User's Manual for the Application of the Dynamic Process Inventory
Contents
1. CALCULATION OF De z lt O u _ H M s X5 Yj co 4 PRINT H and 3 the contributions of each single output batch READ N READ P X CALCULATION Repeat the following procedure for k 14725 oo N A o Select randomly Miye Xip Vay Chk qk according prescribed pdf s Compute H k 2 o l fk Xk Yik Shk Shk CALCULATION of the mean value the standard deviation and the pdf of the random variable Hy from the sample H ck Kal 2405 00 CALCULATION of the H values cor responding to the prescribed P X PRINT the results Fig A3 1 Block diagram of the CC3 computer program nn en en en a e 221 48 Annex 4 The Computer Code MUF The present code has been designed to calculate the p d f probability density function of a random variable defined as analgebraic sum of others random variables with known pdf s Let p and q be independent random variables and fi and f the corresponding pdf s The analytical expressions for the pdf s of the random variables s p q r p q are given respectively by the following convolution integrals g s t s t at h r JE t t dt In this particular case we will express the f s in the form of histograms The previous integrals then become K2 G S 2 F1 K F2 S K Ki Ab 1 J2 H R 2 KFUR I FZ J1 The capital letters us2. D wach tO I N mA IR ad Ja J Gi wad W Ti N 60 Projekt Spaltstoffflu kontrolle User s Manual for the Application of the Dynamic Process Inventory Determination Using Isotopic Step Signals in Reprocessing Plants E Drosselmeyer R Kraemer A Rota Als Manuskript vervielf ltigt F r diesen Bericht behalten wir uns alle Rechte vor GESELLSCHAFT F R KERNFORSCHUNG M B H KARLSRUHE KERNFORSCHUNGSZENTRUM KARLSRUHE Mai 1972 KFK 1583 EUR 472Te Projekt Spaltstoffflu kontrolle User s Manual for the Application of the Dynamic Process Inventory Determination Using Isotopic Step Signals in Reprocessing Plants 1 1 2 E Drosselmeyer R Kraemer A Rota This paper was prepared in the framework of the joint research program of the association EURATOM GfK CEN CNEN RCN contract no 00I 69 I TDR D of safeguards and was presented at the IAEA Working Group Meeting on the Use of Isotopic Composition Data in Safeguards Vienna 10 14 April 1972 1 pernforschungszentrum Karlsruhe 2 joint Research Center of EURATOM Ispra Italy Abstract The manual describes the technical feasibility and procedures of a dynamic heavy material process inventory technique which correlates isotopic com position data of subsequent input and product batches in reprocessing plants This technique was developped for the application in safeguards with the ob jective to close the nuclear material balance
3. 6 3 P MUF lt O f m MUF MUP 0 This is a further information that quantifies the agreement between B and H at the moment of closing the balance Another interesting statement from the point of view of the safeguards control concerns the comparison of the measured MUF with a threshold amount e g the LOA referred to in ref 8 Such a statement is obtained in the identical way in which the provious has been obtained It is sufficient only to substitute the O by the actual value of the threshold Acknowledgement The authors are grateful for the help of Nebojsa Naki enovi who has reviewed the manuscript en T 36 Literature H Winter et al 2 131 hy 5 6 U 8 Determination of In Process Inventory in a Reprocessing Plant by Means of Isotope Analysis KFK 904 July 1969 R Kraemer W Gmelin et al Integral Safeguards Exercises in a Fabricating and a Reprocessing Plant IAEA SM 133 86 1970 R Kraemer W Beyrich et al Joint Integral Safeguard Experiment JEX 70 at the EUROCHEMIC Reprocessing Plant Mol Belgium KFK 1100 EUR 4576e 1970 71 IAEA The Structure and Content of Agreements between the Agency and the States required in Connection with the Treaty on the Non Proliferation of Nuclear Weapons INFCIRC 153 May 1971 E Drosselmeyer R Kraemer A Rota Application of Digital Simulation Techniques for Process Inventory Estim tion IAEA SM
4. show the trends which can be expected with certain parameter variations imate a ears 1h 3 Generation of Adequate Input Signal 3 1 Information Requirements on Fuel Elements The maximum benefit from the use of the illustrated technique is achieved when the physical inventory is measured with the lowest uncertainty A certain number of factors which influence the statistical error of the inventory have been already indicated 7 They concern essentially the dissolution of the fuel elements available for reprocessing and the choice of suitable procedures for the plant operations This second group of requirements was treated in 2 3 The choices which must be made a priori concern a the isotope to be used as tracer b the grouping of fuel elements in individual dissolution batches and c the dissolution sequence of the batches It can be shown 6 that the minimum variance of the inventory is achieved when the ratio re 3 1 r Teze is minimum Here te i 3 2 aad zje Mj ee i Z M J 1J where the sum is performed on j batches of the i th superbatch j is the weight fraction of the tracer isotope in the j th batch of the i th superbatch M is the total mass of the heavy element inside one input batch 15 Here the variances are 2_ 1 jij cij 3 3 oj i2 The expression 2 2 NE ee 0 4t0 is an indicator of the batch to batch variation in the weight fraction of
5. the sample H k k 1 2 N CALCULATION of the H values corz responding to the prescribed P X Fig A2 1 Block diagram of the CC2 computer program PRINT input data Cys Cp PRINT H and the contributions of each single PRINT the results Facies i gp in na ea ran 46 Annex 3 The Computer Code CC3 for H3 Evaluation The code CC3 evaluates the three component contribution H3 to the physical inventory Is is conceived and constructed identically to the CC2 Annex 2 The only obvious differences concern the formula for the H3 calculation 4 7 and the system 4 10 1 11 which defines the distributions of the random variables c and d j 1 2 3 J J Fig A3 1 illustrates the logical flow sheet of the program The list of the input requirements and of the output results is identical to that illustrated for the code CC2 In this case obviously the input batch characteristics must include 3 super batches j 1 2 3 and two weight percent ages of tracer isotopes In particular the program needs d Mine Se Sk where k is the index of the k th batch of the superbatch j 47 READ input data t r 3 u input batch index M x y j three components 37 3779 output batch index Os O 0 x y standard errors of Mis Xo igs ye ya CALCULATION of gt da h 1 2 3 PRINT input data Sn 4
