an agency of the health & safety executive enabling a better working world an agency of the...
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An agency of the Health & Safety Executive Enabling a better working world UK Nuclear generating capacity 19% of the UK’s electricity generating capacity (2014) Magnox: 1 station still operating, closure imminent Advanced gas-cooled reactors: 7 stations, planned closure dates Pressurised water reactor: 1 station, current closure date 2035 Maintenance of this capacity is essential to ensuring adequacy of supply over the next decade until nuclear new build (or alternatives) become availableTRANSCRIPT
An agency of the Health & Safety Executive Enabling a better working worldAn agency of the Health & Safety Executive
Enabling a better working world
Nick Warren July 1st 2015
Prediction of Cracking in the Graphite Core of Advanced Gas Cooled Nuclear Reactors
An agency of the Health & Safety Executive Enabling a better working world
Introduction
Background
Stress analysis using Finite Element modelling
Statistical analysis– Calibration of Finite Element modelling– Predicting cracking
An agency of the Health & Safety Executive Enabling a better working world
UK Nuclear generating capacity
19% of the UK’s electricity generating capacity (2014)
Magnox: 1 station still operating, closure imminent
Advanced gas-cooled reactors: 7 stations, planned closure dates 2016-2023
Pressurised water reactor: 1 station , current closure date 2035
Maintenance of this capacity is essential to ensuring adequacy of supply over the next decade until nuclear new build (or alternatives) become available
An agency of the Health & Safety Executive Enabling a better working world
Reactor design and core structure
UK Advanced Gas cool reactors use graphite as a moderator and are cooled by CO2
Constructed from approximately 3000 graphite bricks: 10 layers x 300 channels
An agency of the Health & Safety Executive Enabling a better working world
Reactor design and core structure
An agency of the Health & Safety Executive Enabling a better working world
Ageing processes in irradiated graphite
• Neutron irradiation leads to a change in dimensions. Graphite will initially shrink by up to 4% before reaching a plateau, after which it expands indefinitely. In AGRs this behaviour occurs over several decades
• Oxidisation of the graphite due to the ionisation of CO2 results in a gradual and continual loss of graphite mass and an associated loss of strength and changes to other material properties
• Differential shrinkage creates internal brick stresses and leads to two types of cracking:• Bore initiated cracks in early to mid-life, which have been observed
• Keyway root cracks in late life, not yet observed but predicted to affect a large number of bricks and expected to be the life limiting factor for all the AGR reactors (about 15% of the UK electricity capacity)
An agency of the Health & Safety Executive Enabling a better working world
Exaggerated deformation of a graphite brick
An agency of the Health & Safety Executive Enabling a better working world
Modelling – requirements of the Licensee and Regulator
Can the reactor operate safely?
• What is the current structural integrity of the reactor core?
• How many cracks has it?
• How many cracks are likely in the future?
• How many cracks can the core safely tolerate?
However, as keyway cracks are yet to be observed, the immediate questions are:
• When will keyway cracking start and how fast will it progress?
• Is the inspection strategy adequate to ensure safety limits will not be breeched?
An agency of the Health & Safety Executive Enabling a better working world
Modelling - methodology
1. Develop FE model for a graphite brick
2. Develop fast approximations to the FE model
3. Calibrate the surrogate model using inspection data
4. Monte Carlo simulation using the optimised (surrogate) FE model to predict stresses and thus estimate the probability of cracking
An agency of the Health & Safety Executive Enabling a better working world
Finite Element modelling of brick stresses
Inputs:• Weight loss, temperature and fast neutron dose
⁻ Calculated values; vary spatially and through time
• Equations that represent how the properties of graphite change over time:
⁻ Shrinkage, elasticity, strength etc.⁻ Empirically derived from Test and AGR reactor data⁻ Highly uncertain
• Loadings from other components
Outputs:
• Changes in brick shape, internal stresses
Computationally intensive
Irradiation dose
An agency of the Health & Safety Executive Enabling a better working world
Evolution of stresses within a brick
Keyway cracking
Stress reversal
An agency of the Health & Safety Executive Enabling a better working world
Inspection data
Inspection data are only obtained during station outages
Cannot measure internal stresses
One channel inspected per day
Video inspection of the channel bore – Identification and classification of cracks– No keyway cracks yet observed
Trepanning device cuts small graphite samples from the bricks – Material property tests, e.g. density, strength
Channel Bore Measurement Unit measures the channel bore diameter
An agency of the Health & Safety Executive Enabling a better working world
Channel bore measurements
An agency of the Health & Safety Executive Enabling a better working world
Statistical model for bore diameters at mid brick height
Sensitivity analysis using the finite element identified mid height diameter as a candidate metric for calibration
– Six parameters were identified as being of primary importance– Three parameters relate to the modifying effect of oxidisation upon graphite
shrinkage in an insert environment
)
Model fitted using MCMC
How to deal with computational burden?
