ML18065B047

TR on Use of Mcbend Code for Calculation of Neutron Fluences in PVs of Lwrs.

ML18065B047
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Issue date:	07/12/1996
From:	Avery A, Chucas S, Carolyn Cooper AEA TECHNOLOGY
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• CONSUMERS POWER COMPANY PALISADES PLANT DOCKET 50-255 TOPICAL REPORT ON THE USE OF THE MCBEND CODE

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FOR THE CALCULATION OF NEUTRON FLUENCES IN-THE PRESSURE VESSELS OF LWRS i.,*

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Report AEAT-0352 AEA Technology AEAT-0352 Topical Report on the Use of the MCBEND Code for the Calculation of Neutron Fluences in the Pressure Vessels of LWRs AF Avery July 1996 NAME SIGNATURE POSffiON DA1E Author Alan Avery Al (,v-1 Shielding Consultant RPS CD Lf(1(?k Checker Steve Chucas

~~

Shielding Product Manager RPSCD \l~~\

Approver Colin Cooper Department Manager, c~~ RPSCD I~ :; .C\G REACTOR PHYSICS, SHIELDING AND CRITICALITY DEPARTMENT PLANT SUPPORT SERVICES GROUP AEA TECHNOLOGY plc WINFiUTH .

UNITED KINGDOM AEA Technology

AEAT-0352 This report was prepared as an account of work carried out by AEA Technology plc in accordance with the contract between AEA O'Donnell Inc. and Consumers Power Company dated 10 October 1994 .

• The information which this report contains is accurate to the best knowledge and belief of AEA Technology pk, but neither AEA Technology plc nor any person acting on behalf of AEA Technology pk make any warranty or representation expressed or implied with respect to the accuracy, completeness or usefulness of this information, nor assume any liabilities with respect to the use of, or with respect to any damages which may result from the use of any information, apparatus, method or process disclosed in this report .

• 1

AEAT-0352 Topical Report on the Use of the MCBEND Code for the Calculation of Neutron Auences in the Pressure Vessels of LWRs AF Avery ABSTRACT The subject of this Topical Report is the application of the Monte Carlo code MCBEND9 to the calculation of neutron fluences in the pressure vessels of light water reactors. It has been prepared for submission for review and acceptance under the NRC licensing topical*report program. Features of the Monte Carlo method and its application to the calculation of neutron fluxes in reactor shields are discussed. The code MCBEND9 is described and details of its verification and validation are presented. The latter include comparisons of predictions against measurements of a range of reaction rates in water, the NESDIP2 benchmark, and H B Robinson Unit 2. In the calculations nuclear data from ENDF/B-VI were used for the materials with cross-sections from the International Dosimetry File, IRDF-90, being adopted as the response functions for the detectors. The NESDIP2 experiment is a simulation of the radial shield of a PWR with measurements being made within the slabs of steel that represent the pressure vessel. The results from H B Robinson provide comparisons with measurements made in a surveillance capsule at the inner surface of the pressure vessel and also in the cavity outside the vessel. The comparisons thus meet the requirements of the Draft Regulatory Guide, DG-1025, that methods must be validated against _a power reactor benchmark that provides in-vessel surveillance capsule dosimetry or ex-vessel cavity measurements or both, and a pressure vessel simulator benchmark that provides measurements at the inner surface and at the T/4 and 3T/4 positions within the vessel wall. The reports which describe the validation comparisons are included as Appendices. They give detailed analyses of the uncertainties associated with the calculations. The results confirm that MCBEND9 with the data from ENDF/B-VI and IRDF.,9Q gives agreement between predictions and measurements which is consistent within these uncertainties. Finally the use of the SENSAK code to adjust the calculated fluxes when reaction rate measurements are available at a plant is described.

AEA Technology pie Plant Support Services Group Reactor Physics, Shielding & Criticality Department Winfrith Dorchester Dorset DT28DH United Kingdom 11

AEAT-0352 0

- * - **- -~ NTE::ODUCTION -** ---- -- - *-* . -*-*. - -- - - ~age ---- - -

2 THE MONTE CARLO METHOD 1 3 THE MCBEND9 CODE 2 3.1 Geometry* 2 3.2 Nuclear Data 3 3.3 Sampling 4 3.4 Acceleration 4 3.5 Scoring 6 3.6 Summary 7 4 QUALITY ASSURANCE 7 5 VERIFICATION 7 6 VALIDATION . 8 6.1 Benchmark Measurements 8 6.2 Water Benchmark 8 6.3 NESDIP2 Benchmark 8 6.4 H B Robinson Plant 9 7 ADJUSTMENT n 8

SUMMARY

12 REFERENCES 13 APPENDIX A . Analysis of the Winfrith Water Benchmark Experiment Using ENDF/B-VI and IRDF-90 Data APPENDIXB The Analysis of NESDIP2 with ENDF/B-VI Nuclear Data and IRDF-90 Response Cross Sections APPENDIXC Further Analysis of the H B Robinson Unit 2 PWR using the Monte Carlo Code MCBEND with ENDF/B-VI and IRDF-90 Nuclear Data APPENDIXD Few-Channel Unfolding in Shielding - The SENSAK Code IV

AEAT-0352

1. INTRODUCTION

-McBEND9(l)isthe mo-strecent veI'Sion of the- ?Vfonk Caifo-cooe which has beencievefope<l by- ---- --

- AEA Technology and applied to problems of neutron and gamma-ray transport over many years.

The subject of this report is its use in the calculation of neutron fluences in the surveillance capsules and pressure vessels for Light Water R~actors.

The method which has usually been employed for this type of work has been based on discrete ordinates codes such as DORT(2) with the synthesis of three dimensional distributions from the results of one and two dimensional calculations. The advantage of the Monte Carlo method is that it can describe the geometry without being restricted toXYZ and R9Z orthogonal arrays of mesh

- points. It also avoids the need to average the nuclear data over wide energy ranges in the preparation of multi-group libraries, and thus removes the requirement to estimate a weighting spectrum for each of the groups.

This report describes the Monte Carlo method and discusses the questions which need to be addressed in its application. It then considers how these are dealt with in calculations carried out with the MCBEND code. The Quality Assurance procedures which are followed in managing the code are described together with a summary of the user documentation. Details of the verification tests which have been performed on the code and descriptions of three validation benchmarks

-relevant to the pressure vessel calculations are presented. Finally the ~djustment procedure which is applied when measw:ed re~tion rates are available to complement the calculations is described

2. THE MONTE CARLO METHOD The possible application of the Monte Carlo method to calculations of neutron transport has long been recognised (3), (4), (5), but its use has become much more widespread with the rapid development of cheap computing power in recent times. This was evident at the 8th International

-* Conference on Radiation Shielding held in April 1994 where 58 papers which referenced Monte Carlo codes were presented (6).

The Monte Carlo approach estimates the population of neutrons within regions of a given configuration of materials by creating typical tracks. If the spatial and energy distribution of the sources of neutrons are known together with the laws which govern their interactions with the nuclei comprising the materials, then it is possible by sampling from the appropriate probability function at each stage to generate a path from birth to death or leakage from the configuration. This sampling is performed by choosing random numbers in the range 0-1 and operating on them so that they correspond to a selection from the particular probability distribution. This reproduces the processes that occur in reality where a neutron path is determined by the probabilities inherent in the physical laws. At any point on its track it is therefore necessary to know the cross-sections and the associated distribution of secondary neutrons which represent these laws. In order to do this the

• code needs to recognise when a boundary between materials has been crossed, but these can be specified in a very-general way so that the method is not restricted to regular geometries. As the energy of the neutron is known at any point along its track it is possible to refer to the cross-sections corresponding to that energy, and to sample directly from the explicit laws governing the

• angular distributions of scatter and the secondary energies rather than representing them by multi-group averages and parametric fits.

For any general source distribution and configuration of materials there are an infinite mimber of possible paths, so that both the actual migration of neutrons and the Monte Carlo simulation of the process will produce finite sets of samples from this distribution and will thus show stochastic variations. These are much more evident in the calculation where the numbers of tracks generated are far fewer than the numbers of neutrons emitted by the true sources, so that the Monte Carlo estimates of neutron fluxes have statistical uncertainties associated with them which are sigriificant.

1

AEAT-0352 A key feature in the application of the method is the extent to which this statistical uncertainty c reduced so that if possible it becomes small compared with the other uncertainties arising from knowledge of the cross-sections, the specification of the materials, and the definition of the sour This is achieved by concentrating the tracking on those paths which are most likely to reach the regions of interest in a problem. This artificial increase in the probability of a track contributing to the score is counterbalanced by a reduction in the weight of the particle which is included as a multiplicative factor in the scoring process. There are many techniques which have been employed for accelerating Monte Carlo calculations; in this report only that adopted when applying MCBEND to the prediction of neutron fluences in LWRs wi~l be discussed. This is included in the description of MCBEND ...

which is presented in the next section.

The Monte Carlo method is a po~erful approach to sol~ng neutron transport problems butwhen performing such calculations there are a number of features which need. to be considered in order to ensure that the results are meaningful. These are listed below.

(a) Geometry. Does the model accurately represent the practical situation? Are there "any poin~ which could lie in more than one region? *

. (b) Nuclear Data. Are the cross-Sections and the laws govemi~g the emission of secondary particles adequately represented? ,: .. , .

. (c) Sampling. Is the random number generator acceptable in its cycl~ length and the distribution of its numbers? Are the algorithms for sampling satisfactory?

(d) Aeceleration. Has the acceleration t.eChnique led to a class of p()ssibly significant

. paths being omitted from th~ sampling process? *

. * . (e) . Scoring. What is the likely distribution of the Scores? .Are the~ ~y high s c o r .

pat~s which are very infrequently sampled? Are the standard deviations acceptably low? .

The way in which the MCBEND9 code is applied to the calculation of neutron. flueri~ in LWRs is

.de5cribed in. the next section where each of the above factors is co.nsidered in more detail.

3.. THE MCBEND9 CODE The facii~ties of the MCBEND9 cod.e as employed in the fluence calculations for PwR pressure vessels are described in the various sub-sections which follow.

' 3.1 Geometry

. The* geometry of the problem is represented in MCBEND by dividing it into zones which are defined by specifying the surfaces which form their boundaries. The latter may be planes, spheres, ellipsoids, cylinders, cones, and tori, with sections of the surfaces being combined to form zones with complicated shapes. The Fractal Geometry system which is employed in MCBEND9(1)

• enables the model to be divided into "parts" with zones being specified to fill each part This sub-

• division can be used to simplify construction of the model; since local co-ordinate systems can be used within each part, or to take advantage of replication which may be present Alternatively the whole model may be one part. The combinations of surfaces are specified in most cases by .

constructing the model from bodies. Cylinders and cones thus have two end faces as well as their curved surfaces, whilst prisms .and boxes have six plane surfaces. The zone is then defined as being outside or inside each of the bodies from* which it is built The exception to this is the plane which can be specified as a single surface with the zone being defined as being on a given side of the plane. A single material fills each zone and this is specified by means of a number which refers to compositions which are listed in another unit of the data input. *

• 2

AEAT-0352 Tracking in MCBEND9 is carried out in the standard way by determining the next boundary to be crossed and the zone which is entered after that crossing. For a neutron entering a zone the distances along its path to its intersection with the surfaces defining that zone ~~c_alc!.!l~ted*_ 'Th~ __ _

-- - -- - * ~--- ---- - - -- shortest distance-is-taken and if this ts less tharf tllerenfaining lerigth of ilie flight of the neutron then this gives the next boundary crossing. If it is not then the position of the particle interaction within the zone is calculated.

Testing of the accuracy of the geometry model is an essential step in checking the input of a Monte Carlo calculation. For MCBEND9 this is performed using the programs SKETCH, VISAGE, VISTA-WIRE, and VISTA-RAY. SKETCH carries out the following functions:

(a) it displays the material, region, or zone numbers at the mid-point of a regular spatial

. mesh in a selected plane, (b) it performs checks for multiply-defined or undefined regions to ensure that each ..

point is uniquely associated with a zone, (c) it estimates zone, region, and material volumes within selected regions of a model, (d) it estimates body surface areas, (e) it performs a detailed qiagnostic trace for a pre-defined track, and (f) it creates a file for detailed analysis using the VISAGE program.

• The essential steps are those in (b) and (f), the latter being equivalent to (a) but giving a display with higher resolution. * *

• VISAGE displays in colour the materials, regions, or zones in a two-dimensional slice through the model. By examining a number of such slices it is possible to check that the model is reproducing the required configurations.

The check for undefined or multiply-defined regions is necessary to ensure that the* model is complete and unambiguous. MCBEND9 will stop if a neutron enters an undefined' region, but it does not recognise the presence of two overlapping regions. In the latter case it could choose.either of the two materials specified for such regions leading to errors if the wrong one is selected.

. SKETCH is therefore used to eliminate any doubly-defined regions from the MCBEND model

. through the checks in (b).

• Volumes are not used in the tracking process but they are needed for track length scoring of fluxes and reaction rates. They can usually be calculated accurately by analytic methods, but facility (c) provides a check by estimating the volume from the mean length of a set of tracks, albeit with a standard deviation associated with the sampling which gives this mean.

Further checks of the geometry may be carried out using the VISTA-WIRE program which generates three-dimensional outlines or shaded views of the bodies which form the model, and VISTA-RAY which produces three dimensional pictures of the model showing materials, regions, or zones. By use of these programs it is possible to ensure that the model accurately represents the practical situation.

3.2 Nuclear Dat~

The neutron cross-sections for the materials in MCBEND9 cakulations for L WRs are based on the ENDF/B-VI library. To facilitate sampling the data are processed into the DICE format as described by Parker (7). The ENDF/B-VI data contain doubly differential distributions in energy and angle 3

AEAT-0352 for Cr0 , Cr 2 , Cr 3 , Cr4, Fe", Fe", Fe58 , Mn 55 , Niss, Ni , Ni61 , Ni62 , Ni64 , um and U238 w -

60 are isotopes of interest in LWR calculations. These data have been converted into independent distributions in energy and angle using the SIXPAK program (8). The simplification of the data this way is not expected to lead to significant errors because the correlations between energy and angle for the non-elastic interactions are only important at energies above 10 MeV. The data have been processed into the DICE format using the NJOY code (9) with a modified ACER module and additional modules CNMONK and MOULD. The route, methods validation, and the production of the* DICE library of ENDF/B-VI data are described by Eaton and Dean (10). This library has been entered into the ANSWERS QA Set following the standard procedure (11) of AEA Technology's ANSWERS Software Service (see Section 4). The cross-sections in the validation comparisons and in the application to calculations for LWRs are represented by the mean values in 8,220 energy bands while the energy loss laws and the angular distributions are expressed as cumulative

• probabilities which are sampled directly at the specific energy of the neutron. _

The uncertainties associated with the cross-sections have been expressed as co-varianre matrices by processing the relevant files from ENDF/B-VI using the ERRORR and COVR modules of NJOY (9). However for hydrogen and oxygen there are no error files in ENDF/B-VI and in these cases the.co-variances have been taken from ENDF/B-V data as processed by Kodelli and Sartori (12).

The compilation of the library of co-variance data is described by Ziver and Earwicker '(13).

The response cross-sections for calculating the reaction rates of detectors have been taken from .

IRDF-90 (14)_, where they are expressed as mean values in the 640 energy bands of the SAND II group .scheme (15). The uncertainties ass9ciated with these response cross-sections have been derived from the IRDF-90 library using the relevant modules of NJOY. *The processing of the IRDF cross-sections and co-variances into the form in which they are used in the MCBEND calculations is also described in reference 13.. * '*

3.3. Sampling . . .. . **

Sampling of the probabilities at each stage in the creation of the rieutro'n tracks is performed using random numbers. The latter are generated by algorithms which give a sequence of numbers which can be identically re-generated if the same starting point is used. They are .thus "pseudo" random numbers, but this is satisfactory for use in Monte Carlo calculations provided that the sequence has been shown to meet conditions of randomness. The latter involve tests in which the numbers are used to sample various probability distributions and then demonstrating that expected_ properties of the distribution are reproduced. The other significant feature of a randoin number sequence is the cycle length, i.e. the number of random numbers which are generated before the sequence starts to repeat itself. Obviously if the calculation is reproducing tracks which h;ive already been followed .

. by earlier -sam pies, then it will not be *generating new information*and the statistical estimation of th~

standard deviation will be too optimistic.

In MCBEND the random numbers are produced by a combination of a Lagged Fibonacci (16) and a -

Linear Congruential generator. This has been shown to satisfy extensive tests of randomness, and it has a cycle length in excess of 1014 numbers. Each Monte Carlo calculation of the flux distribution in an LWR shield requires typically 2 x 108 random numbers so that there is no danger of track duplication. _ . * * * * ,

• 3.4.

• Acceleration ,,'

The Monte Carlo calculations of the neutron fluences at LWRs are accelerated by the use of the standard technique of splitting and Russian roulette .. In the MCBEND code the geometry of the problem is overlaid with an orthogonal spatial mesh in which the neutron "importances" are specified in a number of energy groups. The "importances" are approximate values of the probability of a neutron contributing to the score which is of interest in the particular calculatio.

Accurate values of the neutron importances are given by the solution of the adjoint trarisport 4

AEAT-0352 equation but if these were available they would enable the quantity of interest to be computed directly from a knowledge of the neutron source distribution so that there would be no need for the forward calculation. The derivation of accurate values of the importances is a problem of... _

- ----*complexity similar to that of the forward calculation so tharthey are nofreadilf avmfatile. It is found. however, that approximate values of the importances are effective in accelerating Monte Carlo calculations since they provide sufficient indication of whether a neutron is becoming more or

. less likely to contribute to the score of interest. The MCBEND code has an in-built facility which ..

derives such approximate importances by solving the adjoint transport equation in the simplified form based on a multi-group diffusion treatment. although the group parameters have been adjusted to improve the accuracy at deep penetrations. The irregular three-dimensional model is translated into an orthogonal array of materials for this calculation of the importances by smearing the materials or by adopting the dominant material within a mesh. The importances are then used in the conventional way in splitting and Russian roulette; i.e. when a neutron moves to a region where its importance is increased by more than a factor of 2 it is split into a number of particles which are then tracked separately; conversely when its importance decreases it is killed off with a probability determined by the change. The weights assigned to the neutrons are adjusted after splitting or Russian roulette so that weight is conserved on average. In MCBEND calculations for LWRs, sampling of the source distribution for the initiation of tracks is also controlled by the same importance map so that the weights of all neutrons at a particular location are consistent The use of splitting to accelerate Monte Carlo calculations can be seen as a way of distributing the information obtained from tracking in a more uniform way over the depth of penetration of interest In a straightforward analogue calculation most neutrons would be captured close to the source ~o that the density of tracks there would be high and the statistical uncertainty on the neutron flux~

would be small. Relatively few neutrons would reach. deeper penetrations so that the quality of information there would be poor. By splitting neutrons as they move towards a target region the tracks are distributed more uniformly and the statistical uncertainty is reduced at deep penetrations at the expense of poorer accuracies close to the source. Because the importance map as derived by MCBEND is continuous in space and energy it is very unlikely that any important penetration path will not be sampled. (If it were sampled infrequently then this would be seen in high standard deviations.) With splitting and Russian roulette MCBEND employs natural sampling of the path lengths and the angular distributions of scatter. It does not distort the tracks and is thus more robust than techniques such as path length stretching or angular biasing of the angle of scatter. where emphasis is placed on creating tracks of a particular class, and it is not always possible to justify this choice a priori. The use of adjoint solutions in MCBEND provides a standardised way of_:*

generating the importance maps which control the splitting and Russian roulette. Application of this

. _approach in the validation comparisons, such as that for the H B Robinson plant for example, then gives confirmation of its suitability for general use in calculations of PWR fluences when the same procedure is used.

The use of splitting to give a more uniform distribution of the collisions.being treated in the Monte

• Carlo calculation introduces one possibility for error which would not be present when there was no acceleration. The large number of collisions occurring close to the source in the latter case would generate scattered neutrons covering a wide range of energies and directions of motion. If there .

were a very narrow energy band in which the cross-section was exceptionally small then a scattered neutron moving in the appropriate direction in this "window" could readily penetrate deep into a shield. Such a path has a low probability of being sampled but could give a high contribution to the flux at deep penetrations. In an analogue calculation such a path would be sampled if it were important. When splitting gives fewer collisions close to the source then the probability of

• sampling such a path is reduced and its contribution could be omitted. This would not arise when the approximate adjoint solution recognised the presence of "streaming" in the cross-section window, but this would not be very likely given the nature of the multi-group parameters.

(Similarly in discrete ordinate calculations with multigroup cross-sections the neutron would never "see" the narrow window.) It is therefore possible to postulate a situation in which splitting and Russian roulette as applied in MCBEND could underestimate the fluxes. However in practice this 5

AEAT-0352 has never been found to occur. It would be most likely with thick regions of single materials wh the "window" would extend for distances of very many mean-free-paths for neutrons with energ outside the window. It has not been found in LWR radial shields with their layers of steel and water.

The application of splitting and Russian roulette in MCBEND calculations together with the code's in-built facility for determining the importance maps thus provide a standardised approach for acceleration .. The absence of bias in the use of this technique is demonstrated in the validation calculations for the LWR fluence applications. It has also proved to be a robust and reliable method in a wide range of other calculations of neutron attenuation in shields ( 17), ( 18) ..

3.5 Scoring MCBEND can score the fluxes of neutrons in any specified energy group scheme using either track length, collision density, or point estimators. The first two give the mean values of the fluxes within the volume of the scoring region. For reactor calculations track length scoring is used because it gives results in low density regions (e.g. air) and also in thin regions when spatial resolution is required. Reaction rates are scored during tracking by inultiplying the track length by a reaction cross-section at the energy of neutron for that part of its track. The energy dependence of

.the response cross-sections is specified as a histogram, the standard IRDF library used in the calculations* for L WRs being given in 640. energy groups. The slims of the contributions of the samples to the score in each bin (i.e.-to the response or flux in each scoring region for each of the scoring groups) are accumulated as*are the.sums of the squares of the contributions. This enables

• the mean score and the associated standard error on the mean to be derived at the end of the calculation. *

• The significcmce which can be anach~d *to the standard error depends upon the distribution from

, *which the .scores are sampled. The central limit theorem states that the means of sampl~s taken f any distribution will show a normal distribution provided that sufficient samples are taken and th

• the second order moment of the sampled distribution about the mean is finite. *

.The distribution of scores in MCBEND with automated source weighting will arise from the

• variation in track lengths and the number of particles contributing to the score of the sample (i.e. the

... number of split samples which.reach the scoring region). The weigh~ of the particles will be identical in each group, and if the response .function* has been used as the adjoint source, that weight will be inversely proportional to the* response cross-s~tion _in the group giving a constant product when the two factors are combined; When a compromise adjoint source is used to score several detector responses iri the same calculation, there will, however, be an additional variation sj.nce the factors will i:iot balance exactly for all detectors. *

• The main contributio~s to the variation will thus arise from the path :lengths and the n'umbers of

• particles which score for.each sample. The first will be distributed between zero and a clearly.

defined maximum determined by the size of the scoring region~ while the second will show statistical fluctuations due to the sampling of the probabilities of particles reaching the next splitting boundary. The fatter will also show sharp rises if the probability of a neutron following a particular set of tracks is much greater than is indicated by the importance map. In this case extensive splitting will take place, many secondary particles will reach the scoring regions, and a high contribution will be recorded. This will show in the high standard deviation when a large part of the score is due to one sample. The possible danger is *that discussed in section 3.4 above where the probability of the high scoring path is so low that it is not sampled. As discussed in Section 3.4 there is no evidence which suggests that such paths would be present in calculations for L WR vessel fluences, and none of the extensive calculations which have been carried out for this application show any sudden increase in standard deviation which would symptomise this effect.

6

AEAT-0352 The distribution of scores as discussed above will meet the requirement that the second moment should be finite for the central limit theorem to apply. The number of samples that are needed to meet the other conc!itiol}__c:a!l!!_Clt ~specifi~d a prio_ri. but _experience from calculations has shown --- --

- - -- -that resultS wiili standard deviations of 20%-30% can change by many standard deviations as more samples are scored. However, when the standard deviation is less than 10% the changes are more consistent with those for a nonnal distribution, so that the aim is always to reduce the statistical uncertainty below this level.

MCBEND also includes a scoring option which will give the fractions of a response which are due

• to reactions in each of the scoring groups. This enables the uncertainty due to the response cross-sections to be estimated since these are the sensitivities which are needed to fold with the co-variance data for the response cross-section. The code will also calculate the sensitivity of a response in a given region to the cross-sections of the materials comprising the model of the reactor.

This is achieved during tracking by scoring the differential of the probability of that track with respect to the specified cross-section. The latter can be for any reaction in any element of the reactor materials, and the sensitivities can be derived for a number of energy ranges of the cross-section.

These can again be folded with the co-variance data for the material cross-sections in order to estimate the uncertainties in the calculation of the response due to uncertainties in the nuclear data.

3.6 Summary The way in which the MCBEND code addresses possible errors entering into the Monte Carlo method have been discussed. Steps are taken to eliminate each of the sources of bias so that the calcula_tion produces reliable results. The positive evidence that this has been achieved is contained in the_ benchmark validation comparisons, where application of the same techniques produces good agreement with measurements. These are considered in more detail in a later section. The MCBEND

• • code is described in the comprehensive User Guide (1) which includes descriptions of features of the code and advice on their use as well as the specification of the fonnats for the input data.

4. QUALITY ASSURANCE Quality Assurance (QA) is a requirement for software which-is used to perfonn calculations associated with .the safety of reactors. QA principles embrace all aspects of a software package including development, maintenance and in-service use. In the United Kingdom these requirements led to the establishment of AEA Technology's ANSWERS Software Service which has set up~a comprehensive range of software management QA procedures covering the complete life-cycle-including specification, design, coding, testing and in-use support and maintenance. These standards are employed in the development and validation .of the MCBEND code. The Quality Management System provided by these procedures has been certified against the International Standard ISO 9001.

The source code for version 9 of MCBEND was passed to ANSWERS for testing, commissioning and final distribution as a recognised updated version of the code. The version was formally identified (version 9) and changes made since the previous version and the documentation that supports the changes were recorded and archived. ANSWERS then commissioned the code for a range of standard computer platfonns, the load module for each type being fully tested at commissioning.

• Any further developments of the code will be carried out under the same procedures to provide Quality Assurance. .

5. VERIFICATION Verification of MCBEND9A has been achieved by carrying out the 113 standard tests that have

• been assembled over a period of 10 years in order to check the various functions of the code (19).

7

AEAT-0352 The results were mostly compared with those given by earlier versions of the code, although in few cases analytic solutions were available. This procedure ensures that changes made to the c have not perturbed any of its previous functions, whilst the comparisons for problems with kno answers provide direct tests of the algorithms as programmed in MCBEND. Verification of a subsequent version of the code, MCBEND9B, which contained a number of minor developments has been carried out by running the 113 cases and also by the introduction of additional tests for which there are analytic solutions (20).The latter are based on the use of a library of artificial nuclear data which is written in the formats of the DICE library used in practical calculations with MCBEND, but which contains data for nuclei with simplified properties. Details of this approach are described by Shuttleworth (21). By suitable choice of such nuclei, analytic solutions can be obtained for problems which enable more routines within the*code to be tested in a direct manner rather than against previous results. As MCBEND9B is mostly identical to MCBEND9A, its verification provides additional checking of the earlier version.

6: VALIDATION 6.1 Benchmark Measurements The MCBEND code has been validated against measurements for a range of situations and this has been documented.in a number of reports. Validation of the particular application of MCBEND to the calculation of neutron fl uences in the pressure vessel of L WRs is provided by the comparison with the benchmarks which are described in detail in Appendices A, B and C. These cover penetration in water, the NESDIP2 array of water and steel, and the H B Robinson radial shield for Cycle 9 of the plant's operation. The NESDIP2*experiment is a simulation-of the water, core barrel, and pressti,re vessel of a PWR shield with measurements being made within the steel slabs which represent the

. pre5sure vessel. This comparison thus provides validation of the method for points within the vessel wall as required in reference 22. The results from the individual benchmarks. are summ in the sections below.

6.2 Water Benchmark The detailed description of the comparison of me'asurements and *calculations f9r the water benchmark is given in ApEendix A.. The neutron souree for this experiment was provided by spontaneous fission in Cf- 2 and the attenuation of high energy neutrons, E>2MeV, .was mea5ured with the S 32(n,p )P-12 reaction. The ratios of the calculated to* experimental reaction rates (C/E) for points on the plane of the sources lie between 0.965 and 1.035, with no consistent trend with increasing penetration. The uncertainties on the values of C/E (one standard deviation) are estimated to be between 7.4% and 8.1 % with .the largest' contribution of 6% arising from the .

measurements. The largest uncertainty in C/E due to the cross-sections of water as calculated using the co-variance data (13) is at the deepest measurement position of 355.6mm where it is+/- 2.4%.

The agreement of measurement and calculation to within 4% at all five penetrations suggests that the uncertainty on the measurements was less. than was estimated, confirms that the calculation of fast neutron attenuation is accurate to within 4% over a* penetration of 355mm, and suggests that the .

uncertainties assigned to the cross-sections of hydrogen and oxygen in the library of co-variance data are appropriate with no significant under-estimation of the errors. **

6.3 NESDIP2 Benchmark The NESDIP2 Benchmark was a series of measurements carried out in the ASPIS facility with the source provided by a fission plate which was driven by neutrons from the NESTOR low power reactor operated by AEA Technology at Winfrith. This plate was approximately disc-shaped with a radius of 50cm and it was composed o( enriched U/Al coupons of 2mm overall thickness. The distribution of the source across the plate was measured with manganese foils whilst the absolute

. source was determined from the analysis of the fission products in selected coupons. The shiel array was a series of water tanks and steel slabs of lateral dimensions 1.83m x 1.91 m which 8

AEAT-0352 simulated the radial shield of a PWR, with measurements being made within the region of steel which represented the pressure vessel. The benchmark is described more fully in Appendix B.

The measurements were carried out-using-the three detectors S 32 (n,p )P32; -Jn 11 s(n;n')In 115 m, and Rh to3(n,n')Rh103m.

The sulphur and indium measurements were only made within the pressure vessel region and the cavity region outside of the vessel. For the sulphur detector the values of C/E range from 0.89 +/-

0.10 to 0.99 +/- 0.12 with the major contributions to the estimated uncertainties arising from the cross-sections for iron, the detector cross-sections, and the spectrum of the fission neutron source.

The values of C/E do not show any consistent trend with penetration, and the mean value for the five positions is 0.94 with the individual departures from unity being -1.1, -0.36, -0.08, -0.62, and

-0.29 when expressed as fractions of the standard deviations. Similarly for indium the mean value of C/E at the five locations is 0.95 with the discrepancies being -0.88, -0.63, -0.11, -0.44 and -1.0 when expressed in terms of the standard deviations.

The rhodium measurements were made at the same five locations in the vessel as those using sulphur and indium, but in addition detectors were irradiated in the two regions which simulated the downcomer water on either side of the steel slab representing the thermal shield. In the two regions of water the values of C/E for the twelve measuring positions ranged from 0.88 to 1.08 with a mean of 0.92 and discrepancies of -0.86, -1.0, +0.62, -1.23, -1. 7, -0.50, -1.00, -1.13, -1.38, -1.5, -

1.38 and -1.13 standard deviations. In the pressure vessel location the values of C/E were between 0.88 and 1.02 with a monotonic increase with penetration through the vessel followed by a fall for the measuring position in the cavity. The discrepancies expressed as fractions of the standard deviations for these locations were -1.5, -0.67, -0.11, +0.2, -1.2.

The mean values of bE for the three detectors :ire 0.94, 0.95, and 0.93 which suggests that the*.

absolute normalisation is low by about 6%. The uncertainty on the measurement of the power of the fission plate was estimated to be 3.5% (1 standard deviation). However if the source strength of the plate is increased by 6% then the mean C/Es for the three detectors are very close to unity and only 4 of the 27 individual values differ from unity by more than one standard deviation, the contributions from the source uncertainty having been removed from the latter. The comparisons of the measurements and calculations in NESDIP2 thus confirm the accuracy of the code and the data for calculations in PWR radial shields, and in particular in the simulated pressure vessel for neutrons in the energy range 0.37MeV to 19 MeV over which the three detectors are sensitive:

6.4 H B Robinson Plant Measurements of neutron reaction rates were made during cycle 9 at Unit 2 of the H B Robinson plant with detectors being irradiated in a surveillance capsule at the inner surface of the pressure vessel and in the cavity between the vessel and the primary shield. The reactor is a three loop PWR

. so that the measurements provide data against which the accuracy of calculations can be tested in a practical situation. MCBEND calculations have been carried out using the ENDF/B-VI data and IRDF-90 dosimetry cross-sections, and the results have been compared with the measured reaction rates. Full descriptions of the calculations and the results of the comparisons are given in Appendix

c. . .

The detectors that were used were Ti 46 (n,p)Sc 46 , Fe5:4(n,o)Mn 54 , Fe58 (n,g)Fe59 , Ni 58 (n,p)Co58 ,

Co 59 (n,g)Co 60, Cu6 )(n,a)Co 60 , U 23s(n,fx), U 238 (n,fx), Npb 7 (n,fx), and Sc45 (n,g)Sc 46

• The n,p and n,a reactions are sensitive to neutrons at energies above about 2MeV while the n,g reactions are due mostly to neutrons at thermal or near-thermal energies. The fission reactions cover a ranfe of energies; urn is sensitive to low energy neutrons, U 238 to those above lMeV, and Np23 mostly to those above 0.2MeV although some 5% of its response can be due to energies below this. In the surveillance capsule the Ti, Co, Cu and fission foils were covered with gadolinium to reduce any 9

AEAT-0352 response to thermal neutrons. (In the fast neutron detectors this can alleviate possibl~ problems

• burn-up of the product nuclei or activation through alternative reactions.) Similarly in the cavity Fes4. Niss, Cu 6 , U 238 , and Np 237 foils were encased in cadmium.

Calculations for cycle 9 of the operation of the plant were initially carried out with a source distribution for fissions within the core which corresponded to a time close to the mid-point of the cycle. This distribution was specified as relative powers in each fuel pin together with absolute powers for each fuel assembly. There are l 5x 15 pin locations in each assembly which were grouped into 25 arrays of 3x3 with a uniform source strength being specified within each array. The relationship between the reactor power and the neutron fluxes in the radial shield varies during the course of a cycle for two reasons. Firstly the power distribution changes with burn-up so that a greater proportion of the fissions occur in the peripheral fuel assemblies thus increasing the fluxes in the shield. Secondly the fraction of the power which is being generated by fissions in plutonium also increases with burn-up. This in turn has a number of effects on the neutron source. Firstly the energy released per fission is higher for Pu239 than it is for U 23S so that the number of fissions per watt of reactor power decreases. Secondly the number of neutrons emitted in fission is greater for Pu 239 than it is for um. the combined effect giving an increase of 13% in the neutrons per watt for Pu 239* The third difference is in the spectra of the neutrons emitted in fissipn in the two isotopes, that for Pu 239 being harder and thus giving greater penetration in water than that for um. For the calculation of the fluences (flux x time) at the pressure vessel for the cycle it would be possible to use mean values for the neutron source distributions for the cycle but this is not acceptable for the calculation of the activation of the detectors. The decay of the induced activity during the cycle will

. make the activation of different detectors dependent upon the power distribution at a particular time*

in ways which will be influenced by the half-lives of the product nuclei. It is therefore necessary to consider the variation with time during the cycle of the reaction rate per unit reactor power when calculating the activation produced .in the various detectors at the end of the cycle. In earlier .

MCBEND calculations for H B Robinson plant (23) the reaction rates were obtained for the p o -

, .. distributions and fractions of fiss1.* ons in plu~tonium corresponding to the beg_inning and the end

the cycle as well as for those close lo the middle of the cycle. These calculauons also used

• ENDF/B-VI datri for the materials but the cross-sections for the detectors were taken from IRDF-

85. The factors which related the mid-cycle reaction rates to the end-of-cycle activations of the .

. detectors were derived from the results.of t~e earlier calculations and applied to the mid-cycle results obtained with ENDF/B-VI and IRDF~90 data. It is thus assumed that the calculation of the relative

.time dependence of the reaction rates through the cycle is not sensitive to the changes in the detector cross sections. This assumption is valid because the differences between the cross-sections in the two compilations are small and they would only produce any effect if there were changes in the neutron spectrum during the cycle. The largest contribution* to the time dependence is due to the increase in the fluX/unit power during the cycle arising from the change in the power distribution within the core; the changes in.the neutron *spectrum at the pressure vessel are small. The .

combination of these two small effects makes the time variation effectively* independent of the .

change in the detector cross-sections and justifies the use of the time factors from the earlier calculations. *

• Uncertainties were estimated for the ratios of Calculation/Experiment (C/E) which were derived when the results were compared. Contributions for the calculation arose from the nuclear data, the detector cross-sections, reactor dimensions, material compositions, source strengths, the source spectrum, and the statistical standard deviations from the Monte Carlo method. Typically the latter were less than 4% which was much smaller than the total of those estimated for the other contributing factors. Uncertainties for the measured reaction rates were provided with the published results. * * .

At the surveillance position the comparison of calculation.and measurement gave values of C/E between 0.9 and 1.0 for seven of the nine detectors with the values of 0.85 and 0.89 for the other two reactions, Ti 46 (n,p)Sc 46 and U 238 (n,fx) zrs respectively. Comparisons were not made for.

low energy detectors which were covered with gadolinium because of the difficulty of calcula

• 10

AEAT-0352 the effect of the casing. The uncertainties on C/E are between 23.4% and 26.5% for the detectors at this position with the dominant contribution of 20% arising from the imprecise knowledge of the location of the capsule. This would affect all of the d_ete_<:~o-~_to_aJ>P!O~I)l~(!ly .the srune degree. The

-- mean value-of C/E-was 0:94 which -s-iiggests-tliat factors which affect all the detectors in a similar way, i.e. the capsule position, the source data, and the water density, give a small underestimation which is much less than one standard deviation. Uncertainties which apply to the C/E values for individual detectors, and which contribute to the spread about the mean, are those from the measurements and from the reaction cross-sections. For the Ti foils these are 10% and 5.3%

respectively with corresponding values of 5% and 0.7% for the U 238 results. The discrepancies between the mean value of C/E and the values for the individual detectors are less than one standard deviation from the combined uncertainties due to measurement and detector cross-section for all detectors. The calculations thus give results which are consistent with the measurements to within the estimated uncertainties.

The values of C/E for the comparisons of calculated and measured reaction rates in the cavity range from 0.90 to 1.14 for thirteen of the sixteen detectors with the values for the three neptunium detectors ranging from 0.82 to 0.88. For the fast neutron detectors the standard deviations on these ratios lie between 19.13% and 25.28% with the largest contributions of 11 % to 19% being due to the uncertainties in the cross-sections for iron. For the low energy detectors the latter contributions are less than4.0% with the overall uncertainties being between 14.7% and 17.5%. The values of C/E for the ten fast neutron detectors are between 0.82 and 1.05 with a mean of 0.93, whilst those for the low energy detectors are between 1.04 and 1.14 with a mean of 1.08. This indicates that the fast neutron reaction rates are predicted much more accurately than would be suggested by the standard deviations whilst the low energy fluxes are overestimated. The spread in the results for the individual reactions about the two means exceeds the standard deviations from the combined uncertainties due to the measurements and the response cross-sections in only one case, the C/M being 0.82 for Np237 (n,fx) Cs 137 with a difference from the mean the of 1.05 x the standard deviation. The fact that the results for the high and the low energy detectors fall into two clear groups is attributed to the greater sensitivity of the low energy neutron fluxes to the composition of the concrete. The uncertainty due to the latter has not been quantified but it will have a greater influence on the low energy reaction rates because in this case the neutron fluxes arise from backscatter from the concrete. The results suggest that this l>ackscatter was overestimated with the

' composition that wa.S adopted for the calculations. * .,

The agreement observed between calculations and measurements is thus better than that which would be expected with the estimated uncertainties at both positions and for all detectors. The .

results suggest that the uncertainties due to _the position of the surveillance capsule were overestimated as were those for the cross-sections for iron as obtained from the ENDF/B-VI co-variante files. The consistency between calculation and measurement therefore provides validation for the application of the MCBEND code to the prediction of neutron fluxes in the radial shields of PWRs.