6. where Hi is the contribution to the total inventory of the i th group In the following each single contribution will be evaluated independently In 4 4 4 the evaluation of the whole inventory end its statistical error will be outlined l ween crema pr 26 4 4 1 H Evaluation The contribution of the first group of batches to the inventory is simply given by n 4 2 H E M 1 o where n is the number of batches of the first group and M are the masses of heavy material of the first superbatch only present in the i th output batch The contribution H is independent of the c values weight fractions of tracer isotope so that the statistical error of H may be easily calculated from the errors of the single mass measurements These errors are usually small lt 1 and normally distributed Thus it follows that n 12 4 3 a N 1 i 4 4 2 H Evaluation The definition of H is given see 1 1 by n 2 7C eh Hy Ty Mi ge 1 e ny being the number of batches of the second group All the other symbols have been already defined The use of the weighted average concentrations c and c may have a biased estimate of one Due to the fact that the theory is still not sufficiently developed to indicate how to calculate these values in order to obtain a better estimate of H the following approach may be used we 29 wu Aw reo mn A i Farese private communication 27 Let us
7. 4 10 j 1 2 3 i 4 11 ars Pki kjkj s 1 DE 29 logically justified by the equation 57 the symbols have the same meaning indicates that single values of c and a are obtained as randomly weighted means of the concentrations of the input batches c and d It follows that in every realization of the pair of random variables Cis ds the same contribution of the individual input batches to the means must be considered The use of the same weighting factors oi Rej in both equations of the system assures that the physical correlation existing between c and d inside each single superbatch is respected Similarly to the previous case of H the contribution H is evaluated many 3 times as function of independent variables randomly selected from the mentioned distributions The analysis of the results of this application of the Monte Carlo technique gives the expectation value of Hs its pdf and the error limits according to a prescribed confidence interval These calculations may easily be effectuated by a computer using the computer eode CC3 described in Annex 3 4 4 4 Total Inventory In the previous sections it has been indicated how to calculate the different contributions to the total process inventory and how to interpret each of them The pdf s that have been associated to the measurement of each Hy 1 2 3 represent the confidence that can be attributed to the measured figure When a variable is normally dis
8. to increasing values of the selected isotope concentra tion _no N 0 yes SELECT the m N j elements for the eonstruction of the first SELECT the groups of elements of each batch of the superbatch see the scheme of the procedure in fig Al 2 SELECT the mN elements for the construction of the second superbatch SELECT the groups of elements of each batch of the superbatch superbatch see the scheme of the procedure in fig Al 2 11 MH 123456789012 I STEP 56781012 9 11 HH UI STEP 5678 2 IR 10 1413 Fig Al 2 Scheme of the procedure for batch grouping Case of 12 elements to be divided in groups of 3 oom Annex 2 The Computer Code CC2 for H Evaluation The calculation of the two component contribution H2 to the physical inventory according to the formula 4 4 does notin itself justify the use ofa computer and the construction of a computer code However this becomes unavoidable when further information is required The computer code CC2 has been in fact designed to calculate the measurement uncertainty By a proper use of a Monte Carlo technique the pdf and the distribution function of the parameter Hz are calculated H is considered as the realization of a random variable depending on the set of random variables M Xj Cy C2 as given in 4 4 For each of these variables the code r
9. 133 18 1970 Ref 3 Chapter 4 Ref 3 Chapter 5 W Gmelin et al A Technical Basis for International S feguards A CONF 49 P 773 July 1971 37 Annexes In the following pages a short description of the computer codes suitable for data handling of the DPID is given The listings of such codes written in FORTRAN language may be found together with the solution of sample problems in the external report EUR 4833 e Four Computer Codes for the Dynamic Process Inventory Determination Application in Safeguards by A Rota 1972 38 Annex 1 The Computer Code GROUP The computer code GROUP has been designed to provide the information necessary for the composition of the single input batches when a DPID is planned The problem has been outlined in paragraphs 3 1 and 3 2 The input data which define the problem are the total mamber N of the available fuel elements of the same reactor and approximatively of the same enrichment the number of elements m of which an input batch is composed the total number of batches desired in superbatch 1 and super batch 2 Nj and N respectively the name of each fuel element available for reprocessing together with the calculated values of its content in Pu and U isotopes When both N and N are different from zero the code defines the optimum grouping for the construction of two superbatches When either Nj or N2 is zero only one superbatch is c
10. assume that the independent variables m gt ci an c5 are realizations of random variables each of which has a known prescribed pdf probability density function For the values Me and x the paf s are assumed to be normal with mean values equal to the measured ones and standard deviations equal to the standard errors of the related measurements The variables c and c are given by A ox oR 6 Gy 4 5 cj wai Kop 24 2 EM Rs where the sums are performed on all the input batches of the j th superbatch and Where Me is the input mass of the heavy material contained in the k th batch of the j th superbatch Cys is the weight fraction of the tracer isotope in the same batch and Bis are random numbers extracted from a 0 1 interval with uniform distribution Consequently ei and c5 are also random variables and their mean values and standard deviation may be calculated Note that the previous formula assures that Ee c53 and that 5 lt t lt 4 6 min c lt cj lt max c The repeated use of the formula Lau for a high number of realizations of the independent variables Me X gt e allows the computation of a high number of contributions of type Hy related to the real input signal It is then possible to calculate the frequency curve the distribution the mean value and the variance of the realizations of Hye The frequency curve may be interpreted as the probability density function of t so that it is
11. code has been written for equal amounts of Pu in all the elements see below see section 2 4 17 j is a function that defines the minimum integer number with Q mq as the argument The sufficient quantity constraint can be expressed as 3 5 N gt nem The computer code given in Annex 1 has been written with the constraint that the amounts of Pu and U in all the elements are equal Nevertheless in many actual cases the mass differences of different elements are not so large to render relevant changes in the results It must be recalled that the batch construction is made on the basis of reactor data which can be affected by not negligible errors for this reason in most cases a more sophisticated analysis on such data is useless The n batches must be constructed in such a way that the batch to batch variation of the tracer isotope is minimal This operation must be performed on all of the Pu U isotopes in order to select the tracer isotope This tedious exercise is automatically performed by the GROUP code Appendix 1 For each Pu and U isotope the computer code gives the list if any when N n of the N n elements not considered the optimum grouping of the elements in n batches of each containing m fuel elements the expected relative weight fractions of each isotope in each batch and their expected mean values and variances for the superbatch The latter may be interpreted as a measure o
