Data analysis with uncertainty evaluation for the Ignalina NPP RBMK 1500 gas-gap closure evaluation

Transcription

1 Data analysis with uncertainty evaluation for the Ignalina NPP RBMK 1500 gas-gap closure evaluation M. Liaukonisl &J. Augutis2 Department ofmathematics and Statistics, Vytautas Magnus University, Lithuania. Nuclear Safety Installation Laboratoy, Lithuanian Energy Institute, Lithuania, Abstract This paper presents data analysis with uncertainty evaluation for Ignalina NPP Unit 1 RBMK reactor core lifetime analysis. The closure of the gas gap between the pressure tubes and the graphite bricks is one of the criteria for the evaluation of the reactor core lifetime. The rate of closure of the approximately 1.5mm gaps between the pressure tubes and the graphite is largely a function of accumulated fast neutron dose and graphite operating temperatures. Historical approaches to this problem are briefly discussed and more thorough data analysis performing probabilistic model is presented. For the graphite behaviour the ABAQUS code was used. Non-linear changes of graphite have high influence for further forecast. With the data used for the calculations it was performed uncertainty analysis. It showed confidence in the results. 1 Introduction The RBMK reactor is designed to use a graphite moderator in the form of graphite bricks which surround Zirconium-Niobium channels (or pressure tubes ) containing the nuclear fuel and coolant. The pressure tube is initially positioned in place by a series of graphite rings that are alternately in contact with the inner bore hole of the graphite bricks and the outer perimeter of the

2 426 Risk Analysis III pressure tubes, The initial design was to provide a nominal 2,5-3 mm gap between the pressure tubes and the rings, It is well known that the initial gaps will contract as a result of radiation induced shrinkage of the graphite and outward creep of the pressure tubes. An in-service inspection program has been in place at Ignalina NPP, which is focused on monitoring the rate of gap exhaustion. The gas gap closure problem at the Ignalina NPP- 1 RBMK reactor was first identified by Safety Analysis Report in (SAR [1]). It was followed by another few continuous studies, One common feature of the models developed by different teams until 2000 was that dimensional change model of the graphite bore inner and FC outer diameters were assumed to be linear. It is agreed that linear model is correct for the expansion of the FC tube diameter but experimental data and a known physical phenomenon contradicts the linear graphite shrinkage model. This phenomenon was not accounted in any of the previously used models and caused wrong long-term future projections. This work describes probabilistic model of the gas gap closure accounting for the non-linear graphite behaviour with uncertainty evaluation. The model is used to estimate the gap closure probability and timing. 2 Technical description A typical single fuel channel cell consists of a 7 meters high stack of graphite moderator bricks being located together by the cup and cone arrangements, There are steel bricks at the top and bottom of the column. At the base of the column the bricks are located on a spigot and the top of the column is located in line with a hole in the upper biological shield by means of a telescopic joint, The vertical joints between graphite moderator bricks are staggered in adjacent channels to avoid any horizontal planes of weakness. To prevent the oxidation of the graphite and to improve the thermal efficiency the core is contained in a go~o Helium 10% Nitrogen mixture, The prtxsure tube is located in the moderator brick central hole by a system of graphite split rings. Each ring is alternately tight on the pressure tube or tight in the moderator bore as shown in Figure 1, pressure tube graphite rings graphite brick Figure 1: Graphite and Zr-2.5%Nb pressure tube interaction zone.

3 Risk Analysis III 427 The slots in these rings are aligned together to allow the HeiNj mixture to pass along the channel. The fuel element which consists of an outer ring of 12 and an inner ring of 6 zirconium clad uranium dioxide fuel elements are contained within the pressure tube supported by a central tie bar. The interaction of the fast neutrons leads to dimensional changes in the graphite and the pressure tube materials. For example, in the graphite-moderated reactors, initial accumulation of the fast neutron dose produces a gradual shrinkage of the graphite blocks. For the RBMK reactors this results in a decrease of the bore diameter through which the fuel channel passes. For the pressure tube made of a Zirconium and 2.5~0 Niobium alloy, the effect is opposite, due to thermal and irradiation effects the tube diameter increases, As a result, the gap between the pressure tube and the grapkite, which has a nominal thickness of 1.5-mm, is gradually diminished leading to an eventual closure of the gap. 3 Statistical analysis of the graphite bore and pressure tube outer diameters measurement data Graphite bore diameter and pressure tube diameters are subject to continuous inspection and measurements. An in-service inspection program has been developed recently at the Ignalina NPP, which is focused on monitoring the rate of gap closure. 3,1 Data Analysis In the next sections a new probabilistic approach to deal with the gap closure problem is presented. It is based on the actual gap data analysis. The main feature of the probabilistic gas-gap closure model is that it estimates the gap in each channel separately and investigates the gap in each graphite brick along the channel. The actual gap is calculated as the difference between the graphite blocks diameters and the pressure tube outer diameters at the same channel and the same axial position. This approach eliminates unnecessary conservatism, which arise from comparing extreme diameters. Actual gap in the channel is illustrated in Figure 2. This figure shows the graphite block internal diameter and the pressure tube internal diameter plotted against the distance from the lower zirconium-steel adapter, for the channel 12-10, extracted during the measurements program in 1998.

