An_Investigation_of_the_Effectiveness_of_ Hydrostatic_Testing

Risk Based and Limit State Design and Operation of Pipelines Aberdeen, October 1998

An Investigation of the Effectiveness of Hydrostatic Testing

in Improving Pipeline Reliability

Richard Espiner & Alan Edwards

BG Technology

Gas Research & Technology Centre

Loughborough

LE11 3GR

United Kingdom

SUMMARY

Hydrostatic pressure testing can be used to prove the integrity of a pipeline, either prior

to commissioning or for revalidation of an in-service pipeline.

Probabilistic limit state analysis is used here to investigate the impact of hydrostatic

testing on the overall reliability of an onshore gas transmission pipeline.

Hydrostatic pressure testing is shown to significantly reduce the probability of failure

from time dependent failure modes but has an insignificant effect on randomly occurring

failure modes such as external interference. The merits of the hydrostatic test are

discussed and compared with an alternative method for proving pipeline integrity.

INTRODUCTION

A pre-service hydrostatic test is usually conducted in order to prove the integrity of a

pipeline and remove defects which may fail in service. However, many pipeline failures

occur as a result of defects introduced during the life of the pipeline rather than those

present at the time of commissioning, which limits the value of a pre-service hydrostatic

test. This report describes a probabilistic limit state analysis to investigate the impact of


pre-service hydrostatic testing on each credible mode of failure of onshore gas

transmission pipelines and hence on the overall probability of failure of such a pipeline.

A hydrostatic test may also be conducted during the life of the pipeline in order to

demonstrate that the pipeline integrity has been maintained, i.e. there is still a ‘factor of

safety’ between the operating pressure and the failure pressure. The impact of in-

service hydrostatic testing on the probability of failure for each credible failure mode is

investigated using a probabilistic limit state approach and compared with an alternative

method of proving pipeline integrity (the magnetic flux leakage pig).

The failure modes considered in this study are bursting, external corrosion, fatigue crack

growth and external interference. Operating experience of onshore gas transmission

pipelines has shown that external interference and external corrosion are the most likely

modes of failure [1].

FAILURE PROBABILITY

Bursting

For simplicity and conservatism, bursting of the pipeline is assumed to occur if the hoop

stress exceeds the material yield strength at any point around the pipe circumference.

This will occur if the wall thickness is smaller than a critical value wc given by

wc(Pop,ry ) =PopR

ry (1)

where R is the pipeline radius and Pop is the operating pressure.

Both wall thickness, w, and yield strength, σy, are subject to uncertainty and are

assumed to be independent quantities. Bursting will occur if the combination of values of

w and σy at any point around the circumference lies within the failure space given by


0 [ ry [ ∞ (2)

0 [ w [ wc(Pop, ry)

Therefore the probability of failure of the pipeline, pf, found by integrating the product of

the independent probability density functions over the failure space, is given by

p f(Pop ) = ¶

0

∞

p(ry) ¶0

wc Pop,ry

p(w) dw dry (3)

where p(σy) and p(w) are the probability density functions of yield strength and wall

thickness respectively.

If the pipeline has previously been subjected to a hydrostatic test at pressure Ph without

failure, this additional information can be used to reduce the failure space as it is clear

that the wall thickness cannot be less than wc(Ph, σy). The reduced failure space is given

by

0 [ ry [ ∞ (4)

wc(Ph, ry) [ w [ wc(Pop, ry)

Therefore the conditional probability of failure at the operating pressure Pop, given that

the pipeline has survived a hydrostatic test at a pressure Ph, is

p f(Pop|Ph) =

¶0

∞

p(ry ) ¶w c Ph,ry

wc Pop,ry

p(w) dw dry

1 − ¶0

∞

p(ry ) ¶0

wc Ph ,ry

p(w) dw dry (5)


Fatigue Crack Growth

Failure of pipelines due to fatigue crack growth occurs as a result of defects, introduced

into the pipeline during manufacture and construction, growing to a critical size under the

influence of a cyclic hoop stress. The defects are typically crack-like defects in

longitudinal seam welds. Failure will occur when a defect grows to a critical depth ac

given by [2]

ac(Pop ) =

w 1 −PopR

w1.15ry

1 −PopR

w1.15ryMa

(6)

where Ma is the Folias factor given by

Ma = 1 +0.26 L2

Rw (7)

and L is the defect length.

