4th International CANDU In-service Inspection Workshop and NDT in Canada 2012 Conference, 2012 June 18-21, Toronto, Ontario

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1 4th International CANDU In-service Inspection Workshop and NDT in Canada 2012 Conference, 2012 June 18-21, Toronto, Ontario Methods for Evaluation of Accuracy with Multiple Essential Parameters for Eddy Current Measurement of Pressure Tube to Calandria Tube Gap in CANDU Reactors Shaddy SHOKRALLA 1, Thomas W. KRAUSE 2 1 IMS NDE Projects, Ontario Power Generation, Ajax, ON, Canada, shaddy.shokralla@opg.com 2 Royal Military College of Canada; Kingston, ON, Canada; thomas.krause@rmc.ca Abstract The purpose of inspection qualification of a particular inspection system is to show that it meets applicable inspection specification requirements. Often a requirement of the inspection system is that it meets a particular accuracy. In the case of a system with multiple inputs accompanied by additional influential parameters, calculation of the system s output accuracy can be formidable. Measurement of pressure-tube to calandria tube gap in CANDU reactors using an eddy current based technique is presented as a particular example of a system where multiple essential parameters combine to generate a final uncertainty for the inspection system. This paper outlines two possible methods of calculating such a system s accuracy, and discusses the advantages and disadvantages of each. Keywords: Inspection Qualification, Essential Parameters, Eddy Current Testing, Nuclear 1. Introduction Inspection qualification is an evaluation of an inspection system that determines whether the stated objectives, as outlined in the Inspection Specification, have been achieved [1]. Inspection specifications often require that accuracy of inspection system measurements lie within a specific error band [2]. Although not always stated, an implicit interpretation of this is that the bias in measurement, plus or minus two standard deviations of the error (a gauge of measurement uncertainty), are within the error band. Preparation for inspection qualification first involves identification of essential parameters, which are those parameters that if modified, will affect the inspection outcome in such a way that it can no longer meet its objectives [3]. Therefore, it is important to determine how the essential parameters vary under inspection conditions and evaluate the effect of this variation on the desired outcome of the inspection. The essential parameters, their variation and the effect of this variation on the inspection outcome are considered in the technical justification [3-5]. The technical justification (TJ) is the main document produced by the inspection service provider in the inspection qualification process [4,5]. In the TJ analysis of influential parameters for the inspection system is conducted in order to identify essential parameters that may affect the desired outcome of the inspection. Essential parameters are related to input information, inspection procedure and equipment. An examination of the physical basis of the inspection method provides justification for choice of parameters associated with procedure and equipment with regards to detection or sizing of the particular parameter to be measured with reference to essential parameters. Demonstration that the system is achieving its desired outcome may be accomplished by, experimental evidence, uncertainty analysis including probability of detection studies, parametric studies or prediction by modelling. Evidence is presented in view of the inspection specification objectives. Input on test pieces for practical trials is also provided.

2 The particular application considered in this paper is the measurement of pressure tube to calandria tube gap in the fuel channels of CANDU reactors, since this is a measurement that depends on multiple parameter inputs. In this work the variability and/or uncertainty of the essential parameters and their effect on the gap measurement accuracy is considered. This paper outlines two different approaches to calculation of the mean error (measurement bias) as well as standard deviation of the error. The first approach follows the Guide to the Expression of Uncertainty in Measurement (GUM) [6], while the other approach is that of employing Monte Carlo methods [7]. 2. Inspection Description The fuel channels of CANDU reactors consist of upwards of 400 fuel channels, each consisting of a 6 m long Zr 2.5% Nb pressure tube (PT) with 104 mm inner diameter (ID) lying within a larger 129 mm ID Zircaloy-2 calandria tube (CT). The pressure tube contains the fuel bundles and heavy water used for heat transport. Between the PT and CT is an gas annulus that insulates the hot (~300 C) pressure tube from the colder (~50 C) moderator cooled CT. Pressure, heat and irradiation induced creep produce diametral creep of the PT ID to a maximum of 111 mm and a gradual change in the nominal 4.2 mm wall thickness to an allowable minimum of 3.7 mm. This results in a PT to CT gap that starts with an average of 8.3 mm and which decreases with increasing reactor life. Contact between pressure tube and calandria is initially avoided by 4 garter spring spacers that have either a 5.7 mm (older reactors) or 4.8 mm thickness. However sag of the hotter PT within the cooler CT introduces the potential for contact between PT and CT. Contact for a prolonged period of time introduces the potential for hydride blister formation on the PT outer diameter with a consequent risk of PT cracking. Therefore, PT to CT contact is to be avoided. The separation of PT and CT is monitored by using an eddy current based technique that measures the gap between PT and CT. An example of the parameters of interest and the basic measurement configuration are shown in Figure 1. The technique compensates for wall thickness and inner diameter PT variations using normal beam ultrasonic measurements. The objective of the inspection system is to measure the PT/CT gap with sufficient accuracy so that time-tocontact between PT and CT can first be predicted and second, be avoided. Figure 1. Configuration of pressure tube to calandria tube gap measurement

