A comprehensive framework for evaluation of piping reliability due

to erosioncorrosion for risk-informed inservice inspection

Gopika Vinoda,*, S.K. Bidharb, H.S. Kushwahaa, A.K. Vermab, A. Srividyab

aReactor Safety Division, Bhabha Atomic Research Centre, Mumbai 400 085, IndiabIndian Institute of Technology, Mumbai, India

Abstract

Risk-Informed In-Service Inspection (RI-ISI) aims at prioritizing the components for inspection within the permissible risk level thereby

avoiding unnecessary inspections. The two main factors that go into the prioritization of components are failure frequency and the

consequence of the failure of these components. The study has been focused on piping component as presented in this paper. Failure

frequency of piping is highly influenced by the degradation mechanism acting on it and these frequencies are modified as and when

maintenance/ISI activities are taken up. In order to incorporate the effects of degradation mechanism and maintenance activities, a Markov

model has been suggested as an efficient method for realistic analysis. Emphasis has been given to the erosioncorrosion mechanism, which

is dominant in Pressurized Heavy Water Reactors. The paper highlights an analytical model for estimating the corrosion rates and also for

finding the failure probability of piping, which can be further used in RI-ISI.

Keywords: Risk informed in-service inspection; Erosioncorrosion; Markov model; First order reliability method

1. Introduction

1.1. Background

Piping systems are part of most sensitive structural

elements of power plant. Therefore, the analysis of these

system and quantification of their fragility in terms of failure

probability are of utmost importance. From plant operating

experience, it has been found that various degradation

mechanisms can result in piping failures like thermal

fatigue, vibration fatigue, ErosionCorrosion (E/C), Stress

corrosion cracking, corrosion fatigue, water hammer, etc.

Recent inspections have indicated that carbon steel outlet

feeder pipes in some CANDU reactors are experiencing

wall loss near the exit from the reactor core [1].

Examination has indicated that the mechanism causing the

wall loss is erosion corrosion, at rates higher than expected.

Experimental observation or plant measurements strongly

reveal that E/C also depends on piping layout, local

distribution of flow properties and flow chemistry charac-

teristics. Since CANDU plants have seen various instances

of E/C attack, attention has been given to estimate a realistic

value for piping failure probability due to erosion corrosion.

This paper presents a framework for estimating the piping

failure probability due to erosion corrosion and further

describes model to incorporate the effects of In-Service

Inspection so that realistic estimate can be deduced.

1.2. Objective and scope of the study

This study originated with an aim to find the realistic

failure frequency of piping segments based on the

degradation mechanisms to be employed in Risk Informed

In-Service Inspection studies. Since E/C is one of the

prominent degradation mechanisms, estimation of corrosion

rate due to this mechanism is the scope of the current study.

However, after the corrosion rates have been established,

the rest of the approach can be applied to other corrosion

mechanisms in a similar way. Since First Order Reliability

Method (FORM) is being widely used in Structural

Reliability Analysis problems, the authors also propose

the same approach [2]. After estimating the base failure

probability, Markov approach has been employed as

suggested by Fleming et al. [35]. Markov model finds a

realistic failure frequency, incorporating the effects of In-

Service Inspection and degradation mechanism. Fig. 1

depicts the complete frame work for the flow of activities to

be carried out towards estimation of failure frequency of

piping segment.

2. Estimation of corrosion rates

The PHWR primary piping is made of carbon steel of

grade A-106 GrB operating around 300 8C. Essentiallymajor decrease in erosion-corrosion rate is found as one

approaches near 300 8C. If the pH of the water can be raisedto 9.5, this rate is reduced to a factor of 1001000 compared

to pH of 9.0. Obviously, carbon steel systems are operated at

about 200 8C at velocities greater than 6 m/s with lower pHvalues. Operating experience data on piping failures due to

erosion corrosion from Indian PHWRs are very limited and

not sufficient in suggesting the failure frequency of piping

due to this mechanism. Not much attention has been focused

by researchers for developing models for rates of Erosion

Corrosion since this mechanism is predominant mostly in

PHWRs. Numerous empirical and semi-empirical models

have been developed, which depend on field experience for

some of the factors involved. The main challenge is to

develop a complete mathematical model for erosion

corrosion rate which could effectively and accurately

predict the rate. Once corrosion rate is known, this can be

easily interpreted as crack depth growth rate which can be

used in limit state functions to predict the failure

probability.