It is assumed that the growth of defects is accurately described by a function X, based

on the well known Paris fatigue crack growth law, such that

a(t) = X(a0, t) (8)

where a0 is the depth of the defect at time zero, i.e. at the time of commissioning of the

pipeline. Therefore a defect of critical depth at time t must have been of depth ac0 at

commissioning, where

ac0(Pop ) = X−1[ac(Pop ),t ] (9)


This relationship allows the failure space for the interval (0, t) to be expressed in terms of

the initial distribution of defect depths, viz.

0 [ ry [ ∞

0 [ w [ ∞ (10)

0 [ L [ ∞

X−1[ac(Pop ), t] [ a0 [ w

The probability of failure in the interval (0, t), i.e. the cumulative failure probability is

therefore given by

P f(Pop, t ) = ¶

0

∞

p(ry ) ¶0

∞

p(w) ¶0

∞

p(L) ¶X−1 ac Pop ,t

w

p(a0 ) da0 dL dw dry

(11)

where p(a0) is the probability density function of the depth of construction defects

present at time zero, and p(L) is the corresponding probability density function for defect

length. It is assumed that the length of a given defect is constant, i.e. the distribution of

lengths is not time dependent.

If the pipeline was subjected to a hydrostatic test at pressure Ph at time th without failure,

this additional information can be used to reduce the failure space as it is clear that

defects of initial depth greater than ac(Ph) are not present in the pipeline for t > th. The

reduced failure space is given by

0 [ ry [ ∞

0 [ w [ ∞ (12)

0 [ L [ ∞

X−1[ac(Pop ), t] [ a0 [ X−1[ac(Ph),th ]

Therefore the conditional cumulative probability of failure, Pf[(Pop,t)|(Ph,th)], in the interval

(th, t), given that the pipeline survived a hydrostatic test at pressure Ph at time th, can be

approximated by


Pf (Pop, t)|(Ph, th) = ¶

0

∞

p(ry ) ¶0

∞

p(w) ¶0

∞

p(L) ¶X−1 ac Pop ,t

X−1[ac(Ph),th ]

p(a0) da0 dL dw dry

(13)

External Corrosion

Failure of corrosion defects is governed by plastic collapse. Therefore failure is

assumed to occur when a defect grows to a size such that the stress in the remaining

ligament due to the operating pressure Pop exceeds the material ultimate tensile

strength, σu. This will occur at a critical depth ac given by [3]

ac(Pop ) =

w 1 −PopR

wru

1 −PopR

wruQ

(14)

where Q is a length correction factor given by

Q = 1 + 0.31 L2

Rw (15)

and L is the defect length.

The distributed quantities w, σu, a and L are all assumed to be independent, resulting in

the four-dimensional failure space given below.

0 [ ru [ ∞

0 [ w [ ∞ (16)

0 [ L [ ∞

ac(Pop ) [ a(t) [ w


The defect depth, a, grows with time resulting in a time dependent failure probability,

pf(Pop, t), given by

p f(Pop, t ) = ¶

0

∞

p(ru) ¶0

∞

p(w) ¶0

∞

p(L) ¶ac Pop

w

p(a, t) da dL dw dru

(17)

where p(a,t) is the time dependent probability density function of corrosion defect depth

and p(L) is the time independent probability density function of defect length.

If the pipeline was subjected to a hydrostatic test at pressure Ph at time th without failure,

this additional information can be used to reduce the failure space as it is clear that

defects of initial depth greater than Y[ac(Ph), Th] are not present in the pipeline for t > th,

where the function Y represents the law describing corrosion growth with time given by

a(th) = Y−1[a(t),Th] (18)

and Th denotes the time interval (th, t).

