an agency of the health & safety executive enabling a better working world an agency of the...

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


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


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


Reactor design and core structure


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)


Exaggerated deformation of a graphite brick


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?


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


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


Evolution of stresses within a brick

Keyway cracking

Stress reversal


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


Channel bore measurements


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?


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


Calibrated shrinkage behaviour

Calibration suggests earlier ‘turnaround’


Evaluation of predicted bore shapes


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)


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


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


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


Additional slides


Video inspection – early life cracking


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’)


Effect of varying calibration parameters upon shrinkage


8 9 10 11 12 13 14 15 16

256

257

258

259

260

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

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