7 ADJUSTMENT

• When calculations of the neutron fluxes are carried out for operating plant they are frequently combined with the results obtained from measurements in order to derive the best estimates of the neutron doses received by the pressure vessel and by specimens in surveillance capsules. The uncertainties on measured reaction rates are usually much less than those associated with the

. calculation so that confidence in the values of the doses is increased when the two are taken

• together. The results of the calculation are adjusted to improve their consistency with the measurements and this process usually reduces the uncertainties. (It is not possible to use measurements alone because they cannot be made at all the positions of interest, nor can the dose expressed either as fluence above lMeV or atomic displacements per atom be measured directly in the practical situation.) The process of adjustment of the calculations is not dependent on the method used to calculate the fluxes so that it is not necessary to employ any special technique for treating the 11

AEAT-0352 results from Monte Carlo. In this section details of the SENSAK code (25) which is used in Technology.for performing such adjusunents are given in order to complete the description of approach which is *applied to the calculation of pressure vessel fluences. The report specifying tti equations which are solved by SENSAK is included as Appendix D.

The SENSAK cooe follows the maximum likelihood procedure as discussed in ASTM Standard Guide E 944 (26). The results of the MCBEND calculation are presented as the neutron fluxes and the mean detector-cross-sections in a number of energy groups as specified by the user in his input These are fed into SENSAK togetl1er with their associated uncertainties. For the fluxes the latter are

• expressed separately as the components arising from the source, and those due to other factors with correlations between the groups being provided for this second type of data. Similarly co-variance data are specified for the detector cross-sections. Typical values of these uncertainties as estimated for the H B Robinson calculations are given in Appendix C. The measurements and their associated uncertainties are also specified. The SENSAK code then adjusts the group fluxes to improve the agreement between the measured and calculated reaction rateS and it generates co-variances for the adjusted data. The adjusted fluxes can then be folded wi~ response cross-sections to provide revised values of quantities such as the flux above lMeV and the displacement rate together with their uncertainties. The fatter will be based on the consistency of the measurements and the adjusted calculated reactic;m-rates together with the size of the adjusunents that were required. Because the accuracies of the measurements are usually much better than those of the calculations in the practical.

• situation, this procedure leads to*reduced uncertainties_on the ne\}tron doses. Also in practice the uncertainties on the fluxes* are much larger than those on the detector cross-sections s9 that it is the fluxes which are changed in the adjusunent procedure. An example of the use of SENSAK to improve the accuracy of some very coarse calculations is included in Appendix D.

8

SUMMARY

- The features of the Monte Carlo method have* ~n discussed and the way in which the method

• been implemented in* the MCBEND code has been described. Quality Assurance and verificatio the code have been described and the results of validation benchmarks for the calculation of neutron fluxes in the preS.Sure vessels of LWRs have been presented, with the more detaile.d reports of the

. benchmark comparisons with measurements being included .in Appendi.ces A, B, and C. The

- adjustment code SENSAK which can be used to improve the accuracies of the predicted neutron dos~s when measuremerits are availab.le at the operating plant has also been described.

This report thus provides validation for the application of the MCBEND9 Monte Carlo code to *

. provide accurate calculations of neutron fluxes in the' radial shields of LWRs when the nuclear data*

are taken. from ENDF/B-VI for materials and from IRDF-90 for detector .crossz'sections.

.. ('

'.J.

12

AEAT-0352 REFERENCES

-- -- --~--------- -----*- ---

---

u1 - --MCBENDUserGuide lo Versfon-9A, ANSWER-SfMCBENo(94)15.

[2] TORT-DORT Manual for Two!Three-Dimensional Discrete Ordinates Transport ORNURSIC-CCC-543. Version 2.8.14

[3] Cashwell E and Everett C J. A Practical Manual on the Monte Carlo Method for Random Walk Problems. Pergamon Press 1959

[4] Hammersley JM and Handscomb DC. Monte

. Carlo Methods. Methuen. 1964

[5] Goldstein H. Fundamental Aspects of Reactor Shielding. Addison-Wesley 1959

[6] Proceedings of the 8th International Conference on Radiation Shielding, Arlington, USA 1994.

[7] Parker J B. DICE MkV. The Preparation of Nuclear Data into a Form Suitable for Monte Carlo Calculations using an Electronic Computer. AEEW-27/66

[8] Cullen DE. SIXPAK:* A Code Designed to Check Double-Differential Correlated Data and Calculate "Equivalent" Uncorrelated Data.

UCRL-ID-110241

[9] MacFarlane R E & Muir D W.

The NJOY Nuclear Data Processing System, Version 91 ~

LA-12740-M

[10] Dean CJ & Eaton CR. The 1994 DICE Nuclear Data Library AEA-RS 5697

[ 11 Production of Nuclear Data Libraries for Applied Purposes.

Reactor Physics, Shielding and Criticality Department Procedure 2.306 AEA Technology .

[12] Kodelli I and Sartori E Co-variance Data Library. Z:Z-VITAMIN~J/COV A, NEA1264, OECD/NEADB 1990

[13] Ziver A K and Earwicker J Generation of Variance-Covariance Data from the ENDF-B/VI and IRDF-90 Nuclear Data Libraries. AEA-TSD-0387

[14] Kocherov N P and Mclaughlin P K The International Dosimetry File (IRDF-90), IAEA-NDS-141October1993.

[15] McElroy W N, Berg S and Crockett TA Computer Automated Iterative Method for Neutron Flux Spectra Determined by Foil Activation. AFWL-TR-67-4 Marsaglia G and Zaman A. Toward a Universal Random Number Generator.

Supercomputer Computations Research Institute and Department of Statistics.

The Florida State University, Tallahasse

[17] Locke HF. NEACRP Intercomparison of Codes for the Assessment of Transport Packages:

Solution for the TN12 Benchmark Problem. AEA-RS-1063 13

AEAT-0352

[ 18)

[19)

Wright GA. Analysis of the Winfrith Graphite Benchmark Experiment AEA-RS-5628 The Verification of MCBEND 9A.

NCDIMCANOfIT.119. AEA Technology

[20). Shuttleworth E. MCBEND Verification. Review of Tests NCD/MCANOfIT.1/14. AEA Technology

[21) Shuttleworth E. The Verification of Monte Carlo Codes in Middle Earth.

Proceedings of the 8th International Conference on Radiation Shielding, Arlington, USA

. 1994. pll48

[22) Draft Regulatory Guide 00-1025 Calculation and Dosimetry Methods for Determining Pressure Vessel Neutron Auence. USNRC September 1993

[23) .. Locke (Mrs) H F. Further Analysis of the H B Robinson Unit 2 PWR using the Monte Carlo Code MCBEND with ENDF/B-VI Nuclear Data.

AEARS 5579 .

[24) Lippincott E.P. et al.. Evaluation of Sm:veillance Capsule and Reactor Cavity Dosimetry '

from H B Robinson Unit 2, Cycle 9 WCAP-11104, NUREG/CR-4576 125) McCracken AK. Few-Channel Unfolding in Shielding-The SENSAK Code.

Proceedings of the Third ASTM-EURATOM Symposium on Reactor Dosimeuy;

• 1975. pp 732-742 . .

[26) Standard Guide for Application of Neutron Spectrum Adjushnent Methods in Reactor

.. Surveillance. ASTM E 944

• 14

AEAT-0352 APPENDIX A (AEA-TSD-0392)

---*--- APPENDIX A AEA-TSD-0392 ANALYSIS OF THE WINFRITH WATER BENCHMARK EXPERIMENT USING ENDF/B-VI AND IRDF-90 DATA A KZiver December 1994 AEA Technology Technical Services Division Reactor Physics, Shielding and Criticality Department Winfrith Technology Centre Dorchester Dorset DT2 8DH United Kingdom Telephone 0305 251888 Facsimile 0305 202194

AEAT-0352 APPENDIX A (AEA-TSD-0392)

AUTHORJSATION.

NAME POSffiON SIGNATURE DAlE Author AK Ziver

• Senior Analyst * -f{Yil

. ; ,,. .....; J 7 /1/1i'1~:;

/1 Checked AF Avery Section Head l*(1 - ,, )*/, 11-V.:*1 . I /Cf:_,.

/If .>

Approved CA Cooper . Deparunent

• Manager c -A: Cftr,.r 1s//ci.s Aii

AEAT-0352 APPENDIX A (AEA-TSD-0392)

AEA-TSD-0392 ANALYSIS OF THE WINFRrrfl WATER BENCHMARK EXPERIMENT USING THE ENDF/B-VI AND ffiDF-90 DATA AK Ziver December 1994 Summary This report describes the analysis of the Winfrith water benchmark experiment as part of the validation of MCBEND9A and its associated point data cross-section library based on the ENDF-B/VI compilation.

Results are presented for the high energy S32(n,p)P32 reaction rates which are calculated using the mDF-90 dosimetry library. It is shown that MCBEND9A predictions are within one standard deviation of the experimental results.

• AEA Technology Technical Services Division Reactor Physics, Shielding and Criticality Department Winfrith Technology Centre Dorchester Dorset DT2 8DH United Kingdom Telephone 0305 251888 Facsimile 0305 202194 Aili

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Contents

• ----*- ---*--- -- -- ----- *------ ---- ---- - -- ---- ~ *__ . ---*- - ------ *- - - --------* ----- ------ - -~ ------* ---* - * - - --- -- - --~ --

1. INTRODUCTION 1

2. EXPERIMENTAL DESCRIPTION 1

3. lHE MCBEND MODEL 1

4. RESULTS 2

5. UNCERTAINTIES 2 6; CONCLUSIONS 4 REFERENCES 5 List of Tables Table 1 Options Used in the MCBEND Input Files Table 2Californium-252 Source Spectrum Table 3The Sulphur S32(n,p)P32 Reaction-rates

• Table 4Relative Sensitivities fromMCBEND (DUCKPOND) Calculations Table 5 Experimental and Calculational Uncertainties Table 6Analysis of C/E for the Sulphur Reaction Rates List of Figures Figure 1 Schematic View of the Experimental Set up Figure 2 Model of the Source Capsule Figure 3 Values of C/M for the S32(n,p)P32 Reaction Rate in the Source Plane Figure 4 S32(n,p)P32 Reaction Rate Cross-sections (IRDF-90)

AoDCndix A The MCBEND9 Input Data for the Source Detector Separation 10.16 cm

• Aiv

AEAT-0352 APPENDIX A (AEA-TSD-0392)

1. INTRODUCTION This repon describes the ~I!~Y~i~ Qf_!}l~ ~ing!e _m~te_ri.µ w~~r 1Je11ch_m_ark_~~_periment performed as

• parfof the villidation study for MCBEND9A [ 1] with the ENDF-BNI [2] pomt energy nuclear data in conjunction with the IRDF-90 [3] dosimetry library.

The water benchmark experiment was performed at AEA Technology, Winfrith in the U.K [4] in the early 1980s. The aim of the experiment was to test calculational methods and the validity of cross-section data for materials of imponance in PWR dosimetry analysis. The experiment was set up in a water tank in which eight individual accurately calibrated Californium (Cf252) capsules were used as neutron sources. The Cf252 sources provided spontaneous fission neutrons with a well-known energy distribution. The fast neutron flux was -measured using sulphur detectors with the S32(n,p)P32 reaction rate being determined at distances ranging from 100 to 400mm from the source. This experiment has been studied previously [5], [6] to test the JEF2.2, UKNDL and the ENDF-BNI nuclear data with the IRDF-85 dosimetry library.

A brief description of the experimental set up is given, followed by a full description of the MCBEND input model. The results from the calculations using the ENDF-BNI and IRDF-90 data are compared against the measurements.

2. EXPERIMENTAL DESCRIPTION A water-filled tank containing a light support structure from which various source configurations were suspended was used to perform the experiment Figure 1 shows a schematic view of the experimental set up. The tank was 2280mm by 1770mm in cross section and 1720mm high.

Because the shortest distance between a source and any external boundary was 380mm, which is more than four times the migration length of a 5MeV neutron in water, the whole source - detector arrangement could be considered to be in an infinite bath of water. The detector was placed in an air-filled measurement tube made of aluminium situated at the centre of the support structure, the tube being 75. lmm in radius with a wall thickness of 4.04mm. Measurements were made in the plane of the sources and at 150 and 300mm above and below this plane. The support structure has eight arms from which up to eight sources were symmetrically suspended by thin steel wires at accurately known distances around the measurement tube. The source to detector spacing could be increased by 50.08mm steps from 100.16mm to 500.80mm.

The Californium sources were contained in special capsules. Each consisted of an inner double walled stainless steel capsule (l.6mm in.total thickness) holding the source which was inserted via a plug into an outer cylindrical stainless steel container of 9.5mm radius. The neck of the latter contained a steel screw which was connected by a very fine steel wire to an arm of the support structure. The central region of the source capsule contains a very small amount of air and aluminium. Figure 2 shows the MCBEND9A model of the source container. The absolute calibration of the sources was carried out at the National Physical Laboratory. The estimated standard deviation on the source strengths is 0.5%, with appropriate corrections being made for the decay following calibration. The angular variation of the neutron output of one source was also measured and departures from the average value were found to be well below_ 10%. The Cf252 source spectrum was taken from reference [4].

3. THE MCBEND MODEL The experiment was modelled accurately apart from omitting the light support structure and thin steel support wires. This is not considered significant because of their small volume. Figure 1 shows a schematic view of the experimental model and Figure 2 shows a schematic view of the Al

AEAT-0352 APPENDIX A (AEA-TSD-0392) model of the source container. The model differed from that used in earlier calculations beca detector was explicitly included; previously it had been treated as a scoring region in the void the measurement tube[5] [6]. The sulphur was in the form of a cylindrical block of dens1 y 1.86g/cm3 with its height and diameter both equal to 28mm. As data for sulphur* from ENDF-BNI had not been processed into the library for MCBEND, the detector was represented by aluminium.

Supporting calculations for this model using data from UKNDL showed that there were negligible differences in the predicted reaction rates when the detector was represented as sulphur or aluminium. (Inclusion of the detector reduced the reaction rate by 7% below. that obtained when the scoring region was a void.) Version 9A of the code has been used in this work to predict the detector reaction-rates in the measurement tube at the centre of the source array. MCBEND's complex source option, where the source is described using bodies similar to those used to construct the model of the system, was used to define the source geometry and spectrum. Splitting and Russian roulette were applied to accelerate the calculation, with .the MAGIC adjoint diffusion module in MCBEND being used to. determine the importances in the R, Z and energy dimensions,

• the calculation being accelerated towards the sulphur detector on the source plane. The cross- .

• .sections for the S 3 2(n,p)P~2 reaction were taken from the IRDF-90 response library [3]. Figure 4

• shows the variation of S32(n,p)P32 cross-sections with neutron energy. The input data options used

. in setting up the ~CBEND model are listed in Table 1. The Cf252 source spectrum used in the calculations is presented in Table 2. *

• The calculations were run until the majority of the Monte Carlo standard deviations on the responses

• were less than 5%. The input data necessary to perform sensitivity calculations have been included in the model. The sensitivities to nuclear data (hydrogen, oxygen and detector cross-Sections) are

.required to determine the uncertainties due to these parameters. *'

4. RESULTS The results are given in Table-:J which co~pares the caiculated S32(n,p)P32 reaction-rates with the experimental values for each source-detector configuration. The results show good agreement with the measurements giving 'C/E (ie Caiculation!Exr}eriinent) ratios ranging from 0,95 to *:i.oo.

However the calculations were concentrated on predictjng reaction rates on the source plane {Axial displacement =O) so that the uncertainties due to the Mon~ Carlo statistics are least for these points.

The mel,lSurements and calculations all agree to within 3.6% at these points. The attenuation between 101.6mm and 355.6mm is calculated to be 4.9x 1Q*3 compared with the measured value of.

4.5x I 0*3. For a point kernel, in* spherical geometry this would imply that the attenuation cross-section is known to an accuracy of 3%. *

• . *. i ,

A full analysis of the significance of the comparison, however, requires a detailed sensitivity and uncertainty analysis. This is presented in the next section.  : .* *

5. UNCERTAINTIES.

5 ~:1 Experimental The main uncertainty quoted by the experimentalists arises from the dispersion introduced into the measurements due to the technique of burning the irradiated sulphur* to concentrate the p32 activity thereby increasing the sensitivity of the detector. When combined with the smaller contribution from the. counting statistics the uncertainty is estimated to be 6% on each measurement In addition the experimentalists mention uncertainties in the source strength (0.5%),and in the sulphur deri *

(5% ). An error in the source-detector separation is also quoted as +/-0.25mm. The error

• vertical position of the sources is +/-0.4mm. The changes in the sulphur reaction rate due to A2

AEAT-0352 APPENDIX A (AEA-TSD-0392)

5. 2 Calculational The calculational uncertainties are mainly due to the nuclear data (hydrogen and oxygen cross-sections) and the sulphur S32(n,p)P32 reaction rate cross-sections. The MCBEND model of the experiment is an exact representation of the geometry in three-dimensions, therefore no modelling approximations are present in the analysis. The MCBEND model was checked by the SKETCH geometry visualisation program [7] to ensure that no errors were present in the parameters defining the model. There is an additional uncertainty arising from the errors in the Cf25 2 source spectrum used in the calculations which has a mean neutron energy at 2.164+/-0.062 MeV. The effect of this on the sulphur reaction rates.is calculated to be less than 1%.

The nuclear data uncertainties for hydrogen and oxygen have been determined using the relative sensitivity profile5 obtained from MCBEND folded with the variance-covariance data obtained from the ZZ-VITAMIN COYA library [8]. The sensitivities as calculated by the DUCKPOND module of MCBEND are presented in Table 4. The uncertainties estimated using the WINCOV program [9] to combine the sensitivities and the variance-covariance data are given in Table 5. It was found that the

• main uncertainty is due to the hydrogen elastic scattering cross-section which becomes more significant with increasing separation of the sources and the detector. Below 13MeV the total macro5copic cross-section for hydrogen in water is greater than that of oxygen even at the: narrow resonance peaks in oxygen. At 8 MeV the cross-section is twice as large for hydrogen as for oxygen and at lower energies the average ratio is even higher. Therefore most of the collisions in water are with the hydrogen nuclei. Further, an elastic collision with oxygen does not significantly degrade the neutron energy, whilst at high energies there is a large probability of small angle elastic scattering which has little effect on the penetration. Collisions with hydrogen however will tend to degrade the neutron energy so as to remove it below the threshold for the S32(n,p)P32 reaction.

Hydrogen collisions therefore play the dominant role in the penetration of fast neutrons through water. Hence cal_culations performed for the water benchmark are a test of the accuracy of the hydrogen cross-section. The latter decreases with increasing energy and therefore for greater source

- detector spacings, higher energy neutrons are more important Table 4 is given to show the relative sensitivities of the S32(n,p)P32 reaction to the cross-sections of hydrogen and oxygen.

The uncertainties in the calculated reaction rates which arise from the response cross-sectio~ for the

. sulphur detectors have been calculated using the contributions to the sulphur reaction rate from

. neutrons in 4 energy groups above 0.7 MeV folded with the co-variances obtained from the IRDF-90 data after processing with the NJOY [10] system. The results showed that a 4% uncertainty is due to the sulphur S32(n,p)P32 cross-sections at the positions presen~d in Table_5.

The overall uncertainties on the ratios of the calculated and measured reaction rates range from 7.4%

at 10 l.6mm from the source to 8.1 % at 355.6mm. The large contribution to the uncertainty which arises from the measurements means that it is not possible to provide positive confirmation of the accuracies ascribed to the hydrogen and oxygen cross-sections on the basis of the comparisons.

However the consistency of the better than expected agreement suggests that the contribution of the dispersion from burning to the uncertainty in the measurements has been overestimated. Similarly the absence of any consistent bias suggests that the likely errors in the sulphur reaction cross- ,

sections are less than the 4% standard deviation given in Table 5. This is illustrated further by the data presented in Table 6. The mean value of C/E is 0.997 and the standard deviation for the distribution of the individual values is 3.27%. The discrepancies between calculation and measurement are less than 0.5 of the standard deviations as derived in Table 5 by combining all of the estimated contributions. In the light of these observations and the absence of any consistent

• A3

.i.

AEAT-0352 APPENDIX A (AEA-TSD-0392) trend in the ratio of calculation to measurement With increasing penetration, the results as plo Figure 3 suggest that the attenuation cross-section for water is accurate to within the stan deviations given by the co-variance data from reference 9. These data give an uncertainty of +/-2. v in the fast flux detected by the sulphur reaction after a penetration of 355.6mm of water.

6. CONCLUSIONS The single material water benchmark has been analysed using the Monte Carlo code MCBEND9A with the ENDF/B-VI and IRDF-90 nuclear data as part of a validation programme for the nuclear data library and the calculational method. The accuracy of,the model ensures that there are no errors introduced when modelling the experimental system.

The comparison of the suiphur reaction rates calculated by MCBEND9A against the measurements showed go()d agreement with muimum discrepanCies of 3.5% on the source *plane. Figure 3 gives the values of the ratios of calculated to experimental reaction rates (C/E) for this plane together with the calculated uncertainties. The total maximum. uncertainty has been calculated ~o be around 8%* (1 standard deviation) with the major contributions being those from the measurements and the cross-sections fot the sulphur reaction rate.The agreement is closer and more consistent than would be

, expected from the _calculated uncertainties arid it suggests that the uncertainties on the measurements and the detector cross-sections are overestimated. The variance-covariance data for the cross-sectioris for oxygen and hydrogen give an unceruiinty of 2.4% in the predicted sulphur reaction rate at a penetration of 355.6mm due to the calculated attenuation in the water. While the comparisons carinot provide confirmation.of this degree of accuracy, they.do.indicate that the vari~ce-covariance data are not. seriously uriderestimating.the possible errors in the cross-sections.at

~ .

these energies.

The *results presented *in this repqrt can be used as part of the' validation of MCBEND9A code for the prediction offast neutron attenuation in water. ' . , . . . * *

. I.

A4

AEAT-0352 APPENDIX A (AEA-TSD-0392)

REFERENCES

_______ _[IJ_ __ M~BE]'lp_U_serGl!id~JQ V~rsion 9A. ANSWJ;:R_SM~-B~NQ(9_4)15~ ____________ _

(2) Eaton C R and Dean C J Report on the Extension of the Monte Carlo Nuclear Data Generation Route.

AEA-RS-1246 (3) Kocherov NP and Mclaughlin P K The International Dosimetry File (IRDF-90), IAEA-NDS-141October1993.

(4) Carter MD and Packwood A The Winfrith Water Benchmark Experiment NEACRP-A-628 (5) Locke H F and Wright G A Benchmark Testing of JEF2.2 Data for Shielding Applications. Analysis of the Winfrith Water Benchmark Experiment AEA-RS-1232.

[6) McGuiness J M MCBEND Validation Report No. 3. ANSWERSNALIDATION/MCBEND/3/1.

[7] SKETCH. A Program for Checking Geometry Models used in MCBEND, RANKERN -

and MONK. ANSWERSNISTA(94)2. ,,;

(8) Kodelli I and Sartori E Co-variance Data Library. Z:Z-VITAMIN-J/COVA, NEA1264, OECD/NEADB. 1990

[9] Ziver AK and Earwicker J Generation of Variance-Covariance Data from the ENDF-BNI and IRDF-90 Nuclear Data Libraries. AEA-TSD-0387 (10] MacFarlane R E & Muir D W.

The NJOY Nuclear Data Processing System, Version 91.

LA-12740-M -

A5

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 1. Options used in the MCBEND input files.

---*--- Option.

__ (~_I_!of t~_e fil~s-~sed _tlte s~m_~_ option~) _

Details of option.

Geometry. A large rectangular volume of water.

Type of source particle. Neutron.

Thermal treatment None used. -

Source. Complex source.

Energy Variation Cf-252 user supplied spectrum.

Source weighting .. None.

Acceleration. MAGIC in R, Z and Energy.

Scoring. Track length estimation.

Responses. From the IRDF-90 response library [3].

Sensitivities Elastic and non-elastic cross-sections of hydrogen.oxygen and detector cross-sections.

Nuclear Data From the ENDF/B-VI [2].

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 2 Upper Energy (MeV)

Californium-252 Neutron Source Spectrum Neutrons.

per second Upper Energy (MeV)

Neutrons per second 1.284E+Ol 7.119E-04 8.208E-01. 2.945E-02*

l.133E+Ol 1.625E-03 7.244E-01 3.097E-02 l.OOOE+Ol 3.304E-03 6.393E-01 2.747E-02 8.825E+OO 6.059E-03 5.642E-01 2.417E-02

.7.788E+OO . 1.014E-02 4.979E-01 2.112E-02 6.873E+OO 1.565E-02 4.394E~Ol . 1.833E-02 6.065E+OO 2.222E-02 3.877E-01 1.583E-02 5.353E+OO 2.941E-02 3.422E-01 L361E-02 4.724E+OO 3.684E-02 3.020E-01 1.164E-02 4.169E+OO 4.398E-02 . * . 2.655E-0.1 . 9.835E-03 3.679E+OO 5.033E-02 2.352E::o1 . . 8.134E-03 ..

3.247E+OO 5.547E-02 2.075E-01 6.660E-03 2.865E+OO 5.914E-02 1.832E-01 5.456E-03 2.528E+OO 6.123E-02 L616E-01 4.473E-03.

2.231E+OO 6.177E-02 1.426E-Ol 3.670E-03

• 1.969E+OO 6.090E-02 1.259E-01 3.014E-03 l.738E+OO 5.884E-02

• Ll l lE-01 2.476E-03 1.534E+OO 4.715E-02 . 9.804E-02 2.036E-03 1.353E+OO 3.633E-02 .. 8.652E-02 L676E-03 l.194E+OO 3.329E-02 . 7.635E-02 1.380E-03 l.054E+OO 3.015E-02 6.738E*02 l.137E-03 9.30lE-01 2.702E-02 5.946E-02 ..

1.0

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 3 The Sulphur Reaction Rates (S32(n,p)P32)

Axial Position Experimental reaction-rate.

(Bq/atom/source neutron)

Calculated reaction-rate.

(Bq/atom/source neutron) CJE (mm) 1 s.d. 1 s.d.

1. Source= 1.256E7 n/s 101.6mm from detector.

300 6.71E-31 6.0% 6.46E-31 7.4% 0.963 150 5.37E-30 6.0% 5.28E-30 1.9% 0.983 0 3.13E-29 6.0% 3.02E-29 1.5% 0.965

2. Source= 2.540E7 n/s 152.4mm from detector.

300 3.22E-31 6.0% 3.06E-31 8.4% 0.950 150 2.25E-30 6.0% 2.28E-30 4.0% 1.013 0 7.56E-30 6.0% 7.78E-30 2.2% 1.029

3. Source = 5.260E7 n/s 203.2mm from detector.

300 1.79E-31 6.7% '

150 9.96E-31 3.5%

0 2.45E-30 2.4%

4. Source = l .048E7 n/s 254.0mm from detector.

300 9.5E-32 6.0% 9.41E-32 7.2% 0.991 150 4.36E-31 6.0% 4.31E-31 2.9% 0.989 0 8.55E-31 6.0% 8.39E-31 2.4% -o.981

5. Source = l.046E7 n/s 304.Smm from detector.

300 5.16E-32 6.0% 4.98E-32 8.4% 0.965 150 l.94E-31 6.0% 1.96E-31 3.8% 1.010 0 3.43E-31 6.0% 3.34E-31 .2.6% 0.974

6. Source = 1.048E7 n/s 355.6mm from detector.

300 2.81)3-32 6.0% 2.96E-32 6.6% 1.053 150 8.92E-32 6.0% 9.06E-32 2.8% 1.015 0 1.42E-31 6.0% 1.47E-31 2.6% 1.035

7. Source = l .045E7 n/s 508.0mm from detector.

300 4.48E-33 7.6%

150 1.02E-32 2.9%

0 1.41E-32 2.5%

The errors quoted are due to the dispersion due to the experimental method (experiment) and Monte Carlo stochastic error (calculated).

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 4 Relative Sensitivities from MCBEND (DUCKPOND) Calculations Upper Sensitivity

• Sensitivity

• Sensitivity Energy Group (MeV). Hydrogen 1 s.d Oxygen 1 s.d Oxygen 1 s.d Elastic Elastic Non-Elastic

~ourc;e ~ Detector Spacing = 10.16 cm . ..

1 . i4.92 .. ..;O.i68 . O.Ol 0.011 0.004. -0.017 0.001

.2 .. 4.4 -0.333. 0.01 -o;o3 *0.007. .. -0.004 . 0.001

• 3 . 2.6 . -0.079 0.01 -0.007 0.001' 0 '

. 1.35 ... '

Source -Detect()r Spacing = 25.4. cm " '*

1 *14.92.' .;0 ..987 o.o~* -0.138 .0~02 -0.096*' . 0.01 2* 4.4 -0.8J7' 0.06 '-0.188 *, 0.02 '-0.013 ... 0.01 3 *.* 2 6

-0.123 . 0.02 ~0.016' . 0.01 0

i"

'1.35 .. .. '

.* Source~betector Spacing*= 3?.56 cm. "

1 ., . *'

..

• 14~~2 . -L641. * *0.09 .. -0.280 *0.03 -0.186' 0.01 2 :. .. . ~.4 . -0.881 0.04' ....  :.. ~0.23l . ~- . .0.02. -:0.01'3. 0.01 .

3 2.6 -0.172 0~04 .. -0.025 *0.01 *o ., '

I i.35 .. ' '*

• S~urc~ - Detector Spacing = 50.8 cm ... ..

1 14.92 .* *<-2~so1 0.11 .**_-0.602 0.04. " -0.359:* *0.02 2 4.4 -0.776 . 0.03 ... :.:.0.218 0.01 -0.012 0.01 3 .. 2.6 -0.141 0.04 -0.018 -0~02. 0

. 1.35

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 5.

• Experimental and Calculational Uncertainties Source of Error Uncertainty 1 s.d %

Source - Detector Spacing 10.16 cm Experimental 6.00 Monte Carlo Statistics 1.50 Sulphur Reaction Cross 3.94 Sections Nuclear Data.- Hydrogen 0.50 Nuclear Dara - Oxygen 0.02 Total on C/E 7.37 Source - Detector Spacing 25.40 cm Experimental 6.00 Monte Carlo Statistics 2.40 Sulphur Reaction Cross 3.98 Sections Nuclear Data - Hydrogen 1.67 Nuclear Data- Oxygen 0.29 Total on C/E 7.78 Source - Detector Spacing 35.56 cm Experimental 6.00 Monte Carlo Statistics 2.60 Sulphur Reaction Cross 4.10 Sections Nuclear Data - Hydrogen 2.30 Nuclear Data - Oxygen 0.50 Total on C/E 8.07 Note. Nuclear data uncertainties are calculated using the co-variance data from reference [8]

Uncertainties due to Sulphur reaction rate cross-sections are calculated from reference [9]

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Table 6 Analysis of C/E for the Sulphur Reaction Rates Uncertainty onC/E Distance C/E 1 stnd dev (C/E-1)/a (mm) a 101.6 0.965 0.0737 -0.4749 152.4 1.029 0.0750 0.3867 254.0 0.981 0.0778 -0.2442 304.8 0.974. 0.0790 -0.3291 355.6 1.035 0.0807 0.4337 Mean Value of C/E =0.9968 Standard Deviation of the values of C/E =0.0327

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Figure 1 Schematic View of Experimental Set up

AEAT-0352 APPENDIX A (AEA-Tso:.0392)

Figure 2 Model of the Source Capsule I

I 2.30 1.90.

1.35 L25 1.05.

0.72.

0.50 ..

0.42 0.26

- - 0.0"

-0~2 ....

-0.28

• -0.42

-1.1 I I I I -0.475t -0.161 I

-0.95 -0.5 -0.32 . 0.0 0.24 0.40 0.95 ES) Stainless steel 111 . Califomium-252 D Void All dimensions in cm

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Figure 3 Values of C/E for the S32(n,p)P32 Reaction Rate in the Source

---

P-lane----- ----- -- - --- - -------- ----- ------------ ------------ -----------------------------------

1.15 1.10 -

1.05 -

I I

1.00 I

' I 0.95 -

I 0.90 -

Error bars= I standard deviation (exp.+calc.)

0.85

- 5 10 15 20 25

. 30 35 40 45 SOURCE-DETECTOR SPACING (cm)

AEAT-0352 APPENDIX A (AEA-TSD-0392)

Figure 4 . s*32(n,p)P32 Reaction Rate . Cross-sections (IRDF-90) 0.4,-------------------------.. . . .

r,.',

0.3

. .Q 0

u 0.2 Cll Cll I

Cll Cll

...0

(.)

0.1

.(

O.O+-....;mi~~---r---....,....:-----...,:--_;._...;......~--_J o* 5 10 15 Neutron Energy . (MeV)

AEAT-0352 APPENDIX A (AEA-TSD-0392)

APPENDICES A MCBEND INPUT DATA

& WATER BENCHMARK -------- CASE 1

& SOURCE 10.16CM FROM DETECTOR

&**~***********************************************************************

&UNIT 1 BEGIN CONTROL DATA PROCESS TO STAGE THREE SPLITTING END

&UNIT 2 BEGIN DATASET DEFINITIONS DUMP A 25 DUMP B 26 END

&UNIT 4 BEGIN MATERIAL GEOMETRY CG

&AL MEASUREMENT TUBE (OUTER)

RCCl 0.0 0.0 -90.0 0.0 0.0 180.0 3.755

&AL MEASUREMENT TUBE (INNER)

RCC2 0.0 0.0 -90.0 0.0 0.0 180.0 3.351

&AL TANK RPP3 -114.0 114.0 -88.5 88.5 -86.0 86.0

&SCORING REGIONS RCC4 0.0 0.0 -31.4 0.0 0.0 2.8 1.4 COPY 4 z 4*15.0

&SOURCE CAPSULES (RPP DEFINING CELL) c 1 RPP9 -0.95 0.95 -11.11 -9.21 -+.1 2.3

&BODIES WITHIN SOURCE CAPSULE CELL 1

&SOURCE RCCl 0.95 0~95 0.9 0.0 0.0 0.46 0.24

&LOWER VOID RCC2 0.95 0.95 0.68 0.0 0.0 0.14 0.16

. AEAT-0352 APPENDIX A (AEA-TSD-0392)

&UPPER VOID

&VOID CAP RCC3 0.95 0.95 1. 52 0.0 0.0 0.09 0.24 TRC4 0.95 0.95 1. 61 0.0 0.0 0.21 0.4 0.0

&BULK OF CAPSULE RCC5 0.95 0.95 0.0 0.0 0.0 2.35 0.95 RCC6 0.95 0.95 2 .35 0.0 0.0 0.65 0.475

&LID OF CAPSULE RCC7 0.95 0.95 3.0 0.0 0.0 0. 4.

0.5

&SCREW VOID

.. RCC8 0.95 0.95 2.15 0.0 0.0 0.3 0.32

&SCREW SSTEEL RCC9 0.95 o*. 95 2.45 0.0 0.0 0.55

,~-

0.32 ZONES ALTUBE 20 +l -2 MEASVOID 20. +2 5 7 -8 WATER 20 +3 -1. -9 SCOR-30 20 +4

• SCOR-15 20 +5 SCORO 20 +6 SCOR+l5 20 +7 SCOR+30 20 +8

.EXTVOID 20 -3 CELL 1 SS CASE 20 +5. 1 4 -8 SSCASETOP 20 . +6 9 SSL ID 2.0 +7 SOURCE 20 +l VOIDLOW 20 +2 VOIDUP 20 +3 VOIDCAP 20 +4 VOIDSCREW 20 +8 SS SCREW 20 +9 WATER 20 +0 6 -7 REGIONS SEQUENCE CELL 1

AEAT-0352 APPENDIX A (AEA-TSD-0392)

COMMON ..

--*- --------_______ :~~;~~s __

. 1 0 2 5*5 -2000

- c - - - - - - - - - -- -------- --------- -- ----------

CELL 1

- 3 *3 4 4 *0 3 2 VOLUMES

&EQUAL 1.0 EXCEPT SCORING REGIONS 3*1.0 5*17.24 1.0 CELL 1 UNITY END

&UNIT 5 BEGIN SPLITTING GEOMETRY R 3 0.0 2.5 5.0 150.0 THETA DUMMY z 5

-90.0 -20.0 -5.0 5.0 20.0 90.~

END

&UNIT 6

- END

&UNIT 7 BEGIN ENERGY DATA NEUTRON SPLITTING GROUPS 12.

14.6 13.5 12.5 11.25 10.0 8.5 7.0 6.07 4.72 3.68 ~.8r 1.74 o.639 SCORING GROUPS 20 12.84 8.825 7.788 6.873 6.065 5 .353 4.724 4.169 3.679 3.247 2.865 2.528 2.231 1. 969

1. 738 1.534 1..353 1.194 1. 054 0.930 0.639 THERMAL TREATMENT NONE COMPLEX SOURCE END

&UNIT 8 BEGIN IMPORTANCE MAP DIMENSIONS 3 1 5 12 l* -

CALCULATE TARGETS 1 ZONES 6 STRENGTHS 1.0 USE METHOD D PRINT IMPORTANCE VALUES

-END

.&UNIT 9 BEGIN SCORING DATA MESH SYSTEM CG DIMENSIONS 19 1 1 MATERIAL MESH TRACK LENGTH

AEAT-0352 APPENDIX A (AEA-TSD-0392)

FLUX ALL NOT SOME 1

1 2 3 9 10 11 12 14 15 16 17 18 19 RESPONSES DITTO SENSITIVITY OF FLUX DITTO SENSITIVITY OF RESPONSES DITTO CONTRIBUTIONS TO RESPONSES DITTO END

&UNIT 10 BEGIN RESPONSE DATA FUNCTION S32 (N, P)

& SJ2(N,P) IRDF90 FUNCTION PAIRS

~ee Figure 4 of this report END

&UNIT 11

.BEGIN SENSITIVITY DATA or,*

.. r COMBINATIONS 36 1250296 ' 0 .

1 EXC 1 2

• .-- r*

1250296 0 INC* 1 2

• • , ~,' * *

• I 825, 0 EXC 1 2 ,<,:

825 0 '**.

• '*.: INC 1 2 . '

2631 o.

.. -~-

• EXC 1. 2 *-:.:

2631 .o ' I INC 1 ... 2 1325' 0 EXC 1 2 1325 0 INC 1 2

• 2525 0 EXC: *l 2 2525 0 INC 1 2 2431 0 EXC 1 2

-2431 0 INC 1 .2 2825 0 EXC 1 2

AEAT-0352 APPENDIX A (AEA-TSD-0392).

2825 0 INC 1 2

~

9237 0 EXC 1 2 9237 0 INC 1 2 2625 0 EXC 1 2 2625 0 INC 1 2 2634 0 EXC 1 2 2634 0 INC 1 2 2637 0 EXC 1 2 2637 0 INC 1 2 2425 0 EXC 1 2 2425 0 INC 1 2 2434 0 EXC 1 2 2434 0 INC 1 2 2437 0 EXC 1 2 2437 0 INC 1 2 2831 0 EXC 1 2 2831 0 INC 1 2 2834 0 EXC 1 2 2834 0 INC 1 2 2837 0 EXC 1 2 2837 0 INC 1 2 2843 0 EXC 1 2

AEAT-0352 APPENDIX A (AEA-TSD-0392) 2S43 0 INC 1 2 GROUPS 16 1.492E+l .4.400E+O 2.600E+O l.3SOE+O 7.0SOE-1 S.SOOE-1 4.!lOOE-1 3.09SE-l 2.620E-l 6.200E-2 3.000E-2:

l.SOOE-2 l.SSSE-2 2.14SE-2 l.06SE-S S.043E-6 S.SOOE-7.