3 For the particular example of PT/CT gap the technical justification addresses those essential parameters that will affect the eddy current measurement outcome and, to a much smaller extent, the ultrasonic measurements used compensate PT wall thickness variations. For the eddy current component of the inspection system, the essential parameters may be largely be extracted from the skin depth relation [8], f (1) where is the skin depth, the resistivity, the permeability and f the frequency. The eddy current measurement relies on the penetration of the electromagnetic field through the pressure tube wall, interaction with the calandria tube and a return back to the receiving coil, where it is sensed and recorded by the eddy current instrument. The essential parameters in this case become the operating frequencies of the probe, the resistivity and thickness of the PT and CT, and the respective diameters of PT and CT, since these define the average distance between PT and CT. In addition, the resistivity of both the PT and CT are a function of temperature and therefore, temperature is also an essential parameter of PT/CT gap measurement, particularly since it may vary between inspections and between in-reactor inspection conditions and system calibration. Resistivity may be affected by material processing and variable chemistry conditions during manufacturing. Additional variables in the measurement arise as a result of uncertainties in the calibration configuration, potential lift-off variation of the probe from the PT surface and material or coatings on the PT surface, if they are present. Gap measurement therefore, requires input of multi-variable parameters, the variability of which needs to be identified and potential impact on inspection outcome evaluated in order to identify final sensitivity to inspection parameters. Figure 2 depicts the general format for generating the estimate of gap. Inputs are the calibrated eddy current response that accounts for PT wall thickness, PT diameter and wall thickness as measured by gauging systems. The algorithm assumes constant resistivity for PT and CT, constant CT wall thickness and diameter and a circular PT, all of which are represented in the calibration facility. However, these parameters also have variability that needs to be represented in the final gap estimate. Given the large number of variables, sensitivity tests were performed by experimentally varying parameters over the range expected under in-reactor inspection conditions and gap measurement output was evaluated. Error analysis was performed looking at outcomes due to variation of parameters in order to obtain an estimate of the uncertainty in the measurement. Inputs Calibrated Eddy Current Response PT Diameter PT Wall Thickness Gap Evaluation Algorithm Output Estimated Gap Figure 2. Method for generation of estimated pressure tube to calandria tube gap.

4 3. Measurement of Variability by Experiment The effect of variability of inputs on the gap measurement output was examined experimentally. Systematic error, as well as error induced by variation of the essential parameters of PT resistivity, CT resistivity, and heat transport temperature, were characterized through experiments. A comparison between gap measurement system output and ultrasonic B-Scan of mockup-flooded PT/CT annulus at varying radial positions and gap was used to estimate systematic error. Systematic error was found to be gap-dependent. Gap between pressure tubes with varying resistivity and uniform-resistivity calandria tubes was obtained and relationship between PT resistivity and gap output was determined. Mockup heat transport temperature was varied to estimate the effect of varying heat transport temperature under inspection conditions on output gap. Both PT resistivity and eddy current coil resistivity were affected by change in heat transport temperature. Effect of calandria tube resistivity on output gap was determined by varying CT temperature, which employs the relationship between CT temperature and resistivity. In this particular case calandria tube temperature was varied by wrapping the CT in a floodable jacket with varying temperature. 4. Calculation of System Accuracy This section outlines two different approaches to calculation of the mean error (measurement bias) as well as standard deviation of the error. The first approach follows the Guide to the Expression of Uncertainty in Measurement (GUM) [6], while the second employs Monte Carlo methods [7]. 2.1 GUM Method The following steps outline the GUM method for calculation of inspection system error band. 1. Express mathematically the relationship between the error Y and the error input quantities X i on which Y depends: Y = X 1 +X 2 +: : :+X N. X i is the error contribution to Y from essential parameter variation i. 2. Determine x i, the estimated value of input quantity X i, either on the basis of the statistical analysis of a series of observations or by other means. 3. Evaluate the variance 2 (x i ), of each input best estimate, x i. (x i ) is the standard deviation of x i and is equal to the square root of 2 (x i ). 4. Evaluate the correlation coefficients, r(x i ;x j ), for estimates x i and x j. 5. Calculate the best estimate of the error y, where y = x 1 +x x n. 6. Determine the standard deviation of the error, (y) from the standard deviations and correlation coefficients associated with the error input estimates, through the following relationship, N N 1 N 2 i i j i j i 1 i 1 j i 1 ( y) ( x ) 2 ( x ) ( x ) r( x, x ) (2)