The reduced failure space is given by

0 [ ru [ ∞

0 [ w [ ∞ (19)

0 [ L [ ∞

Y−1[ac(Pop ), Th] [ a(th) [ ac(Ph )

The conditional probability of failure following the successful hydrostatic test, given that

there were no failures on the pipeline prior to the hydrostatic test, is given by


p f[(Pop, t)|(Ph, th) =

¶0

∞

p(ru ) ¶0

∞

p(w) ¶0

∞

p(L) ¶Y−1 ac Pop ,Th

ac(Ph)

p(a, th ) da dL dw dru

1 − ¶0

∞

p(ru ) ¶0

∞

p(w) ¶0

∞

p(L) ¶0

max{ac(Pop),ac(Ph)}

p(a,th) da dL dw dru

(20)


External Interference

External interference defects, in the form of dent and/or gouges, are randomly

introduced into a pipeline during service. No growth mechanism is involved so a defect

will either fail immediately or remain safely in the pipeline (providing the operating

conditions do not alter) and therefore the probability of failure is not time dependent.

Failure of external interference defects occurs by an elastic-plastic fracture mechanism

if the defect is larger than the critical gouge depth ac where

ac = ac(Pop, ry ,w,Cv, L,D) (21)

In the above function L is the gouge length, D is the dent depth and Cv is the Charpy

energy of the pipe material. The function cannot be expressed analytically and must be

evaluated using a numerical method. A full description of the function is given in [4].

The six-dimensional failure space is given by

0 [ ry [ ∞

0 [ w [ ∞

0 [ Cv [ ∞ (22)

0 [ L [ ∞

0 [ D [ ∞

ac(Pop, ry ,w, Cv, L, D) [ a [ w

and the probability of failure by

p f(Pop ) = ¶

0

∞

p(ry ) ¶0

∞

p(w) ¶0

∞

p(Cv) ¶0

∞

p(L) ¶0

∞

p(D) ¶ac(. ..)

w

p(a) da dD dL dCv dw dry (23)


INFLUENCE OF PRE-SERVICE HYDROSTATIC TEST

The preceding limit state analysis has been formulated in terms of a generalised

pressure test to a pressure Ph at time th. For the pre-service hydrostatic test the time th

is equal to zero. In the following sections the influence of the test pressure on the

probability of failure for each failure mode detailed previously is examined.

Bursting

Equation (5) shows that if the critical wall thickness at the pre-service hydrostatic test

pressure, wc(Ph, σy), is larger than the critical value at the operating pressure, wc(Pop, σy)

then the probability of failure will be zero. This will be the case if the hydrostatic test

pressure is greater than the operating pressure.

This result demonstrates that performing a pre-service hydrostatic test proves the

integrity of the pipeline provided that no damage occurs during construction or service.

The test removes the possibility of failure due to a gross error in wall thickness or yield

strength, i.e. it proves that what is in the ground is what was intended to be there.


Equation (13) shows that the cumulative probability of failure depends on the relative

magnitude of the critical values of the initial defect depth at the pre-service hydrostatic

test pressure, X-1[ac(Ph), th] and at the operating pressure, X-1[ac(Pop), t]. Therefore if a

pre-service hydrostatic test is conducted we can write

p f(t ) = f(Ph, Pop, t ) (24)

The function f is such that pf increases with increasing Pop and t but decreases with

increasing Ph.


The probability decreases as the hydrostatic test pressure is raised because the

increased test pressure reduces the critical defect depth at the time of the test.

Therefore the depth of the largest remaining defect will be smaller, increasing the

amount of growth necessary to cause failure at the operating pressure and thus

extending the fatigue life.