4 428 Risk Analysis III Inner pressure tube diameter, mm [nner graphite block diameter, mm %2.03 $+.x,,45 M,W 414 am [,,,! W,m 713 m I, I I, 1, (.,, Z ,5 Mal distance from transition joint, mm Figure 2: Measurements of inner pressure tube diameter and graphite bore diameter in channel, recorded in Probabilistic gas gap closure model Model assumptions and uncertainties Based on the experience of all teams participated in the investigation of the gas gap problem Lithuanian Energy Institute (LEI) developed the probabilistic gap closure model to estimate the remaining gap and closure time. The main feature of the probabilistic gas gap closure model is that it estimates the gap in each channel separately and investigates the gap in each graphite brick along the channel. The probabilistic gas gap closure model is based on the following assumptions: The model accounts for the gas gap in each single graphite block of the graphite brick. Eight middle blocks were used for the calculations, as the rest has significantly small burn-up.. Diameters of the graphite and PT are distributed normally. Graphite mean values are obtained from the deterministic calculations and variation is calculated from the statistics, PT diameter mean value is obtained from the linear trend line and variation is calculated from the statistics. Statistical data compliance with normal distribution was verified using x 2 criterion. Data compliance with normal distribution hypothesis was accepted with high confidence.. Gap closure criterion in the channel is the gap closure in at least one graphite brick, Probability of the gap closure is calculated for each channel. For future projections non-linear graphite model is used, calculated by ABAQUS code,

5 Risk Analysis III 429 The model is affected by the following sources of uncertainty:. Measurement errors are 0,01-0,1 mm. Initial values of PT outer diameter and graphite bore diameters have considerable manufacturing margins: 0,8 mm for PT and 0.23 mm for the graphite, Gap closure probabilistic model Probability of the gap closure in a single graphite brick is calculated by Z? - ([-G(x)) q=l - (1) I -.D& e 2 2 dt Zri - maximal outer PT diameter of the graphite brick, G(x) - graphite shrinkage trend function, G - standard deviation of the graphite brick non-linear trend function. ~= n ~~(di - G(xi))2 - &(di - G(xi))) n(n-1) x - burn-up of the bricks, di - graphite bore diameter measurement, n - number of graphite bricks in the reactor. (2) The model is illustrated in Figure 3, The gap closure probability is an area below -- interception of two normal distributions of graphite and PT diameters. o 2om woo MW4ays Figure 3: Illustration of the gas gap closure probabilistic model,

6 43(I Risk Analysis III Probability of the gap closure in one channel is calculated by Pi-probability of gap closure in i graphite brick. P,. =1- fi(l-<) (3) i=d Probability of the gap closure in at least one channel in the reactor is calculated by P=l-~(l-PTK, ) (4) P~Kj - probabilityof gap closure inj channel. 3.3 Analysis of probabilistic model results Gas gap closure probability was projected for the period until the middle of Calculations were performed for each fuel cell individually and then transformed into the total gap closure probability, Results of the probability estimation in the individual ceils are shown in Figure E-03 IE-04 1E-(I5 le-06 te.r37 1 E-08 <IE-09 P Figure 4: Frequency diagram of the gap closure probability in individual cells until 2002, Probability that there will be no channels with zero gaps in reactor unit 1 until 2002 is not less than Preliminary calculations included sensitivity study of the most important model parameters variance of graphite and PT diameters. The results indicated that graphite variance is the most sensitive parameter in the model. Therefore data uncertainty influence on the graphite behaviour was analysed.

7 4 Uncertainty evaluations Risk Analysis III 431 The uncertainties in the predictions of gas-gap closure have been investigated for various ranges of input parameters. The parametric uncertainty analyses have been carried out assuming the following approach (Hopkinson [2]): Identification and assessment of the uncertain input parameters, This step requires that those parameters to be considered in the analysis are identified and that the ranges and distributions of these parameters are estimated, Input parameter sampling. Each of the parameters is sampled from the range of potential values, taking account of the probability distribution of these values, Many samples are taken for each parameter and these samples are combined, taking account of correlations between different parameters, to form input datasets that contain one sample value of each of the uncertain parameters. Each of these sets of input values is then used to generate a separate set of input data for a single ABAQUS calculation, ABAQUS calculations, The 2D ABAQUS calculation is then run with each of the sets of input data. Analysis of the uncertainties in the predictions of ABAQUS. Finally, the resultant variation in the code s predictions maybe assessed. 4.1 Input data included in uncertainty analysis The calculations required for the uncertainty analysis comprised of th sensitivity of the bore diameter changes with irradiation to variations in th following (Table 1) input data items (Hopkinson [2]). Table 1: Parameters that have influence on uncertainties of result. Virgin: Young s modulus CTE Thermal Conductivity Graphite material properties: Reactor parameters: Geometry Irradiation ~ changes in: Thermal conductivity Secondary creep coefficient Graphite temperatures Gap conductance Coolant temperature Heat transfer coefficient from tube to coolant Graphite bore Tube diameter