12. in adequate time intervals during a running campaign The manual is divided in 7 chapters covering preprocess information require ments on the material balance area and the spent fuel to be processed optimisation procedures for the generation of an adequate isotopic stepsignal and the proce dures to determine with the help of the actual measured input and product signal the physical inventory of heavy material This inventory is compared with the corresponding book inventory by suitable statistical procedures Monte Carlo technique in order to obtain the Material Unaccounted For MUF and its range of uncertainty The annexes give a short description of four com puter codes for suitable data handling of this inventory technique Zusammenfassung Das Handbuch beschreibt die Ma nahmen und technischen Grenzen einer Methode zur dynamischen Bestimmung des Proze inventars von Uran oder Plutonium in Wiederauf arbeitungsanlagen Diese Methode wurde f r die Spaltstoffflufkontrolle ent wickelt mit dem Ziel die Materialbilanz w hrend einer laufenden Aufarbeitungs kampagne in geeigneten Zeitintervallen zu schlie en Das Handbuch ist in 7 Kapitel aufgeteilt die zun chst die Beurteilung der Material bilanzzone und des abgebrannten Kernbrennstoffes im Hinblick auf die Gr e und Beschaffenheit des notwendigen Isotopensprungsignals behandeln Danach werden die Ma nahmen zur statistischen Auswertung Monte Carlo Technik der gemesse
13. may contain either pure inventory material of superbatch I or mixtures of material from both superbatches I and II In the case that the superbatch II was too small to replace completely the inventory material superbatch I three component mixtures may occur including material of a third superbatch This information should be summarized in Fig 5 2 2h The separation of the two or three groups is an important procedure with respect to the inventory evaluation Sec 4 4 Fig 5 2 the grouping can be arranged very quickly With the help of Product batches be longing to group a are roughly within the dashed mixing area of super batch I As soon as the product isotpic vector leaves the mixing area of superbatch I following roughly the dashed line between the weighted averages of superbatch I and II the product batch will belong to group b Complications arise if a third superbatch is involved as the solution of three component mixing equations requires that the coefficient determinant is sufficiently different from zero 1 This condition can be demonstrated graphically in Fig 5 3 Lanse tn BORE tracer isotope wol auxiliary isotope Lulo tracer isotope w o _ Fig 5 3 Three component mixing MMA DE IEA TAD LEAN SLOT ETN MTEL TCE SNL IER fy 7 Po A i H H Pal Lam d 4 g A E u N FEN FR DT N a i N Lo 2 rete m men Ar nenne enter ern r mnt auxiliary isotope w o_ T
14. possible to determine its expectation value and the error limits according to a prescribed confidence interval These operations may be easily effectuated by a computer employing the computer code CC2 described in Annex 2 28 4 4 3 H Evaluation The DPID requires sometimes the use of a three component system three subsequent input superbatches with two selected isotope tracers In this case a further contribution to the inventory is given by T of 3 ye i 1 1 4 7 H D am HB where the sum is performed over the n3 batches of the third group and where 4 8 T x C i i a Yi d d end 1 1 1 en D c4 cz c3 d d c and d j 1 2 3 are the concentrations of two tracers e g Pu 2h1 uv and Pu 242 in the j th input superbatch x and y are the concentrations of the same isotopes in the i th output batch The inadequancy of this theory in respect to the treatment of real cases results from the same reasons pointed out in the case of the two component systems It follows that the evaluation of the experimental data may be ob tained following a procedure similar to the one outlined in the previous paragraph In this case however it is necessary to pay some attention to the fact that the selection of random values for the pairs Ch a must respect the physical correlation existing between these parameters The use of the following systen i 2 8 EMR sc 4 c 5 i MR
15. agraph 113 Physical inventory means the sum of all measured or derived estimates of batch quantities of nuclear material on hand at a given time within a material balance area obtained in accordance with specified procedures 6 ke et By fe Lf foe 3 lt 3 ct 3 ct M a gt Q g 5 n tom z s 27 H en 2 p Inventory Determination DPID 1 2 Basic Considerations For ready reference a short description of the basic principles of this method is given below This technique makes use of the fact that the heavy material inventory between input and product accountability tanks which is replaced by the incoming material can be measured quantitatively in subsequent product batches provided that the isotopic composition of the inventory differs sufficiently from that of the new input material The problem is to generate a step function in the isotopic composition of the input flow by loading the dissolver in such a way that a sufficient number of fuel elements of equal initial enrichment and irradiation history will be followed by fuel elements with isotopic abundances different from the first en It is also possible to use the different isotopic composition of irradiated fuel elements from two different reactor batches which are processed in close sequence The evaluation of the physical inventory is a simple sum up of product batches weighted by a factor which indicates the fraction o
16. aluation Annex 3 The Computer Code CC3 for H Evaluation Annex 4 The Computer Code MUF ee 1 General 1 1 Introduction This manual was prepared after considerable theoretical and experimental work 1 2 3 on the validity of a new inventory determination technique which employs the correlation of isotopic data of subsequent input and output batches This new technique described here had a number of different names in the past some of which are a Dynamic Inventory Determination in order to express the fact that this technique does not need static conditions during inventory taking but may be performed during a running campaign b In Process Inventory Determination in order to emphasize the point that this technique is applicable only in the process area and not in the storage area of a reprocessing plant because it is based on nuclear material flow measurements c Self Tracering Technique because the step signal used for the evaluation of the inventory is the inherent isotopic composition of the heavy material and not an artificial tracer a Finally this technique was simply called Physical Inventory Technique in order to demonstrate the fact that this technique represents an independent inventory measurement which can be compared with the book inventory determination in order to make a statement on MUF Therefore this independent inventory determination meets the specifications de fined in the model agreement 4 par