The fatigue life of the pipeline, T, can be defined as the time at which the calculated

cumulative failure probability reaches some limit of tolerability Pf*, leading to the

functional relationship

T = g(Ph,Pop, Pf& ) (25)

From the above it is seen that, for known Pop and Pf*, the fatigue life of the pipeline is

increased if the hydrostatic test pressure is increased. If the desired life is known then it

is possible to calculate the test pressure which will ensure that the calculated probability

of failure within the design life is below Pf*.

If no pre-service hydrostatic test was carried out the fatigue life of the pipeline would be

governed by the largest defect introduced by the welding process. Adherence to set

welding procedures may limit the size of defects present but the actual size of the

largest defect and therefore the fatigue life would be unknown. Other measures such as

ultrasonic inspection can reduce the probability of failure due to fatigue crack growth but

cannot ensure that the desired fatigue life is achieved. A pre-service hydrostatic test is

necessary to obtain an adequate and known fatigue life. The extension of fatigue life due

to the pre-service hydrostatic test is shown schematically in Figure 1.

External Corrosion

It can be seen from Equation (20) that the probability of failure is governed by the time

dependent distribution of corrosion defect depths. At time zero the probability of failure

will be zero as it is assumed that the distribution of defect depths at this time is given by


p(a, t0) = d(a) (26)

i.e. there are no corrosion defects present at this time. Therefore the pre-service

hydrostatic test will not effect the probability of failure due to external corrosion.


It can be seen from Equation (23) that neither the hydrostatic test pressure nor the time

at which the test is performed have an effect on the probability of failure due to external

interference. This is because of the random nature of external interference defects. Any

failure in service is a result of a dent/gouge defect introduced into the pipeline

immediately before the failure, i.e. after the time of the hydrostatic test. Clearly the pre-

service test has no influence on defects introduced after the test and therefore cannot be

used to reduce the probability of failure.

INFLUENCE OF HYDROSTATIC TEST DURING SERVICE

Bursting

Failure due to bursting is ruled out as a credible failure mode during service due to the

pre-service hydrostatic test. A further test during service is of no additional benefit.


From Equation (13) it can be seen that conducting a hydrostatic test during service will

reduce the failure space and hence the probability of failure for t > th.

However, there is an increase in the probability of failure at the time that the test is

conducted, th, due to the probability of defects of depth greater than ac(Ph) failing during

the test. The additional probability of failure during the test is given by


P f (Ph, th)|Pop = ¶

0

∞

p(ry ) ¶0

∞

p(w) ¶0

∞

p(L) ¶X−1 ac Pop ,th

X−1[ac(Ph ),th ]

p(a0 ) da0 dL dw dry

(27)

The probability of failure before, during and after the test is as shown schematically in

Figure 2.

External Corrosion

From Equation (20) it can be seen that conducting a hydrostatic test during service will

reduce the failure space and hence the probability of failure for t > th.

There is however an increased probability of failure at t = th due to the probability of

defects of depth greater than ac(Ph) failing during the test. The probability of failure

during the test is given by

p f (Ph, th )|Pop = ¶

0

∞

p(ru ) ¶0

∞

p(w) ¶0

∞

p(L) ¶ac(Ph)

ac(Pop)

p(a, t) da dL dw dru (28)

The probability of failure before, during and after the test is illustrated in Figure 3.


As there is no growth mechanism involved with defects introduced from external

interference the defects are stable during normal operation. If a hydrostatic test is

conducted during service there is an increased failure probability due to the probability

of defects that are stable at the normal operating pressure failing at the hydrostatic test

pressure. The additional probability of failure during the test is given by

p f(Ph|Pop) = ¶

0

∞

p(ry) ¶0

∞

p(w) ¶0

∞

p(Cv) ¶0

∞

p(L) ¶0

∞

p(D) ¶ac(Ph)

ac(Pop)

p(a) da dD dL dCv dw dry

(29)


The probability after the test is given by Equation (23), i.e. the probability of failure is

unmodified after the hydrostatic test is performed as shown schematically in Figure 4.

