A PROBABILISTIC MODEL FOR INTERNAL CORROSION OF WET-GAS PIPELINESA PROBABILISTIC MODEL FOR INTERNAL CORROSION OF WET-GAS PIPELINES

Ben Thacker, Narasi SridharAmit Kale, Chris Waldhart

Southwest Research Institute

International Pipeline ConferenceCalgary, Alberta, Canada

October 4 - 8, 2004

2

BackgroundBackground

Wet Gas ICDA Goal“Identify the locations most likely to have the maximum internal corrosion (IC) damage within a pipeline region”

Probabilistic model needed to identify most likely IC locations

Pipeline model to estimate probability of water accumulation (location)Corrosion rate model to estimate probability of corrosion (extent)Updating strategy to calibrate model with inspection data as gathered

3

ObjectivesObjectives

Identify the most probable pipeline locations for ICConsider historical information on the pipeline, uncertainties in the IC models used, uncertainties in the model parameters, and field observations of ICSimple and straightforward methodology

As complex as necessary, but not moreEnable end users to

Identify critical locations Perform trade and sensitivity studiesMake risk-informed decisions

4

Approach – Wet Gas ICDAApproach – Wet Gas ICDA

Obtain Historical Operational

and inspection data

Ranges of input variables(flow rate, pressures,

temperature, inclinations,

gas quality, water,prior corrosion depths, etc.)

Perform flowmodeling to determine

water holdup points

Probability of water holdup

by location

Probability of corrosionby location and depth

Identify digs/ILI

Feedback dig data

Input torisk management models

Current Dry GasMethod

Prioritizedigs/ILI

5

Solution MethodologySolution Methodology

Predict operating conditions and distribution of water deposition in the pipeline (flow model).

Calculate critical angle, α.

Calculate probability of exceeding critical pipe thickness at location i (corrosion model).

Perform inspection at specific location of maximum localized corrosion and update the model.

Calculate probability of water deposition in pipeline at location i (pipeline model).

Calculate most probable locations of corrosion damage failure (systems model).

Next location (i=i+1)

Update model

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Flow ModelingFlow Modeling

CFD simulation performed to obtain flow characteristics and operating conditions, e.g., velocity, temperature, pressure, etc.Water will flow until it reaches a local minimum at which point it will start pooling.Pooling water may fill a local minimum and spill over to next local minimumWater may be carried to the next location

+θ

I

I+3

Flow Direction

+θFlow Direction

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Critical AngleCritical Angle

Critical angle α is the pipe inclination at which water is likely to accumulate.Required data are

Internal diameter of pipe, dID

Operating pressure, PTemperature, TLiquid density, ρl

Critical angle is obtained by solving:

( )2 sinl g ID

g g

gdFV

ρ ρα

ρ−

=

Molecular weight of gas, MWGas density, ρg

Velocity, Vg

Froude number, F

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Uncertainty in Water FormationUncertainty in Water Formation

Uncertainty in prediction of water formation due toUncertainty in pipeline inclination angle due to variations in

– Mapping error– Cover depth– Axial location

Uncertainty in critical inclination angle due to variations in

– Velocity– Pressure– Temperature– Pipe diameter

Uncertainty in measured and critical inclination angles results in all sites having a probability of water formation.

Distance

θ

2

α

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Corrosion ModelsCorrosion Models

Internal corrosion may initiate once water has collectedRelationships have been developed that predict corrosion rates given various flow parameters such as

CO2H2SH20pH levelCorrosion inhibitorsFlow velocityPressure

Many different corrosion rate models available

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Selected Corrosion ModelsSelected Corrosion Models

de Waard-Milliams

de Waard-Lotz

SwRI

( )217105.8 0.67 log pCOTCR e

− + =

( )217105.8 0.67log pCOTCR CF e

− + = ×

( ) ( ) ( )( )( ) ( )( ) ( )( )

( )( )

23 72 2

2 5 32 2 2 2 2 2

32

8.7 9.86 10 1.48 10 1.31

4.93 10 4.82 10 2.37 10

1.11 10

CR O O pH

CO H S CO O H S O

O pH

− −

− − −

−

= + × − × − +

× − × − ×

− ×

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Corrosion Inhibitor ModelCorrosion Inhibitor Model

Corrosion rate CRincreases exponentially with distance from inhibitor injectionCorrosion rate negligible at inlet and will increase as a function of distanceParameters k and aobtained empirically

k - modeling errora - variation in corrosion growth with pipe length due to presence of inhibitor

effect of inhibitor on corrosion growth rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12

distance along pipe length

00 1

a LLC R kC R e

− = −

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Mapping Uncertainty & Terrain RuggednessMapping Uncertainty & Terrain Ruggedness

Mapping inaccuracies are correlated to terrain ruggednessBased on root mean square error between the elevation at a location and eight neighboring locationsLinear fit to error data6σ spread in inclination angle between ±εy

( )8

24

4∑

+=

−=

−

=

ij

ijji yy

TRI

21 CTRICy +×=ε

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Inspections and Model UpdatingInspections and Model Updating

Initial corrosion probability computed using three candidate models

Update model weights and probability using Bayesian updating

This adjusts the overall model commensurate with observed inspection (corrosion depth) data

( ) ( ) ( )1 1 2 2 3 3cr M c M c M cP P a a W P a a W P a a W= ≥ + ≥ + ≥

( )

( )3

1

0|

|0

|

i

M dii

i

M dii

i M di a a

Mi A

i M di a a

i M

P a aW

aW D

P a aW

a

=

==

∂ − ≤×

∂=

∂ − ≤×

∂∑

( )

( )∑=

=

=

∂

≤−∂∂

≤−∩≥∂

=3

1 |0

|0

idaiMa

iM

diMi

daiMaiM

diMciMi

Updated

a

aaPa

aaaaP

P

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Probabilistic Problem StatementProbabilistic Problem Statement

Probability of failure estimated as the probability of exceeding critical corrosion depth times the probability of water formation

Calculation performed at each pipeline location, l

( ) ( )

( ) ( ) ( )

A = Corrosion damageB = Water formation

f

t

p l P A P B

P d d P θ α

=

= ≥ ≥

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Example Problem – Typical Flow ParametersExample Problem – Typical Flow Parameters

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Example ProblemRandom Corrosion Growth ParametersExample ProblemRandom Corrosion Growth Parameters

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Example ProblemExample Problem

Probability of water formation along pipe length with highest probability observed at location 971

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Example ProblemExample Problem

Probability of Corrosion depth exceeding critical depth along pipe length assuming water is present at all locations

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Example ProblemExample Problem

Probability of Corrosion depth exceeding critical depth along pipe length assuming water is present at all locations

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Example Problem – Updating VerificationExample Problem – Updating Verification

• Updating of model weights given synthetic data generated from the input corrosion rate models• Updating process verified to converge to correct model

21

Example Problem – Updating and RepairExample Problem – Updating and Repair

• Results from several successive updates• Corrosion damage is repaired once inspected

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SummarySummary

Preliminary probabilistic wet gas internal corrosion model developed

Spreadsheet based – fast runningMonte Carlo and FORM solution methods

Methodology incorporates flow, pipeline, corrosion and updating with a probabilistic frameworkConcept demonstrated with simple exampleEasily extensible to include cost model. Would allow inspection schedule optimization

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AcknowledgementsAcknowledgements

Office of Pipeline SafetyPipeline Research Council InternationalInterstate Natural Gas Association of AmericaDuke EnergySouthern California GasTexas Gas Transmission