END

&UNIT' 14

.BEGIN MATERIAL DATA MINNIE.

MIXTURES 1 WEIGHT*'*

Ml MN .1. S9S6E:..2 FES4 b.0401 FES6 0.64SS FES7 O.OlSO FESS 0.0021 CRSO O.Ob7S CRS2 0.1S64 CRS3 O.OlSO CRS4 0.0046 N,ISS 6-. 3S7E-2 NI60 2. S4SE-;2 NI61 l .12E"".3 NI62 3.64E-3 NI64 9.6E-4 MATERIALS S

'VOLUME

.1 AL 2 *;.7 1 . 0 2 WATER 1.0 3 Ml 7. 9 1. 0 * '*,'

4 U23S lS.7 1.0 S. AL27 . 1. S6 l. 0 USE MOULD 2S FQR H IN ALL MATERIALS USE MOULD 21 FOR 0 IN ALL MATERIALS .

USE DFN 162S FOR S32 IN ALL MATERIALS

'USE A,DCN FE *FOR FES6 IN ALL MATERIALS .

.USE ADCN FE FOR FES7 IN ALL MATERIALS

• USE *ADC~ FE FOR FES4 IN ALL MATERIALS :.

USE ADGN*FE FOR FESS. IN ALL MATERIALS

' .USE ADCN .CR FOR CRSO IN ALL MATERIALS

• USE ~N CR FO~ CRS2 IN ALL MATERIALS* . '

USE ADCN .. CR FOR CRS3 IN ALL.. MATERIALS USE ADCN CR FOR CRS4 IN ALL MATERIAL~

USE ADCN NI FOR NISS IN ,?\LL MATERIALS USE ADCN NI FOR.'NI60 IN ALL MATERIALS USE ADCN NI FOR N.I61 IN ALL MATERIALS USE ADCN NI FOR NI62 IN ALL MATERIALS

'*' USEADCN NI* FOR NI64 IN ALL MATERIALS

' USE ADCN AL FOR AL27 *IN. ALL' 'MATERIALS END

&UNIT 23

.BEGIN CG SOURCE DATA .

RCA 0.0 -10.16 -0.2 0.0 0.0* 0.46 0.0 0.24

1. 0 1 1 VOLUME* SOURCE ENERGY BOUNDARIES 43 12.S4 11.33 10.0 S.S2S 7,.7SS 6.S73 6.06S S.3S3 4.. 724 4~169'

AEAT-0352 APPENDIX A (AEA-TSD-0392) 3.679 3.247 2.865 2.528 2.231 1.969 1. 738 1. 534 1. 353 1.194

1. 0_5_~_ -- -~ _._3 Ql.E:-1 8.2Q8E-l _7.244E-:_l 6 .-3.93E,,-l 5.642E-l 4.979E-l 4.394E-l 3.877E-l 3.422E-l 3.020E-l 2.665E-l 2.352E-l 2.075E-l l.832E-l

1. 616E-l l.426E-l 1. 259E-l l. lllE-1 9.804E-2 8.652E-2 7.635E-2 6.738E-2 1. OE-20 GROUP IMPORTANCES 10.0 9.6 8.3 7.5 7;~ 6.1 5.0 4.1 3.0 2.2 1.5 1.0 0.8 0.6 0.5 0.3 8*0.001 19*0.0 SOURCE GENERATION GROUPS 1 FLUXES

1. 510E8 CROSS SECTIONS 7 .119E-4 1. 625E-3 3.304E-3 6.059E-3 1. 014E-2 l.565E-2 2.222E-2 2.941E-2 3.684E-2 4.398E-2 5.033E-2 5.547E-2 5.914E-2 6.123E-2 6.177E-2 6.090E-2 5.884E-2 4.715E-2 3.633E-2 3.329E-2 3.0lSE-2 2.702E-2 2.945E-2 3.097E-2 2.747E-2 2.417E-2 2 .112E-2 1. 833E-2 l.583E-2 l.361E-2 l.164E-2 9.835E-3 8 .134E-3 6.660E-3 5.456E-3 4.473E-3 3.670E-3 3.014E-3 2.476E-3 2.036E-3 l.676E-3 l.380E-3 l.137E-3 END

AEAT-0352 APPENDIX B (AEAT-0355)

--*- - -------- -- -~-------------- --~  :------------ -* - - -- -~- ---- -------- --- -- - ---------- - - --- - ------------ - ----------- --

AEA Technology

• AEAT-0355 The Analysis of NESDIP2 with ENPF-BNI Nuclear

- Data and IRDF90 Response Cross Sections.

• A F Avery. S New hon and A K Ziyer June 1996

' ~ "'

Reactor Physics. Shielding and Criticality Depanment Plant Supporj Servi_cc:s Group _ _ _

• __

• _ _- _

AEA Technofogy Winfrith Dorset DT2 8DH

AEAT-0352, APPENDIX B (AEAT -0355)

('

AUTHORISATION NAME .. POSffiON 'SIGNATURE DA1E:

. tc6

• .~ (AcY-'I Author AF Avery* Shielding '*

• Consultant 1'2- (b \ .

Checked SJ Chuca5 Product

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Manager.* ~~~~ v -J Approved CA Cooper Department ..

Manager .. C-A-tmv ,, Ii. G.:'\IO

AEAT-0352 APPENDIXB (AEAT-0355)

_AJ~AJ':-Q3~_s _____ _

AEA Technology The Analysis of NESDIP2 with ENDF-B/VI Nuclear Data and IRDF90 Response Cross Sections.

AF Avery, S Newbon, and AK Ziver June 1996 Sum mazy This report describes a comparison with measurements to validate the Monte Carlo code MCBEND for the determination of neutron penetration through typical PWR radial shields. Calculations were carried out for the NESDIP2 experiment performed in the ASPIS facility of the NESTOR reactor at Winfrith, using MCBEND9A with ENDF-B/VI nuclear data and IRDF-90 response cross-sections.

Results for three reaction rates, ie S32(n,p)P32, In 115(n,n')In 115m and Rh 103(n,n')Rh t03m have been compared with measurements. A detailed analysis of uncertainties using the covariances from the ENDF-B/VI library is included.

In general MCBEND accurately predicts the reaction rates in the region representing the RPV and the cavity and underpredicts in the water regions inboard of the RPV. At the important T/4 and 3T/4 positions in the RPV, the C/M values are within 12% of those at the cavity, showing that accurate predictions of the neutron fluence at these positions can be derived from measurements made in the cavity.

The results provide validation for the use* of MCBEND and the ENDF-B/VI library for this type of calculation, and confirm that the uncertainties assigned to the material cross-sections are appropriate.

Reactor Physics, Shielding and Criticality Department Plant Support Services Group AEA Technology Winfrith

-Dorset DT2 8DH

AEAT-0352 APPENDIXB (AEAT-0355)

CONTENTS

__ Page No .... _ -*-

1 INTRODUCTION 1 2 THE EXPERIMENTAL CONFIGURATION 1 3 THE FISSION PLATE 2 3.1 The Fission-Rate Distribution within the 2 NESDIP Fission Plate Located in the NESDIP 2 Radial Shield Array 3.2 The Low-Energy Neutron Flux Profile 3 Over the Fission Plate 3.3 The Fission Plate Profile 3 3.4 The Z Dependence of the Fission-Rate Distribution 3 3.5 The Absolute Calibration c;>f the Fission Plate 4 4 THRESHOLD REACTION-RATE MEASUREMENTS 4.

4.1 Rhodium Activation Measurements 4 4.2 Sulphur Activation Measurements 4 4.3 Indium Activation Measurements 4 4.4 Core Background Corrections 4 4.5 Activation Results. 5 4.6 Perturbation in the RPV Region 5 5 MONTE CARLO CALCULATIONS 5 5.1 The Geometric Model 5 5.2 The Fission Plate Source Distribution 5 5.3 The Scoring Data 5 5 .4 Nuclear Data 6

5. 5 *Variance-Covariance Data 6 5.6 Acceleration of the Monte Carlo Calculations 6 6 MONTE CARLO RESULTS 6 6.1 Corrections to the Calculated Reaction-Rates 6 6.2 Uncertainties 7 6.3 Comparison of Calculation with Experiment 8 7

SUMMARY

• 9 8 REFERENCES 11

• iii

AEAT-0352 APPENDIXB (AEAT-0355)

TABLES 1 Dimensions and Materials in the NESDIP2 Array 2 Material Compositions 3 The Neutron Source Distribution in the NESDIP Fission Plate L6cated in the NESDIP2 Array 4 Measured Reaction-Rates through the NESDIP2 Radial Shield .

5 S32(n,p) Reaction-Rate Profile in the Cavity 6 Comparison of Activation Measurements in the Cavity with RPV Plates Open and Closed 7 Calculated Responses with ENDF-BNI Data 8 Calculated Reaction-Rates and Uncertainties for Rb103(n,n')Rhl03m

.9 Calculated Reaction-Rates and Uncertainties for fullS(n,n')InliSm 10 :calculated Reaction-Rates and Uncertainties for S32(n,p)P32 11 . Ratio of Calculated and Measured Reaction Rates iv

AEAT-0352 APPENDIXB (AEAT-0355)

---*--------- -~-~Ql!_~s_ -~- -------- --- - - -------

NESDIP2 Configuration 2 NESDIP2 Enriched U/Al Alloy Fission Plate 3 AS PIS VIAl. Alloy Fuel Element 4 Detail of Fuel Loading Pattern 5 Co-ordinate System 6 Fuel Element Configuration and Manganese Foil Measurement Positions

7. NESDIP2 Fission Plate Source Profile 8 Source Mesh Boundaries 9 Measurement Locations in the NESDIP2 Array 10 Relative S32(n,p)P32 Reaction-Rate Axial Profile in the Cavity of the NESDIP2 Array*

11

• MCBEND Model of the NESDIP2 Array APPENDIX A MCBEND lriput

• v

AEAT-0352 APPENDIXB (AEAT-0355) 1 INTRODUCTION The NESTOR Shielding and Dosimetry Improvement Programme (NESDIP) (1) was conceived to study neutron penetration through typical PWR radial shields. The programme encompassed both penetration through the radial shield from the core boundary to the cavity external to the reactor pressure vessel (RPV) and the subsequent transport within the cavity.

An important feature of these experiments was the ability to make measurements at positions within the simulated vessel wall, since in practice the fluxes at penetrations of T/4 and 3T/4,

. where Tis the thickness of the RPV, are required. The first three phases of NESDIP studied the radial penetration to the cavity while Phases 4 and 5 studied streaming within the cavity and in a simulated nozzle and coolant duct configuration.

In Phase 1 of NESDIP an exact replica of the Oak Ridge PCA radial shield benchmark (2) was constructed in a large water tank mounted in the ASPIS trolley of the NESTOR facility at Winfrith in order to investigate discrepancies in the PCA between measurement and calculation. The second phase of NESDIP was a natural extension of the PCA and REPLICA experiments whereby the lateral extent of the configuration was expanded to the full height and width of the ASPIS trolley. The PCA configuration was thereby represented by a combination of slabs and water tanks of 1.8m x l.8m cross-sectional area, the thickness of each region remaining unchanged. To fulfil a major concept of the NESDIP studies, the move away from the REPLICA configuration was carried out in well defined stages. In this phase of NESDIP two series of measurements were conducted. The first series retained the small rectangular fission plate used in the REPLICA experiment; this configuration is known as the NESDIPl radial shield. The second series utilised a large circular fission plate with an effective radius of 56cm; this configuration is known as the NESDIP2 radial shield. Both configurations have common slab components outboard of their respective fission plates. With a spatially large source as in the NESDIP2 configuration the effect of the lateral leakage on the centre-line fluxes is substantially reduced.

The results of measurement.S made within the shields using fast neutron threshold activation foils and neutron spectrometers, along with comparisons against analysis with the Monte Carlo code MCBEND using UKNDL point energy neutron data were reported in reference 3, which considered both NESDIPl and NESDIP2. A later (4) report described the analysis

_ of NESDIP2 with the latest version of the code, MCBEND7B, using the new DICE data library based on ENDF-BNI data. The latter calculations have been repeated using th~

. IRDF-90 library of response functions (5) in place of the IRDF-85 data (6) used previously.

In addition the analysis of the uncertainties in these later calculations is based on co-variances derived from the ENDF-BNI files and IRDF-90.

2 THE EXPERIMENTAL CONFIGURATION The NESDIP2 configuratfon is shown in Figure 1. It consisted of a combination of slabs and water tanks contained within a trolley of mild steel with an aluminium window on the NESTOR side to allow passage of neutrons into the trolley. The region between the window and the fission plate consisted of void and a graphite slab to allow further thermalisation of the n~utrons from the NESTOR source. Beyond the fission plate the array consisted of a water cell divided into two compartments by a thermal baffle, a mild steel block representing the reactor pressure vessel, a 29.4cm wide cavity, a second-water cell and a 6lcm thick ---

concrete slab forming a biological shield. The positioning of the array within the trolley was constrained in order that the front (NESTOR side) of the cavity was aligned with the front face of the roof slot of the ASPIS facility thus allowing the cavity region to extend beyond the height of the trolley so that streaming measurements could be taken. The 12/13 configuration (i.e 12cm of water between the core and the thermal shield and 13 cm between

• thermal shield and the reactor pressure vessel) was constructed from a single water tank Bl

AEAT-0352 APPENDIXB (AEAT-0355) which contained the 6.3cm thick stain.less steel thennal baffle. The above thiekn water are nominal dimensions because the end faces of the cell bowed when the cell filled with water. The baffle was located to maintain *the front water gap at 12.1 cm and the expansion due to bowing was mostly taken up in the rear water compartment which has a

. thickness of 13.2 cm. both dimensions being measured on the centre line. To allow the use of stock components the mild steel block representing the pressure vessel was constructed from 5.08cm thick plates and the 2.5cm plate which fonned the rear wall of the water cell.

Hence the total steel thickness was 22.8cm. The dimensions of the NESDIP2 configuration are given in Table 1. It should be noted that this table differs from that in reference 3 due to a correction to the thickness of the thermal baffle; This can also be seen in the dimensions of

• Figure 11. The material specifications:~ given in Table 2..

• The thicknesses of steel and water in NESDIP2 simulated typical arrangements of the barrel,*

. thennal shield. pressure vessel. and downcomer .water in. a PWR power plant The outer surface of the cavity however was defined by a tank of water. Whilst :some PWRs do have steel and. water primary shields,* it' is more common to find concrete fonning the outer wall

• • of the cavity. Thus while steel an.d water gave well-defined materials for the primary shield .

' ... ' . in the NESDIP benchmark, it should ~e noted that in many practical situati9ns the lack< of an accurate co~position for the concrete would introduce additional uncertainties.

3.

• THE FISSION PLATE

• The .large circular fission plate used in.NESDiP2~ known as the NESDIP fission plate, is shown. in Figure 2. It comprised .an aluminium ..frame which filled the height and width .of the ASPIS trolley. Loeated within the frame were 13 separate fuel elements. An explpded

"* view of an individual fuel element iS shown in Figure 3. Each element had two 12mm thick aluminium cover plates whiCh attac:hed *On eitl1er side o.f .the tc>p and bottom locating

.* * ** pieces leaving a 5mm separation in which U/Al alloy fuel strips were located. The fuel s were of density 3.256g..cm*3 and were 80.% by weight of AI and. 20% by ,weigh( of enriched to 93%. They were nominally 30.5mm wide and Imm thitk and. were screwed to

.the rear cover plate. * *

...... . There*was dept}i*for four fue~ strips within each* element leaving* a Imm clearancegap*neXt to

• • , the *front cover plate; Three coh~mns. of fuel. str~ps laid *side. by side filled. the width of the element. In the NESDIP configuration _only the central two strips in* each column contained

• U/Al .a!loy, the 'Outer tw9 were both blanks* manufactured from aluminium. T9 approximate to

• a disc sourc~ th~. axial fuel loading within each element had been arranged fo the specification of Figure 4 by the substitution of aluminium blanks where n~essary. .

~.I The. Fission-Rate Distribution ~ithin the. NESDIP Fission* Plat~

Located* in the NESDIP 2 Radial Shield Array

• The approach taken to obtafu the absolute.power distribution throughout the fission plate in this phase of NESDIP follows t11e procedure set out in reference 3. In summary this is :

. (a) The measurement of manganese reaction-rates over the front surface of the fission plate

• .. to 'define a thennal .flux profile in the x and y coordinates of the system defined in Figure 5; *

(b) A measurement of the distribution of the U235 content within the fuel; (c) Combining (a) and (b) to provide a relative fission-rate profile in X and Y; B2

AEAT-0352 APPENDIXB (AEAT-0355)

(d) The definition of a relative fission profile in the Z direction through the fuel from fission product decay measurements in irradiated fuel; (e) Normalisation of the fission-rate profile to absolute measurements of the fission-rate per NESTOR Watt in the plate.

3.2 The, Low-Energy Neutron Flux Profile Over the Fission Plate Measurements of the Mn55(n;y)Mn56 reaction-rate on the front and back faces of the fission plate were made with 12.7mm diameter Mn foils. The distribution of foils on the front face of the fission plate is shown in Figure 6. The foils on the back face were positioned directly behind the foils on the front face at the locations which are encircled in Figure 6. The definition of the X-Y flux profile was made using the manganese measurements made on the front face. The fission-rate attenuation in the Z direction through the plate is assumed to be independent of X and Y

• allowing a considerable simplification of the treatment with little loss of accuracy. To support this.assumption it is noted that the average difference in the ratios of the manganese measurements at the front to those at the back is less than 3%

between positions at the centre of the plate and at ~ts edge.

The manganese reaction-rate measurements on the front face of the plate were input to the CRISP code (7) which fitted a continuous surface to them to define the manganese reaction-rate covering the plate. The surface fit is shown in Figure 7. From this surface the average manganese reaction-rate can be defined within the elements of any source mesh overlaid onto the fission plate. To model exactly the boundaries of the plate and to provide adequate *.,

spatial resolution, the source mesh shown in Figure 8 was used. The fractional uncertainty *:1 on the mean manganese reaction-rate in each source mesh due to *the surface fitting and :i integration is estimated to be 2%.

3.3 The Fission Plate Profile The fission-rate profile in X and Y is taken as the manganese reaction-rate profile on the front face of the fuel plate, as shown in Figure 7. In the definition of the fission-rate in each mesh the Z dependence is irrelevant provided it is independent of X and Y. This assumption ,*

has been made and justified in Section 3.2. The uncertainty estimate on the average fission- * .,;j rate in each source mesh is mostly due to the uncertainty of the surface fitting and integration :i~

procedures of the CRISP code with a much smaller contribution from the uncertainty on the ;o' U235 content, giving a total of+/- 2.1 % (2).

3.4 The Z Dependence of the Fission-Rate Distribution The relative fission rates in the two layers of fuel contained within the plate have been derived from measurements performed to establish the absolute power of the plate. The ratio of fission rates in the front and back fuel plates was 1.044+/-0.015. For the calculational analysis of the NESDIP2 radial shield this variation is neglected and the fission-rate in the Z direction is assumed to be uniform over the 2mm depth of the fuel.

It has become customary to provide a spatial neutron source definition which integrates to a total plate power of 1 Watt. Table 3 contains the neutron source distribution for the NESDIP _

plate in the NESDIP2 array normalised in this way; constants of 3.121El0 fissions per Watt and 2.437 neutrons per fission have been used in its derivation. .

B3

AEAT-0352 APPENDIXB (AEAT-0355) 3.5 The Absolute Calibration of the Fission Plate The absolute' power in the fission plate, expressed per NESTOR watt, has been detennine by combining spot measurements of the absolute fission-rate made by counting fission product decay rates with corresponding absolute measurements of the Mn55(n;y) reaction-rate and the fission-rate profile data derived in CRISP. This is fully described in reference 3.

The fission plate power per NESTOR Watt is calculated to be 8.67E-4 Watts, the standard deviation on this value being 3.5%. The latter is due mostly to the 3% uncertainty in the measurement of the absolute fission rate.

4. THRESHOLD REACTION-RA TE MEASUREMENTS The reactiori-rates of three fast neutron threshold detectors.have been measured along the nuclear axis of the *shields. They are the S32(n,p)P32, Inll5(n,n')In115m and Rhl03(n,n')Rh103m reactions. The rhodium reaction-rate was measured over four decades of .

• attenuation through the .water cell, RPV and into the cavity. For measurements in the RPV region, 0.6cm air gaps were opened up* between the slab components to allow the insertion of the ,activation detectors. The indium and sulphur measurements were made in the RPV region and the cavity. In addition, during all irradiations of activation detecto.rs within the .. *

- shields, three sulphur pellets were placed .in locations at the centre of the front face of the

• fission plate to monitor its run~to-run power via the S32(n,p)P32 reaction.

4.1 . Rhodium Activation Measurements The rhodium measurements were 'made under ca~ium to reduce impurity activation. The foils were.located within the water cells on a thiri:perspex jig which-was sprung against cell wall. The positional uncertainty was +/-lm.m. In the RPV .and cavity the foils located on a thin aluminium carrier. The uncertainty associated with the calibration of Nal spectrometer counting system is 3%.

4.2 Sulphur Activadon Measurements_

In the RPV and cavitY 20g sulphur samples were located ~n thin aluminium carriers. To facilitate their inclusion in the RPV, 0.6cm voids were introduced between the 5.lcm thick mild steel components. The activated sulphur is first slowly burnt in a* thin aluminium cup which is subsequently collapsed to' a disc. The residue containing the p32 activity is then .*

• counted. The calibration .of the counting system including counter ~fficiency, .losses due to

• burning, and reference data has a systematic uncertainty of 4%. **

4.3 Indium Activation Measuremeµts The indium samples were located on, the thin aluminium carrier in the* RPV and Cavity. The

• calibration of the counting system for these foils, including Ge(Li) efficiency and reference

- data has a systematic uncertainty of 2%.

4.4 Core Background Corrections A small fraction of neutrons present in the arrays origiflate from leakage from the NESTOR core. The NESTOR reactor is fitted with a boral shutter which is located outside the thennal column, ie adjacent to the front of the ASPIS trolley. It is composed of 1.27cm of boral and when closed it absorbs thennal neutrons which could otherwise enter the trolley. This boral shutter, to a first approximation, shuts down the fission plate leaving only fast n e u .

leakage from the NESTOR core. Work conducted to study the true shutdown factor o f .

B4

AEAT-0352 APPENDIXB (AEAT-0355) plate power when the boral shutters are closed (8) led to value for the background correction of (2+/-1)%. This background correction applies in both the RPV and cavity regions. In the

___ water-cells-the-value oL(J+/-l)~ds_appropriate. ___ ----- - ------ --- - ----- .------. -- ------* --- --- - -*-- ---*- - -- -.

4.5 Activation Results.

The reaction-rates measured on axis in the NESDIP2 array with the corrections and uncertainties described above are shown in Table 4. The foil irradiation locations are defined in Figure 9. *The results of the lateral scans made with the sulphur detectors are shown in Table 5 and Figure 10.

4.6 Perturbation in the RPV Region The RPV region is constructed from four 5.lcm thick mild steel plates and the rear wall of the water cell. To obtain activation measurements through the RPV region four air gaps of width 0.6cm were opened up between these components. The penurbation of activation measurements made at a position 4cm into the cavity when_ these voids are. introduced is given in Table 6 (note that the measurements were made at a constant distance from the rear face of the RPV region irrespective of whether the RPV plates were separated by air gaps or closed up).* The ratios suggest a slight reduction in the measured reaction-rates caused by opening the plates as would be expected, but the reduction is not statistically significant 5 MONTE CARLO. CALCULATIONS The analysis of the NESDIP2 measurements has been performed using versfon 9A of the Monte Carlo code MCBEND (9). A listing of the input data is given in Appendix A.

5.1 The Geometric Model A precise geometric representation of the NESDIP2 radial shield configuration in the ASPIS trolley was achieved using the combinatorial geometry package of MCBEND. The calculational model is shown in Figure 11. The only approximation in the model is the exclusion of the 0.6cm wide voids between the mild steel plates in the RPV region. It is assumed from the evidence presented in Section 4.6 that the activation rates in the cavity are insensitive to the absence of the voids between the plates.

5.2 The Fission Plate Source Distribution The derivation of the source distributio~ for the fission plate has been described in detail in Section 3. The Z dependence of the source between the two fuel strips in the NESDIP plate

.has not been modelled and a uniform source across the thickness of the plate has been used.

The effect of this approximation on the calculated fluxes is trivial but.it does allow a halving of the number of source regions required to 225. The output from the CRISP program which derives the source distribution in the fission plate is formatted in accordance with the input requirements for the source module in MCBEND and has been included directly into the input data. The fission neutron energy spectrum for U23S due to Story and Miller (10) has been used in this analysis. .

- - . 5.3 The Scoring -nata Scoring is in rectangular regions having a 20cm x 20cm cross-sectional area and 2mm depth. The regions are centred on the measurement positions through the shield which have been defined in Figure 9. An additional scoring region at 23.9cm into the cavity region was included. This was used as the target for the MAGIC calculation(see below). In addition to BS

AEAT-0352 APPENDIXB (AEAT-0355) the three measured reaction-rates the reactions *Al27(n.a). Fe54(n,p). ASlM

• displacement and total flux >O.llMeV were scored for comparison with the calcul results of reference 3. The cross-section data were taken from IRDF-90 (5).

5.4 Nuclear Data Reference 3 used UKNDL data presented at 8220 energy points. This exercise uses ENDF-BNI data in the same DICE fonnat in which the nuclear data are represented as averaged partial cross-sections at 8220 energy points. a point being a very fine group, with explicit representation of the energy loss laws and angular distributions of scatter. The data librarie.s are produced from evaluated nuclear data by processing codes contained in the NJOY suite

.of codes. In the case of ENDF-BNI. data the processing includes replacing the doubly differential distribution* for angle and energy, which is present for some isotopes, by

• uncorrelated angular and energy distributions. The production of the DICE Library of ENDF~BNI data is described by Eaton and Dean [12]

5.S.

• Variance-Covariance Data *

.. The variance-covariance data used for matenal cross-secti~ns were based on* the ENDF-BN .

(hydrogen and oxygen) and ENDF-BNl library (iron). The *co-~ariances for the detector cross-sections were generated from the IRDF-90 (5) library which is based on the ENDF-BNI compilation. In estimating uncertainties these co-variance dat.a were folded with the

. sensitivities of the responses to the appropriate cross-section calculated by MCBEND iii 10

. energy grou*ps above 0.028Mey:

5.6 .Acceleration of the Monte *Carlo Calculations The MCBEND module MAGIC was invoked to calc~late .the importance map for ti

. accelerating the MCBEND calculation. This perfonns an adjoint diffusion theory calculau

'in an orthogonal mesh~ in this case RZ, in order to provide the importances used in splitting and Russian roulette. The spatial *mesh,was the same as in reference 3 with 11.R.intervals and*33 Z inter\tals. Material compositions for each mesh were automatically 'determined by MAGIC. The importanceS were calculated in 16 energy groups ranging from 14.6MeV to 0.03MeV. The source for the adjoint calculation was positioned at the outennost. scoring region. with the adjoint source spectrum being spe~ified to be identical iri all energy groups in an attempt to score .all responses with equal statistical accuracy.. * *

• 6 MONTE CARLO RESULTS

• The calculation* w;is perfonried on** a micro VAX3 *running for about

• 15

• hou~ with

.' approximately 1.15 million particles being started.. The results of the calculation* using* the ENDF-BNI data in conjunction with the IRDF-90dosimetry *cross-sections are shown fu

Table 7.'The statistical errors are expressed in terms of one standard deviation (sd).

6.1 .Corrections to the Calculated Reaction-Rates .

In order.to compare the calculated and measured results it is necessary to make the following

. corrections to the calculated results (a ) To correct for the size of the Monte Carlo scoring regions compared to the size of the measurement foils. * . *

• The ratio of the fluxes on the axis to the mean fluxes over the Monte Carlo sc~

regions varies slightly with energy and position, becoming flatter with lower ene.

• B6

AEAT-0352 APPENDIXB (AEAT-0355) and sharper near the source. The ratio for the NESDIP2 calculation has been detennined from the axial measurements of the S32(n,p)P32 reaction in the cavity already shown in

- -Table ,S; A cosine distribution-of width 140cm *was-fitted to -the -measured- profile and from this the maximum to mean ratio of 1.014 for the S32(n,p)P32 reaction-rate in the scoring zone was derived with an uncertainty of 1%. This ratio is assumed to apply for all reactions at all positions.

(b) To normalise the calculation to 1 NESTOR watt.

The fission-plate calibrations detailed in Section 3 give the fission plate power per .

NESTOR Watt as 8.67E-4 Watts.

6.2 Uncertainties In addition to the corrections described above there are other considerations which contribute to the overall uncertainty of the calculation. These are discussed below.

(a) Uncertainty due to the correction for the size of the scoring region A value of 1% as described in section 6.1 is adopted.

(b) Uncertainties due to material cross-sections There are uncertainties in the nuclear data libraries. As part of the MCBEND calculations the sensitivities of the various responses to changes in the total cross-.

sections of hydrogen and oxygen and in the inelastic cross-section of iron were determined in 10 energy groups ranging from 14.9 to 0.03 MeV. The calculat,ed

• sensitivities were folded with co-variance matrices obtained from the ENDF-BM (iron inelastic) and the ENDF-BN (hydrogen and oxygen) to produce the uncertainties which*

are recorded in Tables 8, 9 and 10. (Currently there are no co-variance data in ENDF-BNI for hydrogen and oxygen).

(c) Uncertainties due to material dimensions

~i) Front and rear water gaps in cell 1 Spot measurements made of the front and rear water gaps in cell 1 show a maximum difference from the input water thickness of -0.16cm and +o. lcm and -

0.16cm and +0.37cm respectively. Uncertainties on the calculated results based on the maximum uncertainty in cell width have been determined by extrapolating the calculated results for the input water thickness assuming an exponential attenuation for the response . function. This unce~inty applies to the reaction-rates downstream of the water cells and can be seen in Tables 8, 9 and 10.

(ii) Air gaps The air gaps between the mild steel plates were not modelled. Section 4.6_ states that the slight reduction in the measured . reaction-rate with the gaps open is not

• statistically significant

• B7

AEAT-0352 APPENDIXB (AEAT-0355)

(d) Uncertainties due to detector cross-sections . A The detector cross-sections used in the calculation were taken from the IntemaS Reactor Dosimetry File IRDF-90 (5) whiCh also contains co-variance matrices for the cross-sections in reduced energy group schemes. An uncertainty for each calculated response for the three measured reactions was derived from the co-variance data and the contributions to each response from 27 energy groups.

(e) Uncertainties* due to the representation of the fission spectrum The. calculations used MCBEND's built-in option for providing a

• lJ235 fission spectrum. The formula used to represent the spectrum is the Watt-Cranberg expression x(E) = K e*AE sinhVBE *.,

where E is the neutron energy in MeV, x(E) is the fracti~n of neutrons at E per MeV,

, and A and .B are constants which vary* with nuclide. K. is a normalisation constant

• Uncertainties in the values of A and B lead to uncertainties in the spectrum and hence in the results. 'The. uncertainties in the spectrum are negligible ~t the peak energy of about

. 2MeV, and increase with decreasing energy to about 4% at 0.1 lMeV. Howe.ver, the uncertainties are more significant at higher energies, being about 7% at lOMeV. .

The effect of the .uncertainty in the representation of the fission spectrum has been investigated in an analysis of NESDIP2 with JEF2.2 nuclear data (11). In the cavity, the uncertainty was 4.3% for .sulphur, 3. 7% for indium and 3.5% for rhodium. Jusr inside 'the RPV, the uncertainty w. as 4.1 % for sulphur, 3.3% fo. r indium and 3.2-v r .

rhodium. Near the fission plate the uncertainty on the rhodium result was 2.3%,

at zone 36 immediately beyond the baffle the uncertainty was 2.6%. Uncertain other positions have been determined by linear interpolation between these values.

Uncertainties inboard of the RPV have not'been determined for sulphqr and indium as no merisurements for these two reactions were taken there.

• The*calculated results for the* rhodiu*m, indium, and' sulphur reaction-rates, along with the corrections detailed iil seetion. 5.8 are shown in. Tables 8, 9 and 10 together with the calculated uncert;iinties detailed above.

• 6.3 Comparison of Calculation with Experiment

• The ratios of calculated and measured reaction-rates are shown in Table 11. In the RPV and cavity regions, the average C/M values for the sulphur, rhodium and indium reactions are

_0.94, 0.94 ancl 0.95 respectively. Inboard of the RPV, the CJM values for rhodium along the centre-line of the system vary from 1.08 near the source to 0.89 in the water cells with a mean value of 0.92. This suggests that the absolute normalisation of the calculation is low by about 6%, the estimated uncertainty on the source strength being +/-3.5%.

All .values of CJM for indium and sulphur are within one standard deviation of unity, the rhodium results being within two standard deviations throughout the system. The major components of the uncertainty on the CJM values are due. to the detector cross-sections, the iron* inelastic cross-section, and the fission spectrum.

In the RPV position T/4 corresponds approximately to measurement position 15, and the values of C/M at this point are within 5% of those for the cavity. At position 3T/4, corresponding to measurement position 17, the values of CJM are within 4% of those

• cavity for sulphur and indium, and 14% for rhodium. Therefore normalising _calculati.

B8

AEAT-0352 APPENDIXB (AEAT-0355) measurements made in the cavity of an operating PWR allows accurate prediction of the neutron fluence at the T/4 and 3T/4 positions.

Of the 27 values of C/M given in Table 11 none differ from unity by as much as two standard deviations, whilst in 10 cases the discrepancy exceeds one standard deviation. 1be expected number for a normal distribution would be 9. Most of the instances of large discrepancies are for the rhodium detector where in 53% of the comparisons the differences exceed one standard deviation. compared with 20% for the other two detectors. This suggests that the uncertainty in the rhodium measurements and the detector cross-section have been underestimated and that the remaining uncertainties, including those due to the material cross-sections, are if anything overestimated. The measurements therefore support the uncertainties that have been assigned to the cross-sections for hydrogen, oxygen and iron in the ENDF-BN and ENDF-BNI files.

7

SUMMARY

The NESDIP programme has been briefly described, and details of the NESDIP2 experimental configuration presented. Measurements of three reaction-rates, ie S32(n,p)P32, In l 15(n,n')ln l 15m and Rh 103(n,n')Rhl03m, have been tabulated and compared with the results of analysis using the Monte Carlo code MCBEND with ENDF-BNI nuclear data.

MCBEND predicts the reaction rates with maximum discrepancy of 12%. Within the wall of the simulated vessel the mean value of C/M for the three detectors at four positions is 0.95.

At the important T/4 and 3T/4 positions in the RPV, the C/M values are all within 5% of those at the cavity except for the rhodium at 3T/4, showing that accurate predictions of the neutron fluence at these positions could be derived from measurements in the cavity and calculated ratios. It should be noted that the outer wall of the cavity in the NESDIP2 array was a water tank thus giving well defined materials. In a practical reactor the primary shield is usually composed of concrete with additional uncertainties arising in the fluxes calculated in the cavity because o_f the lack of an accurate chemical analysis.

The results are consistent with the uncertainties assigned to cross-sections in the ENDF-BN and ENDF-BNI~ and they provide validation for the application of MCBEND with its ENDF-B/VI library to the calculation of fluences in PWR vessels.

B9

AEAT-0352 APPENDIXB (AEAT-0355)

[1]

RE.FERENCES

• Review of the NESTOR Shielding and Dosimetry Improve,~~nt Programme (NESDIP)

J Butler et al j* ,*

• • L Reactor Dosimetry: Methods, Applications and Standardisation (Farrar and Lippincott, ed.), STP 1001,ASTM, Philadelphia.PA, USA,1989

[2] The PCA Replica Experiment Part 1. Winfrith Mea5urements and Calculations.

AEEW - R '1736

[3] NESDIP Phase 2. The ASPIS PCA Slab G~ometry Benchmarks Carter MD, Curl I J * *

. PRPWG(SH)P(85)34

[4] The Analysis of NESDIP2 with ENDF-BNI Nuclear Data* .

Newbon S * **

AEA-RS-5591

. ' [5] . The International Reactor Dosimetry File (IRDF,.90)

• Kocherov N P and McLaughlfo P K.

• IAEA,.NDS-14~ . . .

[6] *:. The International Reactor Dosimetry File (IRDF-85)

• Cullen. D.E: & McLaughlin P.K..*. * , ..

. IAEA-NDS:-41 .

. ~-' ' . . . . ' .' . .  : . . . ~*.**. Ji.~ ......

[7] CRISP - A Computer Code to Define Fission~Plate,Source Profiles ,

Curl I J *. . . .* .  ; '. .

. . . 'i ' ..,. "

RPD/IJC/934  ; .* + *

. ..  ; .' ~: . :,~ ~

ASPIS: Correction for NE~TOR Core Bp.ckground *

[8] 0*< ~ **

CarterM D . .' .

RPD/MDC/1048 *

. '[9] MCBEND9 User Guide

.

• ANSWERS/MCBEND(94)l5.

[10] Fission Neutron Spectra for Shielding Calculations Story JS and Miller PC ARPWG/P(81)12 .'

[11] Benchmark Testing of JEF2.2 Data for Shielding Applications Analysis of the NESDIP2 Benchmark Experiment G.A Wright , S.Newbon and J.M Earivicker .

AEA-RS-5629 (12] Eaton C R and Dean C J .

Report on the Extension of the Monte Carlo Nuclear Data Generation Route AEA-RS-1246 BlO

AEAT-0352 APPENDIXB (AEAT-0355)

-Assembly -----

Trolley

-Component---- -Thickness-(cm) 3.2

-- - -Material-Mild Steel 3,8 Material

-Reference---

Numher3 Face with Aluminium Window of radius 56. lcm Void 6.0 0 Graphite 15.0 Graphite 1 Void 1.2 0 Fission coverplate 1.2 Aluminium* 9 Plate void 0.1 0 blank 0.1 Aluminium 9 fuel 0.2 Fuel 7 blank 0.1 Aluminium 9 coverplate 1.2 Aluminium 9 Void 0.4 0 *,,

Water- front face 1.9 Aluminium 9 Cell , .. water gap 12.11 Water 10 No. 1

• thermal baffle 6.3 Stainless 6 Steel .

water gap 13.21 Water 10 rear face 2.5 Mild Steel 4 RPV plate 1 5.12 Mild Steel 5 plate 2 5.12 Mild ~teel *5

plate 3 ' 5.1 2 Mild Steel 5 plate 4 5.12 Mild Steel 5 Cavity 29.4 0 Water 1.9 Aluminium 9 Cell 22.5 Water 10 No. 2 2.5 Mild Steel 5 Biological 61.0 Concrete 2 Shield . --*

1 This dimension is greater than the specification due to cell bowing.

2 A 0.6cm void was opened up in front of this component for activation foil measurements.

3 See Table 2.

Table 1 Dimensions and Materials in the NESDIP2 Array

AEAT-0352 APPENDIXB (AEf.T-0355)

Material Graphite Marerial Reference No.

l Densiry (J?.cin-3) 1.65 Element c

Atom Fraction 1.00 Concrete 2 2.30 Si 0.2044 Fe ' 0.0043 H 0.169

.. ' 0 0.5633 Al 0.0215 Ca 0.0161 Na 0.0119 K 0.0096 Mild Steel 3 7.835' Fe '. *0.9781 Mn 0.011 c I '* 0.0102 Si 0.0007 '*

Mild Steel 4 7.862' .Fe 0.9958 Mn *0.0024 c 0.0018 Mild Steel 5 7.85 fe. 0.98.16 Mn 0.0075 c* 0.0106. . '

H. ' 0.0003 Stainless 6 *'

• 7.90 Fe 0.6?14' Steel c 0.0011 Ni 0.0934.