17. annot be avoided without a washout But since this mixing is small it can be left out With the models which were constructed in order to describe the flow of fissile material 5 relatively good correspondence of the theoretical and experimental results could be ob tained in spite of the fact that these units were neglected 2 3 Operational Limitations Generally speaking the optimization of operations in a given plant with ob jective to allow the application of the DPID method must be solved case by case if there is only a limited quantity of material available Simulation studies which use a proper model of the plant under consideration or historical experience of operation can be of great help The only general rule is that the mixing should be maximized inside the superbatches and minimized between two consecutive superbatches It should be attempted to homogenize the material inside the superbatches as much as possible The simulation studies of the Pu cycle of the EUROCHEMIC plant and their results which were applied during the Mol III experiment give some hints on relevant operation parameters with respect to the influence of mixing The studies were made on 10 a Residual heels in the head end tanks b Mixing procedures in the feed tanks between the accountability units and the first extraction cycle This is possible in a plant with parallel intermediate storage tanks c Recycles to the second pu
18. asibility 2 1 MBA System A definition of Material Balance Area MBA is given in the basic report of the IAEA INFCIRC 153 4 in article 110 MBA means an area in or outside of a facility such that a the quantity of nuclear material in each transfer into or out of each MBA can be determined and bd the physical inventory of nuclear material in each MBA can be determined when necessary in accordance with specified procedures in order that the material balance for Agency safeguards purposes can be established In connection with the application of the DPID the MBA has been defined for two different plants The first one was the American NFS plant the second one was the Belgian EUROCHEMIC where the method was very successful in two integral experiments Fig 2 1 shows the example of the NFS MBA Fig 2 2 shows the EUROCHEMIC example In both cases the MBA system covered the process part only and excluded the product storage area because emphasis has to be laid on the condition that the system response can be measured adequately In addition it is advisable to have only one significant input stream into the defined MBA When the process needs auxiliary inputs of heavy material e g the g re ucing agent in separation units the DPID must be suitably corrected 2 2 Design Limitations In order to allow a fruitful application of the method a few limitations should be kept in mind They apply to the design a
19. ed for the function names and variables correspond to the small letters which indicate continuous function and variables 1 12 Ni lt N define the integer interval outside which lis identically zero and let Noy N32 N N have the same meaning for F2 From these limits it is possible to deduce analogous intervals for the functions G and H 19 te Allen Nat DAN lt a Ny N 25B Naz N Ignoring those terms which certainly do not give any contribution to the sums A4 1 the sum limits become K1 Max N S N K2 min N S N J1 Max N N R J2 min N N R These relationships are used in the MUF computer code to evaluate the sequence of conwolutions necessary for a statement on the material unaccounted for This program however may be used independently of the safeguards problems for the evaluation of any sequence of convolution integrals of the mentioned type Great care must be taken to correctly define the histogram intervals They must be equal for every considered pdf The code uses as input the subsequent pdf s defined through their histograms of through their mean value and standard deviation when they are of normal type The process of the data is sequential a first pdf f p is defined it is read or it is the result of a previous convolution second pdf f q is read together with an indication the possible indications and their significance are the fo
20. equires the definition of its distribution Mo andx i 1 number of output batches are assumed to be random variables with normal distributions individuated by a proper value of the standard deviations Gy Gxi cj and c are random variables the distributions of which are implicitly defined by the equations 4 5 This formalism is used by CC2 It follows that the input batch characteristics Mij ckj must be introduced as input data for the program Further input data for the CC2 are the number N of histories requested for the Monte Carlo procedure the range that should be covered by the error analysis the step magnitude for the frequency distribution and then for the p d f the list of the particular values of the probability for which an error boundary definition is particulary interesting 43 alist of parameters of minor interest initialization values for the random number generation routines print out definitions optional perforation of the results etc Fig A2 1 reproduces a logical flow sheet of the program The output of the program contains the following information a summary of the input batch data a summary of the two component mixture output batch data the median value m f M Xi 1 the contribution to H2 of each output batch the frequency histogram the table of the pdf of H a rough plot of such pdf the table of the distribu
21. etween these two quantities is the well known MUF Material Unaccounted For defined as 6 1 MUF B H The calculation of such a quantity and of its statistical errors is of capital importance for the control activities In fact the article 30 of INFCIRC 153 4 explicitly requires a statement on the amount of material unaccounted for over a specific period giving the limits of accuracy of the amounts stated 6 2 Confidence Intervais As illustrated in 4 4 4 the determination of the limits of accuracy for the MUF is deduced from its pdf Such a function is obtained as in the case of the whole inventory by a suitable convolution between the pdf s associated to H and B The first has been calculated in 4 4 4 the second is Simply a normal distribution the mean value and standard deviation of which have been deduced in sect 5 Indicating by h H and b B such pdf s the pdf for the MUF m MUF is given by 6 2 m MUF Ib MUF x h x dx 4 or by a suitable approximation of this integral w This operation is described in more detail in Appendix 4 where the per formances of a computer code which may be used for calculations are illustrated mp aea 3 6 3 The Statement on the MUF In theory if a facility has a perfect accountancy system for all the in puts and outputs the MUF should be only the eonsequence of cumulated measurement errors Its value if not zero should be consistent with zero The ana
