An agency of the Health & Safety Executive Enabling a better working world An agency of the Health & Safety Executive Enabling a better working world Nick Warren July 1 st 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 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 CO 2 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 CO 2 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

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 ’

An agency of the Health & Safety Executive Enabling a better working world 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 Brick bore diameters: forward predictions