.. Cr'* O;i856 Ti I, 0.0021

... Si* 0.0121 Mn 0.0143**

Fuel 7 3.256 Al 0.9721 U235 0.026 ..

U238 0.0019 Aluminium 8 2.70' Al 1.00 Aluminium 9 2.666 ,. Al ., 0.9959

.... I

,. Si 0.0014 Fe " 0.0027 '*

Water lO 1.00 H 0.6667 0 o.~333 Table 2 Material Compositions

AEAT-0352 APPENDIX B (AEAT-0355)

X-Coordinate (cm)

-49.1S -46.BS -43.32 -37.08 -33.92 -27.SB -11.7S -2.2S 7.2S 16.7S 32.SB 38.92 42.08 48.42 SI.SB .S4.7S Sl.44 0 0 0 0 0 6 3.236E+07 3.277E+07 3.236E+07 0 0 0 0 0 01 47.63 0 0 0 0 0 3.333E+07 3.S72E+07 3.642E+07 3.S91 E+07 3.327E+07. 0 0 0 0 01 40.64 0 0 0 0 3.232E+07 3.693E+07 4.021E+07 4.115E+07 4.0S2E+07 3.71 IE+07 3.245E+07 0 0 0 o, 3S.S6 0 0 0 3.3S6E+07 3.SSIE+07 3.994E+07 4.37SE+07 4.484E+07 4.412E+07 4.022E+07 3.483E+07 3.20SE+07 0 0 y 31.7S 0 *o 3.489E+07 3.729E+07 3.983E+07 4.S31E+07 4.98SE+07 S.llOE+07 S.022E+07 4.S61E+07 3.921E+07 3.S87E+07 3.231E+07 0 c 19.69 0 0 3.S02E+07 3.784E+07 4.079E+07 4.380E+07 S.009E+07 S.Sl7E+07 S.6SIE+07 S.S49E+07 S.032E+07 4.317E+07 3.941E+07 3.S39E+07 3.12SE+07 ol 0 IS.88 I r 3.440E+09 3.6SIE+07 3.973E+07 4.302E+07 4.632E+07 S.307E+07 S.842E+07 S.977E+07 S.861E+07 S.316E+07 4.S62E+07 4.166E+07 3.741E+07 3.304E+07 3.0llE+07 I

d S.29 i 3.482E+07 3.731E+07 4.070E+07 4.428E+07 4.779E+07 S.484E+07 6.029E+07 6.IS9E+07 6.o3SE+07 S.468E+07 4.697E+07 4.29SE+07 3.866E+07 3.42SE+07: 3.129E+07 n -S.29

• I -IS.88 3.319E+07 3.SS3E+07 3.910E+07 4.264E+07 4.610E+07 S.296E+07 S.819E+07 S.937E+07 S.808E+07 S.2S5E+07 4.518E+07 4.139E+07 3.738E+07 3.331E+07 3.062~+07 e 0 3.33SE+07 3.672E+07 4.007E+07 4.334E+07 4.982E+07 S.472E+07 S.S78E+07 S.4SOE+07 4.926E+07 4.238E+07 3.889E+07 3.S24E+07 3.IS9E+07 oi

-19.69 i c 0 0 3.309E+07 3.603E+07 3.891E+07 4.465E+07 4.898E+07 4.986E+07 4.866E+07 4.393E+07 3.789E+07 3.489E+07 3.183E+07 0 o:I m -31.75 0 0 0 3.IS7E+07 3.393E+07 3.869E+07 4.228E+07 4.296E+07 4.186E+07 3.782E+07 3.282E+07 3.043E+07 0 0 O!

-3S.S6 i 0 0 0 0 3.113E+07 3.Sl8E+07 3.82SE+07 3.880E+07 3.779E+07 3.423E+07 2.994E+07 0 0 0 0

-40.64 0 0 0 0 0 3.071E+07 3.296E+07 3.330E+07 3.243E+07 2.963E+07 0 0 0 0 o:

-47.63 0 0 0 0 0 0 2.870E+07 2.883E+07 2.811 E+07 0 0 0 0 0 oi

-Sl.44 Table 3. The Neutron Source Distribution in the NESDIP Fission Plate LocaJed in the NESDIP2 Array (n.cm-Js-1/Plate Watt)

AEAT-0352 APPENDIXB (AEAT-0355)

.Reference In l 15(n,n ')In l 15m S32(n .* p)P32 Location Position Monitor 1 9.94E-22+/-5.41 %

Front 2 8 ..24E-21+/-4.7%

Compartment *3 4.84E-21+/-4. 7%

of water 4 1.88E-21+/-4,7%.

Cell no.I 5. 1.45E-2l+/-4.7% ..

6 7.16E-22+/-4.7%

7 6.15E-22+/-4.7%

Rear 8 2.13E-22+/-4.8%  :

Compartment '* '9 l .06E-22+/-4.8%

of water *. 10 ' 5.82E-23:t5.. Q% *:

Cell no.I* 11 . 3.86E~23+/-5.0%

12' . 2.39E-23+/-5.6%.

1.3 1.87E-23+/-5.3%

RPV 14 1;66E-23+/-5.1 % , 3:39E-24+/-43% 1.ose-24~.8%.

15 9.16E-24+/-5.1%.

• 1.66E-24+/-4.2%

• 4.05E-25+/-6.2%

16 5,04E-24+/-5.6% 7 .93E-25+/-4A% 1.59E-25+/-5.8%

17 2.71E-24+/-5.9% , . 3,75E-25+/-4.5% 6.42E-26+/-5.8%

Cavity l~ , f.18E-'24+/-6.2% 1.36E-25+/-4.6% 2.02E~2()+/-5.8%..

. Table 4 Measured Reaction-Rates thro~gh the NESDIP2 Radial Shield .

• AEAT-0352 APPENDIXB (AEAT-0355)

---*-- Distance from------- - - -

Nuclear Centre (cm)+

Reaction-Rate (dps.atom-lper NESTOR Watt)

Profile

- (Normalised to LO at Nuclear Centre)

~*--

75 3.llE-27 0.15 50 9.05E-27 0.44 25 1.76E-26 0.86 0 2.06E-26 1.00

-25 1.71E-26 0.83

-50 9.28E-27 0.45

-75 2.75E-27 0.13

• Measurements made on vertical axis intersecting the nuclear centre of the trolley and 4cm off the front wall of the cavity.

+ Nuclear Centre is 88.9cm from the floor of the trolley Table 5 S32(n,p) Reaction-Rate Profile in the Cavity*

Reaction-Rate Ratio Reaction (Plates Open/

' Plates closed)

Rh 103(n,n')Rhl03m 0.98+/-0.04 In l lS(n,n')In l 15m 0.95+/-0.04 S32(n,p)P32 0.98+/-0.03 Table 6 Comparison of Activation- Measurements in the Cavity with the RPV Plates Open and Closed

AEAT-0352 APPENDIX B (AEAT.:0355)

Mmsuremem MC11END Rmctim-Ratn AUX>0.11 Mc V (clps.11om*I Ptt PlateWao) l..callmi pmldoo 7.me A127(11,1) . 1111 I OJ(D.D') IDIU(n.n') sl2<n.p) ASTM 800 llHI ~S-ttn.p) (n.cm*la*l per rtf. Number Numbtt Plait Will) 2 30 4.$0E-ll 1.2 l.86E*ll 2.6 1.971!-18 1.4 .S.J2E-19 1.0 1.0691!-14 4.1 6.611E*19 1.0 l.IOE+-07 14.4 Froill . J JI J.121!-U 1.2 .S.14E*ll l.4 1.201!-18 l ..S l.421!-19 1.2 6.J961!-l.S 2 ..S '-l67E,19 1.0 9.8.SEt-06 6.2 w- 4 Jl l.4.Sl!-21

• l ..S l.31E*ll II 4.101!-19 2.7 l.4Jl!-19 1.9 2.J98E-l.S J.9 1.7281!-19 r..s J ..SJEt-06 *9.9

<:uns-tmem .s JJ 1.20!!-21 1.6 IA91!-ll 4.2 J.611! 2.1 1.12E*l9 1..s 1.8096-1.5 J.2 l.JBJl!-19 1.4 2..SBEt-06 9 ..S 6 J4 6.69E-22 1.7 7.IJE-19 2.8 1.796-19 l.l .S.6.SE-20 1.7 l.91.5E-16 2.6 6.8-16E,20 l ..S l.J2Et-06 6.J 7 u* .s.441!-22 I.I 6~.Sl!-19 7.J 1.491!-19 2.7 U9E-20 I.I 7.7186-16 J.2 .S.496E-20 1.6 1.JOEt-06 10.1 I J6 1.511!*22 2.0 2.lJE-19 J ..S 4 ..566-20

• 2.1 1.19E*20 1.7 2.6641!-16 2.1 l ..5<17E*l0 1.6 4.7.SE+0.5 J.7 Ra 9 J7 1.0.SE-il 2.1 l.llE-19 2.8 2.486-20 2.1 7.4JE*21 1.7 l.JJJl!-16 2.1 9.J.S.SE-21 1.6 2.1.SE+0.5 J ..S w- 10 JI 7.20l!-2J 2.1 .S.861!-20 2.7 1.421!-20 2.J '-.59E-21 1.9 7.2786-17 2.2 .S.860E-21 1.7 l.IOE+0.5 4.1 Cali~ II 12 IJ J9 40 41

.S.4'1!-23 J.141!-2J J.78E-23 2.1 2.1 2.2 J.861!-20.

2.42E-20 1.941!-20 2.J J.J 1.9 9 ..S.Sl!-21

.S.981!-21 4.~l!-21 2.0 2.0 1.9 J.29E*21 2.141!-21 l ..54E*21 I.I 4.7806-17 J.0746-17 1.9 2.4.S.SE-17 1.9 2.0 1.9 4.llJE-21 1.6 6.72E+04 2.7961!-21 1.8 4.211!+04 l.960E*21 1.7 3.72E+04 J.O u

J.J 14 42 l.IJl!-2J 2.4 l.66E*20 1.7 ).S7E-21 I.I Ul6E-21 1.9 2.07.SE-17 1.7 1.3611!*21 I.I J.6JE+Ot 2.0 Rl'V IS 4) 7.71E-24 2.1 9.78E*21 1.6 1.80&21 1.7 U2E*22 2.0 1.214&17 1.6 .S..S7JE-22 1.7 2.66E+Ot 1.7 16 4' J.27E*24 ).J .S.71E*21 1..s 1.84&22 1".1 1.786-22 2.2 7.096&18 1.4 2.179E-22 1.7 l.BJE+Ot 1..s 17 4.S l.Jll!-24 J.7 J.IJE-21 1.4 4.111!-22 1.6 6.741!-U 2.4 4.0196-11 1.4 l.6JJE-2l 1.7 l.llE+Ot l ..S CaY!ly 18 46 UJl!-2.5 4.0 l.IBE*21 1.2 1.J9E-22 1.4 2.19E*2l 2..s l..S.56&11. 1.4 2.IOOE*ll 1.4 4.92E+OJ 1.6

. 47 J.71E-2.5 J.9 1.l6E*22 1.2, 9.966-23 l.J l.66E 2l0 2..s 1.129&18 l.J 2.092E*ll l.J J.S71!+0J 1* ...

Table 1 Calculated Responses with ENDF-BNI Data

• AEAT-0352 APPENDIX B (AEAT -0355)

Measurement ~* *- . - u~namues l Ill.II Location position Zone calada1ed reaclion-rale.s/ .sconng maten&I aos.t sections malerial derector uncatailty region dimensions fwion refnuniler Number NESTOR Wall size iron oxygen hydrofen w11er gaps ao" lpCCtlUlll imlaslic loW . IOU sections sd'I> 'I> 'I> 'I> 'I> 'I> 'I> 'I> 'I>

2 30 7./'.IC.-21 2.6 1.U u.ou 0.1 0.1 0.0 3.~ 2.3 ~.o Froilt 3 31 4 ..S2E-21 2.4 1.0 0.00 0.1 0.4 0.0 3 . .S 2.3 4.9 Wiier 4 32 2.03E-21 10.9 1.0 0.00 0.2 0.8 0.0 4.1 2.4 12.0 Co~

6 7

33 34 3.S l.31E-21 6.27E-22

.S.8.SE-22 4.2 2.8 7.3 1.0 1.0 1.0 0.01 0.0.S 0.12 0.2 0.4 o..s 0.9 1.4 J.4 0.0 o.o o.o 3.6 M

4.0 2.4

2. .S 2 . .S 6.2

'-4 8.9 8 36 1.96E-22 3. .S 1.0 0.70 o..s .., o..s 3.9 2.6 6.2 Re. 9 37 9.76E-23 2.8 1.0 0.92 o..s 1.8 o..s 3.6 2.7 .S.8 Wiier 10 38 * .S.ISE-23 2.7 1.0 1.07 0.6 2.1 o..s 3.3 2.8 .S.8 Co~ II 39 3.39E-23 2.3 1.0 1.12 0.7 2.3 o..s 3.4 2.9 .S.8 12 40 2.IJE-23 2.3 1.0 1.22 0.9 2.6 o..s 3.4 3.0 6.0 13 41 l.71E-23 1.9 1.0 1.33 1.0 2.7 o..s 3.4 3.1 6.0 RPV .,

14 16 42 43 44 l.46E-23 8.60E-24

.S.02E-24 1.7 1.6 u

1.0 1.0 1.0 1.69 2.38 2.86 1.0 1.0 1.0 2.7 2.7 2.7 2.2 2.2 2.2 3.6 4.0 4.4 3.2 3.3 3.3 6.6 7.0 7.4 17 4.S 2.7SE-24 1.4 1.0 3.11 I. I 2.7 2.2 4.9 3.4 7.8 Cavity 18 46 l.04E-24 1.2 1.0 3.28 I. I 2.7 2.2 .S.2 l . .S 8.1

- 41 7.3SE-2S 1.2 1.0. 4.30 1.0 2.1 2.2 .S.2 3. .S 8.6 Table 8 Calculated Reaction-Rates and Uncertainties for Rh103(n.n')Rbl03m

AEAT-0352 APPENDIX B (AEAT-0355)

Measurement ~* -- ~* -- Uncertamues lOW wicenainty Location position Zone calculated reaction-rates/ sconng material aoss sections matenal detector region dimensions fission rcfnulllM Number NFSrORWait size iron oxygen hyarogcn water g31>5 aoss spectrum inelastic tocal total sections 2 30 1.1.'1:.-:ll S<l 'k 1.4

'A>

1.U

'A>

u.u

'A>

U.I

'A>

U.I

'A>

u.u

'I>

2.2 '"'- 'I>

l.8

• Front 3 31 1.0SE-21 1..5 1.0 0.0 0.1 0.4 0.0 2.2 3.0 Wakt 4 32 4.22E-22 2.7 1.0 0.0 0.2 0.9 0.0 2.2 3.7 Compartmelt s 33 3.. 17E-22 2.1 1.0 0.0 0.2 1.0 0.0 2.2* 3.2 6 34 1.S7E-22 2.2 1.0 0.2 0.4 1.4 0.0 2.2 3.6 7 35 l.31E-22 2.7 1.0 0.2 0.5 1.5 0.0 2.2 3.7 8 . 36 4.0IE-23 2.-. 1.0 I. I 0.4 1..5 0.6 2.2 3.7 Rear 9 37 2.18E-23 2.1 1.0 1.2 o.s 1.8 0.6 2.2 3.8 Wal.er 10 38 l.2SE-23 2.3 1.0 0.9 0.6 2.1 0.6 2.2 4.0 Compartmelt 11 39 8.40E 2.0 1.0 .. 1.3 0.7 2.3 0.6 2.2 4.2 12 40 5.26E-24 2.0- - LO IA 0.9 2.6 0.6 2.2 4.4

13 41 4.<i4E-24 1.9 1.0 1.5 1.0 2.8 0.6 2.2 4.6 14 42 - 3.14E-24 1.8 _ . 1.0 2.1 1.0 - 2.7 2.6 2.2 3.3 6.3 RPV 15 43 l.58E-24 I. 7 1:0 3.3 1.0 2.7 2.6 2.2 . 3.4 6.8 16 44 7.77E*25 . I. 7 1.0 4.2 1.0 2.7 2.6 2.2 3.S 7.3 17 45 3.61E-25 1.6 1.0 5.0 1.0 2.6 2.6 2.2 3.6 7.8 2.2 Cavity 18 46 l.22E-25 1.4 1.0 -5.5 1.0 2.6 2.6 2.2 3.7 8.3

- 47 8.76E-26 J.3 - . 1.0 5.5 1.0 2.7 2.6 2.2 3.7 8.3 Table 9 Calculated Reaction-Rates and Uncertainties for Jn11S(n,n')Jn11Sm

, AEAT-0352

, APPENDIX D (AEAT-0355)

Measurement ~* - ~* " Unctttamb~ *101a1 Lociuioo position* l.one calculated reaction-rates/ sconng matcnaJ cr~s sed1ons matenaJ <kt~dor uncertainly region dimensions fission refnumbei' Number NESTOR Wall size iron oxygen hyarogcn water gaps cross spectrum inela<tic total total sedions sd 'I> 'I> 'I> 'I> *.ti 'I> 'I>

2 30 4.!>l!t:.-22' 1.0 l.U u.u U.I u.I u.u J. / "" ""

4.U Front 3 31 3.0IE-22 1.2 1.0 0.0 0.0 0.4 0.0 3.7 4.1 Waler 4 32 l.26E-22 1.9 1.0 0.0 0.2 0.8 0.0 3.7 4.2 Compartmcll s 33 9.8SE-23 1.5 1.0 0.0 0.3 0.9 0.0 3.7 4.3 6 34 4.97E-23 1.7 1.0 0.1 o.s 1.3 0.0 3.7 4.4 7 35 3.9SE-23 1.8 1.0 . 0.1 0.6 1.4 0.0 3.7 4.5 8 36 l.OSE-23 I. 7 1.0 I. 7 o.s 1.3 0.8 3.7 4.9 Rear 9 37 6.S3E-24 I. 7 1.0 1.7 0.6 1.6 0.8 3.7 s.o WaJer 10 38 4.04E-24 1.9 1.0 1.8 0.7 1.9 0.8 3.7 S.2 Compartmelll II 39 2.89E-24 1.8 1.0 1.8 0.8 2.0 0.8 3.7 S.2 12 40 1.88E-24 1.8 1.0 1.8 1.0 2.3 0.8 3.7 S.4 13 41 1.3SE-24 1.9 1.0 1.9 I.I 2.4 0.8 3.7 s.s 14 42 9.32E-2S 1.9 1.0 3.0 I. I 2.4 3.2 3.7 4.1 7.9 RPV IS 43 3.89E-2S 2.0 1.0 4.8 1.2 2.3 3.2, 3.7 4.1 8.8 16 44 1.S6E-2S 2.2 1.0 6.7 1.2 2.3 3.2 3.7 4.2 10.0 17 45 S.93E-26 2.4 1.0 8.1 I.I 2.2 3.2 3.7 4.2 I I.I Cavity 18 46 l.93E-26 2.S 1.0 9.8 I.I 2.2 3.2 3.7 4.3 12.6

- 47 l.46E-26 2.S 1.0 9.8 I. I 2.3 3.2 3.7 4.3 12.6 Table 10 Calculated and Measured Reaction-Rates anci Uncertainties for S32(n,p)P32

AEAT-0352 APPENDIXB (AEAT-0355)

Measurement MCBEND Rh l03<n,n')Rh 103m In l 15(n,n')In l 15m S32(n,p )P32 Location position Zone C/M CIM CIM ref number Number

' 2 30 0.94 +/-0.07 Front 3 '- 31 0.93 +/-0.07 Water 4 32 1.08 +/-0.13 Compartment 5 33 0.90 +/-0.08 6 34 0.88 +/-0.07 7 35 0.95 +/-0.10 8 36 0.92 +/-0.08 Rear 9 37, . 0.91. +/-0.08 Water 10 38 0.89* +/-0.08 Compartment 11 39 0.88 +/-0.08 .

12 40 0.89 +/-0.08' '

13 41 0.91 +/-0.08 14 42 0.88 +/-0.08 0.93 +/-0.08 0.89 '+/-0.10 RPV 15 43 0.94 +/-0.09 0.95 +/-0.08 0.96 +/-0.11

'16 44 ,0.99 +/-0.09 0.99 +/-0.09 ' 0.99 +/-0.12 17 45 1.02 +/-0.10 0.96 +/-0.09 0.92 +/-0.13

• • Cavity 18 46 0.88 +/-0.10 ' 0.90 +/-0.10 0.96 +/-0.14 Table 11. Ratio of Calculated and Measured Reaction-Rates

AEAT-0352 APPENDIXB (AEAT-0355)

' ' ' ' ' ' 'Iii N , ' , ' , ' , ' , , ,

E ,' ,' , ' , ' ,' , ' , '

s ,,,,,,

T ,,,,,,,,

0 ,,,,,,,,

A ,,,,,,,.

""'"""'V:"'....."", ', \,',',',','.,

~

,' , ' ,' , ~ , ' , ' , ' ,

-m --

Key stainless steel aluminium water graphite

~

mild steel trolley face

~ concrete fission plate Fig 1 NESDIP2 Configuration

AEAT-0352 APPENDIXB (AEAT-0355)

ALUMINIUM COVER FL.ATE

/ .

i ;i I

Il I!

I

. .1 .

. i  ;

-.*1

,... I I

'/

I i

I i I I I I j I

I j i i I '

I I i i I I . i I i I I

.I ,. '

I i

I I

!'/

I I i j

• i I

I FUEL ELEMENT

~.WMINIUM BODY Fig 2 NESDIP2 Enriched U/A' All~y Fission Plate

AEAT-0352 APPENDIXB (AEAT-mSS) 1mm Ti-il~K U/Al FUE~ SI RIPS

• ~l AL~IJY MS x icm.11 Fig 3 ASPIS U/AI Alloy Fue I Element.

AEAT-0352 APPENDIXB (AEAT-0355) 111 121 Ill 141 151 I:

l

.~I I*. .r. .,_,,.

,n. . r IBl-1911101111111211131

.~.

r .

..... ....:~:-*:: :~~: :;::i::~--

tf1l.l.l=~,iil:.1*11:!.1*~[1.11:1_~,i1~~

J:fMit{IMMtltd=1:tm1nr1~~~~~\lb

~:=~i1:=M=h~rtE.a~:~fili~~:e:~: =~==~=~==~=n

j:;:~;:!:;~:;E~:(:*.J;;:t:+/-;,<:?.::t::t~:~;:.:~;:i::~;;;:N:;:: ;~:;~:~;:t:~:3 NU C' I

i::-

• R * -:.;.: -~:-~:* :<*:*t:;i::..-:c:+.

• FUE1 .~*.:.* *****>* ...... ,,.*~*:i:*c*~*:*.*>:.;

!... - ""'_...:._...:.__ _ _ _...:,.__~:"*:;,;.r:*.;:.;:;.;,***.;,;:*;.;,::1.~:::;,;:::;:;*:~:i;,:::_;;i;:);~:;~ * * * * *':-. ;~::,:;:. ;:~:..:J::*:..:=s:*:*:*.;3:*;;:<;J C::NTRE*

LI NE

• • ~

I I 11

'--~---------------~'*_ _ _ _ _ _ _ _ _ _ _ _ _ _....!....:.)_ ~~'

l NUCLEAR 4'

se9 r.irr.

=--I CENTP.E.

LINE.

Fig 4 Detail of Fuel Loading Pattern

~---*- - --

1

/?

fi~ s co-ordinate system

AEAT-0352 APPENDIXB (AEAT-0355)

I I

x ~ x x x x 51.44 47.63 x x x x

~ 40.64

~I I 35.56 I 31.75

~ x x x x x x x

~ x ~

r-1

-1 19.69 I 15.88 x ~ x x x x ocr/J x x x x ~ x

-1 5.29

• ~

x x x x~ x x x x x ~ x

~I.

. I -5.29 x ~ x x x ~

x x x ~ x x x I -15.88

-1

. I -19.69

-~ x x x x x x x x ~

-35.5 x -40.64

. -47.63

-51.44 J ..

~.,., r-oci...:. ~

~.,.,.,.,

~ _- FRONT BACK MEASUREMENT POSmONS X FRONT ONLY MEASUREMENT ~mONS ND FRONT REFERS TO NESTOR CORE SIDE OF PL.A"IB RJEL BOUNDARY RJEL ELEMENTDOUNDARIF.S All dimensions in ems Fig 6 Fuel Element Configuration and Manganese Foil Measurement Positions

AEAT-0352 APPENDIX B (AEAT-0355)

BOUNDARY Or FISSILE A.RU..

w I-c:::

"'?

a* 20~

i-6 I-L...'

< i-5 r L.:..:

c::: .. Ii" I'<;.

I

- i*2 I L.:..:

I-

• ,*;.,I O*S "L

Ci 0*6 c::

H:IGi-iT

- (c ii',)

W!OTr.

. ( c;;;)

• Fig 7 NESOIP2 Fission Plate Source Profile

AEAT-0352 APPENDIXB (AEAT-0355) 51.44 47.63 40.64 35.5 31.75 e

~

19.69 15.88

~

~ 5.2 q~

-5.29

~

>- -15.88

-19.69

-31.75

-35.5

-40.64

-47.6

-51.4 X-CO-ORDINATES (cm)

Fig 8 Source Mesh Boundaries

AEAT-0352 APPENDIXB (AEAT-0355)

'\t'.ater cell 1

~

E ~

"'~ *-t ~

~ ~ E~

c=-ti

/

c=

i -"'"" c-;"' ~""

Cll

- ;g-"'

t

~

5!

5!

5! -= -""

.g,,

=

ii Cll

~

-"' ~

5!

i E i i i E "'

ii ~

c Q

~

4.0 e position reference number All measurement positions are on an axis that extends through the centre of the fission plate dimensions in cm Fig 9 Measurement Locations in the NESDIP2 Array

AEAT-0352 APPENDIXB (AEAT-0355) 1.0

..... , 0.8 z

u< 0.6

~

N r-.

er.

O...J

,..,,. . 0.2

< HEIGHT OF ?\"ESDIP FISSION PLATE -7 o.o+,~~~;.._-+-~....._~~-r-~~~~-r-~~~~~,.~~~~-r~~~~,

I

-75 -50 -25 0 25 50 75 DISTANCE ABOVE NUCLEAR CENTRE LINE ll"ITI)

Fig 10 Relative S32(n,p)P32 Reaction-Rate Axial Profile in Cavity of the NESDIP2 Array

AEAT-0352 APPENDIXB (AEAT-0355)

--* ="""an

-- =,..)...:

=~-=--

- I 1° I I I

I I II I I I

-0.0

- 28.9

-29.S

- 34.9

- 38.1

- 44.1

-59.1

- 60.3

_63.2

-63.6

-77.6

- 83.9

- 97.1

-99.6 mild steel pressure vessel

- 119.9 cavity

- 147.9

-149.8

- 172.2

- 174.7

- 200.0 all dimensions in cm

• not to scale Fig 11 MCBEND Model of the NESDIP2 Array

AEAT-0352 APPENDIXB (AEAT-0355)

APPENDIX

• -- - -- - --- A- -- --- --- -- ---- --

& NESDIP BENCHMARK EXPERIMENT

& MCBEND ANALYSIS

& ENDF/B-VI and IRDF-90 DATA CARD COLUMN LIMIT 1 80 BEGIN CONTROL DATA PROCESS TO STAGE THREE DUMP INTERVALS 5 SPLITTING END

& UNIT 2 BEGIN DATASET DEFINITIONS DUMP A 40 END

& UNIT 3 BEGIN OUTPUT CONTROL SUPPRESS INFLOWS END

& UNIT 4 BEGIN MATERIAL GEOMETRY CG RP Pl -150.0 150.0 -150.0 155.0 -10.0 210.0 RPP2 -155.0 155.0 -155.0 160.0 -15.0 0.0 RPP3 -155.0 155.0 *-155.0 160.0 -15.0 28.90 RPP4 -155.0 155.0 -155.0 160.0 -15.0 29.50 RPP5 -155.0 155.0 -155.0 160.0 -15.0 34.90 RPP6 -155.0 155.0 -155.0 160.0 -15.0 38.10 RPP7 -155.0 155.0 .-155. 0 160.0 -15.0 44.10 RPP8 -155.0 155.0 -155.0 160.0 -15.0 59.10 RPP9 -155.0 155.0 -155.0 160.0 -15.0 60 .*30' RPPlO -155.0 155.0 -155.0 160.0 -15.0 63 .20 RPPll -155. o* 155.0 -155.0 160.0 -15.0 63.60 RPP12 -155.0 155.0 -155.0 160.0 -15.0 65.50 RPP13 -155.0 155.0 -155.0 160.0 -15.0 77.60 RPP14 -155.0 155.0 -155.0 160.0 -15.0 83.90 RPP15 -155.0 155.0 -155.0 160.0 -15.0 97.10 RPP16 -155.0 155.0 -155.0 160.0 -15.0 99.60 RPP17 -155.0 155.0 -155.0 160.0 -15.0 119.90 RPP18 -155.0 155.0 -155.0 160.0 -15.0 147.90 RPP19 -155.0 155.0 -155.0 160.0 -15.0 149.80 RPP20 -155.0 155.0 -155.0 160.0 -15.0 172.20 R~P21 -155.0. -155. 0 -155.0 160.0 -15.0 174.70 RPP22 -155.0 155.0 -155.0 160.0 -15.0 200.00 RCC23 0.0 0.0 -15.0 0.0 0.0 230.00 56.10 RPP24 -58.50 58.50 -58.50 58.50 -15.0 215.00 RPP25 -91.50 91. 50 -88.90 96.50 -15.0 215.00 RPP26 -93.40 93.40 -92.70 98.60 -15.0 215.00 RPP27 -100.00 100.00 -100.00 110.00 -15.0 215.00

AEAT-0352 APPENDIXB (AEAT-0355)

RPP28 RCC29 RPP30 RPP31 RPP32 RPP33 RPP34

-59.20 2.50

-7.50

-7.50

-7.50

-7.50

-7.50 64.20 0.00 12.50 12.50 12.50 12.50 12.50

-51. 40

61. 70

-10.00

-10.00

-10.00

-10.00

-10.00 51.40 0.0 10.00 10.00 10.00 10.00 10.00

61. 50 0.0 65.00 67.00

70. 90 72.00 75.90

61. 60 0.20 65.70 67.20 71.10 72.20 76.10 56.30 RPP35 -7.50 12.50 -10.00 10.00 77.40 78.00 RPP36 -7.50 12.50 -10.00 10.00 83.40 84.10 RPP37 -7.50 12.50 -10.00 10.00 86.50 86.70 RPP38 -7.50 12.50 -10.00 10.00 89 *30 .8 9

• 5 0 RPP39 -7.50 12.50 -10.00 10.00 91. 50 91. 70 RPP40 -7.50 12.50 -10.00 10.00 94. 30 94 .. 50 RPP41 --7. 50 12.50 -10.00 10.00 96.90 97.40

. RPP42 -7. 50 12.50 -10.00 10.00 98.40 99.80 RPP43 -7.50 12.50 -10.00 10.00 104.60104.80

. RPP44 *7. 50 12.50 -10.00 10. o.o 109.70 109.90 RPP45 -7.50 12.50 -10.00 10.00 114.70 114.90 RPP46 -7.50 12.50 -10.00 10.00 123.80 124.00 RPP47 -7.50 12.50 -10.00 10.00 i43.80 144.00 ZONES

& EXTERNAL VOID 1 20 +l +22 27

• 2 20 +l +2

. 3 20 +l -22

& CONCRETE TROLLEY SHIELD

. 4 20 +27 -26 +22 -4 5 20 +4 -2 +27 -24 6 20 +22 -21 +25 ..

& GRAPHITE BLOCK OUTSIDE. OF THE TROLLEY 7 10 +3 -2 +24

& ALIMINIUM PLATE ON BODY 7 8 10 +4 -3 +24. ' ..

& VOID BEFORE TROLLEY

.9'10 +5 -4 +26

& MILD STEEL TROLLEY WALLS 10 40 +22 ~6 +26 ~25 11 40 +6 -5 +26 ~23 '

& ALUMINIUM TROLLEY WINDOW

.. 12 10 +6 -5 +23

'& VOID AT FRONT OF TROLLEY 13 .10 +7 -6 +25

&

• G.RAPHITE BLOCK INSIDE OF TROLLEY .

14 10 +8 -7 +25

& VOID CORE SIDE OF FISSION PLATE 15 20 +9 -8 +25

& ALUMINIUM FISSION PLATE SURROUND 16 20 +10 -9 +25 29

& VOID IN THE FISSION PLATE 17 10 +28

.& FISSION PLATE 18 10 +29

& VOID SHIELD SIDE OF THE FISSION PLATE 19 10 +11 -10 +25

& CELL 1 l.9cm ALUMINIUM PLATE

AEAT-0352 APPENDIXB (AEAT-0355) 20 10 +12 -11 +25

& CELL 1 12.lcm WATER

__ 21_ l_0 _+13__ -:-12 __+25 _.,._30 _,.._31 _.,..32 -= -34 - - -** --- ---

&CELL 1 5.9 CM STAINLESS STEEL (THERMAL SHIELD) 22 10 +14 -13 +25

& CELL 1 13.2cm WATER 23 10 +15 -14 +25 37 39 41

&CELL 1 2.5cm MILD STEEL 24 10 +16 -15 +25

& 4*5.1 cm MILD STEEL BLOCKS (RPV WALL) 25 30 +17 -16 +25 43 45

&CAVITY 26 10 +18 -17 +25 47

& CELL 2 1.9 cm ALUMINIUM 27 10 +19 -18 +25

& CELL 2 22.4 cm WATER 28 10 +20 -19 +25

& CELL 2 2.5 cm MILD STEEL 29 10 +21 -20 +25

& 30 -47 ARE 20 cm SQUARE SCORING REGIONS 30 10 +30 -12 31 10 +31.

32 10 +32 33 1*0 +33 34 10 +34 35 10 +35 +13 36 *10 +36 -14 37 10 +37 38 10 +38

39 10 +39 40 10 +40 41 10 +41 +15 42 10 +42 -16 43 10 +43 44 10 +44 45 10 +45 46 10 +46 47 10 +47 .

REGIONS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46-47 MATERIALS

-2000 -2000 -2000 2 2 2 1 8 0 3 3 8 0 1 0 9 0 7 0 9

• 10 6 10 4 5

AEAT-0352 APPENDIXB (AEAT-0355) 0 10 10 10 0

VOLUMES 9

10 10 5

0 10 10 10 5

4 10 10 5

1.0 10 10

' 10 5

• 1.0 1.0 1. 0 1. 0

1. 0 1. 0 1. 0 1.0 1.0

1. 0. 1.0 1.0 1. 0 1. 0

1. 0 1. 0 1.0 1.0' 1. 0 1.0 1. 0 1.0 1.0 1. 0

1. 0 1. 0 1.0 *so. o..

80.0 80.0 80.0. 80.0

• ao.o 80.0 80.0 "80 .. 0 80.0 80.0 80.0 80.0 80.0 10.0 20.0 29.5 '34_.9 '38.1 44.,1 ,49.1 54.1' 65.5 .71.6 77.6 83.5 90.1 96.7 99.2 104.3 il9.5.128.8 138.2 143.3 143.7 147.5 149.4 156~9 164.

AEAT-0352 APPENDIXB (AEAT-0355)

MATERIAL MESH TRACK LENGTH

• --*** . --.--**-* .. _ .. __ .. FLUX .....

SOME 1 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 RESPONSES DITI'O SENSITIVITY OF RESPONSES DITI'O CONTRIBUTIONS TO RESPONSES DITI'O END

& UNIT 10 BEGIN RESPONSE DATA

& RESPONSE FUNCTIONS FROM IRDF90

& rh103(N,N') irdf90 END

& UNIT 11 BEGIN SENSITIVITY DATA 7

&FE 2631 0 2 1 2 -1 2

&NI 2825 0 2 1 2 -1 2

&CR 2431 0 2 1 2 -1 2

&H 125 0 3 TOTAL 1 2 -1 2

&O 825 0 4 TOTAL 1 2 -1 2 1 107

&AL 1325 0 2 1 2 -1 2

&C 600 0 2 1 2 -1 2

& NO OF ENERGY GROUPS BOUNDARIES 16 l.'492E+l 4.400E+O 2.600E+O 1.350E+O 7.080E-l 5.800E-1*4~100E-1 3.095E-l 2.620E-1 6.200E-2 3.000E-2 1.500E-2 1.585E-3 2.145E-4 l.068E-5 5.043E-6 5.500E-7 END

& UNIT 23 BEGIN CG SOURCE DATA BOX -49.75 -51.44 61.70 104.5 0.0 0.0 0.0 102.88 0.0 0.0 0.0 0.2

1. 0 1 1 VOLUME SOURCE SUBDIVIDE 15 -0~0303 0~0303 0.0606 o.o303 0.0606 0.1515*0.0909 0~0910

0. 0909 0 .1515 0. 0606 0. 0303 0. 0606 0. 0303 o:. 0303 15 o.63703 0.06794 o.04938 0.03703 0.11122 o.03703 0.10294 0.10206 0.10294 0.03703 0.11722 0.03703 0.04938 0.06794 0.03703 1 -1. 0 IMPORTANCES

0. o. 0. 0. 0. 0. 1. 1. 1. 0. 0. 0. 0. 0. 0.

AEAT-0352 APPENDIXB (AEAT-0355)

0. o. 0. o. o. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0.

o. o. o. o. 1. 1. 1. 1. 1. 1. 1. o. o~ o. o.

0 . 0 . 0 . 1 . 1 . 1 . 1 . 1 . 1 . 1.. 1 . 1. 0. 0. 0.

0. 0. 1. 1. 1.* 1. 1. 1. 1. 1.*l. 1. 1. 0. 0.

0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0.

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

1. 1. 1. 1. i . 1. 1. 1. 1. 1. 1. 1. *1. 1. 1.

0. 1. 1. 1. 1. 1. 1. 1~ 1. 1. 1. 1. 1. 1. 0.

o. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0.

o. o. o. 1. 1. 1. 1. 1. 1. 1. L 1. o. o. o.

o. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0.

0. 0. o. 0. 0. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0.

o. o.* o. o~* o. o. i. i. i. o. o. o. o. o. o.

SOURCES 1 1 ' 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 1'22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1 30 1 31 1 32 1 33 1 34 1 .. 35 1 36 1 37 1 38 1 39 1 40 1 41 1 4 2 1 43 1 4 4 1 4 5 1 .4 6 1 4 7 1 4 8 l 4 9 1 5 0 1 51 1 52 i 53 i 54 1 55 1 56 1 57 1 58 1 59 1 60 1 61 1 62 1 63 1 64 1 65 1 6~ 1 67 1 68 1 69 1 70 1 71 1 72 1 73 1 74 1 75 1 76 1 77 1.78 1 79 1801 81 1. 82 1 83 1 84 1 85 1 86 1 87 1 88 1 89 1 90 1 91 1 92 1 93 1 94 1 95 1 96 1 97 1 98 1 99 1 100 1 101. 1 102 1 103 1 104 1 105 1 106 1 107 1 108 1 109 1 110 1 1111 112 11131114 1 115 1 116 1 117 1 118 1*119 1120 1 121 1 122 1 123 1 124 1 125 1 126 1 127 1 128 1 *129 1 130 1 131 1 132 1 133 1 134 1 135 1 136 1 137 1 138' 1 139 1 140 1

. 141 1 142 1 143 1 144 1 145 1 146 1 147 1 148 1 149 1 150 1 151 1 152 1 153 1 154 1 155 1 156 l J,.57 i 158 1 159 1 160 1.