22. f element expressed in grams available isotopic measurements in weight percent C Specify the single input batches forming the two superbatches as given in section 3 D Select that particular tracer isotope which shows the smallest ratio r P as given in equations 3 1 3 3 E Plot the weight fraction of the tracer isotope versus the mass of the element of subsequent input batches for the two superbatches as in Fig 5 1 tracer isotope w o_ mass of element Fig 5 1 Isotopic input signal gives already a first estimate of the relative standard deviation of DPID Tmin pt 22 F Select one additional auxiliary isotope which shows the second smallest ratio r G Plot the weight fractions of the tracer isotope vers the auxiliary isotope of all input batches forming the two superbatches and establish the maximum possible mixing area according to Fig 5 2 superbatch II g 6 ri p 3 k a p 5 f a maximum possible ns mixing area v ee eee Ne 5 p O Nn ord 2 h o single input batch Y g B weighted average of a superbatch product batches auxiliary isotope weight fraction Fig 5 2 Mixing area of two superbatches 4 2 Analysis of the Measured Product Signal The main problem in this analysis of the measured product signal is the t of the cut off batch which will not show any significant fraction of inventory material Consequentl
23. f the batch to batch variation When more than n batches can be constructed with the N elements it is suggested to run the code for superbatches composed also of nti n 2 batches In fact it is possible that no significant change in c mean value of the tracer weight fraction and no increase in its variance occur In this case the use of a larger superbatch is advised because this guarantees that the sufficient quantity constraint is better satisfied Re ass ATAA n 18 The calculation described heretofore must be performed for both superbatches independently When the results for all the isotopes are available the proper choice of the optimal Pu isotope to be used as tracer can be made Obviously that tracer will be chosen for which the ratio 3 1 is minimized In the second case b the problem consists in the construction of two super batches with minimum quantities Q and Qo by putting the N available elements in groups of m In this case the two superbatches will consist respectively of Bes i Ga and 2 n j Ga batches The sufficient quantity constraint can be expressed as N n n m The following results for each Pu and U are obtained when the proper values of the input parameters of the GROUP program are used the list if any when N gt n n m of theelements nottaken into consideration for the determination of the superbatches the optimum grouping of the elemen
24. f the inven 4 t A 2 x d as gt 7 x L y tory material in each individual product batch according to equ 1 1 de 1 1 gt Mm i 2 ke U Pu7 H t L KE U ae L i t gt t 2 t time of introducing the step input signal MF product batch size kg U Pu cjo weight fraction of the tracer isotope in the two consecutive superbat ches which form the step signal ae X weight fraction of the tracer isotope in product batch i La iin Vi merbetch is defined by a certain number of input batches with similar weight fraction of the tracer isotope The weight factor of subsequent product batches illustrates the operator s individual material management during the passage of the signal through the plant Simulation studies and also experimental results indicate that this factor converges to zero in a similar way as an exponential function does The dispersion of the input step singal can be minimized if the operator runs the process according to a small number of specified procedures mainly by special operation of the headend and product catch tanks but only during the residence time of the signal in the plant This technique may also be applied when the use of three superbatches and consequently two tracer isotopes is necessary In this case the proper formalism is more complicated 1 but its derivation does not need the introduction of further basic concepts ae een 2 Technical Fe
25. he figure on the left demonstrates the conditions of an unsolvable equation system where the three components I II III are linear dependent The figure on the right shows an example of a where the coefficient determinant which is proportional solvable equation systen to the shadowed mixing area is sufficiently different from zero 25 It is recommended to avoid the three component mixing system by enlarging the size of superbatch II Only for reasons of completeness the relevant procedures for the evaluation of the inventory including a three component mixture is also outlined in the following section Product batches which contain components of three superbatches can be identified by plotting the corresponding isotopic data in Fig 5 3 In case of a solvable equation system figure on the right the product point is located clearly within the maximum possible mixing area 4 4 Evaluation of the Physical Inventory From the analysis of the measured input signal Sec 4 1 it is possible to perform the final choice of the tracer isotope or isotopes when three superbatches must be considered The analysis of the output signal allow the separation of the output batches in two or three groups according to their content Sec 4 2 and 4 3 The results of the previous analysis allow a simplification in the deter mination of the inventory In fact the inventory value H may be expressed as 41 4 1 HSH H H
26. llowing when the pdf of the random variable s p qis required 1 2 when the pdf of the random variable s p q is required 2 1 when the pdf of the random variable s q pis required For every convolution the code delivers the table of the resulting pdf together with its relevant parameters mean value standard dev etc 50 on request the following further specifications may be obtained a rough plot of the resulting pdf a rough plot of the resulting distribution function the table of the s values corresponding to the prescribed values of the probability as described in Annex 2 for the code CC2
27. lysis of the MUF measurements must then state a conclusion about such consistency The determination of the required statement is straight forward when the error distribution the pdf around the MUF the mean value of such a distribution is given Let p be the value fixed a priori of the probability level requested for the statement 3 With the employment of the same technique reported in 4 4 4 it is possible to define the two error limits m and m for the 4 measured value of MUF s Two cases must be considered a MUF m lt O lt MUF m t MUF m gt 0 In the case a it is possible to state that the measured MUF is consistent with O with a confidence p in the case b the measured MUF is not con sistent with O with a confidence p A third case is theoretically possible MUF m lt 0 This last case in spite of the fact that it gives a piece of information on the safe side from the safeguards point of view should impose deeper investigation on the process accountancy techniques measurement ineluded or on hidden inventories inside the process area one yorking group meeting on quantitative data and results of systems analysis and integral tests Vienna 4 8 10 71 suggested values of p in the range 90 99 usually 95 is adapted 35 In the case a mentioned before it is possible to calculate the probability that the MUF is equal or lower than O Such value is simply 0
