2817 presentation 2004ipc04probwetgasicda
TRANSCRIPT
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
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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
22
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