161 1 162~116311S4 1 16511661167 1.168.l 169 1 110 1 111 1 172 1 173 1 174 1 175 1 176 1 177 1 178 1 179 1 180 1 181 1 182 1 183 1 184 1 185 1 186 1 187 1 188 1 189 1 190 1 1~1*1 192 1 193 1 194 1 i95 1 196 1 197 1 .198 1 199 1 200 1 201 1 20.2 1 203 1 204 1 205 1 206 1 2.07 1 208 1 209 1 210 .1

• • 211 1 212 1 213 1 214 1 215 1 216 1 217 1 218 1 219 1 220 1 221 1 222 1 223 1 224 1 ~25 1 ENERGY BOUNDARIES 52 1.3499E+l 1.2214E+l 1.1052E+l 1.0000E+l 9.0484E+O 8.1873E+O 7.4082E+O 7.0469E+O 6.7032E+O 6.3763E+O 6.0653E+O 5.4881E+O 4.9659E+O 4.7240E+O 4.4933E+O

4. 0657E+O .3*. 6788E+O 3. 3287E+O

• 3. 0112E+O** 2. 7253E+O 2. 4660E+O 2.3460E+O 2.2313E+O 2.0190E+O 1.8268E+O 1.6530E+O 1.4957E+O 1.3534E+O 1.2246E+O 1.1080E+O 1.0026E;O 9.0718E-1 8.2085E-1 7.4274E-1 6.7206E-1 6.0810E-1 5.5023E-l 4.9787E-1 4.5049E-l 4.0762~-1 3.6883E-1 3.3373E-1 3.0197E-1 2.7324E-1 2.4724E-1 2.2371E-1 2.0242E-1 1.8316E-1 1.6573E-1 1.4996E-1 1.3569E-1 l.2277E-1 l.1109E-1 GROUP IMPORTANCES 2.30E-1 7.3E-2 2.60E-2 2*8.lOE-3 2*3.2E-03 3*1.80E-3 *.

3*9.00E-4 3*3.90E-4 3*2.lOE-4 6*1.0E-04 10*3.0E-05

AEAT-0352 APPENDIXB (AEAT-0355) 5*7.60E-6 12*2.lE-06 SOURCE GENERATION GROUPS 1

_____ --------**- _FLUXES _____ -- - - ----- ----- -- -- -- -- --------- -- --- - - - - - -- ----------- --- -- - -- - -*-- -------------- -- ----- - -----

& Y BOUNDS -51.44 -47.63 ~40.64 -35.56 -31.75 -19.69 -15.88 -5.29

& 5.29. 15.88 19.69 31.75 35.56 40.64 47.63 51.44

& X-MESH BE'IWEEN -49.75 AND -46.58 1.0000E-10 1.0000E-10 l.OOOOE-10 l.OOOOE~lO l.OOOOE-10 l.OOOOE-10 3.3194E+07 3.4821E+07 3.4471E+07 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10

& X-MESH BE'IWEEN -46.58 AND -43.32 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l:ooOOE-10 l.OOOOE-10 3.3347E+07 3.5528E+07 3.7134E+07

• 3. 6506E+07

3. 5023E+.07 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10

& x-MESH BE'IWEEN -43.32 AND -37.08 l.OOOOE-10 l.OOOOE-10 l.OOOOE-10

-1. OOOOE-10*

3.3094E+07 3.6719E+07 3.9095E+07 4.0704E+07 3.9732E+07 3.7844E+07

AEAT-0352 APPENDIXB (AEAT-0355) 3.4890E+07 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10

& X-MESH BETWEEN -37.08 AND -33.92 1.0000E-10 l.OOOOE-10 1.0000E-10 3.1570E+07 3.6028E+07 4.0073E+07 4.2640E+07 4.4277E+07 4.3025E+07 4.0791E+07 3.7289E+07 3.3557E+07 1.0000E-10 1.0000E-10 1.0000E-10

& ~-MESH BET-EEN -33.92 AND -27.58

1. o*oooE-10 1.0000E-10 3.1129E+07 3.3930E+07 3.8913E+07 4.3345E+07 4.6100E+07 4.7791E+07 4.6322E+07 4.3802E+07 3.9826E+07 3.5509E+07 3.3234E+07 1.0000E-10 1.0000E-10

& X-MESH BE'IWEEN -27.58 AND. -11.75 1.0000E-10 3.0709E+07 3.5185E+07 3.8688E+07 4.4654E+07 4.9825Et07 5.2964E+07 5.4838E+07 5.3073E+07 5.0094E+07 4.5306E+07

AEAT-0352 APPENDIXB (AEAT-0355) 3.9940E+07 3.6932E+07

____________3_.333 3_E:t:_0_7________________ _ ------------- - - - - - - - ----*-- -- -- --- ---------*--- ----------*-------------------*

1.0000E-10

& X-MESH BE'IWEEN -11.75 AND -2.25 2.8695E+07 3.2959E+07 3.8254E+07 4.2275E+07 4.8979E+07 5.4722E+07 5.8190E+07 6.0290E+07 5.8416E+07 5.5174E+07 4.9853E+07 4.3755E+07 4.0207E+07 3.5724E+07 3.2358E+07

& X-MESH BE'IWEEN -2.25 AND 7.25 2.8830E+07 3.3303E+07

_3. 8804E+07 4.2959E+07 4.9864E+07 5.5779E+07 5.9368E+07 6.1594E+07 5.9771E+07 5.6531E+07 5.1100E+07 4.4841E+07 4.1154E+07 3.6423E+07 3.2773E+07

& X-MESH BETWEEN 7.25 AND 16.75 2.8110E+07 3.2434E+07 3.7793E+07 4.1862E+07 4.8658E+07 5.4505E+07 5.8081E+07 6.0350E+07 5.8641E+07 5.5491E+07 5.0223E+07 4.4119E+07

AEAT-0352 APPENDIXB (AEAT-0355) 4.0522E+07

3. 5909E+07

• 3.2360E+07

& X-MESH BE'IWEEN 16.75 AND 32.58 1.0000E-10 2.9626E+07 3.4234E+07 3.7822E+07 4.3934E+07 4.9257E+07 5.2551E+07

. 5. 4676E+07 5.3160E+07 5.0322E+07 4.5609E+07 4.0216E+07 3.7112E+07 3.3266E+07 1.0000E-10

& X-MESH BE'IWEEN 32.58 AND 38.92 1.0000E-10 1.0000E-10 2.9939E+07 3.2819E+07 3.7886E+07 4.2376E+07*

4.5182E+07 4.6970E+07 4.5619E+07 4.3169E+07 3.9214E+07 3.4832E+07 3.2446E+07 1.0000E-10 1.0000E-10

& X-MESH BE'IWEEN 38.92 AND 42.08

• 1. OOOOE-10 1.0000E-10 1.0000E-10 3.0427E+07 3.4889E+07 3.8886E+07 4.1391E+07 4.2951E+07 4.1660E+07 3.9411E+07 3.5870E+07 3.2047E+07 1.0000E-10

AEAT-0352 APPENDIXB (AEAT-0355) 1.0000E-10 1.0000E-10

& X-MESH BE'IWEEN 42.08 AND 48.42 1.0000E-10 1.0000E-10 l .*OOOOE-10 1.0000E-10 3.1830E+07 3.5244E+07 3.7384E+07 3.8657E+07 3.7415E+07 3.5388E+07 3.2315E+07 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10

& X-MESH BE'IWEEN 48.42 AND 51.58

1. OOOOE 1. 0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 3.1588E+07 3.3310E+07 3.4245E+07 3.3043E+07

. 3 .1252E+07 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10

& X-MESH BE'IWEEN 51.58 AND 54.75 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 3.0616E+07 3.1292E+07 3.0108E+07 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10 1.0000E-10

AEAT-0352 APPENDIXB (AEAT-0355) l.OOOOE-10 CROSS SECTIONS l.364E-4 3.257E-4 7.019E-4 1. 377E-3 2.4SSE-3 4.1S6E-3 2.911E-3 3 .'SSSE-3 4.349E-3 5.203E-3 l.329E-2 l.761E-2 1. OS4E-2 1. l 7SE-2 2.71SE-2 3.195E-2 3.637E-2 4.032E-2 4.326E-2 4.S66E-2 2.33SE-2 2.37SE-2 4.772E-2 4.7S7E-2 4.666E-2 4.520E-2 4.325E-2 4.097E-2 3. S~.4E-2 3.S70E-2 3.296E-2 *3.019E-2 2.. 749E-2 2.4S9E-2 2.243E-2 2;012E-2 l.797E-2 l.S99E-2 l.419E-2 1.2SSE-2 l.107E,..2 9.743E-3 S.S53E-3 7.497E-3 6.561E-3 S.731E-3 4.99SE-3 4.3S4E-3 3 . .7 S9E-3 3.293E-3 2.S62E-3 2.4SlE-3 END SOURCE END

&***************. UNIT 14 ***********************

BEGIN MATERIAL DATA.

• MINNIE MIXTURES 10

& MAT 1 GRAPHITE

.WEIGHT M 1 C l.O

& MAT 2 CONCRETE WEIGHT M 2 SI .3920S FE54 .OOOS63

.

• FES.6 . 013914

.FES7 . 000324 '.*

FESS .000044 ' 1'"

H . 010743 016 ' . Sl 7S3 AL . * . 0365S5

'CA . 040696 NA .0172S4

& MAT 3 TROLLEY MILD STEEL WEIGHT M 3 FES4 ;562316E~Ol.

FE56 .906316 FE57 .21111SE-al FESS . . 2S6091E-02 MN .010914 C .22126E-02 SI .35507E-03

& MAT 4 WATER CELL MILD STEEL WEIGHT M . 4' 'FE54 .056~46 FE56 .916220 FES7 .021342 FESS .002S92 MN .22662E-02 c .430S4E-03

AEAT-0352 APPENDIXB (AEAT-0355)

& MAT 5 STANDARD 2 INCH MILD STEEL PLATES

- - - * - -- - - --- M --~~~~~4-FE56

- .--564425E-01-- --- *-

.909743 FE57 . 211914E-01 FESS .287177E-02 C .22999E-02 H .54624E-05 MN .007443

& MAT 6 WATER CELL STAINLESS STEEL WEIGHT M . 6 FE54 .4014E-01 FE56 .6469 FE57 .1507E-01 FE58 .2042E-02 c .24021E-03 NI58 .66996E-01 NI60 .26699E-01 NI61 .11764E-02 NI62 .38184E-02 NI64 .10069E-02 CRSO .007316 CR52 .14685 CR53 .01697 CR54 .004299 SI .61786E-02 MN .014283

& MAT 7 FUEL IN FISSION PLATE WEIGHT M 7 AL .79988 U235 .18633 U238 . 01379

& MAT 8 PURE ALUMINIUM WEIGHT M 8 AL 1.0

& MAT 9 WATER CELL ALUMINIUM WEIGHT M 9 AL .99297 SI . 001453 FE54 .31761E-03 FE56 .51191E-02

. FE57 .11924E-03 FE58 .16159E-04

& MAT 10 WATER CELL WATER WEIGHT M 10 H .11192

• 016 .88808 MATERIALS 10

1. M 1 - 1. 650 1. 0 2 M 2 2.300 1.0 3 M 3 7.835 1. 0 4 M 4 7.862 1.0 5 M 5 7.850 1.0 6 M 6 7.900 1. 0 7 M 7 3.256 1. 0

AEAT-0352 APPENDIXB (AEAT-0355) 8 M 8 2.700 1.0 9 M 9 2.666 1.0 10 M 10 1.000 1.0 USE MOULD 12 FOR H IN ALL MATERIALS USE ADCN FE FOR FES4 IN ALL MATERIALS USE ADCN FE FOR FES6 IN ALL MATERIALS USE ADCN FE FOR FES7 IN ALL MATERIALS USE ADCN FE FOR FESS IN ALL MATERIALS USE ADCN NI FOR NISS IN ALL MATERIALS USE ADCN NI FOR NI60 IN ALL MATERIALS USE ADCN NI FOR NI61 IN ALL MATERIALS USE ADCN NI FOR NI62 IN ALL MATERIALS USE ADCN NI FOR NI64 IN ALL MATERIALS USE ADCN CR FOR CRSO IN ALL MATERIALS USE ADCN CR FOR CRS2 IN ALL-MATERIALS USE ADCN CR FOR CRS3 IN ALL MATERIALS USE ADCN CR FOR CRS4 IN ALL MATERIALS USE ADCN 0 FOR 016 IN ALL MATERIALS END

AEAT-0352 APPENDIXC (AEAT-0468)

AEA Technology AEAT 0468 Further Analysis of the H B Robinson Unit 2 PWR using the Monte-Carlo Code MCBEND with ENDF/B-VI and IRDF-90 Nuclear Data.

AF Avery, HF Locke and AK Ziver June 1996 I,

I_.

Reactor Physics Shielding and Criticality Department Plant Support Services Group * . . *

'AEA Technology plc "

Dorset DT2 8DH United Kingdom

AEAT-0352 APPENDIXC (AEAT-0468)

The infonnation which*this repon contains is accurate to the best knowledge and belief of AEA Technology, hut neither AEA Technology nor any person acting on behalf of AEA Technology make any warranty or representation expressed or implied with respect to the accuracy, completeness or usefulness of this irifonnation: nor assume any liabilities with respect to the use of, or with respect tc;> any damages which may result from the use of any infonnrition. apparatus. *method or process disclosed in this repon .

... ..r Name Position Signature Date Author .AF Avery .Shielding*C~nsultant 14*1,4~~, f'5/6/<?G

-~ (;~\/\1,,-'.*'-"

Checked SJ Chucas Product M:rnager* . I. \

. ~

\\\\c\\

Approved CA Cooper Department Manager . CA.~~.v . 2.. ."1.~

Ci ....

AEAT-0352 APPENDIXC (AEAT-0468)

- AEA T -0468- - - ----- - -- - - - -

Further Analysis of the H B Robinson Unit 2 PWR using the Monte-Carlo Code MCBEND with ENDF/B-VI and IRDF-90 Nuclear Data.

-AF Avery, HF Locke and AK Ziver Summaiy This report describes the validation of the Monte Carlo code MCBEND for determining neutron fluence in the radial shield of PWRs .. Calculations were performed for the H.B.Robinson Unit 2 PWR, at dosimetry positions in the reactor cavity and the surveillance capsule, using MCBEND with ENDF/B-VI nuclear data and the predicted reaction rates are compared with extensive measurements. This report is an extension of the work reported in AEA-RS-5579 with the use of data from IRDF-90 for the calculation of the detector responses and their associated uncertainties. A detailed analysis of all the uncertainties in the calculation route is included.

MCBEND accurately predicts the reaction rates in the cavity and surveillance position, with the ratio of calculated reaction rate to measurement (C/M) lying within

- one standard deviation of unity. The average value of C/M is 0.94 at the surveillance position whilst in the cavity it is 0.93 for the threshold reactions which detect high energy neutrons (E>O.l MeV) and 1.08 for those which are sensitive to the low energy fluxes.

Reactor Physics Shielding and Criticality Department Plant Support Services Group AEA Technology pie Dorset DT2 8DH United Kingdom Cii

AEAT-0352 APPENDIXC (AEAT-0468)

• CONTENTS

- *-~* ---- --- -- - * - -- - -- -- --- -- - ----- ----- - ----------- - --- - ----------*---- ----- -- - -- --------- - --- -- -----*- -

Page INTRODUCTION 2 THE MEASUREMENTS 1 3 THE MCBEND MODEL 3 3.1 Geometry 3 3.2 Materials 3 3.3 Source 3 3.3.1 X-Y Solirce Intensities. 4 3.3.2 z Profile 5 3.3.3 Source Spectrum 5 3.4 Scoring 6 3.4.1 . Cavity Scoring Region , . 6 3.4.2 Surveillance Capsule Scoring Region 7 3.4.3 Detector Responses* 7

. 3.5 Nuclear Data 7 3.6 Variance Reduction 7 4 TIME DEPENDENCE .. 8 5 CORRECTION FACTOR 9 6- RES ULTS OF THE CALCULATIONS 10 7 UNCERTAINTIES.

7.1 Cross-Sections 10.

7 .1.1 Surveillance Capsule . 10 7 .1.2 Cavity Position 11 7.2 Dimensions 11 7.3 Radial Variation of the Flux 11 7.4 Material Compositions 11

. 7.5 Core Smearing 12 7.6 Source Iritensity 12.

7.7 Core Source Data 13 7.8 Fission Spectrum 13 7.9 Detector Response Functions 13 7.10 Total Uncertainties 13 8 COMPARISON OF CALCULATION AND MEASUREMENT 8: 1- Surveillance Position 14 8.2 Cavity Position 14 9

SUMMARY

15 REFERENCES Civ

AEAT-0352 APPENDIXC (AEAT-0468)

TABLES 1 Power History for Cycle 9 2 Derivation of Activations Measured at the End of the Cycle.

3 Material Compositions 4 Initial and Final Bum-up Distributions for the 9th Cycle.

5 Fuel Composition at the Beginning, Middle and End of the 9th Cycle 6 *Calculation of Sotirce Intensity

• 7 Source Spectra for Fresh Fuel Assemblies in Peripheral Locations 8 Comparison of Reaction-rates at the Beginning, Middle and End of the 9th Cycle (Taken from Calculations with IRDF-85 data (Ref 5)) *

.9 Ratios of the End-of-Cycle Activities to the Reaction Rates at Mid-cycle 10 Calculated Reaction Rates 11 Calculated Uncertainties arising from Cross-sections 12 Uncertainties Due to the Detector Cross-sections 13 Correction Factors and Uncertainties 14 Comparison of Calculated and Measured Activations FIGURES 1 Plan View showing Sector Modelled and Measurement Positions 2 Plan View of the Model showing Materials 3 Plan View of th~ Model showing Dimensions 4 Side View of the Model showing M~terials 5 Side View of the Model showing Dimensions 6 Core Sources Modelled 7 Scoring. Regions Modelled 8 Power Variation through the 9th Cyde for Assemblies adjacent to the Cavity and Surveillance Positions * * * * * ** * * * .

9 Variation of Response through the 9th cycle - Cavity Position 10 Variation of Response through the 9th cycle - Surveillance Position APPENDIX MCBEND9 INPUT DATA Cv

AEAT-0352 APPENDIXC (AEAT-0468)

INTRODUCTION The H B Robinson Unit 2 (HBR-2) station is a three-loop 665 MW(e) Westinghouse PWR. It is owned by the Carolina Power & Light Company (CP&L), and is located on the shore of Lake Robinson at Hartsville, South Carolina, USA. It has been)identified as a reactor likely to be susceptible to pressurised thermal shock. This susceptibility occurs when irradiation by neutrons causes embrittlement of the pressure vessel wall. To ameliorate this problem previously burned fuel was loaded into the locations on the flats of the core at the start of cycle 9. As the neutron sources in these regions contribute heavily to the fluence in the pressure vessel wall, the introduction of the irradiated fuel reduces this fluence level significantly. In order to validate the effectiveness of this low-leakage core arrangement, special dosimetry was introduced into the surveillance position in the downcomer annulus and into the reactor cavity.

The extensive range of measurements carried out during cycle 9 provides an opportunity to evaluate the Monte Carlo code MCBEND (reference 1) for radial shield calculations on PWRs. Previous calculations for the reactor cavity (reference 2) and the surveillance capsule (reference 3) used cross-sections from the UKNDL. Calculations for both dosimetry positions carried out with ENDF/B-VI data and detector response cross sections from IRDF85 (reference 4) were reported by Locke (reference 5). This report describes a repeat of those calculations using MCBEND9 with response cross-sections from IRDF-90 (reference 6) and compares the results with the measurements. In contrast with the earlier comparisons, the present results are given as the activities of the detectors at the end of the cycle rather than the reaction rates at mid-cycle.

2 THE MEASUREMENTS Measurements were made in the reactor cavity and in a surveillance capsule located between the thermal shield and the pressure vessel. The sensor packages were inserted at the start of cycle .9. In the cavity they were placed at 4 azimuthal positions and 5 axial positions centred on the reactor core mid-plane; however those of interest to this analysis are at the mid-height of the core at the 0° position shown in figure 1. The smveillance capsule was positioned at 20°.

The measurements are presented in reference 7 as the saturation reaction rates derived from the activations of the detectors by making the assumption that the ratios between reaction rates and the power of the reactor remained constant through the cycle. Estimated corrections were subsequently applied to account for changes in this ratio for the results for the detectors in the cavity, these being based on the measurement of the activities of several fission products with differing half lives, and the adoption of a linear variation with bum-up for the flux/power ratio, It was shown in reference 5 that the changes in the power distribution within the core during the cycle gave a non-linear variation for this ratio. For the comparisons with the present calculations the uncorrected measurements have been converted back into the activations at the end of the cycle by carrying out a reversal of this process.

Cl

AEAT-0352 APPENDIXC (AEAT-0468)

Thus A(T) = f R(t)P(t)Ae-A.<T-i>dt T '

0 where A(f) = Activation at the end of the cycle,

. '.!~

R(t) = Reaction rate for full power (2300MW) at time t in the cycle, . * . *

• P(t) *- Reactor power (fraction of full power) at time t

..t = Decay constant for the activity, and T =

• Duration of the cycle.

• The assumption made previously for the uncorrected results in reference 7 was that R was .

. independent of burn-up. The cycle history is given in that reference as the mean p_owers in

.18 time intervals, and this is reproduced in Table 1. The above equation for the cycle is then reduced to a summation over the jntervals. ** * *

. . 18 ,,.~. . . *' .

A(T) Re-A.TIP; J).eA.tdt 1 .,, .

18 ..

= Re-A.TL',P;<eA.t,., -:e.v')

1 where ."i'; . . - ' Mean power in the*iui-interva:l; Time at. the start of the iui interval, arid*

Time at the end of the iui interval (t19=T).

!~'-

v*

Values of the ratio A(f)/R were derived using the power history of Table l. The resulting ratios are given in Table 2 as scaling factors for each detector. Also presented in Table 2 are the measured values of R taken from reference 7 together with the resulting values of A(T) when the calculated factors are applied. *The table also gives the estimated standard de.viatioris on the measurements as taken from reference 7.

• The measurements were made with some ofthe detectors being covered with gadolinium in the surveillance position and with cadmium in the cavity. This provided shielding against low energy neutrons and thus reduced

• C2

AEAT-0352 APPENDIXC (AEAT-0468)

(i) reactions which would arise from impurities in the detectors e.g. Co59(n,g)Co60 from cobalt in the copper foils and U235_(n.f~) fr~!11_ t~~ce~f U7~5_ in U2)8, _

-~ ~ -- . - - ----- ----*- - --------- --* - -~ --

(ii) the background count from other reactions e.g. Fe59 for the Fe54(n,p) reaction, and (iii) the bum-up of Co58 by the (n,g) reactions.

The accuracy of the high energy measurements will be improved by the presence of the covering and therefore, where there is a choice, the results which are included in Table 2 for these detectors are those given with the covers present. For the low energy reactions the results given in the table are for the bare detectors except for Co59(n,g)Co60 and U235(n,fx) in the surveillance position where the only measurements were made with gadolinium covers.

3 The MCBEND Model 3.1 Geometry A 45° sector of the reactor core and shield was modelled using combinatorial geometry, as shown in figures 1 to 5. The reactor has eight-fold symmetry, so that it may be modelled by a 45° slice with reflective boundaries at its sides. The full height of the reactor was modelled, although approximations were made at regions away fr,om the core mid-height (Most of the measurements were taken at the mid-height.) Most of the dimensions were ' ! ;~

taken from reference 8, although some of the heights were taken from reference 9.

Although the shield, baffles, and pressure vessel were modelled exactly, the core region was smeared.

3.2 Materials The materials data and compositions were taken directly from reference 8 which specifies them in terms of number densities. The core region consists of fuel (U0 2), fuel pin cladding (Zircaloy), ft.lei assembly supports and sheathing (lnconel and SST304), and boronated water smeared together. The maierial compositions are given in Table 3. Iron, nickel and ,*

chromium are present in the ENDF/B-VI library in isotopic form and so the composition of each material is defined using the relevant isotopes.

3.3, Source The calculation was performed for a single time interval with burn-up and power distribution appropriate to the core at a time which was close to half way through the cycle.

Neutron source data were provided in reference 10 for one quarter of the reactor core at a near-mid-cycle burn-up of 5,500 MWd!fe, this being representative of a cycle averaged distribution. Not all of this source was needed for the 45° sector, as can be seen in figure 6.

The effect of the variation of the source due to changes in the burn-up and power distribution through the cycle were examined in reference 5 where additional calculations were performed with sources appropriate to the beginning and end of the cycle as well as for those corresponding to the near mid-cycle condition. The time dependence of the ratio of reaction rate to power was thus calculated in reference 5 for each of the detectors, the nuclear data being taken from END FIB-VI for the material cross-sections and IRDF-85 for the response functions. The present calculations were restricted to the burn-up of 5,500MWd!Te and the effects of the variation of the source distribution during the cycle were derived from the results given in reference 5. The assumption is thus made that the factors which allow for the time dependence of the source distribution are not sensitive to the changes in the response functions between IRDF-85 and IRDF-90. This is valid because the corrections are mostly due to the increase in the absolute fluxes per unit power and the C3

AEAT-0352 APPENDIXC (AEAT-0468) effect of the latter would be independent of the response cross-section. There changes in the neutron spectra during the cycle which could be given different weigH by the two sets of dosimetry cross-sections but these are both small differences which in combination are expected to produce an insignificant effect An XYZ source configuration was used, with Z being the vertical axis. In Monte Carlo calculations the efficiency is improved if sampling of the source is biased in energy and position to concentrate on those neutrons which are most lik~ly to contribute to the fluxes of interest. MCBEND's optiori for "Automatic" source weighting was used which meant that the importance map specified for accelerating the tracking was also .used to generate source importances. The source intensity was specified as two *components, namely intensities for each source area in the X and Y directions, combined with a single Z profile.

3.3.1 X-Y Source Intensities Two sets of data were produced by CP&L and provided in reference 10.. They were:

.1) *

• Relative pin powers, calculated using the code"PDQ7..

2) Assembly averaged relative powers measured at a reactor.power of 1782.9MW(t),

processed using INCORE .. * * * * *** * * * ': "

• These measurements are considered to be better than the calculated assembly averaged powers (reference 11). The PDQ7 pin* powers were re-nonnalised ~o the INCORE assembly

• averaged powers by using the following equation for' each pin: *

. I0

= Pxy-

• Qa where Pxy is the relative pin power for pin x,y as calculated using PDQ7. DiviSion of Pxy by*

Qa. the mean pin power in the assembly containing pin x,y as calculated using PDQ7, * * *

. normalises the calculation to unit mean pin power in the assembly. Multiplication by Ia~ the .

mean pin power in the assembly containing pin x,y as calculated using INCORE with

• normalisation to unit mean pin power for the whole core, results in rxy being the relative pin ** .

power for pin x,y normalised to unit mean pin power over the whole core.

• The values of rxy were multiplied by *the mean absolute power .per pin (S, meas.ured in MW), and by a factor n relating the number of neutrons emitted to the power produced (measured in neutrons s*l MW-1), to give source strengths in neutrons s*l per pin. Because sou~ce strengths are speeified for MCBEND in terms of ne~trons s:1 cm-3, the st~ngth for each pin needs to be divided by the volume of the MCBEND. source for the pin. At this

• stage, the source strengths for each pin were divided by the area of the source, *the height of the pin being considered with the ~xial profile (see below).

• Therefore,

~ S rxy Sxy , = Axy where Sxy is the absolute source density for pin x,y (neutrons s*l cm-2) and Axy is the area occupied by pin x,y including the space around it ,which forms the MCBEND source m .

(cm2). *

• C4

AEAT-0352 APPENDIXC (AEAT-0468)

There are 32028 pins in the full source and the total reactor p_ow~~ \V_~__17?_7.9M_W(n,

---giving a mearrpin-power of0;05567-MW. The source for-each pin occupied an area 1.43cm square. The pin powers were converted to source rate densities using a value of (7.96+/-0.13)El6 neutrons s*I MW-I as described in section 7.6.

To reduce the amount of data required to describe the source, groups of 3 pins by 3 pins were combined into single large source regions. Thus each as~mbly (containing 15x15 pins) was modelled by a 5 by 5 array of sources. Therefore,

=

y=l where Sr is the absolute source density for the region r containing the 9 pins with x=l to 3 and y=l to 3 (neutrons s*l cm-2).

3.3.2 Z Profile ..

The axial (Z) profiles are stated in reference 10 to be independent of Y, and almost

• independent of X. For the purpose of the calculation, the Z profile was assumed to be independent of both X and Y, and a mean figure was taken. The profile was supplied in 57 vertical intervals, but to reduce the amount of data required to describe the source, these intervals were combined into sets of three to give 19 larger intervals over the full height of the source. The Z profile was then normalised to unity.

• Because source strengths must be specified for MCBEND in terms of neutrons .s*Icm-3, the "I factor for each vertical interval was divided by. the height of* the interval' (the other

:,[_

dimensions of the sources having been considered wi.th the X-Y component). Combining the source strengths for each XY region (neutrons s*l

• cm-2), with the factors for each Z interval (cm* 1) .. gives the complete source for the core .

.Although the source was produced for one *quarter of the core, only one eighth of the core was modelled. The source was reduced in area to omit those regions in the X direction lying entirely outside the eighth modelled. This still leaves some source regions outside the model. MCBEND will automatically ensure that any particles started outside the model are absorbed immediately, thus not affecting the source normalisation. Figure 6 shows the source areas used.

3.3.3 Source Spectrum

• • MCBEND9 has the capability of generating sources with spectra arising from a mixture of fission in U235 and Pu239, the fraction of neutrons created from each of the two spectra being specified for each source mesh. This facility was adopted for the present calculations.

The fractions of the fissions occurring in each of the isotopes were obtained from the calculations described below.

C5

AEAT-0352 APPENDIXC (AEAT-0468)

In cycle 9 for H B Robinson some of the fuel assemblies had considerable bum-up hence contained substantial proportions of plutonium, so the source will have consiste some neutrons with a plutonium fission spectrum, with the remainder having that appropriate to uranium. The additional information that is required for input_ to MCBEND is the fraction of neutrons with a plutonium spectrum in each source mesh. It is assumed that U 238 produces the same fission spectrum as U 235 with the plutonium spectrum applying to both Pu 239 and Pu 241 , these being the four main fissionable isotopes.

Table 4 shows the distribution of bum-up within the core at the beginning and' end of the 9th cycle. It can be seen_ that there are regions of very high bum-up on the flats, which are nearest to the main 0° dosimetry position, and low bum-up at the other edge regions. The remainder of the core consists of a range of bum-up histories. The assemblies were considered in groups with comparable histories as follows:

High bum-up assemblies on the flats:- _

Inner -22,000 to -26,500 MWcf/tonne

• outer -29,000 to -33,000 MWd/tonne Low bum-up assemblies near surveillance capsule:-

Inner 0 to -10,000 MWcl/tonne Outer 0 to -7,700MWd/tonne_

Rest of the core:-

- 7 ,500 to*_ -20,000 MW cf/tonne

_ -11,000 to .... 23,000 MWcf/tonne

-18,500 to * -30,000 MWd/tonne

• -0 tO -8,000 MWd/tonne

-0 to -11,000 MWcl/tonne Fission fractions were obtained .from_ bum-up calc~lations carried out ~ith the -nuclide inventory code FISPIN (reference 12) for 3.1 % enriched fuel for this range of bum-up histories. Table 5 gives the fission fractions at the beginning, middle and end of the 9th

• cycle for the five regions above (the "rest of the core" is treated as orie region), with average values being presented for the fifth* region. The fraction of neutrons with a plutonium spectrum was then determined, knowing the neutrons produced per fission (reference IJ);

and this is also shown. The calculated fission rates for the highest .rated fuel are in reasonable agreement with tho5e given in Table 33 of reference 14, for 3;2% U 235 -with fuel--

discharged at bum-ups approaching 30,000 MWd/tonne. The variation of the source per MW with plutonium content is shown in. Table 6 for fuel assemblies at the positions illustrated in figure 6, these being based on the energy released per fission taken from __

reference 15. Table 7 gives the variation in the neutron spectrum emitted during cycle 9 by a

• fresh fuel assembly which was loaded into a peripheral core position at the start of the cycle.

3A. Scoring The reaction rates were scored in the reactor cavity and at the surveillance capsule position, as shown in figure 7.

3.4.1 Cavity Scoring Region For scoring, the cavity was divided by planes at the following distances above and below _

the core centre line: +/-9lcm, +/-l22cm, +/-145cm, +/-175cm, +/-206cm and +/-221cm. Only the mid-height region is of interest in this exercise. The cavity was also divided into wedges.

around the circumference of the reactor. These included a 12° wedge centred on the 0° C6

AEAT-0352 APPENDIXC (AEAT-0468) position, an 8° wedge centred on 30° and a 12° wedge centred on 45°. The 0° and 45° wedges were actually only 6° wid.e__,_the _~_f}~~!9n pJane.~ gi~iog the effect of the other half. Each ----- - --- -

storing region covered the full width of the cavity. Most of the measurements were made at 0° at the core mid-height. The scoring regions were chosen to provide as large a scoring volume as possible around each measurement position, but with 10% or.less variation in measured detector response across them (based on the axial and azimuthal measurements of reference 7).

3.4.2 Surveillance Capsule Scoring Region The surveillance capsule was modelled accurately as shown in figure 7. The measurements of reference 7 show that there is little variation in flux over the 60cm height of the capsule, so the scoring region covered the entire central carbon steel region of the capsule.

3.4.3 Detector Responses The following detector responses were scored:

Ti 4 6(n.p) Fe 54 (n,p) Fe 58 (n,y) Ni58(n,p)

• Co59(n,y)

Cu63(n,ci) U235(n,fx) U238(n,fx) Np237(n,fx) Sc 4 5(n,y)

The cross-sections for these reactions were taken from the International Reactor Dosimetry Files IRDF-90 (reference 6). They are used in MCBEND in the 640 energy group scheme in which they are presented in the files. These data do not take the gadolinium or cadmium covering into account, the effect of which is discussed later.

3.5 Nuclear Data The nuclear data were processed from ENDF/B-VI into the DICE format used by MCBEND, which expresses cross-sections at 8220 energy points and has an explicit representation of the angular distributions and the energy loss laws. The doubly-differential representation of the energy and angle dependency of the scatter laws present for some isotopes in the ENDF/B-VI data was_ replaced by two independent distributions, the former representation being incompatible with the DICE format. The route for preparing the data was that described by Dean and Eaton (16) in which the SIXPAK (17) code is used to change the doubly-differential data, and the files are then processed with NJOY (18) to convert them to the DICE format designed for Monte Carlo tracking of neutrons. The calculations also included a detailed treatment of thermal neutron scattering using S(a,~) data (reference 19).

3.6 Variance Reduction The MCBEND module MAGIC was invoked to calculate the importance map for use in accelerating the MCBEND calculation. This performs an adjoint diffusion theory calculation in an orthogonal mesh, in this case XYZ, in order to provide the importances used in splitting and Russian roulette. The spacing of the mesh was determined from consideration of the attenuating properties of the materials in the system and of the penetration path from source to detector, e.g. C<?~ser meshes were used at the axial extremities of the model bec-~mse the importances are not required to be very accurate in these regions. Material compositions for each mesh were automatically determined by MAGIC by identifying the material in the MCBEND model at a number of points within the mesh, and combining the materials in the appropriate proportions. The importances were calculated in 28 energy groups.

C7

AEAT-0352 APPENDIXC (AEAT-0468)

Importance maps were generated for both detector positions separately. The source f adjoint calculation was specified at either the 0° cavity position or the surveillance cap ,

the adjoint source spectrum being identical in all energy groups in an anempt to score the high and low energy responses with equal statistical accuracy.

4 TIME-DEPENDENCE During the cycle the source distribution changes, with more power being produced by the peripheral assemblies towards the end of the cycle. This leads to an increase in the ratio of the flux levels outboard of the core to reactor power over the duration of the cycle, the effect being greater near the assemblies with high bum-up than near those containing fresh fuel (reference 20). When there is this variation with time there is no straightforward. definition of a mean reaction rate for the cycle and the results in the present comparisons are therefore given as the activations of the detectors at the end of the cycle~

The source terms used in the calculations with ENDF/B-VI and IRDF-90 data corresponded to a burn-up of 5500MW cl/tonne, i.e. about half way through the 9th cycle; The effects of the time de~ndence ,were taken from the calculations described, in reference 5 and the relevant results and data are reproduced from that report. In those calculations MCBEND cases were run with source strengths appropriate to the power distributions at the beginning and end of the 9th cycle as well as for those at 5500MWd!fe. The mid-cycle sources were

.. adjusted by multiplying them by the ratio of the appropriate assembly powers at the beginning/end of the .cycle to those in the middle of the cycle to give the relevant source strengths. No allowance was made for the change in neutrons released per MW through the cycle due to the increased plutonium content. This is considered separately (see section 7.6).

The power distribution was that supplied in reference 21 ~ and figure 8 shows the varia

• for assemblies adjacent to the cavity and surveillance positions. The effects on the s spectra of differences in the amount of plutonium through the cycle *were taken into by specifying the fractions of the sources arising from plutonium at the beginning and en of the .cycle calculated as described in section 3.3.3. The reactor power was kept constant for these calculations at l 782.9MW(t).

Table 8 and figures 9 and 10 are reproduced from reference 5. They compare the results of the MCBEND calculations for l 782.9MW(t) at the beginning, middle and end of cycle. 9 for both detector positions. It can be seen that the responses in general do not vary linearly with time, as is often assumed, although this could be considered valid for the surveillance capsule..

• The plutonium contents in assemblies adjacent to the cavity position, i.e. those on the flats ~t the edge of the core, show little change throughout .the cycle (see Table 5) and so the variation in the reaction rates is due to differences in the source ,strength, Figure 8 shows

• that the power, and hence source strength, in the assemblies adjacent to the cavity, increases linearly over the first -350 days (from 70% to 110% of the value at mid-cycle) and then fJ.attens .out. The calculated reaction rates show the same variation. The peripheral assemblies adjacent to the surveillance position were fresh .at the start of cycle 9 so that the plutonium content increases during the cycle. The calculated reaction rates will thus be dependent on* the change in both spectrum (for high energy reactions) and source strength over the cycle. The maximum change in spectrum however (see Table 7) is -6% at the very .

high energies which is less than,,the source strength variation. The change in the spectrum is much less than 6% for the lower energies at which most of the neutrons are emitted. The source strength for the assemblies close to the surveillance position shows less increase (from 85% to 103%) than did those relevant to the cavity reaction rates and this is reflected in the calculated time profile through the cycle.

• C8

AEAT-0352 APPENDIXC (AEAT-0468)

Following the equation given in Section 2 above the activation Am at the end of the cycle is given by *

--- ---- - *-- --- --~ -- --- -- --- - - - -- ~-- -------- ----*

A(T) = f R(t)P(t)A[A.<T-r>dt T

0 where A(T) = Activation at the end of the cycle, R(t) = Reaction rate for full power (2300MW) at time t in the cycle, P(t) = Reactor power (fraction of full power) at time t

,t = .Decay constant for the activity, and T = Duration of the .cycle.

When this is re-written for the representation of the power history by the mean powers in 18 intervals it becomes 18 A(T) = e-A.T,LP;R;(eA.r,., -eA.r')

1 where = Mean reaction rate at full power in the ilh interval

= Mean power (fraction of full power) in the ilh interval,

= Time at the start of the ilh interval, and

- Time at the end of the ith inrerv3..I (t19=T).

The. ratio of the end-of-cycle activation to the reaction rate in interval 9, i.e. that

. corresponding to 5500MW dffe, is then given by .,

-A.T 18

_e_'° PR.(eA.r,., -eA.r')

= ~ f' II '_,'r

?.**

. -i The results from reference 5 have been used to evaluate the relationships between A(T) and

~ for each detector at the surveillance position and in the cavity and the ratios are given in Table 9. These ratios, which are based on the IRDF-85 dosimetry cross-sections, are then applied to the current results for the ~ reaction rates obtained with IRDF-90 data in order to derive the end of cycle activations. As discussed in Section 3.3 a~ove the ratios are expected to show only small sensitivities to the differences between the two sets of response cross-sections so that this procedure should not introduce any significant error..