28. nd the operation of the plant in question and to the material which is to be reprocessed Of course there are interconnections between these parameters e g it is BIER MBA for Process Inventory Fuel Element Storage Mechanical Treatment ED YY Process Area U Product CA En Pu Product Dissolver Area Fig 2 1 Definition of Material Balance Area for Process Inventory in NFS USA ei Dissolver Process A MBA 12 MBA 21 Waste storage MBA 50 Fig 2 2 Scheme of Pu flow and MBA system for Process Inventory in EUROCHEMIC MOL BELGIUM evident that when large amounts of heavy material are mixed in big tanks the superbatches must also be large The limiting quantities for the superbatch sizes become smaller when the mixing of material inside the plant is reduced As far as the design is concerned the following parameters must be taken into account a The main influence on the dispersion of the step signals comes from the mixing inside the tanks with a great hold up of heavy material as buffer tanks evaporators or product catch tanks b A second contribution is due to the heels in the tanks which can be inherent in the plant design or can be operation parameters The con dition of low heels in order to have low mixing should be mainly respected during the passage of the step through the respective units c Mixing inside the continuously working units of the plant as mixer settlers c
29. nen Isotopensignale im Eingangs und Produktstrom beschrieben mit dem Ziel den realen Bestand an Uran bzw Plutonium zu bestimmen ber den Vergleich mit dem entsprechenden Buchbestand erh lt man quantitativ das nicht nachgewiesene Material MUF und dessen Unsicherheitsbereich Im Anhang werden 4 Rechenpro gramme zur statistischen Auswertung von Teilproblemen dieser Inventurtechnik beschrieben Menuskript einger 29 5 1972 List of Content 1 General 1 1 Introduction 1 2 Basic Considerations 2 Technical Feasibility 2 1 MBA System 2 2 Design Limitations 2 3 Operational Limitations 2 4 Material Requirements 3 Generation of Adequate Input Signal 3 1 Information Requirements on Fuel Elements 3 2 The Determination of Super Batches 3 3 The Determination of the Input Sequence 3 4 Practical Problems 4 Procedures to Determine Process Inventory 4 1 Analysis of Measured Input Signal 4 2 Analysis of Measured Product Signal 4 3 Separation of Mixing Types in the Relevant Product Batches 4 4 Evaluation of the Physical Inventory 5 Book Inventory Determination Procedures 5 1 Definition of the Time Interval 5 2 Evaluation of Book Inventory 5 3 Determination of the Variance of Book Inventory 6 Procedures to Determine MUF 6 1 Book Physical Inventory Difference 6 2 Confidence Intervals 6 3 The Statement on the MUF 7 Literature Annexes Annex 1 The Computer Code GROUP Annex 2 The Computer Code CC2 for H Ev
30. onstructed If N 0 the superbatch is constructed in such a way that the higher tracerconcentrationis selected When N 0 the minimum tracer concentration is selected Note that when both Nj and N are different from zero the first superbatch will be constructed with the minimum tracer concentration and the second with the maximum one When a going down step is desired the two superbatches selected by the code willbe usedin inverse order T I1 1e grouping of the element for each batch of the The selection of t required superbatches is made for each isotope both of U and Pu present in the burned fuel elements For each of these isotopes and according the specifications required N N2 N the GROUP code gives 39 the list of the elements not utilized when Nj N3 eK N the list of the groups of fuel elements which constitute a batch for every constructed batch the expected abundance of each Pu and U isotope for every superbatch the mean values and the standard deviations of such abundances The block diagram of the code is reported in fig A1 1 Fig A1 2 shows an example of batch grouping for a case of 12 elements which are to be divided in groups of 3 mm EN 10 READ N N N m READ The name and the characteristics of each fuel element PRINT the input data REPEAT the following procedure for each U and Pu isotope ORDER the fuel elements according
31. rification cycle ad a Increasing the mixing in the head end tanks by enlarging the heels can help to achieve a smoothing of the tracer concentration within one superbatch Obviously the prescription of minimum heels at the step passage must be kept Heels of 1 and 10 were studied ad b Since the study of the mixing strategy in the feed adjustment tanks of the first extraction cycle was connected with the variation of other process parameters like the quantity of recycled material or the number of batches taken into account for the calculation of the concentration mean values for the superbatches the results are not completely clear There seems to be a tendency by which the variance of the measured inventory is lowered by the mixing strategy 5 ad ce Reprocessing campaigns with 5 and without continuous Pu recycling have been studied The results show no significant differences The only important remark concerns the magnitude of the superbatches a Pu recycle obviously increases the mixing so that larger superbatches are needed in order to estimate the process inventory with the same accuracy Two further important points are a It has been shown in 6 that the DPID method can also be applied success fully in case of additional inputs as e g uy streans this strategy for the input accountability tank has been called external mixing in 5 11 It is possible to adjust the model for additional inpu
32. section 4 represents the inven tory situation within the defined MBA at the time t when the isotopic step signal is introduced As this time t is very important for closing the material balance more specifications must be given Case I The input accountability tank IAT is located outside the defined MBA system The relevant time point is defined at the beginning of the transfer of the first input batch of the second superbatch from the IAT to the next process unit Case II The IAT is located inside the defined MBA which is sometimes so the case that the adequate shipper receiver differences can be established The relevant time point is defined at the beginning of the transfer of the first input batch of the second superbatch from the dissolver tank to the IAT In the case that there are relatively great heels in the IAT one has to relate the isotpic signal to the incoming material and not to outgoing material as it is done in case I Correspondingly the book inventory B which is to be compared with the physical inventory H determined according to the procedures specified in section 4 has to be related to the time point defined above 5 2 Evaluation of Book Inventory The evaluation of the book inventory is a well known procedure which needs not to be specified in detail here The relevant equation is given below z 2 zu Da 7 i I P a W kg heavy element_ 5 1 Br BI 1 o 32