2.1. About erosioncorrosion

Erosion-corrosion of the material is a complex phenom-

enon, which is dependent on solution chemistry, properties

of impacting particles and flow environment. The action of

erosion may cause removal of passive corrosion film

thereby removing the ability of the material to withstand

corrosion. On the other hand the effect of the chemical

environment may reduce the ability of material to resist

mechanical attack and cause this latter effect, the so called

synergistic effect, which is still not well understood.

When water reacts with iron, an oxide film is formed on

the surface of the metal. This oxide layer consists of

magnetite when water is deoxygenated. The magnetite layer

is porous and slightly soluble in water, which makes it less

protective. The solubility of magnetite is a function of

temperature, hydrogen activity, and solution composition.

According to Sweeton-Baes experiments [6], four different

ferrous ion complexes can be formed upon dissolution of

magnetite. The chemical equation describing this process is

Fe3O4 322 bH 3FeOH22bb 42 3bH2O2:1

where b 0; 1; 2; 3: The equilibrium constants Kb; werecalculated from a relationship derived by least square fit to

experimental data.

Kb FeOH22bb =H22bP1=3H2 2:2FeOH22bb is the activity of bth ferrous ion complex,[H] is the activity of the hydrogen ion in the solution, PH2is the pressure of molecular hydrogen gas.

2.2. Determining the relevant hydrodynamic

parameters for E/C

Mathematical models for the estimation of rate of

erosion corrosion depend on large of parameters. Since

these parameters are interrelated, complexity has been

increased further in deriving these parameters. Recent

advance in understanding of erosioncorrosion mechanism

Fig. 1. Framework for failure frequency estimation.

188

rate has been focused in identification of regimes of

behavior of this mechanism using quantitative technique.

As a result of large number of experimental works

conducted, several key variables are identified that

influence the rate of attack [6]:

Fluid velocity Fluid pH-level Fluid oxygen content Fluid temperature Component geometry Component chromium, copper and molybdenum

content.

The decision concerning the prioritisation of various

classes of piping components such as elbows, bends etc.,

from most to least susceptible to erosion-corrosion is very

complicated. It depends on the interaction of several

variables with weighing factors applied to each of the

variables. Empirical models are formulated, which con-

siders all the variables responsible for erosion corrosion to

happen. These models can predict the rate of E/C with

considerable accuracy. This predictive capability helps to

avoid nonproductive inspection efforts.

2.3. Steady state model for erosion corrosion

The erosion corrosion of carbon steel in water of low

dissolved oxygen content occurs mainly due to flow

assisted dissolution of normally protective magnetite film

that forms on the surface. M. Abdulsalem, proposed a

steady state model for erosion corrosion of feed water

piping [6]. It has been discussed that the rate of erosion

corrosion is dependent on two factors (i) oxide dissolution

and (ii) mass transfer based on the oxide dissolution. The

kinetics of erosion corrosion is governed by two steps that

operate in series. The first step is the kinetic rate of oxide

dissolution, Rk:

This rate can be expected to be governed by an Arrhenius

relationship given by:

Rk R0 exp2Ek=RTemp 2:3where

Ek activation energy 31,580 cal/molR0 9:55 1032 atoms=cm2 sTemp temperature in KR universal gas constant 2 cal/mol/K.The second step involved is the estimation of mass

transfer limited rate RMT;

RMT KCs 2 Cb 2:4where

K : mass transfer coefficient DO2 =d0:0791Ud=nx n=DO2 0:335 2:5

x 0:86 in straight pipes 0.54, when flow is fully turbulent 0.67, when flow is developing in the downstream

DO2 7:4 1028 Temp 2:6 180:5=2900:6 2:6d diameter of the pipeU flow velocityn kinematic viscosity

Cs : Surface concentration X

FeOH22bb X

KbH22bP1=3H2 exp22FE=3RT 2:7

F faradays constant 96,400 C mol21E potential in equilibrium systemCb a given bulk concentrationTotal erosion corrosion rate can be defined as by

Rate R21K R21MT21 2:8This rate can be used in models for limit state functions of

pipe failure for estimating the failure probability.

3. Markov model for incorporating effects of ISI

and degradation mechanisms

3.1. Discrete state Markov model for pipe failures

The objective of Markov modeling approach is to

explicitly model the interactions between degradation

mechanisms and the inspection, detection, and repair

strategies that can reduce the probability that failure

occurs or the failure will progress to rupture. This

Markov modeling technique starts with a representation

of piping segment in a set of discrete and mutually

exclusive states [35]. At any instant of time, the system

is permitted to change state in accordance with whatever

competing processes are appropriate for that plant state.