5 CORRECTION FACTOR The calculations were for one eighth of the core,

• and did not take account of any asymmetry. This is not significant for the surveillance capsule; however the 0° measurement

• position is right on the reflection plane in the MCBEND model, so half the flux reaching it will* be* due to the eighth that was not modelled. Of the three assemblies nearest the measurement position (A7, A8 and A9 in figure 6), .the right hand one (A9), which was included in the calculation, had a power 3.5% higher than the left liand one (A7), which was not included. Assuming that sources from these three assemblies dominate the fluxes and that each contributes equally to the responses measured in the cavity, a correction can be derived.

• C9

AEAT-0352 APPENDIXC (AEAT-0468)

Effective relative source in calculation =centre source+ 2 x right hand source

= 0.468 + 2 x 0.355

= 1.178 True source = left source+centre source+right source

= 0.342 +0.468 + 0.355

= 1.165 Comparing the two indicates that the calculated responses should be multiplied by a factor of 0.989.

6 RESULTS OF .THE CALCULATIONS The results of the MCBEND9 calculations with data from ENDF/B-VI and IRDF-90 are given in columns 2 and 5 of Table 10. These are the reaction rates calculated for a reactor power of 2300MW(t) *with the source distribution corresponding to the bum-up of 5500MWd!fe. The standard deviations that are given in columns 3 and 6 of that table are those derived by MCBEND from the statistics of the Monte Carlo scores. Also induded in the table are the end-of-cycle activations as derived from the reaction rates by applying the factors of Table 9. For the activations in *the cavity* the correction factor from Section. 5 has also been applied. .

• 7 UNCERTAINTIES There are* several factors which contribute to the overall uncertainty of the calculation

• addition to those arising from the Monte Carlo statistics as given in Table 10. These uncertainties assocfated. with the cross-sections of the materials in the reactor, dimensions of its components~ maferial compositions, smearing of the model of the core; source data and the detector cross-sections. These are *considered individually in the following sections where the analysis is mostly taken from reference 5 with modified values for the uncertainties.arising from the data for iron in ENDF/B-VI and for the detectors in IRDF-90. .. .

• 7.1 Cross-Sections*

To determine the uncertainty in the results due to uncertainties in the ENDF/B-Vl cross-

. section data for the reactor materials, each MCBEND calculation generated the sensitivities.

of the various responses tO changes in the total cross-sections of hydrogen and oxygen and for* the elastic. arid non-elastic cross-sections of ir:on, the latter being of particular *

• importance. For iron the calculated sensitivitie5 were folded with the covarianee *matrices derived by Ziver from* the data in ihe ENDF/B-VI library (22) to produce the uncertainties presented. in Table. 11 for both the cavity position and surveillance capsule, the correlations between the two partial cross-sections being taken into account in this process. The remaining uncertainties in Table 11 are those derived previously using co-variances from*

ENDF/B-V because these data are not present for hydrogen and oxygen in ENDF/B-VI. The uncertainties due to the cross-sections of iron were considered separately .in two areas of steel: the pressure vessel and the material comprising the barrel, baffle and thermal shield.

7 .1.1 Surveillance Capsule

. The.most important contribution to the total uncertainty for fluxes in the surveillance capsule comes from the uncertainty in the* cross-sections of iron in the stainless steel of the ba baffle and thermal shield. The relative importance of this material compared with the s ClO

AEAT-0352 APPENDIXC (AEAT-0468) the pressure vessel is due to the positioning of the surveillance capsule between the two regions. The smaller uncertainties due to the iron cross-section assigned to the low ~ne~gy_ _

reactions_ are_due .to the-lower sensitivity -of--these -fluxes* in the* su-r\ieillance *capsule to changes in the inelastic scatter cross-section because neutrons below the inelastic scatter threshold can migrate large distances. The contributions to the total uncertainties from hydrogen and oxygen are both less than that from the iron and apply equally to all reactions.

7 .1.2 Cavity Position The most important contribution to the total uncertainty in the fluxes in the cavity comes from the uncertainty in the cross-section of iron in the pressure vessel for the high energy reactions, with a significant contribution over all energies from the iron in the stainless steel of the barrel, baffle and thermal shield. The low energy reactions are not sensitive to the cross-section in the pressure vessel because the thermal flux in the cavity is determined by local downscatter of neutrons with energies below the inelastic scatter threshold. Such neutrons can migrate large distances in iron and the fluxes emerging into the cavity at these energies are not therefore sensitive to the positions of inelastic scatter events. In contrast, any increase in the inelastic cross-section leads directly to a decrease in the high energy r:esponses. The contributions to the total uncertainties from hydrogen and oxygen are both _

_less than that from the iron and apply equally across all energies.

7 .2 Dimensions No information was available on the as-built dimensions of the reactor, and nominal

- dimensfons were used in the model. Reference 8 examines the effect of varying the dimensions within the given manufacturing tolerances, and concludes that the maximum

.effect on the neutron fluence at the surveillance position is +/-2.5%. This value is taken as the uncertainty at both measurement locations.

Reference 20 states that the radial position of the surveillance capsule is known to Within 0.5in, resulting in an uncertainty of approximately 20% being applied to the fluxes in the capsule. In the cavity, measurements had been made at several axial and azimuthal positions (reference 7) so the MCBEND scoring regions were chosen such that there was 10% or less variation in measured detector response across them (section 3.4.1) and this uncertainty is applied to the fluxes in the cavity.

7:3 Radial Variation of the Flux Radial variation of the fluxes within a scoring region is only significant for the surveillance capsule which has a radial width of 3.17 5cm. The MCBEND result represents the mean flux over the radial width and this may be different to the true flux at the mid-point where the detectors are located. If the flux is assumed to vary exponentially through the steel capsule with distance from the core then there is a -3% difference between the mean and the mid-point value (calculated using a cross-section for iron averaged over the fission spectrum). It is recognised that this effect is energy dependent but, as it is small, the above value is

~pplied to all results.

The axial variation in flux is taken into account in the uncertainties applied to the measurements. - -

7.4 Material Compositions Reference 8 examines the plant-specific atomic number densities for the steels in the reactor, and concludes that using these would have no significant effect on the neutron fluences .

Reference 20 considers the effect of uncertainties in the coolant density and ascribes a Cll

AEAT-0352 APPENDIXC (AEAT-0468) standard deviation of approximately 6% for flux predictions at both measurement loca The results of the sensitivity analysis described in section 7.1 imply that all responses equally sensitive to the hydrogen and oxygen total cross-sections and so thiS value has been applied to all of the results. Similarly taking the analysis from reference 20 for the effect of the. density of the steel, a 3% uncertainty is applied to the *responses at the surveillance position with corresponding values in the cavity of 6% for the high energy detectors and 3%

for those at low energies.

Measurements made in the cavity will be influenced by the backscatter of neutrons from the concrete of the primary shield particularly for those detectors which are sensitive to neutrons at thermal or near thermal energies. No data are available at present which enable an estimate to be made of the uncertainty in the calculated reaction rates due to possible errors in the

. composition of the concrete. The existence of a likely contribution from this source should however be noted. * * ** *

• 7 .5 Core Smearing The core components (fuel, *clad, supports, and water) were smeared in the model because including all fuel pins explicitly would be impractical (there are more than 35,000 pin locations in the reactor). However this approximation is. not expected to** introduce any significant error because neutrons reaching the detectors leave the core with high energies where there is very little fine structure in the flux in the pins and moderator. Smearing is therefore justified. Moreover, as most of the flux received at both measurement locations is from those assemblies on the edge of the core where there has been only a short penetration through the core material, any small error in the treatment of attenuation will not be magnified by being applied over large distances. Evidence on the validity of smearing fuel pins is provided in reference 23.

7.6 Source Intensity

. The.estimated uncertainties on the calculation of the neutron* source per MW are given in.

Table 6. The FISPIN uncertainty on the calculation of the fission fractions is estimated as 5% (reference 24). The fission fractions quoted for the "rest of the core" are average values (see section 3.3.3) and therefore the uncertainty stated in Table 6 includes the. standard deviation on the values used to determine the average. The calculated total souree interµ;ity is (7.96+/-0.13) 10 16 ns*lMW-1. This value is used t<;> convert pin powers. to source rate den~ities so that an uncertainty of 1.6% is appropriate. for the source strength per unit

• power.

• There is an increase in *neutrons released per unit power throughout the cycle due to the increase in plutonium content. This was not taken* into ,account 'ih the change in source strength used in calculations at the beginning and end of the cycle (see section 4) .. The resultant uncertainty on total source strength can be. estimated from the values given for n/MW in Table 6. For assemblies adjacent to the surveillance capsule, which contribute about 78% of the result at that positiqn, it can be seen that the mid-cycle source is lower than the adopted mean value of 7.9.6x10 16 ns*lfMW by about 3% and there is a -2% variation from the mid-cycle value. Thus an additional uncertainty of 4% should be applied to the results. For assemblies adjacent to the cavity position the number of neutrons emitted per unit power does not change significantly during the cycle, but at 8.2xl0 16 ns*lfMW the source is higher than the adopted mean by 3%. An uncertainty of 3% is therefore assigned to the results for the cavity due to this variation in the source of neutrons per unit power.

C12

AEAT-0352 APPENDIXC (AEAT-0468) 7.7 Core Source Pata * -

In reference 8 ~~ _u_nq;J1ainties on _the measured -power- distributions -from INCORE -are-

-considered: ihe assembly-averaged powers are ascribed a standard deviation of +/-2.3% and the axial distributions a standard deviation of+/- 1.0%. The accuracy of the PDQ7 calculated pin powers is estimated as +/-1.5%.

In defining the source data each assembly was divided into groups of 3x3 pins. This introduces an averaging of the source over the group with an associated uncertainty. By estimating the contributions made by individual pins to the result in the scoring regions, uncertainties due to the averaging have been quantified and found to be -0.5% at both scoring positions. Thus the total uncertainty due to core source data is 2.9%.

7 .8 Fission Spectrum The calculations used MCBEND's built~in option for providing a U235 and Pu239 fission spectrum. The formula used to represent the spectra is the Watt-Cranberg expression x(E) = K e*AE sinhVBE where E is the neutron energy in Me V, x(E) is the fraction of neutrons at E per Me V, and A and B are constants which vary with nuclide. K is a normalisation constant Uncertainties in the values of A and B lead to uncertainties in the spectrum and hence in the results. The uncertainties in the spectrum are negligible at the peak energy of about 2MeV,*and increase, with decreasing energy to about 4% at 0.1 lMeV. The uncertainties a(e more significant at higher energies, being about 7% at lOMeV.

The effect of the uncertainty in the representation of the fission spectra has been investigated in a Study of an experimental benchmark whose configuration was similar to the radial shield of a PWR (reference 25). For high energy reactions, the uncertainty on results in positions equivalent to the cavity was about 4%. The value for locations equivalent to the surveillance position was about 3.5%. These values have been used for the high energy reactions in this study, with no uncertainties being.applied to the low energy reactions as they are much less sensitive to the detailed structure of the fission spectrum. **

7. 9 Detector Response Functions .

The cross-sections for the ~ctions for which measurements were made were taken from the International Reactor Dosimetry File IRDF-90 (reference 6) which also contains variance-covariance data. The uncertainties on the calculated reaction rates due to the IRDF-90 response cross-sections have been derived by folding the energy dependence of the reaction rates with these covariance data as presented in matrix form by Ziver (22). The co-variance data for the Fe 58 (n;y)Fe 59 reaction in IRDF-90 however contain errors and the uncertainty of 5% has been taken from reference 5 for this reaction. The uncertainties obtained in this way are given in Table 12.

7.10 Total Uncertainties The uncertainties due to the- above factors are summarised in Table 13. The data from Tables 11, 12 and 13 have been combined in quadrature with the variances arising from the Monte Carlo calculation to give the total uncertainties on the calculated reaction rates .

• C13

AEAT-0352 APPENDIXC (AEAT-0468) 8 COMPARISON OF CALCULATION AND EXPERIMENT The calculated activations at the end of cycle 9 are compared with the measured values in Table 14 where values of the ratio of Calculation/Measurement (C/M) are presented together with the uncertainties based on the analysis given in Section 7. The results are discussed separately for the surveillance position and the cavity .

. 8.1 Surveillance Position The measured values which are included in Table 14 for the U23S(n,fx) and Co59(n;y) reactions at the surveillance position are for the gadolinium covered detectors. As this was not taken into account in the calculated responses. it is not possible to make meaningful C/M comparisons for these detectors. * -

Of the remaining nine responses, the MCBEND results show values of CIM in the range 0.90 to 1.00 for seven of the detector~. The remaining two, Ti46(n,p) and U238(n,fx)Zr95, give ratios of 0.85 and 0.89 respectively. The average CIM value is 0.94. All of the responses have values pf C/M which are within one standard deviation of unity, the values of the standard deviation for the ratios being about 25%. The uncertainties mostly arise from the 20% assigned to the doubt about the radial position of the capsule which, as suggested in reference 20, may be too large. The variation of C/M between the detectors with the mean value of 0.94 for CIM suggests that the factors which contribute to the uncertainties for all detectors in an approximately similar way, such as the those due to the material cross-

.sections, the source data, the capsule position, and the material densities/dimensions, give a

'. small underestimate with the remaining spread being due to the uncertainties associated with particular reactions, i.e. the measurements and the detector' cross-sections. For Ti46(

these are 10~ and 5:3% which gives a combined uncertainty of 11.3%, so tha departure from the mean is 0.85 standard deviations. The values of CJM. for the reactions are closer to the mean and the differences are all less than one standard deviat.Ion due to the combined measurement and detector cross-section uncertainties. The measured and calculated reaction rates are thus consistent within the uncertainties assigned to the input paraineters.

• 8.2* Cavity Position

.The results for the detectors in the cavity as given in Table 14 'show values of CIM in the

• range 0.82 to 1.05 for the fast neutron reactions-with a mean of 0.93. The differences between the values of C/M and the mean for this group of detectors are again less than one standard deviation due to the combined uncertainties arising from the measurements and the detector cross-sections exeept in one case. For the neptunium reaction the uncertainty on the measurement is 5% whilst the uncertainty due to the detector is 9.2% giving a standard deviation of 10.5% for the combined uncertainties pertaining solely to that detector. The CIM for the* Np 237 (n,f)Cs 137 reaction is 0.82 so that its departure from the mean is just greater than one standard deviation. The mean of 0.93 for the high energy detecto*rs in the cavity is close to the value of 0.94 at the surveillance position so that 'the results suggest that the attenuation through the vessel is being calculated more accurately than*is indicated by the uncertainties of 11.5% to 18.45% due to the iron cross-sections which were obtained from the ENDF/B-VI co-variance data.

The *results for the six low energy reactions, Fe 58 (n,y)Fe 59 , Co 59 (n,y)Co 60 , U 235 (n,f)Zr95 ,

U 235 (n,f)Cs 137 , U 235 (n,f)Ru 103 , and Sc 45 (n,y)Sc 46 give values of CIM of 1.14, 1.13, L04, 1.10, 1.03, and 1.04 respectively. These show that the low energy fluxes are overestimated with a mean value of C/M of 1.08. The fluxes in the cavity at low energies arise from A scatter of the neutrons leaking from the pressure vessel at intermediate energies a n w Cl4

AEAT-0352 APPENDIXC (AEAT-0468) therefore more sensitive to the composition of the concrete primary shield than those which contribute to the reaction rates of the high energy detectors. The co~~_c>sit,ign__ Qf _lh_e____

________ __ _ ___ concrete, and-in-particular-its-hydrogen content~- is nocknown p*recisely so that there is an

---

-- -- - *---- additional uncertainty in the calculated results for the low energy detectors which it was not possible to quantify in the analysis of section 7.4. The comparis.ons suggest that the back-scatter of low energy neutrons is overestimated with the composition of the concrete that has been adopted in the present calculations. The embrittlement of the pressure vessel is usually correlated against neutron fluxes either through the_ fluxes above lMeV or the atomic displacement rate (dpa). The cross-section for the production of displacements falls with decreasing energy down to lkeV and then shows a 1/v variation at energies below this, with the cross-section at thermal energies being lower than that at lMeV by a factor 0.015. The embrittlement in the pressure vessels of PWRs is thus dominated by the higher energy neutrons so that it is the values of CIM for the threshold detectors which are the more relevant indicators of the accuracy of the calculations for predicting such damage effects.

9

SUMMARY

Calculations have been performed for the H B Robinson Unit 2 PWR, at dosimetry positions in the reactor cavity and the surveillance capsule, using MCBEND with ENDF/B-VI nuclear data. The calculations show a slight underestimation of the reaction rates at the inner surface of the vessel at the surveillance position with a mean value of C/M of 0.94+/-0.02, where the uncertainty is the standard error on the mean. In the cavity there is a similar underestimation of the reaction rates of the threshold detectors with a mean value of C/M of 0.93+/-0.02.

The values of C/M for the low energy detectors in the cavity are all above 1.0 with a mean of 1.08+/-0.02. This distinct difference between the results for the high and low energy deteciors is attributed to the greater sensitivity of the latter to uncertainties in the composition of the concrete which forms the outer region bounding the cavity. The results suggest that the back-scatter of neutrons by the concrete is overestimated in the calculations with the composition that is currently specified.

The uncertainties in the calculational route have been quantified. The major contributions are the uncertainties due to the iron inelastic cross-section, the water density. and the radial position of the surveillance capsule. The similarity of the mean values of C/M in the two measurement positions suggests that the error is most likely due to a common* cause such as the water density o*r the source data. The departure of the mean C/Ms from unity is less than one standard deviation arising from such common uncertainties. The agreement suggests that the uncertainties assigned to the radial position of the surveillance detectors and the cross-sections of iron which each affect one position more than the other are too large.

In most cases the discrepancies between the values of C/M for the individual detectors and the mean values are less than one standard deviation based on the combined uncertainties due to the measurements and the detector cross-sections, i.e. the uncertainties which are relevant to that C/M alone. The only exception is the result for one of the three neptunium fission measurements in the cavity where the difference is just over one such standard deviation. The measurements and calculations are therefore consistent with each other.

These results show that MCBEND with data from ENDF/B-VI can be used to predict the

• neutron fluence in PWR pressure-vessels to a high degree of accuracy .

• C15

AEAT-0352 APPENDIXC (AEAT-0468)

REFERENCES 1 MCBEND User Guide for Version 9 ANSWERS /MCBEND(94) 15 2 S.W. Power. An Analysis of the H B Robinson Unit 2 PWR using the Monte Carlo Code MCBEND RSWG/P(89)25 3

• S. Newbon &.S.J. Chucas. Further Analysis of the H B Robinson Unit 2 PWR using the Monte Carlo Code MCBEND SESD/6028/3.17 4 The International Reactor Dosimetry File (IRDF-85)

Cullen D.E. & McLaughlin P.K.

IAEA-NDS-41

.5 .Locke (Mrs) HF. Further Analysis of the H B Robinson Unit 2 PWR using the Monte Carlo Code MCBEND with ENDF/B-VI Nuclear Data..

AEARS 5579 6 Kocherov N P and McLaughlin P K. The International Dosimetry File (IRDF-90),

IAEA-NDS-141October1993. .

7 Lippincott E.P: .et al. ~valuation of Surveillance Capsul~ *and R~ctor Cavity Dosi*

. from H B Robinson Umt 2, Cycle 9 . * . . * * * * *

• WCAP-11104, NUREG/CR-4576 .* . * . * * . . .

8 Anderson S.L. Summary of H B Robinson PTS Analysis RSAC-CPL-170 9 * .. IAEADirectory of Reactors 10 Maerker R.E. . * . - ', .

Private Communication *,

• 11 Kam. F.B.K. * .

Private Communication .

.12 : Burstall 'R.F. & Webb S.G. FISPIN-6 IMAC/P(82) 106 13 Nash G.

Private Communication 14 Nash G. A Fuel Management Study on a Pressurised Water Reactor AEEW-R802 15 James M.F. The Relation between Power and ~ux in Inventory Codes IMAC(83)/Pl20 .

Cl6

AEAT-0352 APPENDIXC (AEAT-0468) 16 Dean CJ & Eaton CR. The 1994 DICE Nuclear Data Library AEA-RS 5697

• - -- - 7 - -*-cuIIeifffE~ SIXPA:R: A Code Designed to Check Double-Differential Correlated Data and Calculate "Equivalent" Uncorrelated Data.

UCRL-ID-110241 18 Macfarlane RE & Muir D W.

The NJOY Nuclear Data Processing System, Version 91.

LA-12740-M 19 Bendall D.E. New Thermal Treatment for MONK Proceedings of the ICNC 91. International Conference on Nuclear Criticality Safety.

20 Maerker R.E. LEPRICON Analysis of Pressure Vessel Surveillance Dosimetry Inserted into H B. Robinson-2 during Cycle 9 NUREG/CR-4439 21 Maerker R.

Private Communication 22 Ziver AK and Earwicker J Processing of the Variance-Covariance Data from the ENDF/B-VI and IRDF-90 Nuclear Data Libraries for use with the MCBEND Code.

AEA-TSD-0387 23 NEACRP Comparison of Codes for the Radiation Protection Assessment of Transportation Packages. Solutions to Problems 1-4.

NEACRP-L-331 Table 43 (i) 24 Burstall R.F. Thermal Reactor Validation Work for the FISPIN Code AEA RS 1138 (March 1992) 25 Newbon S.(Mrs.) The Analysis of NESDIP2 with ENDF/B-VI Nuclear Data.

AEA RS 5591 (February 1994)

• Cl7

AEAT-0352 APPENDIXC (AEAT-0468)

Table 1 - Power History for Cycle 9 Cumulative Mean Cumulative Fraction Period Days days Power MWd(e) MWd(e) of Cycle MW(e) 1 20 20 334.94 6698.8 6699 0.03 2 3 23 0 0 6699 0.03 3 78 101 511.96 39932.88 46632 0.22 4 2 103 48.98 97.96 46730 0.22 5 29 132 533.92 15483.68 62213 0.30 6 2 134 75.24 . 150.48 62364 0.30 7 89 223 496.78 44213.42 106577 0.51 8 4 227 45.79 183.16 106760 0.51 9 24 251 465.76 11178.24 117939 0.57 10 29 280 0.1 2.9 117942 0.57 11 100 380 507.67 50767 168709 0.81 12 16 396 11.95 191.2 168900 0.81 13 4 400 323.75. 1295 170195 0.82 14 39 439 521.79 20349.81 190545 0.92 15 36' 475 1.83 65.88 190610 0.92 16 16 491 286.15 . . 4578:4 195189 0.94 17 7 498 503.43 3524.01 198713 0.95 18 26 524 363.22 9443.72 208157 1.00

AEAT-0352 APPENDIXC (AEAT-0468)

Table 2 - Derivation of Activations Measured at the End of the Cycle Surveillance Position Cavity Scaling Measured End-of Std Measured End-of Std Cycle Dev Saturation Cycle Reaction Factor* Saturation Activity Activity Dev

.Activity (%)

• Activity (%)

(dps/a) (dps/a)

(dps/a) (dps/a)

Ti 46 (n,p)Sc 0 0.490 7.08E-16 3.47E-16 10 6.63E-18* 3.25E-18 10 Fe 54 (n,p)Mn 54 0.389 3.86E-15 l.50E-15 10* 3.67E-17 1.43E-17 5 Fe 51 (n,y)Fe 59 0.465 4.42E-14 2.06E-14 12 2.93E-15 1.36E.:15 8 Ni 58 (n,p)Co 58 . 0.483 5.35E-15 2.58E~l5 10 5.85E-17 2.83E-17 10 Co 59 (n,y)Co 60 0.102 6.81E-l3 6.92E~14 5 l.20E-13 1.22E-14 5 Cu 63 (n,a)Co 60 0.102 . 3.98E-17 4.04E-18 10 .3.96E-19 4.02E-20 5 uzJs(n,f)Zr9s 0.478 "3.33E-12 l.59E-12 5

• 1.26E-12 6.03E-13 *: 5 U 235 (n,f)Cs 137 0.019 3.21E-12 6.22E-14 5 1.lOE-12 2.13E-14 5 uzJs(n,f)Ru 103 0.463 ,

• 1.29E-*12 5.97E-13 uz31(n,f)Zr9s 0.478. 1.90E~i4

• 9.09E-i5 5 3.09E'."16 1.48E-16 .5 uz31(n,f)Cs1J1 , . 0.019 1.80E-14 3.49E-16 5 2.87E-16 5.56E-18 5 U m(n,f) Ru 103 0.463 3.24E-16 l.SOE-16 5 Np2J1(n,f)Zr9s . 0.478 l.22E-13 5.84E-14 5 7.34E-15 3.51E-15 5 Np231(n,f)Cs1J1 0.019 1.18E-13 2.29E~15 5 7.23E-15 1.40E-16 5 Np2J1(n,f)Ru103. 0.463 7.82E-15 . 3.62E-15 5 Sc 45 (n,y)Sc 46 0.490 5.77E-14 2.83E-14 10

• The scaling factor is the ratio of the activity of a detector at the end of the cycle to the saturation activity derived assuming the power history of Table 1 and a constant proportionality of reaction rate and reactor power.

AEAT-0352 APPENDIXC (AEAT-0468)

Table 3 - Material Compositions

& MAlERIALS FOR H.B.ROBINSON PWR (FROM WESTJNGHOUSFJCPL DOT MODEL)

& K REMOVED FROM CONCRElE MINNIE MIXTIJRES 5 WEIGHT

& CORE REGION Ml U235 0.20647E-Ol U238 0.62565 0 0.180760 H 0.11840E-01 BIO 0.65507E-04 FE54 l .32525E-04 FE56 2.13598E-03 FE57 4.9755E-05 FE58 6.74250E-06 MN 0.42278E-04 CR50 5.2033E-05 CR52 l.04441E-03 CR53 I.20662E-04 .. j CR54 3.05711E-05 N158 l.98361E-03 N160 7.9Q492E-04 N161 3.48312E-05 NI62 1.13054E-04 N164 2.98312E-05 ZR 0.15447 M2

& WAlER H 0.88799 00.11191 BIO 0.99829E-04

• M3

& STAINLESS SlEEL SST304 FE54 3.933E-02 FE56 6.339E-Ol FE57 l .4766E-02 FE58 2.00lE-03 MN 0.19995E-Ol CR50 7.923E-03 CR52 l .5903E-Ol CR53 1.8373E-02 CR54 4.655E-03 N158 6. 72067E-02 NI60 2.67827E-02

.. Nl61 l.l8012E-03

. NI62 3.83038E-03 Nl64 1.0IO1 E-03

AEAI-0352 APPENDIXC (AEAT-0468)

Table 3

• Material Compositions continued M4

& CARBON STEEL AS33B C 0.24999E-02 MN 0.12996E-Ol FE54 5.58030E-02 FE56 8.99407E-Ol FE57 2.09506E-02 FE58 .2.839 IOE-03 NI58 3.69640E-03 NI60 l.47306E-03 Nl61 6.49071E-05 NI62 2.10673E-04

-MS

& CONCRETE

& POTASSIUM (K) REMOVED TO SAVE SPACE

& (ELIMINATED BY DISTRIBlITING ITS FRACTION AMONG~T TIIB OTIIBR

& ELEMENTS)

H 0.50903E-02 C 0.10183E-02

.. 0 O.Sll89

',,J NA 0.162R8E-Ol MG 0.22130E-02 '.

AL 0.34S30E-Ol SI 0.346230 .

CA 0.442S6E-Ol FES4 2.l 9364E-03 FE56 3.S3562E-02 FES7 8.23S79E-04 FES8 l.111607E-04 MATERIALS 6 CORE REGION #100 1 Ml 4.2632 1.0

& EXCORE STAINLESS STEEL #200 2 M3 8.03 1.0

& EX CORE WATER #300 3 M2 0.7886 1.0

& EXCORE CARBON.STEEL #400 4 M4 7.83 1.0

& INSULATION #500 S M3 0.241 1.0

& CONCRETE #600 6 MS 2.20 . 1.0

AEAT-0352 APPENDIXC (AEAT-0468)

Tahle 4 - Initial and Final Burn-up Distrihutions for the 9th Cycle p - r- I E c I R I N I f\ I I L K I 1 I H I G I D I D  :\  !

I I I I I 294S8 22092 29122 I I I I I 2 I I I 0 o I o I o o 0 I 0 I I I I 3 I I* 0 I 7496 6880 I 1873 7 23046 I .J S7S4 I 690'1 I 7439 I 0 I I I 4 I 0 I o 12016 196321 1254 I 19069 7196 194:7 21850 I 0 I 0 I 5 0 I 7400 I 12236 I 22054 11951123149 0 22933 113.Wl21446\119SOl 7523 I 0 6 0 I 6941 I 19746111917 19513110360 2194S 10100 19755 11S97 I 19299 I 1021 I 0 7 29286 0 I 187S6 I 7132 22787 10247119607 8280 19626 10~12 2324S I 724S I 18762 I 0 29302 8 21143 0 I 23006 I 18885 0 22293 I 8325 21170 8474 21792 0 I 19190 I 22733 I 0 21351 9 29064 0 I 13920 I 7344 22947 10266 I 19454 8290 19428 1('186 I 23054 I 72S2 I 185S9 I 0 29194 10 0 I 6934 I 19819 I 11918 19578110173 21729 10112 19343 I 11611 I 19619 I 1020 I 0 11 0 I 7548 I 12051I21592l 11809l 22801 0 \ 23117 113L"*7 I 21876 I 12142 I 75S4 I 0 12 I I 0 I 0 I 11868 I 19430 I 7287 I 18794 7333 I 196G1 117S5 I 0 I 0 I 13 I I I 0 I 7507 I 6949 I 18618 23052 187521 6S+4 75Sl I 0 ! I i 14 I  ! I I I 0 0 I 0 I 0 0 I 0 i 0 I I I I 15 !  ! I I I I I 29058 22121 j 29211 I  ! I I I I . i I I I I I. I I I I I I I I I I i I  ! I I ... I I L___ J_L __ I  !

I i I R I p I ;--; I M I L I K I 1 I H I G I F I E i D i c ! B I A 1 I I I I I I I 33102 I 26798 I 32689 I I I i I I 2 I I I I I 7705 I 10479\ 11298\ 11988l 11179\ 10208I iiori I i I I 3 I I

I I I 8622 I 19365 200121 29978 33468 I 30031 I 20020 19360 I 8588 I I 41 I I 8646 112384 I 23939 3os20 I 20290 30225 20209130746 24075112661 I 8704 I 5 I I 1~::0 I 19312 I 24274 \ 32490 23678133927113506 33691 I 23701 I 32176124283 i 19~2 7658 I 6 i I 10375 I 20025 I 30931123658 30403 I 22544 I 32792 22241 I 30594 23643 I 30484 / 19908 10017 I 1 I 32962 I 11 ::991 30059 I 20010 \ 33290 22195 I 30566 20758 30573 22253 33843119838 I 29698 10881 32S16 8 I 25984 I 12011 I 33556 I 30027 I 13109 32375 I 20190 31894 20915 I 32636113396 I 29949 J 32831 11656 26080 I 9 I 32729 I 112S4 I 30.J90 I 20322133761 22171130243 20439 30276 22220 33810 I 20143129654 11058 32833 10 I I 1015S I 19756 I 31046j 23921 30443 I 22057 32215 21963 I 30033 I 23425130977 I 20133 10180 i 111. I ns-: I 1934-1 I 24165 I 32343 23561133250 13152 33686 23410 32374 \ 24205 I 19533 7743 121 I I 8653 J 12540 J 24345 30564 I 19870 29607 I 20069 30633 23781112444 I 8599 13 I I I I 8615 I 19118 19680 I 29527 33149 29734 19689 19517 I 8697 I 114 I I I I I 7691 10285111373 11862 11076 10248 7814 I I I 15 I I I I I I 32748 27443 32842 I I I LJ I I I I I I I I I I ---*--*

The numhering of the assemhlies is in the scheme used hy Westinghouse.

AEAT-0352 APPENDIXC (AEAT-0468)

Table 5 - Fuel Composition at the Beginning. Middle and End of the 9th Cycle Fission fractions Fraction of source neutrons n/MW U235 U238 Pu239 Pu241 U235 U2J8 Pu239 Pu~41 Pu Total Avern ge for rest of core Initial 0.658 0.071 0.240 0.030 0.620 0.011* 0.267 0.035 '0.302 7.87El6 Middle 0.548 0.076 0.324 0.051 0.507 0.081 0.354 0.058 0.412 7.98El6 Final 0.457 0.081 0.386 0.076' 0.416 0.085 0.414 0.085 0.499 8.01El6 A:;1;emhlies adjacem to suryeB!ance capsule inner Initial 0.940 0.060 0.000 0.000 0.931 0.069 . 0.000 0.000* 0.000 7.59El6 Middle 0.763 0.066 0.167 0.004 0.732 0.073 0.190 0.005 0,195 7.77E16 Final 0.634. 0.071 0.273 0.022 0.595 0.077 0.303 0.025 0.328 7.90El6 outer Initial 0.940 0.060 0.000 0.000 0.931 0.069 0.000 0.000 0.000 7.59El6

Middle 0.804 0.064 0.130 0.002 0.778 0.072 0.148 0.002 0.150 7.72El6 Final 0.701 0.068 0.220 0.011 0~665 0.075 0.247 0.012 0.260 7.83E16 8_51;i;:mbJil::S lldill!;;l::D! l!l QO S!;;QDD~ PQSili!lll outer Initial 0.352 0.087 0.454 0.107 0.314 0.089 0.479 0.117 0.596. '8.20E16 Middle 0.328 0.089 0.468 ' 0.115 0.292 0.091 0.491 0.126 . 0.617 8.22E16 Final 0.307 0.090 0.480 . 0.123 0.272 0.092_, 0.503 0.134 *0.636 8.25E16 inner Initial . 0.460 0.080 0.390 0.070 0.419 0.084 0.419 0.078 .. .0.497 8.08E16 Middle 0.434 0.082 0.406 0.078 0.393 0.086. 0.435 0.086 0.521 8.11E16 Final 0.397 0.084 . 0.428 0.091 0.357 0.087 0.455 0.100 0.555 8.l5E16 Neutrons~r 2.43 2.8 2.87 2.97 fission ,.

n/s nerMW 7.53El6 8.54El6 8.54El6 8.72El6 The positions of the "inner" and "outer" fuel assemblies for the 0° and 20° scoring positions are shown in figure 6.

• AEAT-0352 APPENDIXC (AEAT-0468)

Table 6

• Calculation of Source Intensity

--- Fission Energy/fi~sion Neutrons/fissi Neutrons/MeV Neutrons/s/MW on fraction unc. (MeV) unc. unc. unc. unc.

U235 0.548 0.152 201.7 0.6 2.43 0.01 6.60E-03 3.35E-5 U238 0.076 0.008 205.0 0.9 2.80 0.01 l.04E-03 5.87E-6 CORE Pu239 0.324 0.110 210.0 0.9 2.87 o.oi 4.43E-03 2.45E-5 129* Pu241 0.051 0.035 212.9 1.0 2.97 0.01 7.llE-04 4.llE-6

' All 1.000 205.0 2.63 l.28E-02 2.51 E-4 7.98E+l6 1.57E+15 U235 0.328 0.016 201.7 0.6 2.43 0.01 3.95E-03 2.0IE-5 U238 0.089 0.004 205.0 0.9 2.80 0.01 l.22E-03 6.88E.6 CAvrIY Pu239 0.468 0.023 210.0 0.9 2.87 0.01 6.40E-03 3.53E-5 INNER Pu241 0.115 0.006 212.9 1.0 2.97 0.01 l.60E-03 9.27E-6

-4*

All 1.000 207.2 2.73 1.32E-02 5.03E-5 8.22E+l6

• 3.14E+l4

",*(

U235 0.434 0.022 201.7 0.6 2.43 0.01 5.23E-03 2.66E-5 U238 0.082 0.004 205.0 0.9 2.80 0.01 I. I 2E-03 6.34E-6 CAvrIY - Pu239 0.406 0.020 210.0 0.9 2.87 0.01 5.55E-03 3.06E-5 OlJIER Pu241 0.078 0.004 212.9 1.0 2.97 0.01 l.09E-03 6.29E-6 8*

All 1.000 206.2 2.68 l.30E-02 5.46E-5 8.10E+l6 3.41E+l4 U235 0.763 0.038 201.7 0.6 2.43 0.01 9.19E-03 4.67E-5 I. I SURV. U238 0.066 0.003 205.0 0.9 2.80 0.01 9.0lE-04 5.lOE-6 CAPSULE Pu239 0.167 0.008 210.0 0.9 2.87 0.01 2.28E-03 l.26E-5 .,

INNER Pu241 0.004 0.000 212.9 1.0 2.97 0.01 5.58E-05 3.22E-7 8*

All 1.000 203.3 2.53 l.24E-02 7.84E-5 7.76E+l6 4.89E+l4 U235 0.804 0.040 201.7 0.6 2.43 0.01 9.69E-03 4.92E-5 SURV. U238 0.064 0.003 205.0 0.9 2.80 0.01 8.74E-04 4.95E-6 CAPSULE Pu239 0.130 0.007 210.0 0.9 2.87 0.01 1.78E-03 9.81E-6 OlJIER Pu241 0.002 0.000 212.9 1.0 2.97 0.01 2.79E-05 l.61E-7 8*

All 1.000 203.0 - 2.51 1.24E-02 8.21E-5 7.72E+l6 5.12E+l4 Total. Neutrons/s/MW 7.96E+l6 1.29E+l5

• number of assemblies

=

unc. uncenainty The positions of the "inner" and "outer" fuel assemblies for the cavity and surveillance capsule scoring positions are shown in figure 6 .

AEAT-0352 APPENDIXC (AEAT-0468)

Table 7 - Source Spectra for Fresh Fuel Assemblies in Peripheral Locations Fraction in energy group Energy Upper Initial Midcycle Final l.o.i1.ia.l UnBl

.Group El_'lergy Mid Mid (MeV) 100%U 20%Pu 30%Pu 1 1.46E+Ol 4.30E-05 4.48E-05 4.57E-05 0.960 ).020 2 l.35E+o1

• 9.IOE-05 9.48E-05 9.67E-05 0.960 r.020' 3 1.25E+Ol 3.28E-04 3.41E-04 3.48E-04 0.961 1.019 I

4 1.13E+Ol 7.69E-04

• 7.96E-04 8.IOE-04 0.966 1:017 5 1.00E+Ol 2.74E-03 2.82E-03 2.87E-03 0.969 1.016

'6; *8.50E+OO 8.72E-03 8.97E-03 9.IOE-03 0.972 l.Oi4 7 ' 7.00E+OO l.25E-02' l.28E-02 l.29E-02 0.976 '1.012 8 6.07E+OO 4.20E-02 4.28E-02 4.32E-02 0.980 1.010 9 4.72E+OO 7.15E-02 7.26E-02 7.31E-02 0.986 1.007 10* 3.68E+OO 9.59E-02 9.68E-02 9.73E-02 0.991 1.005 11 2.87E+OO 2.35E-Ol 2.36E-Ol 2.36E-Ol ' 0.997 1.002, 12 1.74E+OO . 3.66E-Ol 3.64E-Ol 3.63E-Ol 1.006 0.997 13 6.00E-01 7.08E-02 7.00E-02 6.96E-02 1.012 0.994 14 3.90E-Ol 7.74E-02 7.63E-02 7.57E-02 1.015 0.993

' 15 l.IOE-01 7.99E-03 . 7.85E-03 7.79E-03 1.017 0.992 6.74E-02 ..

AEAT-0352 APPENDIXC (AEAT-0468)

Table 8

• Comparison of Reaction-rates at the Beginning. Middle and End of the

• * *9th* Cycle**fTaken *rr-onr*catcufati<ins with --IRDF~85 dafa <Ref 5ll.

