accuracy for the pressure-bend tests. Some of these variations are due to an averaging of material properties for all specimens, when some specimens had exhibited properties different from average. Also, the prediction method does not consider the orientation of the test specimen ovality with respect to the plane of bending. It would seem logical to assume that lower critical strain test results would be obtained for a pipe specimen in which the minimum diameter is located in the plane of bending.

SUMMARY An introduction to the factors affecting tubular collapse

strength has been provided to gain an understanding of the parameters normally considered in the development of collapse prediction methods. A method was then presented that allows for the accurate prediction of tubular collapse strength when subject to axial tension and external pressure. Modifications to this method were then presented in order to predict the critical bending strain causing collapse while under constant external pressure and increasing bending. The method was then used to predict the test results from both the Oman-India and Blue Stream ultra-deepwater pipeline collapse test programs. The predictive results have also been compared to the methods found in DNV OS-FlOl (2000) and API RP 1111 (1999).

Suggested improvements to the method include the use of two stress-strain curves for the load combination of axial tension and external pressure, and further validation of the method using more data for the load combination of external pressure and bending. In addition, the method is expected to adequately predict the collapse of tubular members subject to axial tension, external pressure and bending (T,P^>B), but proper benchmarking to test data is required.

NOMENCLATURE B = bending cov = coefficient of variation = standard deviation/mean D = average mean diameter, = OD-t Dm(ix = maximum diameter Dmtn = minimum diameter E = elastic modulus E = secant modulus E, = tangent modulus ID = average inside diameter k = ratio of ZD to OD, = ID/OD n = Ramberg-Osgood hardening parameter OD = average outside diameter P = external pressure P = applied external pressure Pc = collapse pressure for a pipe with no imperfections Per = collapse pressure Per = modified collapse pressure

Perl = collapse pressure using circumferential compressive material properties

Pcr2 = collapse pressure using axial compressive material properties

Pe = elastic collapse pressure Py = yield pressure R = mean pipe radius, = D/2 Se = ratio of circumferential yield to axial yield stress T = axial tension t = average wall thickness tmax = maximum wall thickness tftim = minimum wall thickness a = imperfection parameter Gfab = DNV OS-FlOl (2000) fabrication factor X = wall thickness eccentricity A = ovality £ = effective strain £cr = critical maximum bending strain while under

external pressure £y = yield strain = 0.5% 1 = plasticity factor V = Poisson's ratio, elastic or plastic Ve = elastic Poisson's ratio, = 0.28 VP = plastic Poisson's ratio, = 0.47 ae = effective stress

= stress at the proportional limit <yx = axial stress

°> = yield stress = stress at 0.5% strain

Oe = circumferential stress ae,op = optimum residual stress

REFERENCES API BUL 2U 1987. Bulletin on the Stability Design of

Cylindrical Shells. American Petroleum Institute Production Department, First Edition, May.

API BUL 5C3 1994. Bulletin on Formulas and Calculations for Casing, Tubing, Drill Pipe, and Line Pipe Properties. American Petroleum Institute, Sixth Edition.

API RP 1111 1999. Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design). American Petroleum Institute, Third Edition.

API RP 2A 1993. Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms. American Petroleum Institute, Twentieth Edition, July.

API RP 2T 1997. Recommended Practice for Planning, Designing, and Constructing Tension Leg Platforms. American Petroleum Institute, Second Edition, August.

Avakov, V. 1998. Collapse Data Analysis and Coiled Tubing Limits. SPE/IcoTA Coiled Tubing Roundtable, SPE 46004, Houston, pp. 43-49.

Bai, Y., Igland, R. and Moan, T. 1993. Tube Collapse Under Pressure, Tension and Bending Loads. Proceedings of the International Journal of Offshore and Polar Engineering, Vol. 3, No. 2, June.

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de Winter, P.E., Stark, J.J.B. and Witteveen, J. 1985. Shell Structures Stability and Strength, Ch. 7 - Collapse Behaviour of Submarine Pipelines. Elsevier Publishing.

DeGeer, D. 1991. Collapse Strength of Cylinders Subject to Axial Tension and External Pressure. Department of Civil Engineering, University of Alberta, Edmonton, Canada.

" D N V OS-FlOl 2000. Submarine Pipeline Systems. Det Norske Veritas Offshore Standard, January.

Edwards, S.H. and Miller, C.P. 1939. Discussion on the Effect of Combined Longitudinal Loading and External Pressure on the Strength of Oil-Well Casing. Drilling and Production Practice, American Petroleum Institute.

Ellinas, C.P., Supple, W.J. and Walker, A.C. 1984. Buckling of Offshore Structures. Granada Publishing.