In this application of Markov model the state refers to

various degrees of piping system degradation or repairs,

i.e. the existence of flaws, leaks, or ruptures. The

processes that can create a state change are failure

mechanisms operating on the pipe and process of

inspecting or detecting flaws and leaks, and repair of

damage prior to progression of failure mechanism to

rupture.

The basic form of Markov model is presented in

Fig. 2. This model consists of four states of pipe segment

reflecting the progressive stage of pipe failure mechan-

ism: the state with no flaw, development of flaws or

detectable damage, the occurrence of leaks and occur-

rence of pipe ruptures. As seen from this model pipe

leaks and ruptures are permitted to occur directly from

the flaw or leak state. The model accounts for state

189

dependent failure and rupture processes and two repair

processes. Once a flaw occurs, there is an opportunity for

inspection and repair to account for in-service inspection

program that search for signs of degradation prior to the

occurrence of pipe failures. Here the Leak stage L does

not indicate actual leak, but represents a stage in which

remaining pipe wall thickness is 0:45 t to 0:2 t (pipewall thickness).

The Markov model diagram describes the failure and

inspection processes as discrete state-continuous time

problem. The occurrence rates for flaw, leaks and ruptures

are determined from limit state function formulation. The

repair rates for flaws and leaks are estimated based on the

characteristics of inspection and mean time to repair flaws

and leak upon detection. The Markov model can be solved

by setting up differential equations for different states and

finding the associated time dependent state probabilities.

These equations are based on the assumption that the

probability of transition from one state to another is

proportional to transition rates indicated on the diagrams

and there is no memory of how current state is arrived at.

Assuming the plant life of 40 years, state probabilities are

computed for the plant life.

Inspect and repair flaw rate, v

v Pf1PFD=TI TR 3:1Pf1 probability that piping element with a flaw will beinspected per inspection interval. The value will be 1 if it

is in the inspection program or else it will be 0.

PFD probability that a flaw will be detected given thiselement is inspected. This is the reliability of inspection

program and equivalent to Probability of Detection. For

most Non Destructive Examination, its values are

between 0.84 and 0.95.

TI mean time between inspections for flaw, itstypically 10 years for nuclear power plants

TR mean time to repair once detected, is in order ofdays, 200 h.

Repair rate

m PLD=TI TR 3:2PLD probability that leak in the element will bedetected per detection period (Typically assumed as 0.9)

3.2. Piping failure probability estimation using FORM

To determine the different transition rates f; lf rL and rf ;limit state functions, based on strength and resistance, are

used. The first limit state function is defined as the difference

between the pipeline wall thickness t and depth of corrosion

defect. This limit state function describes the state of depth of

the corrosion defects with a depth close to their maximum

allowable depth before repair could be carried out that is 85%

of the nominal pipe wall thickness 0:45 t:The probabilitythat pipe fall thickness reduces to 0:45 t will occur at a rate,f; which is defined as occurrence of flaw. So, f representstransition rate from state S, in which flaw is less than 0:125 t; to state F in which flaw is 0:45 t: The limit state functioncan be defined as

LSF1d;T 0:45 t 2 d rate T 3:3d undetected flaw 0:125 t:T time of inspection usually 10 years.The second limit state function is formulated to

estimate the transition rate lf : lf represents transitionrate from state F, which is already crossed the detectable

range i.e. 0:45 t; to the leak state L, i.e. 0:8 t: The LSF

Fig. 2. Markov model for pipe elements with in-service inspection and leak detection.

190

for this case would be

LSF2 0:8 t 2 0:45 t rate T 3:4There is a probability for the piping reaching directly

the rupture state, R from the flaw state, F, because of

encountering the failure pressure in the flaw state. For this

case, a different limit state function needs to be

formulated. The third limit state function is defined as

difference between pipe line failure pressure Pf and

pipeline operating pressure Pop [2].