Surveillance position

Response

Initial Middle Final dps/atom sci(%) dps/atom sci(%) dps/atom sci(%)

Tl46(n,p) 4.36E-16 2.2 4.83E-16 2.1 5.03E-16 1.9 Fe54(n,p) 2.56E-15 1.4 2.82E-15 1.3 2.97E-15 1.2 Fe58(n,y) 2.79E-14. 2.7 3.14E-14 2.9 3.32E-14 2.8 Ni58(n,p) 3.40E-15 1.3 3.76E-15 1.3 3.95E-15 1.1 Co59(n,y) . 1.25£-12 2.4 1.42E-12 2.3 1.47E-12 2.2 Cu63(n,a) 2.83E-17 3.7 3.18E-17 3.5 3.20E-17 3.1 U235(n,fx) 1.21E-11 3.0 l.36E-11 3.1 1.45£-11 3.0 U238(n,fx). l.12E-14 1.0 1.24E-14 0.9 1.30E-14 0.8 Np237(n,fx) 8.00E-14 0.7 9.02E-14 0.7 9.36E-14 0:6 .

Sc45(n,y) 5.81E-13 3.0 6.54E-13 3.2 6.93E-.13 3.1 Cavity position

Response

Initial Middle Final dps/atom sci(%) dps/atom sci(%) dps/atom sci(%)

Ti46(n,p) 3.76E-18 2.0 5.37E-18 1.7 5.65E-18 2.2 Fe54(n,p) 2.26E-17 1.4

• 3.20E-17 1.2 3.41E-17 1.4 Fe58(n,y) 1.82E-15 2.6 2.35E-15 2.6 2.52E-15. 4.2 Ni58(n,p) 3.52E-17 1.1 4.95E-17 0.9 5.29E-17 1.1 Co59(n,y) 7.99E-14 2.1 1.03E-13 2.3 1.13E-13 3.2 Cu63(n,a) 2.71E-19 2.7 3.96£-19 2.5 4.15E-19 3.2 U235(n,fx) 7.44E-13 2.9 9.61E-13 3.1 1.04E-12 4.8 U238(n,fx) 1.53E-16 0.8 2.14E-16 0.7 2.31E-16 0.8

. Np237(~,fx). 3.49E-15 0.4 ... 4.81£-15 .o.4 5.18E-15 0.4 Sc45(n,y) 3.49E-14 3.0 4.49E-14 3.1 4.87E-14 5.0

AEAT-0352

. APPENDIXC (AEAT-0468)

Table 9 - Ratios of the End-of-Cycle Activities to the Reaction Rates at Mid-cycle Ratio of End-of Cycle Acti~ity to Reaction Rate at Mid-c*~cle Reaction Surveillance Cavity Position Ti 46 (n,p)Sc 46

• 0.5024' 0.5029 Fe 54 (n,p)Mn 54 0.3924 0.3832 Fe 58 (n,y)Fe 59 0.4874 0.4931 Ni 58 (n,p)Co 58 0.4999 0.5045 Co 59 (n,y)Co 60 0.1003 0.1001 Cu 63 (n,a)Co 60 0.0995 0.0966 U 235 (n,f)Zr 95  :

0.4953 ' '0.5053 U 235

( n,f)Cs 137 0.0193 0.0187 u23s(n,f)Ru 103 '0.4824 ' 0.4947 u23s(n,f)Zr's 0.5016 0.5067 U 238 ( n,f)Cs 137 0.0193 0.0189 u23s(n,f)Ru103 0.4895 0.4959 N p 237 (n,f)Zr 95 0.4913 0.5044 Np 237(n,f)Cs137 0.0191 0.0187 Np 237 (n,f)Ru 103 0.4781 '0.4937 Sc 45 (n,y)Sc 46 0.5082 0.5150 The factors in the Table were derived using the power history of Table l together with the variation of the ratios of reaction rates to power as calculated in Reference 5. These reaction rates were .obtained with IRDF-85 data at three stages during the cycle and they are reproduced in Table 8.

• AEAT-0352 APPENDIXC (AEAT-0468)

Table 10 - Calculated Reaction Rates Reaction Surveillance Position Cavity Calculated Std Calculated Calculated Std Calculated End-of- End-of-Reaction Dev Reaction Dev Cycle Cycle Rate (%) Activity Rate (%) Activity (dps/a) (dps/a) (dps/a) (dps/a)

Ti 46 (n,p )Sc 46 5.89E-16 0.9 2.96E-16 6.43E-18 2.6 3.19E-18 Fe 54 (n,p)Mn 54 3~81E-15 5.6 1.50E-15 3.76E-17 1.5 1.43E-17 Fe 58 (n,y)Fe 59

• 4.lOE-14 2.9 2.00E-14 3.17E-15 2.1 1.55E-15 Ni 58 (n,p)Coss 5.19E-15 7.6 2.59E-15 5.09E-17 1.3 2.54E-17 Co 59 (n,y)Co 60 1.78E-12 3.0 1.78E-13 1.39E-13 3.6 1.38E-14' Cu 63 (n,a)Co 60 3.66E-17 1.0 3.64E-18 4.41E-19 0.8 4.22E-20 U23s(n,f)Zr9s 1.72E-l 1 3.1 8.63E-12 1.25E12 2.1 6.26E-13 u2;1s(n,f)Cs137 1.72E-11 3.1 3.32E-13 1.25El2 2.1 2.34E-14 U 235 (n,f)Ru 103 l.72E-11 3.1 8.42E-12 1.25E12 2.1 6.13E-13 U 238 (n,f)Zr 95 l.63E-14 2.7 8.07E-15 2.87E-16 5.6 1.40E-16 u23s(n,f)Cs'31 1.63E-14 2.7 3.14E-16 2.87E-16 5.6 .5.3QE-18 um(n,f)Ru 103 1.63E-14 2.7 7.86E-15 2.87E-16 5.6 1.41E-16.*

Np 237 (n,f)Zr 95 1.14E-13 4.0 5.60E-14 6.21E-15 0.9 3.lOE-15 Np231(n,f)Csm l.14E-13 4.0 2.18E-15 6;21E-15 0.9

• I.15E-16 N p231(n,f)Ru 103 1.14E-13 4.0 5.45E-14 6.21E-15 0.9 3.03E-15 Sc 45 (n,y)Sc 46 8.17E-13 3.2 4.15E-13 5.SOE-14 2.1 2.95E-14 The standard deviations are those given by the Monte Carlo statistics.

. The calculated reaction rates are for the mid-cycle power distribution normalised to 2300MW The activations at the end of the cycle are derived by applying the factors given in Table 9.

The activations at the end of the cycle for the cavity .detectors include the correction factor of

- 0.989 for asymmetry of the assembly power as discussed in section 5.

AEAT-0352 APPENDIXC (AEAT-0468)

Table 1 t - Calculated Uncertainties arising from Cross-Sections Surveillance position Reaction Oxygen Hydrogen Iron Iron Total Total Total (pressure vessel) (inrier steel) uncertainty Ti46(n,p) 0.89 1.38 0.47 5.6 6.29 Fe54(n,p) 0.84 1.63 0.3 4.6 5.23 Fe58(n,y) , 0.68 1.44 0.01 1.1 1.94 Ni58(n,p) 0.83 1.66 0.28 4.6 5.22 Co59(n,y) ... 0.68 1.39 0.01 .1 1.85 Cu63(n,a) 0.92 1.17 0.51 6.1 6.78

• U235(n,fx) *0.68 1.44 0.01 1.1 1.94

• U238(n,fx) 0.73 1.92. 0.25 3.3 4.10 Np237(n,fx) 0.78 1.85 0.11 ,2.79 3.44 Sc4S(n,y)

• 0~'68 1.44 0.01 1.1 1.94

.Cavitl'. pQsithm Reaction Oxygen. Hyd'rogen Iron - *Iron Total Total Total (pressure vessel) {inner steel) uncertainty Ti46(n,p) 0.87 1.21 11.4 5.6 17.07 Fe54(n,p) 0.83 1.43 8.8 .4.8 .13.70 Fe58(n,y) 0.86. . 1.88 . 0.33 3 3.92 Ni58(n,p) 0.8 1.51 . 8.4 4.7 13.21 Co59(n,y) 0.86 J 1.9 0.44 2.9 3.94 Cu63(n,a) 0.9 1.05 12.4 6 18.45 U235(n,fx) 0.84 1.89 0.3 3.1 . 3.98 U238(n,fx) 0.72,, 1.74 6.96 4.4 11.52 Np237(n,fx) 0.77 1.85 2.80 '3.44 4.87 Sc45(n,y) 0.84 1.89 0.29 3.1 3.97

AEAT-0352 APPENDIXC (AEAT-0468)

• Table 12 - Uncertainties Due to the Detector Cross-sections

Response

Surveillance Uncertainty 1 s.d%

Cavity Uncertainty 1 s.d%

Ti46(n,p) 5.3% 5.2%

Fe54(n,p) 4.2% 3.1%

FeSS(n,.y) 5.0% 5.0%

NiSS(n,p) 4.3% 4.1%

Co59(n,y) 1.0% 1.0%

Cu63(n,a) 3.8% 3.6%

U23S(n,fx) 0.2% 0.2%

U238(n,fx) 0.7% 1.0%

Np237(n,fx) 9.9% 9.1%

Sc45(n,y) 3.9% 3.9%

AEAT-0352 APPENDIXC (AEAT-0468)

Table 13 - Correction Factors and Uncertainties Surveillance* position Reason for Uncertainty Described m Uncertainty section:  %

Cross-sections 7.1 see Table 11 Dimensions 7.2 2.5 Radial variation of flux 7.3 3.0 Radial position 7.3 20.0 Coolant density 7.4 6.0 Steel density 7.4 3.0 Source intensity

• 7~6 4.0 Core source data 7.7. 2.9 Fission spectra (High energy reactions only) 7.8 3.5 Detector response function 7.9 see Table 12 Cavity position Reason for Correction/Uncertainty Described in Correction Uncertamty section: factor '%

Correction Core Asymmetry 5 0.989 Uncertainty Cross-sections 7.1 see Table 11 Dimensions 7.2 2.5 Scoring Region 7.2 .10.0 Coolant density * . 7.4 6.0 Steel density* High Energies 7.4 6.o*

Low Energies 3.0 Source intensity 7.6 3.0 Core source data 7.7 2.9 Fission spectra (High energy reactions only) 7.8 4.0 Detector response function 7.9 see Table 12

AEAT-0352 APPENDIXC (AEAT-0468)

Table 14 - Comparison of Calculated and Measured Activations Reaction Measurement Std Calculation Std Dev CIM Std Dev Dev (dps/a) (%) (dps/a) (%) (%)

Surv~illan~~ Position 46 Ti (n,p)Sc

• 46 3.47E-16 10 2.96E-16 23.83 0.85 25.84 54 Fe (n,p)Mn 54 l.50E-15 10 l.50E-15 24.00 '1.00 26.00 Fe 58 (n,y)Fe 59 2.06E-14 12 2.00E-14 22.90 0.97 25.85 Ni 58 (n,p)Co 58 2.58E-15 10 2.59E-15 24.55 1.00 26.51 59 Co (n,y)Co 60 6.92E-14 5 l.78E-13 22.37

• 63 Cu (n,a)Co 60 4.04E-18 10 3.64E-18 23.68 0.90 25.71 U23S(n,f}Zr9S l.59E-12 5 8.63E-12 22.37

• U 23s( n, f)Cs 131 6.22E-14 5 3.32E-13 22.37

• U23s(n,f)Zr9s 9.09E-15 5 8.07E-15 22.89 0.89 23.43 u23s(n,f)Cs131 3.49E-16 5 3.14E-15 22.89 0.90.' 23.43 Np231(n,f)Zr9s 5.84E-14 5 5.60E-14 25.02 0.96 25.51 N p231 (n,f)Cs131. 2.29E-15 5 2.18E-15 25.02 0.95 25.51 Cavity Ti 46 (n,p )Sc 46 3.25E-18 10 3.19E-18 23.22 0.98 25.28 Fe 54 (n,p)Mn 54 l.43E-17 5 1.43E-17 20.34 1.00 20.95 Fe 58 (n,y)Fe 59 1.36E-15 8 l.55E-15 14.70 1.14 ' 16.73

. Ni 58 (n,p)Co 58 2.83E-l 7 10 2.54E-17 20.18 0.90 22.52 Co 59 (n,y)Co 60 l.22E-14 5 l.38E-14 14.17 1.13' 15.02 Cu 63 (n,a)Co 60 -4.02E-20 5 4.22E-20 23.84 1.05 24.36 U23S(n,f}Zr9S 6.03E-13 5 6~26E-13 13.84 1.04 14.71 u23s(n,f)Cs131 2.13E-14 5 2.34E-14 13.84 1.10 14.71 U 235 (n,f)Ru 103 5.97E-13 5 6.13E-13 13.84 1.03 14.71 U 238( n,f)Zr9s 1.48E-16 5 l.40E-16 . 19.47 0.95 20.10 u23s(n,f)Cs131 5.56E-18 5 5.30E-18 19.47 0.95 20.10 u23s(n,f)Ru103 1.50E-16 5 l.41E-16 19.47 0.94' 20.10 Np231(n,f)Zr9s 3.51E-15 5 3.lOE-15 19.13 0.88 19.13 N p231(n,f)(:s131 1.40E-16 5 l.15E-16 19.13 .. 0.82 19.13 Np 231 ( 0 , f) Ru 103 3.62E-15 5 3.03E-15 19.13 0.84 19.13 Sc 45 (n,y)Sc 46 2.83E-14 10 2.95E-14 14.37 1.04 17.51

• The effect of the gadolinium covers fitted to the detectors for these measurements was not included in the calculations and therefore no meaningful values of CIM can be derived.

AEAT-0352 APPENDIXC (AEAT-0468) r --7 100 15°

• 31

' I I

I

/

/

/

I I

, /

~

Notes: Various directions have been used as 0° on H.B.Robinson, the system given here is that throughout this report.

In the calculation the core is assumed to be symmetrical and the 315°

. position is replace by a 45° position.

Figure 1

• Plan View showing Sector Modelled and Measurement Positions

en 0

=-

!. () <

0 8.

~

= ~ 0.

ri o.

AEAT-0352 APPENDIXC (AEAT-0468)

~~) tb\d<n= 0.64 61.34

, affle thickness 2.86 All dimensions in cm Figure 3 - Plan View of the Model showing Dimensions

AEAT-0352 APPENDIXC (AEAT-0468) l',',',',',',',,,,,,,,,',',',',',',',',r'r'#'

~

~

,,,~,,,,,,,,,,,,,,,,,,,,,,,

,' ,' , ' , ' , ' , ' ,' ,' , ' , ' , ' , ' , ' , ' ,' ,' , ' , ' , ' , ' , ' ,' ,' ,~,' ,

,' , ' , ' ,' , ' ,' ,' ,' , ' , ' , ' ,' , ' ,' ,' , ' , ,~, ,,,,,,,,,,,,,,,

,',',';',';',', M aten*ais

'' ~ '

<';';';';<,; A Core (fuel/water) ,;<,;

' ' ' ' ' ' ' lDlll

,,,,,,, II l'!!!!I Carbon Steel ,;,;<

,,,,,,,, i ,,,

',',',',',',', Stainless steel ',,,,',',

'' ~

',',',',',',',' Wt a er ',',','

' ' ' ' ' ' ' ,;, vo*d ' ,,,

,,,,,,, concre I te

~''

' , , , , Th erm 1nsu ai* 1 a** ' a on ,

~, ',', ' , ' , ' , ' , ',', ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' ,,,, ,,

Figure 4 - Side View of the M.odel showing Materials

AEAT-0352 APPENDIXC (AEAT-0468)

• I

~

I

---

-..: II I

222.6:*

I 11 203.9 182.9 **** .; ..,..

I

• • C/L 182.9 **  ;

203.9  :* "

• 234.6,*

I 487.7 I- - - - ~v- -----.. -_:

I---- ---------.

t

• • • • 41.T********t I

Figure 5

• Side View of the Model showing Dimensions

AEAT-0352 APPENDIXC (AEAT-0468)

AREA OF SOURCE FOR WHICH /

......,-,,,,-~D~A~TA~W~A~S~A~V~A~l~LA~B~L~E~-/--

45°

• A inner outer' ,

.  :=::;::::::::::::::::

mncr ou1er

, /

---90°

. , a* s 10 n 12 13 14 -1s--

• • Low burn-up assemblies nearest the.surveillance capsule

• High burn-up assemblies on the flats, nearest the cavity position *

• • Remainder of the core The numbering of assemblies is in the scheme used by Westinghouse Figure 6 - Core Sources Modelled

\

AEAT-0352 APPENDIXC (AEAT-0468)

II MCBEND Scoring Regions 15° dosimetry position 30° dosimetry position

z..---45° dosimetry position

....-***-**---*****-..*':=&a1111111111111111111111111111111111111111il11

\

\

/

\

/

/"

Expanded View of Surveillance Capsule Figure 7

• Scoring Regions Modelled

AEAT-0352 APPENDIXC (AEAT-0468)

Cavity position.

1.2 1.1 t*

-=

1.0 0.9

• inner 0.8

':

• outer 0.6 0 100 200 300 400 500 600 days Surveillance capsule.

1.2

1.1

' --" 1.0 0.9

~

0.8 1:1 inner

....::>

• outer

~ 0.7 0.6 0 100 200 300 400 500 600 days Figure 8 - Power Variation through the 9th cycle for Assemblies adjacent to t Cavity and Surveillance Positions.

AEAT-0352.

APPENDIXC (AEAT-0468)

Low energy reactions 1.1 u.....

CJ 1.0 "Cl '

s

-- Cll 0.9 Cll

.c 0 El Fe58 GI

• Co59 c

0 c.

0.8

• 0 U235

"'...GI Sc45

...0

.s 0.7

=

=:

0.6 0 100 200 300 400 500 600 days High energy reactions 1.1 4i

~

CJ 1.0 s-=

--Cll

- 0.9 Cll

.c El Ti46

~

• Fe54 GI

"'c 0 0.8 0

Ni58

c. Cu63

"'...GI CJ U238 Np237 0

.s

=:

Cll 0.7 0.6 0 100 200 300 400 500 600 days Figure 9 - Variation of Res,onse through the 9th cycle - Cavity Position

AEAT-0352 APPENDIXC (AEAT-0468)

Low energy reactions 1.1

~

~

~

.c, 1.0 i

I ll Ill 0.9

.c e

II m Fe58 c

e c.

0.8

• II Co59

"'...II U235.

...e 0 Sc45.

0.7

~

. OI ci::

0.6 0 100 200 300 400 500 days High energy reactions 1.1

. Gi u....

~

I 1.0 "Cl i

I ll 0.9 Ill

.c e

. II c 0.8 m Ti46 II Fe54 e Ni58

c. 0 Cu63 II

...e

• c U238 0.7 Np237

,g o:i

• ci::

. 0.6 0 100 200 300 400 500 600 days Figure. 10 -Variation of Response through the 9th cycle

• Surveillance Position

AEAT-0352 APPENDIXC (AEAT-0468)

APPENDIX MCBEND9 INPUT DATA

& Case with ENDF-B/VI/IRDF-90 data COLUMNS 1 80 BEGIN CONTROL DATA PROCESS TO STAGE THREE SAMPLE LIMIT 10 DUMP INTERVALS 1

& CHIME 3600 SPLITTING END

& UNIT 2 BEGIN DATASET DEFINITIONS DUMP A 25

& SAVE NUCLEAR DATA 31 END

& UNIT 3 BEGIN OUTPUT CONTROL SUPPRESS INFLOWS END

& UNIT 4 BEGIN MATERIAL GEOMETRY CG

& H..B.ROBINSON PWR, 45 DEGREE SLICE.

& BODIES

& 45 DEGREE SLICE WED 1 0.0 1000.0 -2000.0 0.0 -1000.0 0.0 1000.0 0.0 0.0 0.0 0.0 5000.0

& CORE BAFFLE I:t-;JNER RPP 2 -32.304 32.304 -161.342 161.342 -210.0 210.0 RPP 3 -75.331 75.331 -139.857 139.857 -210.0 210.0 RPP 4 -96.840 96.840 -118.349 118.349 -210.0 210.0

-& CORE BAFFLE OUTER RPP 5 -35.162 35.162 -164.200 164.200 -210.0 210.0 RPP 6 -78.189 78.189 -142.715 142.715 -210.0 210.0 RPP 7 -99.698 99.698 -121.207 121.207 -210.0 210.0

& CORE BARREL INNER RCC 8 0.0 0.0 -276.3 0.0 0.0 724.5 170.023

& CORE BARREL OUTER RCC 9 0.0 0.0 -318.0 0.0 0.0 766.2 175.184

& THERMAL SHIELD INNER RCC 10 -o.O 0.0 -300.0 0.0 0.0 600.0 181.135

• & THERMAL SHIELD OUTER RCC 11 0 . 0 0 . 0 - 2 3 4 .. 6 o. o.*o. o 457.2 187. 960*

& R. P. V. *cLAD INNER RCC 12 0.0 0.0 -400.0 0.0 0.0 1100.0 197.485

& R.P.V. CLAD OUTER (MAIN VESSEL INNER)

RCC 13 0.0 0.0 -400.0 0.0 0.0 1100.0 198.041

AEAT-0352 APPENDIXC (AEAT-0468)

& PRESSURE VESSEL OUTER RCC 14 0.0 0.0 -305.0 0.0 0.0 915.0 221.099

& INSULATION INNER RCC 15 0.0 o.o -400.0 0.0 0.0 700.0 222.964

& INSULATION OUTER RCC 16 0.0 0.0 -385.0 0.0 0.0 615.0 230.584

& SPARE - LEFT FOR BIOLOGICAL SHIELD LINER.

RCC 1 7 3 5 0 . 0 3 5 0 . 0 0 . 0 0 . 0 0 . 0 1 . 0

• 1. 0

& BIOLOGICAL SHIELD INNER RCC 18 0.0 0.0 -730.0 0.0 0.0 3000.0 . 238.760

& 0 DEGREE EXCORE WELL LINER OUTER BOX 19 19.050 319.405 -200.0

-100.0 0.0 0.0 0.0 -100.0 0.0 0.0 0.0 800.0

. & 0 DEGREE EXCORE WELL LINER INNER BOX. 20 18. 415 318. 770 -200. 0

-100.0 0.0 0.0 0.0 -100.0 0.0 0.0 0.0 800.0

& 0 DEGREE EXCORE WELL CHAMFER LINER OUTER BOX 2*1 0.0 264.795 -200.0

-100.0 -100.0 0.0 100.0 -100.0 0.0 0.0 0.0 800.0

& 0 DEGREE EXCORE WELL CHAMFER LINER INNER BOX 22 O.D 263.897 -200.0

-100.0 -100.0 0.0 100.0 -100.0 0.0 0.0 0.0 800.0.

& 45 DEGREE EXCORE WELL LINER OUTER BOX 23 212.383 239.324 -200.0

-100.0 -lbO.O 0.0 100.0 -100.0 0.0 0.0 0.0 800.0

& . 45 DEGREE EXCORE WELL LINER INNER BOX 24 212. 393: 238. 426 ...:200. 0

-100.0 -100.0 0.0 100.0 -100.0 o~o 0.0 0.0 800.0

& 45 DEGREE EXCORE WELL CHAMFER LINER OUTER BOX 25 187.238 187.238. -200.0

-100.0 0.0 0.0 0.0 -100.0 0.0 0.0 0.0 800.0

& 45 DEGREE EXCORE WELL CHAMFER LINER INNER BOX 26 187.238 186.603 -200.0

-100.0 . 0.0 0.0 o.o -ioo.o o.o 0.0 0.0 800.0

& INSTRUMENT CAPSULE IN 0 DEGREE WELL OUTER RCC 27 0.0 252.174 -10.635 0.0 0.0 21.27 9.525

& INSTRUMENT CAPSULE IN 0 DEGREE WELL INNER RCC 28 0.0 252.174 -10.0 0.0 0.0 20.0 8.890

& INSTRUMENT CAPSULE IN 45 DEGREE WELL OUTER

AEAT-0352 APPENDIXC (AEAT-0468)

RCC 29 178.314 178.314 -10.635 0.0 0.0 21.27 9.525

& INSTRUMENT CAPSULE IN 45 DEGREE WELL INNER RCC 30 178.314 178.314 -10.0 0.0 0.0 20.0 8.890

& BIOLOGICAL SHIELD OUTER RCC 31 0.0 0.0 -1100.0 0.0 0.0 1650.0 422.0

& SURROUNDING REFLECTOR RCC 3 2 0 . 0 0 . 0 -115 0 . 0 0 . 0 0 . 0 40 00 . 0 600 . 0 .

& SURROUNDING VOID RCC 33 0.0 0.0 1000.0 0.0 0.0 2000.0 600.0

& TOP CLAD INNER SPH 34 0.0 0.0 579.0 197.485

& TOP VESSEL INNER SPH 35 0.0 0.0 579.0 198.041

& TOP VESSEL OUTER .

SPH 36 0.0 0.0 579.0 218.9

& BOTTOM CLAD INNER SPH 37 0.0 0.0 -285.0 *197.485

& BOTTOM VESSEL INNER .

SPH 38 0.0 0.0 -285.0 198.041

& BOTTOM VESSEL OUTER SPH 39 0.0 0.0 -285.0 216.3

& ACTIVE CORE RCC 40 0.0 0.0 -182.88 0.0 0.0 365.76 169.0

& CORE BAFFLE TOP & BOTTOM PLATES INNER RCC 41 0.0 0.0 -203.9 0.0 0.0 407.8 169.0

& CORE BAFFLE TOP & BOTTOM PLATES OUTER RCC 42 0.0 0.0 -206.8 0.0 0.0 413.6 169.0.

& WEDGES FOR CAVITY SCORING REGIONS

& 0 DEGREES WED 43 -26.132 248.630 -220.98 26.132 -248.630 0.0 52.848 5.555 0.0 0.0 0.0 441.96

& 15 DEGREES WED 44 47.702 245.407 -220.98

-47.702 -245.407 0.0 34.489 -6.704 O;O 0.0 0.0 441.96

& 30 DEGREES WED 45 109.593 224.699 -220.98

-109.593 -224.699 0;0 31.579 -15.402 0.0 0.0 0.0 441.96

&. 45 DEGREES WED 46 157.330 194.286 -220.98

-157.330 -194.286 0.0 41.297 -33.441 0.0 0.0 0.0 . 441.96

& SLABS FOR CAVITY SCORING REGIONS

& CENTRE CAPSULE RPP 47 -250.0 250.0 ~250.0 250.0. -91.0 91.44

& UPPER CAPSULE RPP 48 -250.0 250.0 -250.0 250.0 0.0 121.92

& LOWER CAPSULE RPP 49 *-250.0 250;0 . -250.0 250.0 -121.92 0.0

AEAT-0352 APPENDIXC (AEAT-0468)

& TOP CAPSULE RPP 50 . ~250.0 250.0 -250.0 250.0 205.74 230.0

& BOTTOM CAPSULE RPP 51 -250.0 250.0 -250.0 250.0 -230.0 -205.74

& WIRE RPP 52 -250.0 250.0 -250.0 250.0 144.78 175.26

& WIRE RPP 53 -250.0 250.0 -250.0 250.0 150.0 210.0

& WIRE RPP 54 -250.0 250.0 -250.0 250.0 120.0 150.0

& WIRE RPP 55 -250.0 250.0 -250.0 250.0 -175.26 -144.78

& WIRE RPP 56 -250.0 250.0 -250.0 250.0 -210.0 -150.0

& WIRE RPP 57 -250.0 250.0 -250.0 250.0 -150.0 -120.0

& SuRVEILANCE CAPSULE OUTER BOX 58 61.768 178.478 -31.0 5.638 -2;052 0.0 1.493 4.102 0.0 0.0 0.0 62.0

& SURVEILANCE CAPSULE INNER BOX.59 . 63.095 178.761 -30.48

. 3~47~86 -1.26547 0.0 1.08591 2.98352 0.0 0.0 0.0 60.96 END

& ZONES 1-5 COREl 20 +1 +2 +40 CORE2 20 +1 +3 -2 +40 CORE3 20 +1 +4 -3 +40 NOZZLESl 20 +1 +2 -40 +41 NOZZELS2 20 +1 +3 -:-2 -40 +41

& ZONES 6-10 NOZZELS3 20 +1 +4 -3 -40 +41 AXIALBAFLl 20 +1 +2 -41 +42 AXIALBAFL2 20 +1 +3 -2 -41 +42 AXIALBAFL3 20 +1 +4 -3 -41 +42 BAFFLEl 20 +1 +5 6 +42

& ZONES 11-15

. BAFFLE2 20 *. +1 +6 2 -7 +42 BAFFLE3 20 +1 +7 3 +42 WATERlIN 20 +1 +8 6 -7 +9 +42 WATERlOUT 20 +1 +8 +9 -42 BARREL 20 +1 +9 -8

& ZONES 16.,.20 WATER2 20 +1 +10 -9 +11 THERMAL SH 20 +1 +11 -10 WATER3 20 +1 +12. 9 +14 -58

. WATER3TOP 20. +1 +34 -9 -14 WATER3BOT 20 +1 +37 -9 -14

&. ZONES 21-25 CLAD 20 +1 +13 -12 +14 CLADTOP 20 +1 +35 -34 -14*

CLAD BOT 20 +1 +38 -37 -14

AEAT-0352 APPENDIXC (AEAT-0468)

VESSEL VESSELTOP 20 VESSELBOT 20 VOIDl INSULATION 20 20 ZONES 26-30 20

+1

+1

+1

+1

+1

+14

+36 -35

+39 -38

-13

+15 +16 14

+16 -15

..:.14

-14 CAVITY 30 +1 +18 14 -39 +31 44 -

45 -46 WELLINERO 20 +1 +19 22 +31.

} ZONES 31-35 CHAMFLINO 20 +1 +21 19 -18 +31 WELLO 20 +1 +20 -27 -18 +31 CHAMFERO 20 +l +22 -20 -18 +31 CAPSULEO 20 +l +27 -28 INSTRMNTO 20 +l +28

& ZONES 36-40 WELLINER45 20 +l +23 26 +31 CHAMFLIN45 20 +1 +25 23

-18 +31 WELL45 20 +1 +24 -29 -18 +31 CHAMFER45 20 +l +26 -24  :-18 . +31 CAPSULE45 20 +l +29 -30

& ZONES 41-45 INSTRMNT45 20 +l +30 CONCRETE 20 +l 23 25 -18 +31 BLACK 20 +1 +32 39 14 REFLECTOR 20 +32 -1 CAVOOCENTR 10 +1. +18 -16 +43 +47

& ZONES 46-50 CAVOOTOP 10 +l +18 -16 +43 +50 CAVOOUPPER 10 +l +18 -16 +43 +48 -47 CAVOOLOWER 10 +l +18 -16 +43 +49 -47

• . CAVO 0 BOTTM 10 +l. +18 -16 +43 +51 CAVOOWIREl 10 +1 +18 -16 +43 +53 52

& ZONES 51-55 CAVOOWIRE2 10 +1 +18 -16 +43 +52 CAV00WIRE3 10 +1 +18 -16 +43 . +54 52 CAVOOWIRE4 10 +1 +18 -16 +43 +57 55 CAVOOWIRE5 10 +l +18 -16 +43 +55 CAVOOWIRE6 10 +l +18 -16. +43 +56 55

& ZONES 56-60 CAV15CENTR 10 +l +18 -16 +44 - +47 CAV15TOP 10 +l +18 -16 +44 +50 .*

CAV15UPPER 10 +1 +18 -16 +44 +48 -47 CAV15LOWER 10 +1 +18 -16 +44 +49 -47 CAV15BOTTM 10 +1 +18 -16 +44 +51

& ZONES 61-65 CAV15WIRE1 10 +1 +18 -16 .+44 +53 .,.50 -52 CAV15WIRE2 10_ +1 .-+:18 - -16 +-44 +52 CAV15WIRE3 10 +1 +18 -16 +44 +54 52 CAV15WIRE4 10 +1 +18 -16 +44 +57 55 CAV15WIRE5 10 +l +18 -16 +44 +55

& ZONES 66-70 CAV15WIRE6 10 +l +18 -16 +44 +56 55 CAV30CENTR 10 +1 +18 -16 +45 +47 CAV30TOP 10 +1 +18 -16 +45 +50

AEAT-0352 APPENDIXC (AEAT-0468)

CAV30UPPER 10 +1 +18 -16 +45 +48 -47 CAV30LOWER 10 +1 +18 -16 +45 +49 -47

& ZONES 71-75 CAV30BOTTM 10 +1 +18 -16 +45 +51 CAV30WIRE1 10 +1' +18 -16 +45 +53 52 CAV30WIRE2 10 '+1 +18 -16 +45 +52 CAV30WIRE3 10 +1 +18 -16 +45 +54 52 CAV30WIRE4 10 +1 +18 -16 +45 +57 55

& ZONES 76-80 .,,

CAV30WIRE5 10 +1 +18 -16 +45 +55 *..;.*

CAV30WIRE6 10 +1 +18 -16 +45 ~56 55 CAV45CENTR 10 +1 +.18 -16 +46 +47 CAV45TOP 10 +1 +18 -16 +46 +50 CAV45UPPER 10 +1 +18 -16 +46' +48 '-47

& ZONES 81-85 CAV45LOWER 10 +1 +18 -16 +46 +49 -47 CAV45BOTTM 10 +1 +18 -16 +46 +51 CAV45WIRE1 10 +1 +18 -16 +46 +53 52 CAV45WIRE2 10 +1 +18 -16 +46 +52 CAV45WIRE3 10 +1' +18 -16 +46 +54 ~48 -52

& ZONES 86-90 CAV45WIRE4 10 '+1 +18 -16 +46 +57 55

• CAV45WIRE5 10 +1 +18 -16 +46 ' +55 CAV45WIRE6 10 +1 +18 -16 +46 +56 55 SURvEYINNR 10 +1 +59 SURVEYOUTR 10 +1 +58 -59 END

& REGIONS

& CORE! . CORE2 .. CORE3 NOZZLES! NOZZELS2

& NOZZELS3.

• AXIALBAFLl AXIALBAFL2 AXIALBAFL3 BAFFLE!

& BAFFLE2 BAFFLE3 WATERlIN WATERlOUT BARREL

& WATER2 THERMALSH WATER3 WATER3TOP WATER3BOT

& CLAD. CLADTOP

• CLADBOT 'VESSEL VESSELTOP

& VESSELBOT' VOIDl INSULATION CAVITY WELLINERO

& CHAMFLINO WELLO CHAMFERO CAPSULEO IN$TRMNTO

& WELLINER45 CH.AMFLIN45 WELL45 CHAMFER45 CAPSULE45

& INSTRMNT45 CONCRETE BLACK REFLECTOR CAVOQCENTR

& CAVOOTOP " CAVOOUPPER CAVOOLOWER CAVOOBOTI'M CAVOOWIREl

& CAVOOWIRE2*CAVOOWIRE3 CAVOOWIRE4 CAVOOWIRE5 CAVOOWIRE6

& CAV15CENTR CAV15TOP CAV15UPPER CAV15LOWER CAV15BOTI'M

& CAV15WIRE1 CAV15WIRE2 CAV15WIRE3 CAV15WIRE4 CAV15W~RE5

& CAV15WIRE6 CAV30CENTR CAV30TOP CAV30UPPER CAV30LOWER

& CAV30BOTTM CAV30WIRE1 CAV30WIRE2 CAV30WIRE3 CAV30WIRE4

& CAV30WIRE5 CAV30WIRE6 CAV45CENTR CAV45TOP CAV45UPPER

& CAV45LOWER CAV45BOTTM CAV45WIRE1 CAV45WIRE2 CAV45WIRE3

& CAV45WIRE4 CAV45WIRE5 CAV45WIRE6 SURVEYINNR SURVEYOUTR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 so:

51 52 53 54 55 56 57 58 59 60

AEAT-0352 APPENDIXC (AEAT-0468) 61 62 63 64 65 71 72 73 74 75 81 82 83 84 -as-MATERIALS 1 1 1 2 2 2 2 3 3 2 2 2 2 4 4 66 67 68 69 70 76 77 78 79 80 86 87 88 89 90 2

3 4

2 2

0 2

3 5

2 3

0 2

3 4

4 0 0 2 0 4 4 0 0 2 0 6 -2000 -3000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4

& VOLUMES 1.0 1.0 1.0 1.0 1. 0 1.0 1.0 1.0 1.0 1. 0 1.0 1.0 1.0 1.0 1. 0 1.0 1.0 1.0 1.0 1. 0 1.0 1.0 1.0 1. 0 1.0

.1. 0 1. 0 1. 0 1.0 1.0

1. 0 1. 0 1.0 1. 0 4965.73

1. 0 1. 0 1. 0 1. 0 1. 0 4965.73 1. 0 1. 0 1.0 36744.89 3062.07- 6124.15 6124.15 3062.07 6124.15 6124.15 4593.11 4593.11 6124.15 6124.15 48993.19 4082.77 8165.53 8165.53 4082.77 8165.53 8165.53 6124 .. 15 6124.15 8165.53 8165.53 48993.19 4082.77 8165.53 8165.53 4082.77 .8165.53 8165. 53 . 6124.15 6124.15 8165.53 8165.53 36744.89 3062.07 6124.15 6124.15 3062.07 6124.15 6124.15 4593.11 4593.11 6124.15 6124.15 716.128 1623.780 END

& UNIT 5 BEGIN SPLITTING GEOMETRY

.x 17 O.OOOOOOOE+OO 19.353 36.556 49.458 62.360 75.262 83.864 92.465 0.1023478E+03 0.1076878E+03 0.1156978E+03 0.1256977E+03 0.1398176E+03 0.1562976E+03 0.1787776E+03 0.1987776E+03 0.2187775E+03 0.42500E+03 y 31 O.OOOOOOOE+OO 19.353 27.955 . 40.857 49.458 58.os9-- *

• 70.961 79.563 o.8999988E+o2 0.9999986E+02 109.668 118.269 0.1258668E+03 135.472 0.1427047E+03 0.1473647E+03 156.975 0.1642027E+03 0.1692127E+03 0.1742227E+03

AEAT-0352 APPENDIXC (AEAT-0468) .