33. the rule number 1 is respected case 2 and case 3 of the figure it is preferable to shift the maximum tracer oscillations towards the first batches of the superbatch case 3 of the figure must be preferred to case 2 er 20 3 4 Practical Problems Sometimes it happens that the required grouping of elements for the construction of the different batches and or the prescribed input sequence can not be fulfilled because of handling difficulties in herent to the storage location of the reprocessing plant In such cases the inventory taking should be planned sufficiently early to solve the problems indicated at 3 2 and 3 3 before the fuel element shipment In this case the shipment and the storage may be in time planned in such a way that the handling difficulties at the reprocessing storage pond are overcome 2i 4 Procedures to Determine Process Inventory 4 1 Analysis of the Measured Input Signal Because of the lack of adequate shipper data the realized input step signal may show considerable differences from the provided input signal as specified in section 3 All further evaluations will be based on the measured input signal Thus we proceed as follows A Specify the nuclear material U or Pu which is to be balanced by book and physical inventory comparison B Make a chronological list of relevant input batch data batch identification date and hour of transfer as specified in 5 1 total mass o
34. the tracer isotope and le c is the step size 1 2l As long as every isotope of fissile material of Pu or of U may be used as tracer a suitable analysis of the material to be reprocessed must be performed For this reason the following information must be avail able for proper treatment The number of fuel elements to be reprocessed divided according to the type of reactor and of initial enrichments if they differ The number of fuel elements of each type that are dissolved together as a single batch Final quantities of Pu and U contained in each fuel element or assembly and their isotopic composition as calculated by the reactor operator The above mentioned data are usually communicated as shipner data by the reactor operators to the reprocessing plant management and for power reactors it seems that there is no reason for their classification On the basis of these data the batches will be constructed and ordered in those cases where the results of input analysis show that another tracer is more suitable the tracer can be different from the one chosen on a priori basis anaemia meth ee ani 16 3 2 The Determination of Super Batches When our method of inventory determination is used the first constraint of sufficient quantity of material must be satisfied In practice two cases are possible a The step in the weight fraction of the tracer isotope will take place bet
35. tion of H2 a rough plot of such distribution the main characteristics of the statistical analysis H2 TH relative standard deviation the table of the values of Hy corresponding to the prescribed values of the probability The last table can look e g like this P X X H X 1 2 5 528 93 2320 94 2 5 0 433 08 2416 79 3 10 0 332 67 2517 20 4 20 0 209 17 2 640 70 5 80 0 179 53 3 029 40 6 90 0 261 62 3 111 49 7 95 0 321 26 3171 13 8 97 5 365 57 3 215 44 The values of the column P X are input data In this sample case they have been choosen in order to select confidence intervals of manner pam zike 95 90 80 60 in fact the error limits for a 95 confidence are located at P X 2 5 and 97 5 this gives H 365 57 528 93 The same procedure is used for the other confidence intervals 45 READ INPUT DATA Mes c j input batch index M i gt Xi i Two components output batch index N at ate o Gy 0 standard errors of M MS a 1 L mg and x 3 1 CALCULATION of the weighted values Cy and cy CALCULATION of H oO om z F M X Cys cy READ N READ P X CALCULATION Repeat the following procedure for k 1 2 N o Select randomly Mayo Xka Cik and Cop according prescribed pdf Calculate H k z EM KK CCa CALCULATION of the mean value the standard deviation and the pdf of the random variable Hy from
36. tributed its pdf is simply specified by the value of the standard deviation parameter This is the reason that io or 20 values are often used when confidence intervals are given The approximation of the pdf of H and H with a normal function is generally not valid Therefore a more sophisticated error propagation analysis is given below Finally the pdf must be calculated for the whole inventory H This will give an immediate picture of the measurement significance This kind of pdf is obtained by subsequent convolutions of the pdf s of the addends His H and Hz The definition of these Convolutions is given in Appendix 4 For the moment however it is sufficient to remember that in this case the pdf s are given in form of histograms and that the convolutions reduce to simple sums The pertinent formulae are also given in Appendix 4 een terete 30 However it is important to stress the physical significance of the formalism connected with the pdf of the quantity H In the figure an example of such a type of function h H is plotted The area under the curve is by definition equal to 1 H a H H 4 H As expectation value the mean value H is choosen The error limits connected with a prescribed confidence p are the values H q and Htays such that omer ome H H q H q E D 31 5 Book Inventory Determination Procedures 5 1 Definition of the Time Interval The physical inventory determined by DPID
37. ts either by modification of the input or of the output signal e A further operation requirement is to avoid batchwise recycling of heavy material as far as possible 2 4 Material Requirements It has been mentioned before that one of the most important conditions for the application of the DPID method is the availability of enough material in each of the superbatches To give an estimate of the required superbatch sizes one needs either practical experience with the plant or a rough model of the different mixing mechanisms According to Fig 2 3 it can be deduced 5 that for the case of two superbatches the first one should not be smaller than 9 and the second one not smaller than RaR Here Qo is the quantity of material which is produced up to the introduction of the step Q the quantity between the introduction of the step and the first influence of the concentration c in the product and Qa the quantity of material 2 which is produced up to the point where only material of superbatch 2 comes out It is quite clear that the difference Q 78 gives the amount of material which is in a mixed state of superbatches 1 and 2 For the EUROCHEMIC plant this amount is about 3 times as large as the biggest heavy material hold up of any unit of the plant In order to get some more detailed information simulation studies on the EUROCHEMIC plant under normal operation conditions beginning with an empty plant and for a certain t