LSF3Pf Pf 2 Pop 3:5

For determining failure pressure, different models are

available. For the scope of this paper, two models namely

modified B31G and Shell 92 are addressed. According to

modified B31G model, Pf is defined as [2]:

Pf 2YS 68:95tD

12 0:85 dTt

12 0:85 dTt

M21

!

for G 0:893 LTDt

p

, 4 3:6

where

M 1 0:6275 LT

2

Dt2 0:003375

LT2D2t2

s

forL2

Dt# 50 3:7

M 0:032 LT2

Dt 3:3 for L

2

Dt. 50 3:8

According to Shell-92, the failure pressure can be defined

as [2]:

Pf 1:8UTStD

12 dTt

12 dTt

M21

!3:9

where

M 1 0:805 LT

2

Dt

s3:10

D out side diameter of the pipe.L length of corrosion.t thickness of the pipe.UTS ultimate tensile strengthYS yield strength of the pipe material.T time of inspection usually 10 years.LT axial length of the corrosion defectdT the depth of corrosion.

The rupture stage from flaw stage is identified when the

nominal wall thickness is 0:55 t:

For this case, the depth of corrosion is defined as

dT 0:45 t rate T 3:11Both failure pressure models are used to calculate the

rupture frequency from flaw stage. The results are obtained

from software COMREL [8], which represents the failure

probability over the entire life of the plant. So the failure

frequency or transition rate rf is found out by dividing thisprobability by designed plant life time, typically 40 years.

Similarly, for calculation of rL both the failure pressuremodel of Modified B31G and Shell 92 are used. In this case,

the failure probability is found out by considering the fact

that the state transition is occurring from state L to state R

which is the rupture stage, over a period of 40 years. The

state transition rate rL is obtained by dividing theprobability obtained from COMREL by designed plant

life time. The corrosion depth for this case is computed as

dT for this case 0:8 t rate T : 3:12Normal distribution has been assumed for load and

resistance variables. For longer service periods, it has been

found that Shell -92 model gives higher probabilities of

failure while modified B31G gives smaller estimate.

4. Case study

4.1. Corrosion rate estimation

The PHWR outlet feeder piping system is taken as a

typical case study. There are 306 number of small diameter

pipes of diameter ranging from 40 to 70 mm and length

222 m that connects outlet header to the steam generator.

The feeder pipe considered in this case study is made of

carbon steel A106GrB, with a diameter d of 70 mm andthickness t of 6.5 mm. This feeder is subjected to a flowvelocity U of 1500 cm/s, in a PH of 10.2 at a temperature,280 8C. The kinematic viscosity, n is taken as 0.0179 cm2/s.The case study attempts to determine the erosion corrosion

rate for one such feeder pipe. Following the methodology

described in Section 2.3, the rate of erosion corrosion was

found to be 0.051 mm/year, which is the mean value for the

rate. The variance of the rate can be calculated by using

Taylor series expansion.

Corrosion rate f T ; pH;U; dTable 1

Parameters mean values and variances

Parameters Mean Variance

Temperature 553 K 25 K

pH 10.2 0.5

Velocity 1500 cm/s 50 cm/s

Diameter 70 mm 1.48 mm

Rate 0.051 mm/year 0.015 mm/year

191

s 2rate f =T2s 2T f =pH2s 2pH f =U2s 2U f =d2s 2d 4:1

It has been assumed that all the process parameters are

normally distributed. The developed model can be simulated

to get optimum design parameters, by considering the

process variables of interest as the fixed parameters and

adjusting the others. Table 1 presents the mean and variance

value calculated for the corrosion rate depending on the mean

and variance of specific parameters. Figs. 36 present the

variation of erosion-corrosion rate with parameters such as

flow velocity, temperature, PH and diameter, respectively.

4.2. Piping failure probability estimation

After estimating the corrosion rate, it has to be

applied in the suitable limit state function to estimate the

failure probability. Table 2 presents mean and variance

values for various parameters appearing in the limit state

functions.

The software package for structural reliability analysis,

STUREL, has been used to estimate the failure probabilities

from the limit state functions. The solutions obtained from

COMREL module of STUREL are used to estimate the

various transition rates, which are presented in Table 3.

These transition rates are applied on Markov model

shown in Fig. 2. Software MKV 3.0 [9] is used for

determining the various state probabilities in the Markov

model, as shown in Table 4. Modified B31G estimates are

considered for rf and rl in Markov model.Depending on our definition of failure, state probability

of either the leak state or the rupture state, can be considered

as failure probability of the feeder. The failure frequency of

Fig. 4. E/C rate vs. temperature.

Fig. 5. E/C rate vs. pH.

Fig. 6. E/C rate vs. diameter.

