Nuclear Safeguards Analysis. Nondestructive and Analytical Chemical Techniques 9780841204492, 9780841205710, 0-8412-0449-7

Table of contents :
Title Page......Page 1
Half Title Page......Page 3
Copyright......Page 4
ACS Symposium Series......Page 5
FOREWORD......Page 6
PdftkEmptyString......Page 0
PREFACE......Page 7
1 Safeguards Needs in the Measurement Area: the Realm of Measurements......Page 9
BACKGROUND AND EVOLUTION......Page 10
RATIONALE FOR AN EFFECTIVE SAFEGUARDS MEASUREMENT SYSTEM......Page 12
THE REALM OF MEASUREMENTS......Page 13
SUMMARY AND THE MEASUREMENT CHALLENGE......Page 24
ABSTRACT......Page 26
LITERATURE CITED......Page 27
2 Standards for Chemical or NDA Measurements for Nuclear Safeguards—a Review......Page 28
Literature Cited......Page 33
3 Nuclear Safeguards and the NBS Standard Reference Material's Program......Page 35
4 Decision Analysis for Nuclear Safeguards......Page 42
DECISION ANALYSIS......Page 44
PROBLEM STATEMENT......Page 47
THE LIKELIHOOD RATIO......Page 48
SEQUENTIAL DECISIONS......Page 49
SOME DECISION TESTS......Page 50
The One-State Kalman Filter Statistic......Page 51
The CUSUM Statistic......Page 53
The Two-State Kalman Filter Statistic......Page 54
CORRELATIONS......Page 56
Procedure......Page 58
Displaying the Results......Page 59
The Process......Page 60
The Materials Accounting System......Page 63
Results......Page 64
LITERATURE CITED......Page 69
Method......Page 73
Abstract......Page 77
Literature Cited......Page 80
AUTOMATES FOR DIRECT ANALYSIS......Page 81
DATA PROCESSING......Page 82
CONCLUSIONS......Page 84
Introduction......Page 90
Isotopic Functions and Ratios......Page 92
Pu/U Ratio Method(5)......Page 93
Recent Developments......Page 98
Data Base......Page 99
Literature Cited......Page 102
I. TECHNIQUE DESCRIPTION......Page 103
A. Radioisotopic Sources......Page 107
B. Bremsstrahlung Sources......Page 119
III. FUTURE APPLICATIONS......Page 123
C. Portable Instrumentation......Page 128
REFERENCES......Page 130
9 Application of On-Line Alpha Monitors to Process Streams in a Nuclear Fuel Reprocessing Plant......Page 132
EXPERIMENTAL......Page 134
RESULTS......Page 141
CONCLUSIONS......Page 147
Literature Cited......Page 150
10 Uranium and Plutonium Analyses with Well-Type Ge(Li) Detectors1......Page 152
Plutonium Analysis with the Well-Type Ge(Li) Detectors......Page 153
Uranium Analysis with Ge(Li) Detector......Page 157
Discussion......Page 163
Literature Cited......Page 164
B. Radioactive Decay and Sample Specific Power......Page 166
C. Air-Chamber Calorimeters......Page 170
D. Small-Sample Calorimeter......Page 173
E. Data Analysis......Page 180
F. Results......Page 182
ABSTRACT......Page 185
LITERATURE CITED......Page 186
12 Performance of an Accountability Measurement System at an Operating Fuel Reprocessing Facility......Page 187
OVERVIEW OF FUEL PROCESSING AT THE ICPP (1)......Page 188
INTERFACE TO THE ACCOUNTABILITY MEASUREMENT SYSTEM......Page 189
Sample Preparation and Homogeneity Checks......Page 192
Mass Spectrometry......Page 197
Sampling......Page 198
Final Product Measurement Sampling and Archive Samples......Page 199
QUALITY CONTROL PROGRAM......Page 200
Sample Throughput......Page 202
Analytical Measurements......Page 204
STUDIES IN PROGRESS......Page 205
LITERATURE CITED......Page 207
A......Page 209
D......Page 210
F......Page 211
I......Page 212
M......Page 213
N......Page 214
P......Page 215
S......Page 216
T......Page 217
X......Page 218
Z......Page 219