Galambos, T.V. 1998. Guide to Stability Design Criteria for Metal Structures (Fifth Edition). John Wiley and Sons.

Gerard, G. 1962. Introduction to Structural Stability Theory. McGraw-Hill Book Company.

Ju, GT. and Kyriakides, S. 1990. Bifurcation Buckling Versus Limit load Instabilities of Elastic-Plastic Tubes Under Bending and External Pressure. Proceedings of the Offshore Mechanics and Arctic Engineering Conference (OMAE).

Kyriakides, S. and Corona, E. 1991. On the Effect of the UOE Manufacturing Process on the Collapse Pressure of Long Tubes. Proceedings of the 23rd Offshore Technology Conference, Houston, May, pp. 531-543.

Langner, C.G 1984. Design of Deepwater Pipelines. TNO-IWECO 30th Anniversary Symposium on Underwater Technology, The Netherlands, May.

Luft, H.B, Wright, R., Lallemand, F. and Kis, P. 2000. Development of Collapse Ratings for High Temperature and Pressure Coiled Tubing Applications. SPE 60736, presented at the SPE/ICoTA Coiled Tubing Roundtable, Houston, April.

Madhavan, R. 1988. On the Collapse of Long Thick-Walled Circular Tubes Under Biaxial Loading. Ph.D. Thesis, California Institute of Technology, California, 128 p.

Mehdizadeh, P. 1975. Casing Collapse Performance. Journal of Engineering for Industry, American Society of Mechanical Engineers, Paper 75-PET-41, pp. 1-8.

Miller, C.D. 1981. Buckling Design Methods for Steel Structures - A State of the Art. Second International Symposium on the Integrity of Offshore Structures, University of Glascow, Scotland, July, pp. 397-418.

Mimura, H., Tamano, T. and Mimaki, T. 1987. Finite Element Analysis of Collapse Strength of Casing. Nippon Steel Technical Report No. 34, July, pp. 62-69.

Pattillo, P.D. and Huang, N.C. 1982. The Effect of Axial Load on Casing Collapse. Journal of Petroleum Technology, Society of Petroleum Engineers, January, pp. 159-164.

Pattillo, P.D. and Huang, N.C. 1985. Collapse of Oil Well Casing with Ovality. Journal of Energy Resources Technology, American Society of Mechanical Engineers, 107, May.

Ramberg, W. and Osgood, W.B. 1943. Description of Stress-Strain Curves by Three Parameters. National Advisory Committee for Aeronautics, Technical Note 902, pp. 1-28.

Shoemaker, A.K. 1984. The Effects of Plate Stress-Strain Behavior and Pipemaking Variables on the Yield Strength of Large-Diameter DSAW Line Pipe. ASME Journal of Engineering Materials and Technology, Vol. 106, April.

Simonen, F.A. and Shippell, R.J. 1982. Collapse of Thick-Walled Cylinders Under External Pressure. Experimental Mechanics, February, pp. 41-48.

Stark, P.R. and McKeehan, D.S. 1995. Hydrostatic Collapse Research in Support of the Oman India Gas Pipeline. Proceedings of the 27th Annual Offshore Technology Conference, OTC 7705, Houston, May, pp. 105-120.

Stuiver, W. and Tomalin, P.F. 1959. The Failure of Tubes Under Combined External Pressure and Axial Load. Proceedings of the Society of Experimental Stress Analysis, 16 (2), pp. 39-48.

Tamano, T., Mimura, H. and Yanagimoto, S. 1982. Examination of Commercial Casing Collapse Strength Under Axial Loading. Proceedings of the First Offshore Mechanics/Arctic Engineering/Deepsea Systems Symposium, American Society of Mechanical Engineers, 1, pp. 113-118.

Timoshenko, S.P. and Gere, J.M. 1961. Theory of Elastic Stability (Second Edition). McGraw-Hill Book Company.

Tokimasa, K. and Tanaka, K. 1986. FEM Analysis of the Collapse Strength of a Tube. Journal of Pressure Vessel Technology, American Society of Mechanical Engineers, 108, May, pp. 158-164.

Williams, D.N. and Elsea, A.R. 1977. Studies of the Bauschinger Effect in Pipe Steels. American Gas Association NG-18 Report No. 108, April.

Workman, G. 1982. User's Guide for PIPEWALL. Applied Mechanics Incorporated, Columbus, Ohio, 19 p.

Yeh, M.K. and Kyriakides, S. 1986. On the Collapse of Inelastic Thick-Walled Tubes Under External Pressure. Journal of Energy Resources Technology, American Society of Mechanical Engineers, 108, March, pp. 35-47.

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