5 7. The range y-2 (y) to y+2 (y) is the error band of the measurement, where 2 (y) is a measure of the uncertainty. 2.2 Monte Carlo Methods Monte Carlo methods can be described succinctly in the following manner [7]. Let Y be the error, which is the sum of error input quantities X 1,X 2,...X N such that Y = X 1 +X X N. A value is generated at random from each input probability density function (i.e. frequency distribution). The error input quantities probability density functions may be independent of each other or may be correlated, in which case joint probability density functions are used. The process is repeated many times, to obtain M estimates of the output. These M values are sorted into nondecreasing order to yield a frequency distribution, which can be interpreted as the probability density function of the output, Y. The error band y-2 (y) to y+2 (y) can be obtained from the output probability density function. 5. Discussion Statistical significance of test data will dictate which of the above mentioned methods are more appropriate for calculation of the system output error band. If a large amount of test data is available, probability density functions can be determined for error input quantities, which facilitates use of the Monte Carlo Method. This is not a prerequisite however as probability density functions can be assumed to have a specific distribution (e.g. Gaussian). A large amount of test data will also facilitate use of the GUM (Guide to Expression of Uncertainty in Measurement) method, since uncertainties (e.g. standard deviation) can be calculated from derived probability density functions. However, the GUM method can make use of a limited set of test data so that the variance and standard deviation can be calculated directly, or in some cases, these quantities can be calculated analytically. Table 1 lists the differences in the GUM and Monte Carlo Methods for calculation of inspection system error band. Although calculation of inspection system accuracy using the GUM method is simpler than using Monte Carlo methods, the GUM method does suffer drawbacks in terms of flexibility. Monte Carlo methods allow for input error distributions that can be modified slightly and corresponding changes in output error distribution can be identified. With respect to quantifying inspection system accuracy, both GUM and Monte Carlo methods are viable. The appropriate choice of method will depend on the suitability of the method for the particular accuracy characterization problem at hand. Table 1: Differences in the GUM and Monte Carlo Methods for Calculation of Error Band Attribute GUM Method Monte Carlo Methods Low High Necessity for large Low or amounts of test data High Calculation Complexity Low High Flexibility in Modelling Low High Error Distribution Identification of Output Error Band Frequency Distribution Not Present Present or

6 In the case of the PT/CT Gap measurement system, the GUM method was used to calculate output error distribution. This was due primarily to the ease with which standard deviations of input error distributions (due to essential parameter variations) could be calculated. A secondary consideration for not using Monte Carlo methods was the additional task complexity in calculating output error distribution, had these methods been employed. 6. Conclusion The purpose of qualification of a particular inspection system is to show that it meets the applicable inspection specification requirements. In the case of a system with multiple inputs accompanied by additional influential parameters, the requirement of calculating the system s output accuracy can be a challenge. Given the large number of variables involved in generation of pressure tube to calandria tube gap output, sensitivity tests were performed by experimentally varying parameters over the range expected under in-reactor inspection conditions. This included variation of PT and CT resistivity and temperature under variable gap and wall thickness variations. The resulting gap measurement output was evaluated. Error analyses were performed looking at outcomes due to variation of parameters in order to obtain an estimate of the uncertainty in the final gap measurement. Acknowledgements The authors wish to thank Ontario Power Generation and Bruce Power for funding work towards this paper. References 1. The European methodology for qualification of non-destructive testing. Second Issue, EUR EN, published by the European Commission, Brussels-Luxembourg, S. Xu, N. P. Singh, L. Gutkih, M. Elmoselhi, I. Balbaa, and A. Karpelson, Inspection specification for CANDU fuel channels, Tech. Rep. COG-JP-4027-V10- R01, CANDU Owner s Group, Toronto, Canada, ENIQ Recommended Practice 1 Influential/Essential Parameters, Issue 2, ENIQ Report No 24, European Communities, Luxemburg, June ENIQ Recommended Practice 2 Strategy and Recommended Contents for Technical Justifications, Issue 2, ENIQ Report No 39, European Communities, Luxemburg, June Jang, K., CIQB Instructions for the Contents of a Technical Justification Rev. 0, CIQB-INS-03, JCGM, Evaluation of measurement data - Guide to the expression of uncertainty in measurement, first ed., M. G. Cox, M. P. Dainton, A. B. Forbes, P. M. Harris, H. Schwenke, B. R. L. Siebert, and W. Woger, Use of Monte Carlo Simulation for Uncertainty Evaluation in Metrology. New Jersey: World Scientific Publishing Company, Cecco VS, Van Drunen, G & Sharp, FL 1983, Eddy Current Manual, Volume 1, AECL- 7523, Chalk River Laboratories, Atomic Energy of Canada Limited. Shaddy Shokralla (P.Eng.) earned his B.A.Sc. and M.A.Sc. degrees in 2004 and 2006, respectively, from the Faculty of Electrical Engineering at the University of Toronto. Shaddy s research interests include novel methods for non-destructive testing. He is currently employed by Ontario Power Generation.