ALTERNATIVE METHODS OF PIPELINE INSPECTION

There are various types of on-line inspection tools available that are able to detect

incidences of metal loss to a high degree of accuracy. The effect of the on-line

inspection on the failure probability for each failure mode is discussed below. For

brevity the analysis is restricted to the magnetic flux leakage (MFL) pig.

Magnetic Flux Leakage Pig

The reduction in failure probability is dependent on the repair criterion adopted by the

operating company. The effect of the on-line inspection on reliability will be compared to

the effect of the hydrostatic test on reliability, therefore it is assumed that all defects

greater than or equal to the critical depth at the hydrostatic test are detected by the MFL

pig and subsequently repaired.

Bursting

Failure due to bursting is ruled out as a credible failure mode during service due to the

pre-service hydrostatic test. The on-line inspection vehicle detects defects so has no

effect on the bursting failure mode.



The magnetic flux leakage pig does not detect crack-like defects so has no effect on the

probability of failure due to fatigue crack growth. Other tools (e.g. elastic wave pig) can

detect cracks which may be then be repaired as necessary.

External Corrosion

The probability of failure following an on-line inspection, given that no failures occurred

prior to the inspection, is given by

p f[(Pop, t)|ti ] =¶0

∞

p(ru ) ¶0

∞

p(w) ¶0

∞

p(L) ¶Y−1[ac(Pop),T i]

amax

p(a, ti) da dL dw dru

¶0

∞

p(ru ) ¶0

∞

p(w) ¶0

∞

p(L) ¶0

ac Pop

p(a, ti) da dL dw dru (30)

where amax is the maximum size of defect left unrepaired in the system following an on-

line inspection, ti is the time of the inspection and Ti denotes the interval (t,ti). If the value

of amax is chosen such that it is equivalent to the critical defect size at the hydrostatic test

ac(Ph), and the inspection time ti is equal to th, then it can be seen that Equation (30) is

equivalent to Equation (20). The probability of failure before and after the inspection is

illustrated in Figure 5. The probabilities of failure are compared with those associated

with an in-service hydrostatic test.


Due to the random nature of incidences of external interference the probability of failure

following an on-line inspection is given by Equation (23). Therefore the probability of

failure is unmodified following an on-line inspection.


DISCUSSION

It has been shown how the effect of the pre-service hydrostatic test on pipeline reliability

in service can be quantified. It has been shown that the test can eliminate any probability

of failure due to bursting and extend the fatigue life of the pipeline. However, the pre-

service test has no influence on the probability of failure due to either external corrosion

or external interference.

The effect of conducting a hydrostatic test during service on pipeline reliability has also

been examined. It is shown that the test will actually increase the cumulative failure

probability of the time dependent failure modes of fatigue crack growth and external

corrosion. This increase in failure probability is offset by the fact that the precise time of

failure is known and mitigating activities may be put in place at this time. The annual

probability of failure for all times following the test for these failure modes will be

reduced. However, the test is shown to have no influence on external interference which

is the mode of failure of greatest concern for many pipeline operators. The cumulative

probability of failure due to a defect introduced through external interference actually

increases if a hydrostatic test is conducted in service.

The effect of the hydrostatic test during service on pipeline reliability is compared to the

effect of performing an on-line inspection. It can be seen from Figures 3 & 5 that an on-

line inspection has a more beneficial effect on pipeline reliability than an in-service

hydrostatic test. This is because there is no probability of failure associated with

conducting the inspection (the probability of the inspection tool becoming trapped in the

pipeline etc. has been neglected).

There are fewer logistical problems associated with on-line inspection compared to

hydrostatic testing, such as water supply, drainage and pipeline drying. The financial risk

associated with the hydrostatic testing is significantly higher than with on-line inspection

as all defects greater than the critical size will require repair before the pipeline can be

recommissioned following the test.


The probability of failure due to external interference is seen to be unmodified both

during and after the on-line inspection.

Experience of the operation of onshore transmission pipelines [1] has shown that

external interference and external corrosion are the two most likely modes of failure.