8 432 Risk Analysis III 4.2 Identification of distribution type and level of uncertainty Values for uncertain input parameters need to be quantified in terms of the range and shape of their uncertainty distributions. Each variable required by ABAQUS has an associated default value for which has been used in the base case analysis (brick 4 calculation). Quantifying the range of values gives an estimate of the variability of an input parameter. For most parameters, a normal distribution has been assumed, or for some parameters where only rough data are available, a triangular distribution has been assumed as this introduces less bias in the results. 4.3 Method for generation of input parameters For the uncertainty analyses performed with the ABAQUS 2D model, a Latin Hypercube Sampling (LHS) scheme has been used. LHS is a stratified scheme that is designed to ensure that, for each uncertain parameter considered, the sampling procedure covers the full range of the distribution, The advantage of this stratified scheme over traditional Monte Carlo sampling is that coverage of the full range of parameter values is guaranteed by much smaller numbers of samples, thus resulting in less runs of the model being required for the analysis, The number of code calculations depends on the requested probability content and confidence level of the statistical tolerance limits used in the uncertainty statements of the results, The required minimum number n of these calculation runs is given by the Wilks formula (Wilks [3]). For two-sided statistical tolerance intervals the formula is: l-d - n*(l- IX)*rx -]>=~ (5) ~ is the confidence level (%) that the maximum code result will not be exceeded with the probability a x 100 (%) (fractile) of the corresponding output distribution, which is to be compared to the acceptance criterion (Glaeser [4]). The cotildence level is specified to account for the possible influence of the sampling error due to the fact that the statements are obtained from a random sample of limited size. The minimum number of calculations can be found in Table 2. Table 2: Minimum number of calculations n for two-sided tolerance limits, plct

9 Risk Analysis III 433 In case a = ~= 0.9 it is enough n=38. For this study, a set of 40 runs has been performed based on sampling of 16 input parameters. 4.4 Uncertainty analysis results Variation of bore diameter with time of operation for all calculations are shown in Figure 5, L Figure 5: Variation of bore diameter with time of operation for all calculations. Following the completion of the n runs of the code for each analysis, the uncertainty in the results of the predictions of gas-gap closure from the 2D model may be assessed. Uncertainties in the results of the 2D model can be estimated from the results of the uncertainty analysis. For each of the ABAQUS calculations, a separate profile is generated for each of the input samples. This means that for any particular endpoint (or result parameter) of interest, n separate profiles are generated, Consequently at each simulation time step n ABAQUS prediction of the endpoint have been produced and the range of these prediction represents the range of uncertain y in that endpoint at that time step. From these results upper and lower bounds have been determined based on the runs that have been carried out to date. When a and ~ equals 0.9, confidence intervals with probability of 0,9 are shown in Figure 6.

10 434 Risk Analysis III tt4, ~~4,2y r 114 h i, $$3.8 F S,6. &. upper 1,.,1 :. m 1!3, Lower 1,. (I. : 113,4-4f2,8-, ~ % -.=_ Years of opera%n Figure 6: Confidence limits, 5 Conclusions According to Technical Specification: Plant must show that with confidence 0.95 there will be no channels with zero gap until next outage including data collected during current planned preventive maintenance, Technical Specification requirements for gas gap closure are fulfilled. The estimated probability of the gas gap closure until 2002 is close to boundary probability. Uncertainty analysis confirmed gas-gap presence until In-depth probabilistic and engineering analysis of the gas gap closure needs to be performed also in Ignalina Unit 2, References [1] [2] [3] [4] SAR., Ignalina Safety Analysis Report, Final Edition, Vattenfall Nuclear Project AB for the Ignalina Nuclear Power Plant, Hopkinson, K. L,, Marsden, B. J,, Dundulis, G., Kopustinskas, V. & Liaukonis, M., The implications of gas-gap closure in the Ignalina NPP. AEAT/RJCB/RDOl /001, Issue 1, 2001, V7ilks, S. S., Statistical prediction with special reference to the problem oj tolerance limits, American Mathematical Society, 1942, Glaeser, H. G., Uncertainty Evaluation of Thermal-hydraulic Code Results, International Meeting on Best-Estimate Methods in Nuclear Installation Safety Analysis (BE-2000), Washington, DC, USA, 20 p,, 2000.