Table 2

Parameters for failure pressure model with mean and variance

Parameters Mean values Variance

Yield strength (MPa) 358 25

Thickness of the pipe (mm) 7 0.148

Ultimate tensile strength (MPa) 455 32

Outer diameter of the pipe (mm) 72 1.5

Rate of erosion corrosion (mm/year) 0.051 0.015

Load (MPa) 8.7 0.9

Time (year) 40

Length of defect (mm) 300

Fig. 3. E/C rate vs. flow velocity.

192

the feeder can be estimated by dividing this probability by

the design life of the component, which value can be further

employed in RI-ISI for determining its inspection category

[7] for In-Service Inspection.

5. Conclusions

The paper has considered the Abdulsalam model for

estimation of erosion-corrosion rate. However, these

estimates should be verified against operating experience,

if available, before employing in such application. If the

reduction in pipeline safety is assumed for long elapsed

time, then special care must be taken in characterizing

accurately the coefficients of variation of the load and

resistance parameters. The following priority scheme must

be used for determining the actual coefficient of variation:

rate of corrosion, thickness of the pipe, operating pressure,

material yield strength, and pipeline diameter. The sensi-

tivity of the failure frequencies increases with increased

pipeline elapsed life. The failure pressure models con-

sidered here to define the LSF lead to similar failure

probabilities for short pipeline service periods. Various

parameters are assumed here to be normally distributed, but

in actual practice this may not be the case. Nevertheless, the

COMREL module has the facility to account for any kind of

distribution. Instead of applying directly the probabilities

obtained from limit state function in RI-ISI evaluation, it is

recommended to find the state probabilities using MAR-

KOV model, since it incorporates the effect of repair and

inspection works in the pipeline failure frequency. Markov

model also allows formulating a proper inspection program

and period depending on the operating condition of the plant

at any given time.

Acknowledgements

The authors wish to thank the reviewers for their critical

review and constructive suggestions to improve the quality

and readability of this paper.

References

[1] Burnill KA, Chelugel EL. Corrosion of CANDU outlet feeder pipe.

AECL 11965 1999.

[2] Caleyo F. A study on reliability assessment methodology for pipelines

with active corrosion defects. Int J Pressure Vessels Piping 2002;79:77.

[3] Fleming KN, Gosselin S, Mitman J. Application of markov models and

service data to evaluate the influence of inspection on pipe rupture

frequencies. Proc ASME Pressure Vessels Piping Conf, Boston, August

15 1999.

[4] Fleming KN, Mitman J. Quantitative assessment of a risk informed

inspection strategy for BWR weld overlays. Proceedings of ICONE 8,

Baltimore, MD; April 26, 2000.

[5] Gosselin, SR, Fleming KN. Evaluation of pipe failure potential via

degradation mechanism assessment. Proceedings of ICONE 5, Fifth

International Conference on Nuclear Engineering, Nice, France; May

2630, 1997.

[6] Abdulsalam M, Stanley JT. Steady-state model for erosioncorrosion

of feed water piping. Corrosion 1992;48:587.

[7] TR-112657, Revision B-A, EPRI Revised Risk-Informed In-Service

Inspection Evaluation Procedure; December 1999.

[8] STRUREL, www.strurel.de, licensed software for Structural

Reliability Analysis.

[9] MKV 3.0, www.isograph.com, demo version for Markov model

solutions.

Table 4

State probabilities from MKV 3.0

States State probability

Success (S) 0.9956

Flaw (F) 4.362 1023Leak (L) 9.303 1027Rupture (R) 3.147 1027

Table 3

Transition rates obtained from COMREL modules

Parameters Values (/year) LSF method

f 3.812 1024 LSF-1lf 2.435 1025 LSF-2rf 0.115 1027 LSF-3: modified B31G

0.112 1026 LSF-3: Shell-92rl 1.486 1022 LSF-3: modified B31G

8.77 1022 LSF-3: Shell-92

193

A comprehensive framework for evaluation of piping reliability due to erosion-corrosion for risk-informed inservice inspectionIntroductionBackgroundObjective and scope of the study

Estimation of corrosion ratesAbout erosion-corrosionDetermining the relevant hydrodynamic parameters for E/CSteady state model for erosion corrosion

Markov model for incorporating effects of ISI and degradation mechanismsDiscrete state Markov model for pipe failuresPiping failure probability estimation using FORM

Case studyCorrosion rate estimationPiping failure probability estimation

ConclusionsAcknowledgementsReferences