Therefore any measures taken to improve the reliability of a pipeline must have a

significant effect on one of these two modes. The pre-service hydrostatic test is thus of

little benefit in improving the in-service reliability of onshore gas transmission pipelines.

However, from Figure 1 it can be seen that the pre-service hydrostatic test has the effect

of eliminating fatigue crack growth of construction defects as a credible failure mode

during the design life of the pipeline.

Hydrostatic testing during service has the effect of reducing the pipeline reliability due to

the increased failure probability during the test. It is demonstrated that on-line inspection

will reduce the probability of failure due to external corrosion and therefore will improve

the overall pipeline reliability.

CONCLUSIONS

1. If the pipeline survives a pre-service hydrostatic test at a pressure above the

subsequent operating pressure, the probability of failure in service due to bursting

will be zero.

2. A pre-service hydrostatic test is necessary to obtain an adequate and known fatigue

life as it eliminates fatigue crack growth of construction defects as a credible failure

mode during this time. Increasing the pre-service test pressure increases the known

fatigue life.

3. The pre-service hydrostatic test does not have any effect on the probability of failure

due to external corrosion or external interference, which are the two most likely


modes of failure for an onshore gas transmission pipeline.

4. The overall pipeline reliability is reduced if an in-service hydrostatic test is

conducted. The annual reliability after the test is seen to improve as the probability of

failure due to an external corrosion defect is reduced.

5. Methods other than the in-service hydrostatic test are available that will improve the

reliability of the pipeline but carry fewer logistical problems and lower financial risks.

REFERENCES

1. Anon., Report on the European Gas Pipeline Incident Data Group (EGIG), 19th

World Gas Conference, Milan 1994.

2. Keifner, J.F., Fracture Initiation, 4th Symposium on Linepipe Research, AGA, 1969

3. Batte, A.D., Fu, B., Kirkwood, M.G. & Vu, D., New Methods for Determining the

Remaining Strength of Corroded Pipelines, 16th International Conference on

Offshore Mechanics and Arctic Engineering, Yokohama 1997

4. Francis, A., Espiner, R., Edwards, A.M., Cosham, A. & Lamb, M., Uprating an In-

service Pipeline Using Reliability Based Limit State Methods, 2nd International

Conference on Risk Based and Limit State Design and Operation of Pipelines,

Aberdeen 1997

ACKNOWLEDGEMENT

The authors would like to thank BG plc for permission to publish this paper.


extension of fatiguelife due to test

FIGURE 1: Extension of Fatigue Life due to Pre-Service Hydrostatic Test

Pf*

Pf

no test with test

t

Cum

ulat

ive

prob

abili

ty o

f fai

lure

durin

g se

rvic

e

Pf

t

FIGURE 2: Effect of In-Service Hydrostatic Test on the Probability of Failure due to Fatigue Crack Growth of Construction Defects

th

Eqn (11)

Eqn (27)

Eqn (13)

Cum

ulat

ive

prob

abili

ty o

ffa

ilure

dur

ing

serv

ice


Pf

t

Pro

babi

lity

of fa

ilure

per

an

num

dur

ing

serv

ice

FIGURE 4: Effect of In-Service Hydrostatic Test on the Probability of Failure due to External Interference

th

Eqn (23)

Eqn (29)

Eqn (23)

Pf

t

FIGURE 3: Effect of In-Service Hydrostatic Test on the Probability of Failure due to External Corrosion

th

Eqn (17)

Eqn (28)

Eqn (20)

Cum

ulat

ive

prob

abili

ty o

ffa

ilure

dur

ing

serv

ice


Pf

t

Cum

ulat

ive

prob

abili

ty o

ffa

ilure

dur

ing

serv

ice

FIGURE 5: Effect of On-Line Inspection on the Probability of Failure due to External Corrosion

th

Eqn (17) Eqn (13)

In-ServiceHydrostatic Test

OLI

An_Investigation_of_the_Effectiveness_of_ Hydrostatic_Testing

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