0.1802226E+03 0.1871226E+03 ~.1928226E+03 0.2025325E+03 0.2163224E+03 0.2358624E+03 0.2458624E+03 0.2633623E+03 0.2808621E+03 0.2983618E+03 0.3208613E+03 0.42500E+03 z 14

-1000.0 -280.0 -220.0 -200.0 -182.878

-146.956 -80.0 -20.0 20.0 80.0 146.956 182.878 200.0 260.0 2850.0 END

& UNIT 6 BEGIN SOURCE GEOMETRY x 23 0.000 2.150 6.451 10.752 15.052 19.353 23.654 27.955 32.255 36.556 "40.857 45.157 49.458 53.759 58.059 62.360 66.661 70.961 75.262 79.563 83.864 88.164 92.465 96.766 y 38 0.000 2.156' 6.451 10.752 15.052 19.353 23.654 27.955 32;255 36.556 40.857 45.157 49.458 53.759 58.059 . 62 .360 66.661 70.961 75.262 79.563 83.864 88.164 92.465 96.766 101.066 105.367 109.668 113.968 118.269 122.570 126.870 131.171 135.472 139.773 144.073 148.374 152.675 156.975 161.277 z 19

-182.878 -166.550 -146.956 -127.362 -:107.768

-88.174 .-68. 580 -48.985 -29.391 -9.796 9.796 29.390 48.984 68.580 88.174 107.768 127.362 146.956 166.550 182.878 END

& UNIT 7 BEGIN ENERGY DATA NEUTRON SPLITTING GROUPS 15 14.6 13.5 12.5 11.25 10.0 8.5 7.0 6.07 4.72 3.68 2.87 1.74 0-6 0.39 0.11 6.74E-02 SCORING GROUPS 4 14.6 5.0 1.0 0.5 6.74E-02 THERMAL TREATMENT NONE SIMPLE SOURCE FISSION WEIGHTING AUTOMATIC SPECTRUM LIMITS 14.6 6.74E-02 END

& UNITS BEGIN IMPORTANCE MAP DIMENSIONS 17 31 14 15 1 CALCULATE TARGETS 1 ZONES 45 STRENGTHS 1.0 USE METHOD D

AEAT-0352 APPENDIXC (AEAT-0468)

DOMINANT MATERIAL END

& UNIT 9 BEGIN SCORING DATA MESH SYSTEM CG DIMENSIONS 90 1 1 MATERIAL MESH TRACK LENGTH FLUX SOME 1 35 41 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 RESPONSES DITTO SENSITIVITY OF RESPONSES SOME 1 45

& CONTRIBUTIONS TO RESPONSES DITTO END

& UNIT 14 BEGIN MATERIAL DATA

& MATERIALS FOR H.B.ROBINSON PWR (FROM WESTINGHOUSE/CPL DOT MODEL)

& K REMOVED FROM CONCRETE MINNIE MIXTURES 5 WEIGHT

& CORE REGION M1 U235 0.20647E-01 U238 0.62565 016 0.180760 H 0.11840E-01 BlO 0.65507E-04 FE54 1.32525E-04 FE56 2.13598E-03 FE57 4.9755E-05 FE58 6.74250E-06 MN 0.42278E-04 CR50 5.2033E-05 CR52 l.04441E-03 CR53 i.20662E-04 CR54 3.05711E-05 NI58 1.98361E-03 NI60 7.90492E-04 NI61 3.48312E-05 NI62 l.13054E-04 NI64 2.98312E-05

AEAT-0352 APPENDIXC (AEAT-0468)

ZR 0.1S447 M 2

& WATER H 0.11191 016 O.SS799 BlO 0.99S29E-04 M3

& STAINLESS STEEL SST304 FES4 3.933E-02 FES6 6.339E-01 FES7 1.4766E-02 FESS 2~001E-03

.MN 0*.1999SE-01 CRSO 7.923E-03 CRS2 1.S903E-01 CRS3 1. S373E-02 CRS4 4. 6SSE""'.03 NISS 6 .. 72067E-02 NI60 l.67S27E-02 NI61 1.1S012E-03 NI62 3.S303SE-03 NI64 1.0lOlE-03 M4

& CARBON STEEL AS33B C 0.24999E-02 MN 0.12996E-01 FES4 S.SS030E~02 FES6 S.99407E-01 FES7 2.09S06E.:.02 FESS 2.S391QE-03.

NISS 3.69640E-03

• NI60 1.47306E-03 NI61 6.49071E-OS NI62"2.10673E-04

. NI64 S.SS5561E~os M5

• & CONCRETE .

& POTASSIUM (K) REMOVED TO SAVE SPACE

& (ELIMINATED BY DISTRIBUTING ITS.FRACTION AMONGST THE OTHER.

& ELEMENTS)

H O.S0903E-02 C O.i01S3E-02 016 Q.S11S9 NA 0.162SSE-01 MG 0.22130E-02 AL 0.34530E-0],

• SI 0.346230 CA 0.442S6E-01 FE54 2.19364E-03.

FE56 3.53S62E-02 FES7 S.23S79E-04 FESS 1.111607E-04 MATERIALS 6 .

& CORE REGION #100

AEAT-0352 APPENDIXC (AEAT-0468) 1 Ml 4.2632 1.0

& EXCORE STAINLESS STEEL #200 2 M3 S*. 03 1. 0

& EXCORE WATER #300 3 M2 0.7SS6 1.0

& EXCORE CARBON STEEL #400 4 M4 7.S3 1.0

& INSULATION #SOO S M3 0.241 1. 0

& CONCRETE #600

• 6 MS 2.20 1.0 USE MOULD 2S FOR H IN ALL MATERIALS USE ADCN 0 FOR 016 IN ALL MATERIALS USE ADCN FE FOR FES4 IN ALL MATERIALS USE ADCN FE FOR FES4 IN ALL MATERIALS USE ADCN FE FOR FES6 IN ALL MATERIALS USE ADCN FE FOR FES7 IN ALL MATERIALS USE ADCN FE FOR FESS IN ALL MATERIALS USE ADCN CR FOR CRSO IN ALL MATERIALS USE ADCN CR FOR CRS2 IN ALL MATERIALS USE ADCN CR FOR CRS3 IN ALL MATERIALS USE ADCN CR FOR CRS4 IN ALL MATERIALS USE ADCN NI FOR NISS IN ALL MATERIALS USE .ADCN NI FOR NI60 IN ALL MATERIALS

• USE.ADCN NI FOR NI61 IN ALL MATERIALS USE ADCN NI FOR NI62 IN ALL MATERIALS

, USE ADCN NI FOR NI64 IN ALL MATERIALS END

&

• UNIT . lS.

BEGIN *soURCE STRENGTH

& SOURCES SUPPLIED BY D. MAERKER DIMENSIONS 23 3S 19 1 1 SEPARABLE COMPONENT X Y 1~8S7SOE+lS l.88139E+1S 2 .12459E+15 2.37558E+15 2.18132E+15 2*; 191SOE+lS 2. 2S963E+1S 2.55529E+l5 2.13517E+15 1.90959E+15

1. 91846E+1S L 992S4E+1S 2.34192E+l5 2.S9716E+15 2.56099E+15 2.66330E+1S 2.SS761E+lS 2.96464E+15 2.29931E+15 2.03235E+ls*

1.99446E+1S 2.0089SE+1S 2.25052E+15 1.8S080E+15 1.90694E+15 1.89072E+lS 2.10078E+15 2.212S9E+lS 2.21689E+15 2.29723E+15 2.26076E+15 1.S9395E+15 1.92714E+15 l.93628E+l5 2.01383E+15 2.07804E+15 2.41S92E+15 2.735SOE+15 2.57229E+15 2.76605E+15 2.47693E+lS 2.03423E+15 2.05723E+l5 2.02042E+15 2.04177E+15 2.00659E+15 2.12126E+15 1.SSS25E+l5 1.88011E+15 2.05201E+15 2~12606E+15 2.44136E+15 2.19677E+15 2.19313E+15 1.8674SE+15 1.89719E+15 2.16866E+15 1.97721E+15 2.03743E+15 2.43409E+15 2.428SOE+15 2.92103E+1S 2.45714E+l5 2.49493E+l~ 1.99295E+1S 2 .-Ol611-E+l5 2. 27100E+15 2.01755E+l5 1.99771E+15 2.2970aE+15 2.03142E+15 1.984SOE+15 i.96723E+15 l.98269E+15 2.21871E+15 l.96008E+1S 1.92234E+15 2.00792E+lS 2.06227E+lS 2.36S73E+1S 2.1443SE+15 2.1S896E+1S 1.94055E+l5 l.97772E+15 2.24105E+15 2.00488E+lS l.99605E+15 2.19172E+lS 2.26078E+1S 2.58870E+15 2.31764E+lS 2.290SOE+15 2.10804E+l5 2.13866E+lS 2.05478E+1S 1.97S06E+l5 1.9S432E+15 1. 93526E+15 1.94361E+15 1.89828E+15

AEAT-0352 APPENDIXC (AEAT-0468) 2.04912E+15 2.14069E+15 2.14762E+15 2.23388E+15.2.23686E+l5 1.93603E+15 l.97294E+1S l.96470E+15 2.00535E+15 2.00148E+l5 2.23928E+15 2.36856E+15 2.37722E+15 2.46188E+15 2.40061E+15 2.11674E+15 2.14119E+15 2.35769E+15 2.20555E+15 l.92787E+15 1.88052E+15 1.88362E+15 2.09930E+15 2.31301E+l5 2.11460E+15 2.12814E+15 2.20369E+15 2.51704E+15 2.16238E+15 1.93523E+15 1.92892E+l5 l.97181E+15 2.24714E+15 2.54391E+15 2.35716E+15 2.37854E+15 2.45715E+15 2.75682E+15 2.18149E+15 2.21761E+15

.2~11983E+15 l.94200E+15 1.92692E+15 1.87620E+15 1.87833E+15 1.83925E+15 2.04493E+15 2.14569E+15 2.15653E+15 2.24491E+15 2.23001E+15 1.91276E+15 1.94886E+15 1.94439E+15 l.99410E+15

• 2.00288E+15 2.26783E+15 2.42522E+15 2~44181E+15 2.53903E+l5 2.46806E+15 2.46584E+15 2.18133E+15 2.11528E+15 1.89671E+15 1.87339E+15 2.08275E+15 1.83253E+15 1.80360E+15 1.99956E+15 2.06854E+15 2.38284E+15 2.15809E+15 2.17005E+15 1.88661E+15 1.91968E+15 2.18279E+15 1.97069E+15 1.99355E+15 2.2~030E+15 2.37208E+15 2.73378E+15 2.45867E+15 2.41465E+15 2.06892E+15 1.83515E+15 1.80939E+15 2.no267E+15 2.04468E+l5 2.30915E+15

2. 04279E+15 1. 99871E+15, 1. 80076E+15 1. 84079E+15 2 ..10553E+15 1.90582E+15 1.92713E+l5 2.11870E+15 2.14526E+15 2*;41573E+15 2.14776E+15 2.12016E+15 2.11182E+15 2.14553E+t5 2.41712~+15 2.14966E+15 2.11448E+l5 1.84986E+15 1.86683E+15 1.83815E+15

2. 05727E+15 2 .13592E+15 2 .11047E+15 2 .14228E+l5 2 .. 06?47E+15 1.83413E+l5 1.88149E+l5 1.88683E+15 1.94602E+15.1.95797E+15 2.13044E+l5 2.20077E+15 2.16594E+15 2;2Q686E+15 2.1488~E+15

~.10810E+l5 2.13543E+l5 2.10112E+15 2.12683E+15 2*.08932E+l5 1.85827E+15 1.81558E+l5 2.10115E+15 2.36070E+15 2.14325E+15 2.12398E+15 2.15249E+l5 2.37913E+152.08927E+151.87955E+15:

1.88121E+15 1.93334E+15 2.21170E+15 2.37778E+15 2~14610E+i5 2.12271E+15 2.15702E+l5 2.40514E+15 2.3j626E+15 ~.06770E+15 2._03957E+l5 2.06486E+l5 2.32225E+15 1.92972E+l5 1.95037E+15 1.91574E+l5 2.14040E+15 2.22980E+15 2.19951E+15 2.24036E+15 ..

2.15380E+15 1.88143E+l5 1.92957E+15 1.92593E+l~ 1.97941E+15.

1.97409E+l5 2.08365E+15 2.15590E+15 2.12947E+l5 2.17103E+15

2. ll:i19E+l5 2. 04710E+15 2. 06094E+15

• 2. 03363E+ls* 2. 06~41E+15.

2-.04345E+15 2.26898E+l5 ~.Oi370E+15 1~97500E+15-~.18554E+15.

2.23324E+l5 2.51254E+15 2.22534E+15 2.16485E+l5 ~.90239E+15 1.94017E+l5 2~19B21E+15 1.96905E+l5 1.95699E+l5 2.02571E+15 2;06949E+l5 ~.34408E+l5 2.08945E+15 2.06265E+15 1.99589~+15 1.99968E+15 2.25558E+15 2.01396E+15 2.00700E+l5 2.87737E+15 2.40209E+15 2.41734E+15 1.93445E+15 1 .. 92957E+15 2~15450E+15 1.90493E+l5 1.87795E+l5 2.02969E+l5 2.04090E+l5 2.2?852E+15 1.99770E+l5 1.94364E+l5 1.81711E+15 1.84890E+15 2:11272E+15 1.91623E+l5 1.95402E+l5 2.09899E+15 2.16768E+l5' 2.47805E+15 2.22447E+l5 2.20695E+l5 2.54530E+15 2.71891E+l5 2.41352E+15 1.97244E+l5 l.96708E+15 1.92873E+15 1.94136E+15 1.91132E+15 2.05584E+15 2.10843E+15 2 .. 05557E+15 2.06472E+l5 1.98226E+15 l..83627E+l5 1.87568E+l5 1.88662E+15 1.95400E+l5 1.99202E+15 2.14992E+15 2.25161E+l5 2.24643E+15 2.30807E+15 2.25806E+15 i.6488BE+15 2.55847E+l5 2.90471E+15 2.23629E+l5 l.95971E+15 1.92313E+l5 1.93751E+15 2.17381E+15 2.31541E+l5 2~07481~+15 2.03212E+15 2.03713E+l5 2.24129E+15 2.07198E+l5 1.86161E+15 1.87369E+l5 1.94011E+15 2.25487E+15 2.44798E+l5 2.23804E+15 2.23577E+l5 2*.28660E+l5 2.55542E+15 2.57606E+15 2:75306E+15 2.44566E+l5 2.00194E+15 2.00131E+15 1.96670E+15 l.98765E+15

AEAT-0352 APPENDIXC (AEAT-0468) l.96298E+l5 2.05899E+l5 2.11392E+l5 2.06416E+l5 2.07506E+l5 l.99538E+l5 l.85157E+l5 l.89324E+l5 l.90743E+l5 l.98155E+l5 2;02789E+l5 2.19302E+l5 2 .. 29607E+l5 2.28508E+l5 2.33957E+l5 2.27123E+l5 2.95349E+l5 2.46829E+l5 2.48489E+l5 l.99447E+l5 l.99875E+l5 2.24247E+l5 l.99721E+l5 l.98633E+15 2.03306E+15 2.05858E+15 2.30137E+15 2.02006E+15 1.96950E+15 1.84575E+15 1.88258E+15 2.15876E+15 1.96992E+l5 2.02465E+15 2.18432E+15 2.25446E+15 2.56502E+15 2.27922E+15 2.24074E+15 2.28917E+15 2.02491E+15 1.98306E+15 2.13803E+15 2.18320E+l5 2.47856E+15 2.20785E+15 2.19879E+15 2.01833E+l5 2.01301E+15 2.22880E+l5 1.95075E+15 l.90b30E+15 2.06767E+15 2.11892E+15 2.41503E+15 2.16730E+15 2 .16113E+15 2.53719E+15 2.50050E+15 2.96881E+15 2.44589E+15 2.45418E+15 2.02565E+l5 2.05010E+15 2.00822E+15 2.20753E+15 2.31105E+15 2.29823E+15 2.36253E+15 2.30871E+15 2.Ci5121E+15 2.03975E+15 1.97376E+15 1.96565E+15 1.90587E+15

• 2.13601E+15 2.21899E+15 2.20718E+15 2.26712E+15 2.22879E+15 2*. 49865E+15 2.76881E+15 2.52171E+15 2. 664 63E+15 . 2.31023E+15 1.99060E+15 2.01612E+15 2.26497E+15 2.53073E+15 2.32177E+l5 2.32093E+15 2.38041E+15 2.66257E+15 2.31215E+15 2.00827E+l5 1.94836E+15 1.94161E+15 2.15269E+15 2.44542E+15 2.21695E+l5 2.20731E+15 2.25756E+15 2.53609E+15'2.96622E+15 2.52079E+l5 2.54315E+15 2.35419E+15 2.63186E+15 2.00871E+l5 2.04095E+15 2.01541E+15 2.26921E+15 2.40710E+15 2.39968E+15 2.47694E+15  ;

2,39628E+15 2.05748E+15 2.03410E+15 1.97398E+15 1.97178E.tl5 l.92431E+15 2.19771E+15 2.28037E+l5 2.25955E+15 2.~1288E+l5 2.25418E+15 2.44349E+15 2.66327E+l5 2.35367E+15 2.42038E+15 F 1.97774E+15 2.25553E+15 2.01035E+15 1.99933E+15 2.24697Ei-15 ---..

2.35058E+15 2.69512E+15 2.40978E+15 2.35519E+l5 2.02551E+15 2.00011E+15 2.22196E+15 1.95463E+15 1.91951E+15 2.l8218E+15 2.23265E+15 2.52689E+15 2.24634E+15 2.21666E+15 2°.45218E+15 2.30888E+15 2.63101E+15 1.97746E+15 1.81094E+15 2.05650E+15 l.83193E+15 1.82550E+15 2.06762E+15 2.11503E+15 2.39285E+15 .',,.

2.13022E+15 2.09459E+15 2.22134E+15 2.27320E+15 2. 5'77 85E+15 ,;

2.29576E+15 2.29517E+15 2.23515E+15 2.29191E+l5 2.59071E+15 !t 2.29672E+15 2.27129E+15 2.36241E+15 2.33586E+l5 2.45375E+l5 '"t 1.93487E+15 1.48011E+15 1.83203E+15 1.85659E+15 1.83500E+15 2.05217E+15 2.09871E+15 2.07373E+15 2.10736E+15 2.. 06907E+l5

• 2.29353E+15 2.39904E+15 2.37800E+15 2.44154E+l5 2.39169E+15 2.28936E+15 2.36153E+15 2.30686E+15 2.33783E+15 2.25311E+l5 2.31572E+15 2.29661E+15 2.04088E+15 1.83314E+l5 1.31289E+15 1.81469E+15 1.83615E+15 2.06241E+15 2.27064E+15 2.02344E+l5 2.00202E+15 2.03119E+15 2.28391E+15 2.62053E+15.1.39611E+15 2.38418E+15 2.43692E+15 2. 72201E+15. 2. 57645E+15 2. 29497E+l5 2.22889E+15 *2.22172E+15 2.41488E+15 2.41408E+15 2.02638E+l5 1.78396E+15 1.55734E+15 1.27412E+15 1.84764E+15 1.87234E+l5 1.84504E+15 1.99621E+15 2.01463E+15 1.98692E+l5. 2.01550E+l5 1.99108E+15 2.34299E+15 2.47120E+15 2.44395E+1S*2.50320E+l5 2.40144E+15 2.25728E+15 2.~9873E+15 2.19821E+15. 2.16170E+15 1.97280E+15 L 89750E+15* 1. a*oaOSE+15 1. 54737E+15 1. 31258E+l5 8.79700E+l.4 2.09742E+15 1. 86.781E+15. 1. 860l6E+lS* 1. 96234E+15 1.95155E+15 2.18902E+15 1.94455E+15 1.93347E+15. 2.31981E+l5 2.39973E+15 2.71671E+15 2.39418E+15 2.30259E+l5 2.19362E+l5 2.17730E+15 2.34999E+15 l.94086E+15 1.68848E+15 1.43561E+l5 l.28548E+15 1.25771E+15 8.74314E+14 6.00154E+14 2.81540E+15 2.49486E+15 2.41760E+15 2.43192E+15 2.47949E+15 2.80133E+l5

AEAT-0352 APPENDIXC.

(AEAT-0468) 2.47358E+15 2.42566E+15 2:42997E+15 2.49799E+15 2.78813E+l5 2.43958E+15 2.31749E+15 2.20485E+15 2.16255E+15 2.26899E+15 1.80696E+15 1.38766E+15 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 2.33780E+15 2.57229E+l5 2.46056E+15 2.45426E+l5 2.38044E+15 2.27652E+15 2.34346E+15 2.38160E+15 2.37786E+15 2.44615E+15 2.18221E+15 2.35621E+15 2.20715E+15 2.09461E+15 2.06958E+15 1.84608E+15 1.67231E+15 1.20803E+l5 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO Q.OOOOOE+OO 2.32071E+15 2.22201E+15 2.64458E+l5 2.63718E+15 2.15431E+l5 2.22128E+l5 2.08641E+l5 2.48076E+l5 2.4j369E+15 1A97759E+l5 2.01873E+15 1.87216E+15 2.18824E+l5 2.06787E+15 1.75291E+15 1.56273E+15 l.38155E+15 1.14262E+l5 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 2.04126E+15 2.26724E+15 2.15178E+15 2.11566E+15 2.01127E+15 1.89527E+15 1.90798E+15 1.90105E+15 1.85646E+15 1.87017E+15 1.60525E+15 l.73611E+15 1.59664E+15 1.49920E+15 1.47745E+l5 1.30031E+15 1.12600E+15 7.65956E+14.0.00000E+OO O.OOOOOE+OO O,OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 2.17929E+15 1.91746E+l~ 1.83652E+15 1.81279E+15.

1.79548E+15 1.98607E+15 1.65008E+15 1.50166E+15 1.33724E+15 1.30439E+15 1.42371£+15 l.18462E+15 1.09333£+15 1:01743E+15 9.72363£+14 9.97015E+14 7.16569£+14 5.03903E+14 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 1.55237E+15 1.38231£+15 1.34983E+15 1.25601£+15 1.21531E+15.1~28468E+15 1.06816£+15 .8.87599E+14 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+Ob O.OOOOOE+OO O.OOOObE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 1.13670£+15 1.14918E+15 1.11685E+15 1.02031E+15 9.72470E+14 8.92220E+14 8.19297E+14 6.~3382E+14 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO

9. 09864£+14 9.. 12571E+14 9. 99514E+l4 8 .* 91565E+1'4 7. 46038E+14 6.81278E+l4 6.10016£+14 5.40626£+14 O.OOOOOE+OO O~OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 0.00000E+OO o*.oooooE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 7 .. 15587E+14 7.11571E+14 6.74228£+14 5.90156E+14 5.59258E+l4 5;08441E+l4 4.40363£+14

3. 29725£+14 0. OOOOOE+OO 0. OOOOOE+OO 0. OOOOOE+OO 0. OOOOOE+OO * *

0. OOOOOE+OO 0. OOOOOE+OO O*. OOOOOE+OO 0. OOOOOE+OO 0. OOOOOE.+00 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 5.40465£+14 4.64012E+l4 4.45617E+14 3.81856£+14 3.55271£+14 3.67085E+14 2 .. 71727E+l4 2.07674£+14 O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO 0.00000E+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO O.OOOOOE+OO COMPONENT Z 1.20051£-03 2.01117E-03 2.54674E-03 2.79905E-03 2.87465E~03 2.85916£-03 2.94752E-03 2.96756£-03 2.92117E-03 2.98851E-03 3.03041E-03 3.02768£-03 2.98669£-03 3.06593£-03 3.0964~E-03 2.96756E-03 2.88740E-03 2.54128E-03 1.69874E-03

&FISSION FRACTIONS PLUTONIUM FRACTION .*.

&ROW H 69*0.412

AEAT-0352 APPENDIXC (AEAT-0468)

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW .B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0*.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 ~ :1 8*0.412 5*0.195 5*0.150 5*0.0 ..

'\'*

8*0.412 5*0.195 5*0.150 5*0.0 ,\

&ROW A 3*0.521 5*0.617 15*0.0  :,.

3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 .i

&ROW H 69*0.412

'ti

&ROW G to C .f!

115*0.412 115*0.412 115*0.412 115*0.412 115*0 :412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

'8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 .5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

AEAT-0352 APPENDIXC (AEAT-0468) 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521* 5*0;617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412* 115*0.412.

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.b 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0.

3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0*. 0

&ROW H 69*0.412

&ROWG to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5'*0. 0

'8*0. 412 5*0.195 5*0.150 5*0.0 8*0~412 5*0.195 5*0.150 5*0.0 8*0 ..412 5*_0 .195; 5*0 .150 5*0;0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617* 15*0.0

'3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 *~ i.

&ROW H 69*0.412'

&ROW G to C 115*0.412 115*0.412 115*0 .4'12 115*0 .. 412 115*0.412 ..

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.19? 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

AEAT-0352 APPENDIXC (AEAT-0468)

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A

• 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to c*

115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0'.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

. &ROW -H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

AEAT-0352 APPENDIXC (AEAT-0468) 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

.3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B ,,

8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0 .*O 3*0.521 5*0.617 15*0.0 ..*,

Ill 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

- 3*0 .-521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0

&ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B

AEAT-0352 APPENDIXC (AEAT-0468)

&ROW A 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 "5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0 .. 617 15*0.0 3*0.521 5*0 .. 617 15*0.0

• &ROW H 69*0.412

&ROW G to C 115*0.412 115*0.412 115*0.412 115*0.412 115*0.412

&ROW B 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0.412 5*0.195 5*0.150 5*0.0 8*0 .. 412 5*0.195 5*0.150 5*0.0 8*0.412 5*0 .. 195 5*0.150 5*0.0

&ROW A 3*0.521 5*0.617 15*0.0

• 3*0.521 5*' 617 15*0.0 3*0.521 5* 617 15*0.0 3*0.521 5*0.617 15*0.0 3*0.521 5*0.617 15*0.p END

& UNIT 10 BEGIN RESPONSE DATA '.,

& INSERT IRDF-90 DOSIMETRY CROSS-SECTIONS HERE END

& UNIT 11 BEGIN SENSITIVITY DATA COMBINATIONS 6 2631 2 EXC 1*2 2631 2 INC 1 2 2631 4 EXC 1 2 2631 4 INC 1 2 1250296 3 TOTAL 825 3 TOTAL GROUPS 15 14.6 10.0 6.06531 3.67879 2.23130 1.35335 0.82085 0.49787 0.30197 0.18316 0.11109 0.06738 0.04087 0.02480 0.01503 0.00912 END

AEAT-0352 APPENDIXD FEW-CHANNEL UNFOLDING IN SHIELDING-THE SENSAK CODE*

A K McCRACKEN Radiation Physics & Shielding Group, Atomic Energy Establishment. Atomic Energy Authority, Winfrith, Dorchester, Dorset, Un.ited Kingdom.

1 INTRODUCTION

. Information available for the unfolding of flux spectra from detector counting-rates

.; will usually include some knowledge (albeit sometimes imprecise) of the.nature of the spectrum sought. In the case of a Standard Field this knowledge may be of very high quality~ In reactor work - and particularly in shielding - we shall usually have some calculation which, even using the best available methods, may be subject to quite large

• uncertain ties.

An experienced worker will be able to give an estimate of this uncertainty - which is worth more than an uninformed guess.(Comparison of calculated and measured counting rates of detectorswhich span different energy ranges will in itself give a rough idea of the Qncertainties in the calculated spectrum). The introduction of correlations between group fluxes in these difficult situationsmight seem unjustified but we do have, the knowledge that calculated spectral shapes are roughly correct locally in energy and mutilation of these shapes during unfolding can be inhibited by the introduction of positive correlation*

coefficients of, say, 0.5 and 0.25 between first and second group flux neighbours. Although

'*: arbitrary, this is more sensible than treating calculated fluxes as independent.

. Some tests with a prototype code SENSAK I using the above type of spectral information were.carried out using numerical minimisation subroutines to derive unfolding spectra, and work on the estimation of uncertainties on the output spectrum by introducing Monte Carlo sampling of the probapility density functions (p. d. f s) of the measured parameters was initiated .. This approach which is obligatory in many-channel unfolding,

• Paper presented at the Third ASTM-EURATOM Symposium on Reactor Dosimetry held at Ispra, Italy in 1979.

01

AEAT-0352 APPENDIXD is, however, considerably less efficient for few-channel unfolding than the purely algeo method of Perey (1) employed in STAYSL. SENS AK II seeks to solve the same problem as SENSAK I with the efficiency inherent in the latter approach.

The speed and directness of this method have obvious appeal. Disadvantages are:-

. (i) With strong long-range correlations in the parameter covariance matrix (and with many detector results) the inversion of an ill-conditioned matrix may arise.

(ii) The linear methods adopted are unsuitable without modification for dealing with large perturbations in an unfolding.

The latter implies some step-length limitation by scaling together w.ith iteration. Only further experience with practical problems will show whether such a modification method is preferable to the method of 'black-box' minimisation with Monte Carlo sampling, 2 METHOD

'Jlle caiculation of the satur~ion counting-rate C; of the ith detector'. in' a ~eactor irradiation experiI;nent can be expressed by

• C; =Sf; L X;/Pi =L X;j<Pj *,

j j where S is a source-strength is the efficiency of the counting system to radiation from the i1h dete*ctor

• is the reaction cross-section of detector i to f).ux i11' ,' '

~ro'up j, is the calculated flux in group j per unit source s!fength. *

' The form of equation 1 recognises two things:-

(i) We me.asure counting-rates - not reaction-rates*

(ii) We are normally given a fission-source per unit power to start a calculation; estimation of the power leads to uncertainty in the source strength S.

To each of the variables* S LX.JJL is ascribed a variance-covariance matrix V and it is presu'med that the above variates are mutually independent.

D2

AEAT-0352 APPENDIXD From equation 1 we find I

8C. = Jjf~ x .. AA..

~ llVOf"I

+/;~

I~

-& ll'f'I

.. 11.. [Sf;

+ -f; +OS] -

s C. I 2

I . . I which can be written 3

where f_is the vector of parameters to be adjusted in the unfolding.

The form of Gof_ (illustrated for two detectors) is Sq,

!if 0 XT qJ 0 0!1

(

ft!1T -1 ft!i <P.

0!2 4 f2!i 0 J; <P.~ 0 XT qJ

-2_ h!i <P. of OS s

N otin~ that (o<;.8<;.r)= Ve where ( ). denotes the expectation, the dispersion matrix of C..is found in terms of that off_ to be where VP has the form (for two detectors)

~I vp = 6 This form of VP - shows the cross-sec-tions -o(different detectors as independent -if information to the contrary is available the individual matrices Vxi . can be replaced by a single matrix Vx. V, is simply a 2 (S)/S 2 and v, will be taken as diagonal if correlations within a counting system are ignored or unknown.

03

AEAT-0352 APPENDIXD Maximum likelihood agreement between calculation C.,and measurement .M.can no sought by choosing of_and hence oC.,such that z2 = (£'.-M +8£fV;1(f-M +8£'.)+8fTV~ 8f 1

=a minimum 7 where v;' the inverse dispersion of matrix of M.is diagonal.

Setting the derivative w.r. t BC.of equation 7 equal to zero gives 8

and :.

Writing f =f.+8f. we find (E. P.T) =VP= Vp- VpGT(Vc + VM r 1 GVJ 10 for the dispersion matrix of the adjusted variables £.:whose first components are the unfolded group fluxes. Equations 7 and 8 give for the minim.um value o( X2  :~;. .

and if C..is an unbiassed estimator of M.

(z!LN) =NM the number of independent measurements. 12 Thus f (~.!.[.s) and VP are established.

In many practical reactor situations the improvement of an imprecise first estiinate ~ to ~ with its associated part of VP will be the most important product of the adjustment with [. !. S regarded as slightly refined by-products.

If we require X~rN to be equal to NM all the variance matrices' Ve Vm and hence VP can be scaled by the factor a= z!LN/NM without changing the values of the unfolded parameters - this operation is performed in SEN SAK II. With the exception of the.

scaling, which needs discussion, the above algorithm represents a simple - in some w oversimple - solution to the few-channel unfolding problem.

D4

AEAT-0352 APPENDIXD

• An example of its use is now given before consideration.

necessarily brief in this. paper, of some of the implications of this type Of unfolding in situations where accurate calculation is d ifficu It.

3 AN UNFOLDING Fourteen activation detectors were irradiated in the ASPIS facility of the NESTOR reactor operated in the Core Source mode with the fission-plate removed. The experimental shield comprised a boral sheet followed by 10 centimetres each of lead and water. The neutron flux spectrum in this position was calculated in twenty groups with ANISN in spherical geometry. Detector cross sections were taken from the SAND-II library with the exception of those for 103 Rh(n.n') 103 MRh which were taken from the UK Nuclear Data Library (DFN 94).

Uncertain ties in the detector cross-sections were taken from SAND-II values

• quoted by Zijp (2) and for lack of any other information first neighbours of group cross-sections were statistically related with a correlation coefficient of +O. 5. Fractional standard deviations of 0. 3 and 0. 05 were ascribed to the source strength and detector counting efficiencies respectively and of 0.5 and 0.3 to the top-energy ten and bottom-energy ten groups respectively of the calculated fluxes which were statistically related to their first and second neighbours with correlation coefficients of +0.5 and +O. 25 respectively. A fractional standard deviation of 0.05 was uniformly applied to all saturated counting rates - this number is a realistic rounding of observed standard deviations. Table 1 shows some of the principal results of two unfoldings in the first of which all fourteen detectors were included in the unfolding. and in the second of which seven detectors -

arbitrarily chosen - were omitted.

Table-2 gives the group structures employed and the flux spectrum before and after unfolding which included all fourteen detectors. (All the input parameters were perturbed but generally by an insignificant amount; these and output dispersion matrices are not x

shown for lack of space). The value of 2 per measurement fell from 279 to 1.10 for the first unfolding and from 235 to 0.96 for the second unfolding.

The important thing about Table 1 is not the good agreement between measurement and calculation of those detectors which were included in the unfolding but the in:iprovement. sometimes striking, in the ability to predict measurement of each of the seven detectors which were excluded from the unfolding. This is precisely what a foil unfolding code will be required to do in practice. The c. p. u. time taken on an IBM 3033 for the fourteen detector unfolding was 30 seconds and the storage requirement was 500 Kbytes.

D5

AEAT-0352 APPENDIXD TABLE 1 AGREEMENT OF CALCULATION AND MEASUREMENT BEFORE AND AFTER UNFOLDING Calculated/Measured Fractional S. D Reaction Reaction -Rates on Calculations Before After< 1> After< 2> Before After<_2>

58 Ni(n, p) 58 Co 2.06 1.02 1.0

• 191 Au( n, 'Y) 19s Au 0.60 0.98 0.64 0.41 0.25

• 59 Co(n, y ) 6°Co 0.71 0.98 0.80 0.39 0.20 63 Cu(n, y ) 64 Cu 0.85 1.01 0.98

• 54 Fe(n, p) 54 Mn 2.02 1.00 1.01 0.42 0.38

• S(n,p) 1.58 0.98 0.80 0.42 0.42 24Mg(n,_p) 2.51 0.99 1.00

• 47 Ti(n, p) 1.72 1.00 1.00 0.43 0.46 231Np(n, t) 1.06 0.98 0.98 23sU(n,f) 1.54 1.01 1.01

• 27 Al(na) 24 N a 3.14 1.01 1.50 0.50 0.25

11sln(n, n')11sMin 1.34 1.00 1.00 103Rh(n,.n') 1oJMRh 1.37 1.01 1.01

• 23SU(n,f) 0.75 0.99 0.82 0.34 0.13 (1) All detectors-included in the unfolding (2) Detectors marked

• not included in the unfolding 06

AEAT-0352 APPENDIXD TABLE 2 AN UNFOLDING WI1H FOURTEEN DETECTORS Upper Flux/Lethargy Ratio Fractional S. D.

Group Energy Before After After/Before Before After.

MeV

' l* 12.2 5.85 3.75 0.64 0.50 0.72 2 . 10.0 . 27.2 8.53 0.31 0.50 0.86 3 8.18 77.5 12.6 0.16 0.50 1.70 4 6.36 158 38.1 0.24 0.50 1.40 5 4.96 195 . 101 0.52 . 0.50 0.62 6 4.06 186 122 0.66 0.50 0.60 7 3.01 401 267 0.67 0.50 0.65 8 2.46 599 386 0.64 . 0.50 0.69' 9 2.35 628 353 0.56 0.50 0.59 10 1.83 696 . 560 0.80 0.50 0.35 11 1.11 797 857 .1.08 0.30 0.19.

• 12 0.55 558 572 1.03 0.30 *0.28 ..

13 0.11 '222 204 0.92 0.30 0.28 14 3.35,-3. 184 196 1.06

.. ., 0.30 . 0.24.

15 5.83,-4* 203 263 1.29 0.30 0.15 '

16 1.01, -4 222 273 1.23 0.30 0.21 17 2.90,-5 194 258 1.33 o.3o

• 0.20 18 1.07,-5 210 327 1.55 0.30" 0.10 19 3.06,-6 229. 299 1.31 . 0.30 0.21 20 1.12, -6 234 247 '1.06 0.30 0.26 0.41,-6 D7

AEAT-0352 APPENDIXD 4 DISCUSSION No attempt was made to provide a precisely modelled definitive calculation of the type that might have been achieved by extensive running of Monte Carlo for example.

Nevertheless this calculation is of no worse quality than would be found in many shielding applications. The standard deviations ascribed to the calculated fluxes are little more than informed guesses based on the calculator's experience and a cursory inspection of the calculated to measured reaction-rate ratios. A more detailed inspection of the latter might have improved these guesses but the fact remains that in many situations we may reasonably expect v... v, and Vs to be more soundly based statistically than v*. For the case where we feel that v. is as well-known as the other components of the covariance matrix of the parameters (in which case X~tN is unlikely to differ significantly from NM ) it is entirely reasonable to scale all the covariance matrices in the way described in Section 2

. - the covariance matrix and the distribution means, are both estimated parts of an unknown joint pn;>bability density function and are subject to adjustment When v. is not statistically soundly based we may choose to ascribe a discrepancy between X~tN and NM entirely to a bias in the flux calculations. Uncertainties in the cross-sections of materials used in the calculation of the flux spectrum are the only source of uncertainty int_ which can be treated statistically - in this case by uncertainty analysis. Other important sources of error in a flux calculation"' those due to modelling, method inadequacies etc. cause the calculations .C.. to be biased estimators of the measurements. This bias is prop~rly attributed to v. and account may be taken of it in a rather simplistic manner as follows:-

13 "'

where a= X!w/NM

• 14 15 is the matrix to be added to Ve .

. VM is left unaltered. We can isolate the 'statistical' part of Ve by writing 16 where a. for example can be seen from equation 4 to be D8

AEAT-0352 APPENDIXD Now isolating v. as the source of the discrepancy between z~IN and NM we seek a correction matrix F to v. such that .

17 We find after a little manipulation

.F = - 1 - [ G,T( Vc+VM )-1 G- 1-1 18" a-1 This type of variance updating is not at present inco..Porated in SENS AK pending further testing of unfoldings in difficult environments - highly improbable values o( X~rN will demand some such treaunerit *

• It is interesting to note that only minor: change5 in.the input/output format of SENSAK are required to adapt it to a philosophy previously proposed by the*author (3) which.- although limited in application and more expensive to carry out, appears to have r:narked advantages over the directmethod of Section .2, In.any situation.where the sensitivities of the calculated count'rates to the data used in the flux c;alculation can be found write *

• ac.

h..IA =dZ I:

where hit is the sensitivity of the'ith measure~ent to t_he k.th item of data In the sensitivity matrix G replace . . * * .

' [g]

by Gz = ~i and in VP replace v. by Vz which will be derived from uncertainty files. The unfolding' proceeds precisely as before but the output vector f._now contains Z..instead of an adjti~ted value of flux for its first elements.

The unfolded spectrum is now given by a flux calculation using updated data~.

The advantages of this approach are: *

(i) The replacement of v. by V 2 where the latter may be more soundly based statistically. In this case the term F would be added to V2 before solution and would represent approximately those biases on the calculated reaction-rates caused solely by errors in

=

the method of calculation. ( V~ Vz + F would n.m..

of course, be regarded as an improvement in V 2 )

D9

AEAT-0352 APPENDIXD

• (ii) Where a few detectors provided rather incomplete coverage of .the spectral energy range all parameters which are statistically based would be included and z._ would vary over the whole energy range. At present only the correlations between calculated group fluxes which in some cases may be rather arbitrary cause adjustments of flux spectrum in energy regions of low detector information.

5 CONCLUSIONS The unfoldings described included all the information available to the author; the calculation, by design, was not intended to match the quality of the measurements - a situation which will occur commonly in practice. The algebraic solution has worked well in these cases but some experience is needed in environments more hostile to accurate calculations - questions of scaling and iteration may well arise.

ACKNOWLEDGEMENTS Mr A Packwood supplied the measurements and the initial calculations: *Mr V Sumner is thanked for the efficient programming of SENS AK II. The influence of Dr F Perey through his writing and in discussions is gratefully acknowledged.

REFERENCES (1). Perey, F. G. 'Least-Squares Dosimetry Unfolding: The Program STAYSL'. ORNUTM-6062, 1977.

(2) Zijp, W. L 'Review of Activation Methods for the Determination of Neutron Flux Density Spectra' R.M.G. Note 75119, 1975.

(3) McCracken, A K. 'Foil Activation Detectors - Some Remarks on Unfolding of Flux Spectra' IAEA-208, 1976.

• DlO

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