An agency of the Health & Safety Executive Enabling a better working world
Bayesian emulators
Complex models are built in many scientific fields to approximate complex real world systems.
– Examples in climatology, oceanography, vegetation, health economics, finance etc.
– Programs may take a matter minutes, hours, days or even months to execute.
An emulator is a statistical approximation to the complex model
– built using runs of the finite element according to a Latin Hypercube design– for a deterministic model the emulator should interpolate the outputs from
the training runs– Relatively few model runs required (100)– based upon Gaussian processes– fast, computationally efficient approximation to the complex model
An agency of the Health & Safety Executive Enabling a better working world
Calibrated shrinkage behaviour
Calibration suggests earlier ‘turnaround’
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Evaluation of predicted bore shapes
An agency of the Health & Safety Executive Enabling a better working world
Predicting cracking
Keyway root crack is considered to occur when stress>strength (fractional remnant strength)
FE model allows a deterministic comparison of stress vs. strength
To calculate a probability of cracking a distribution for stress and strength is required
Use nested Monte Carlo simulation:– Outer loop - sample global (uncertain) parameters (i.e. parameters that are the same
for all bricks) from defined distributions – Inner loop
• Simulate bricks in layers 3-9 of the central 256 channels• sample quantities that vary between bricks, e.g. dose, weight loss, strength• using an emulator for stress at the keyway calculate the fractional remnant
strength at all eight keyways (strength varying within-brick between the keyways)
An agency of the Health & Safety Executive Enabling a better working world
Prediction: time of onset and rate of cracking
Takes approximately 2 fpy to go from 10% to 70% cracking
Compared with the Licensee’s forecasts cracking starts earlier and progresses more slowly
An agency of the Health & Safety Executive Enabling a better working world
Summary
Presented a methodology for calibrating a complex deterministic model to observational data– Using a Gaussian Process Emulator to overcome the computational barriers
The methodology has improved confidence in predictions of keyway cracking in the AGR reactors
Provides the Office for Nuclear Regulation with an alternative modelling capability that is independent of the Licensee– Challenges, but ultimately supports the Licensee’s safety claims
An agency of the Health & Safety Executive Enabling a better working world
Acknowledgement
Work carried out by:– Health and Safety Laboratory– School of Material Properties, University of Birmingham– The Nuclear Graphite Research Group, University of Manchester
Funded by the Office for Nuclear Regulation
An agency of the Health & Safety Executive Enabling a better working world
Additional slides
An agency of the Health & Safety Executive Enabling a better working world
Video inspection – early life cracking
An agency of the Health & Safety Executive Enabling a better working world
Emulator: validation
Normally validate a model using an analysis of residuals
– However, as the emulator interpolates the data the residuals are not defined.
– Emulators are usually evaluated using cross validation (‘leave one out’)
An agency of the Health & Safety Executive Enabling a better working world
Effect of varying calibration parameters upon shrinkage
An agency of the Health & Safety Executive Enabling a better working world
8 9 10 11 12 13 14 15 16
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core burnup [TWd]
mid
-bric
k di
amet
er [m
m]
HPB-R3: layer 7 fit to BOTH data
Best parameters95% CI
Brick bore diameters: forward predictions