38. ts in the two superbatches of n and n batches respectively containing m fuel elements each 1 2 the expected relative weight fractions of all the isotopes for both U and Pu in each batch and their expected mean values for each superbatch and variances When more than n n batches may be constructed with the N available elements it is an to run the computer code increasing the parameters n and or Ny and to decide from the examination of the results if an increase in the quantities Q and or 9 is possible However it must be recalled that this increase of the minimum quantities is possible and advisable only when no significant increase of the ratio 3 1 occurs 19 3 3 The Determination of the Input Sequence The problems concerning the tracer isotope selection and the composition of the single dissolution batches have been solved The last decision that must be taken before the dissolution is the determination of the input sequence for the batches of the two superbatches Two rules should be respected 1 The regression lines which approximate the histogram of the tracer weight fraction versus total material quantity must be as flat as possible for both superbatches It has been demonstrated that any divergence of the regression line from the horizontal decreases the precision of the final result Avoid the case 1 illustrated in the figure L p ee FE a A CASE 1 CASE 2 CASE 3 2 When
39. ween the reprocessing of two different types of reactor fuels b The step will be created by suitable selection and ordering of the fuel elements of one reactor The two cases are conceptually not different but in practice it is better to follow two different approaches In both of them it will be possible to profit from the use of a computer code illustrated in Annex 1 It is necessary to stress that the optimization procedure that will be described in the following pages allows the optimal sequence determination for the measurement of the Pu or U inventory Nevertheless it is possible that the best input sequence for one of the elements Pu e g is apt to generate a step useful for the other element inventory This second step however is not necessarily optimal Let us assume that a Pu inventory measurement is required In the first case a we have the following problem There are N fuel elements of equal type that must be used to create a superbatch containing at least a prescribed quantity of Pu In other words the minimum number of batches n which are necessary to create a superbatch of the prescribed quantity Q can be cal culated as follows 3 4 nej a In this formula the following quantities are given number of batches for the construction of a superbatch n Q quantity of Pu inside this superbatch m number of fuel elements in one batch q mean quantity of Pu in one element the computer
40. where BI beginning inventory at time to I P W input product and waste batches a 1 D W number of input product and waste batches between to and step time t as defined in section 5 1 The input accountability stops with the last bateh of the first superbatch However only those product and waste batches are accounted for which are completely transfered out of the defined MBA between to and t 5 3 Determination of the Variance of Book Inventory The Relative Standard Deviation RSD associated with each flow can be cal culated with 62 62 2 2 re 2 2 e 6 6 6 5 2 F a e t n loime c n nanaiyeis RSD weight where Sa calibration error RSD Sn precision of the measurement number of batches number of analyses per batch Equ 5 2 is valid if all the batches have equal volumes weights and concentrations This assumption appears to be justified Calibration error and precision have to be estimated from the experience of quality control procedures The resulting variance of the book inventory is the sum of all the variances 2 5 3 B 5 IF F 1I P W BI z F 33 6 Procedures to Determine the MUF 6 1 Book Physical Inventory Difference From the point of view of the safeguards control the main interest of the DPID is the comparison between the measured value H and the accoun tebility value B usually referred to as book inventory The difference b
41. y all the following product batches will also not give any contribution to the inventory We 23 therefore propose to proceed as follows A Make a chronological list of all relevant product batch data 4 3 The a b c starting from the first product batch after initial physical inventory measurement at time to batch identification day and hour when the transfer out of the defined MBA is finished total mass of element in grams available isotopic measurements in weight percent Find the first product batch after the step time t as given in 5 1 Plot the weight fractions of the tracer isotope and the auxiliary isotope of the subsequent product batches which are released from the MBA after t see B t Note that every product point must be in the indicated maximum possible mixing area if the isotopic measurements are un biased and no other material than the fuel of both superbatches is mixed together Proceed plotting as specified in C until the isotope vector merges with the weighted average point within the dashed mixing area of superbatch II If the next few product batches come roughly to the same point one can be sure that all inventory material passed the product accountability tank The cut off batch is consequently defined to be the first product batch which reaches the weighted average of superbatch II ypes_in the Relevant Product Batches relevant product batches
42. ype of material have been done in order to estimate the amounts of material in superbatches 1 and 2 which should be present for a predetermined recovery of the inventory The results are condensed in Table I 12 l l ni Py 20 Q2 Qo lt lt om on ome eee only total Pu in gt total Pu out of the DPID method 13 Table I Minimum size of the two superbatches No of output Percentage of _ Superbatch size ke of Pu batches considered the inventory I II measured Q 9 Q 2 A 70 6 11 32 O 5 86 9 14 15 r 2 83 6 96 9 16 98 5 66 T 99 4h 19 82 8 50 8 99 90 22 65 11 34 9 99 98 25 47 14 15 10 _ 100 i 28 30 16 98 So if 97 of the inventory is to be measured superbatch 1 should contain 17 kg and superbatch 2_ 6 kg of Pu For reasons given in section 4 2 it is not meaningful in actual situation to increase the superbatch size so that the recovery would be 100 Analogous results for the U cycle of the EUROCHEMIC are given in 3 They are dependent on the strategy of recycling or not recycling With recycling and that means with a greater mixing the superbatches have to be much larger for the determination of a prefixed percentage of the inventory All these numbers are results which come out for a specific plant under specific operation conditions They are given in order to indicate the order of magnitude of the superbatches in a plant of this size and to
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