Citation preview

Nuclear Safeguards Analysis Nondestructive and Analytical Chemical Techniques

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Nuclear Safeguards Analysis Nondestructive and Analytical Chemical Techniques E . A r n o l d H a k k i l a , EDITOR Los Alamos Scientific Laboratory

Based on a symposium sponsored by the Division of Nuclear Chemistry and Technology at the 175th Meeting of the American Chemical Society, Anaheim, CA, March 13-17,

1978.

79

ACS SYMPOSIUM SERIES

AMERICAN WASHINGTON,

CHEMICAL D.

SOCIETY C.

1978

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

TK 9360 .Ν854 Copy 1

Nuclear safeguards a n a l y s i s

Library of Congress

Dat

Nuclear safeguards analysis. (ACS symposium series; 79 ISSN 0097-6156) Bibliography: p. 214 + x. Includes index. 1. Nuclear fuels—Testing—Congresses. 2. N u ­ clear fuels—Analysis—Congresses. 3. Atomic energy industries—Security measures—Congresses. I. Hakkila, E. Arnold, 1931. II. American Chemical Society. Division of Nuclear Chemistry and Technology. II. Series: American Chemical Society. ACS symposium series; 79. TK9360.N854 ISBN 0-8412-0449-7

621.48'35 78-12706 ACSMC8 79 1-214 1978

Copyright © 1978 American Chemical Society A l l Rights Reserved. The appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective works, for resale, or for information storage and retrieval systems. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by A C S of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, repro­ duce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED IN THE UNITED STATES OF AMERICA

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ACS Symposium Series Robert F. G o u l d , Editor

Advisory Board Kenneth B. Bischoff

Nina I. McClelland

Donald G . Crosby

John B. Pfeiffer

Jeremiah P. Freeman

Joseph V . Rodricks

E. Desmond Goddard

F. Sherwood Rowland

Jack Halpern

Alan C. Sartorelli

Robert A . Hofstader

Raymond B. Seymour

James P. Lodge

Roy L. Whistler

John L. Margrave

Aaron Wold

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

FOREWORD The ACS SYMPOSIUM SERIES was founded in 1974 to provide

a medium for publishin format of the Serie parallel g IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

PREFACE Nuclear

safeguards is becoming an increasingly important factor in the

public acceptance of nuclear energy, particularly at the end of the nuclear fuel cycle where strategic nuclear materials ( S N M ) in the form of high-purity plutonium and enriched uranium are available in concentrated forms that are attractive to a potential divertor.

Effective safe-

guarding of nuclear materials relies on a combination of physical security, materials control, and material No materials control or accountability system can be considered adequate without suitable measurement techniques. Measurement methodology must provide timely, rapid, precise, and accurate means of determining location and quantity of S N M . In-line or at-line measurement techniques rely heavily on nondestructive analysis ( N D A ) , x-ray, gamma-ray,

including

or alpha-particle emission or absorption, active

passive neutron interrogation, or calorimetry.

or

These N D A methods are

complemented by conventional analytical chemical methods that, although are often not as rapid, are capable of providing improved precision and accuracy.

Finally, it must be recognized that no measurement system is

complete without a standards program whereby data can be correlated to precisely known reference materials which can be traced to a national standards program. This symposium on nondestructive and analytical chemical techniques in nuclear safeguards was organized to review some of the methodology required for an effective measurement program. The overall safeguards program in the national laboratories is directed from the Department of Energy, Office of Safeguards and Security ( D O E - O S S ) .

Chapter One

reviews safeguards needs as assessed by D O E - O S S while the following two chapters review the standard-materials programs operated by the New Brunswick Laboratory and the National Bureau of Standards, respectively. Chapters Four and Five discuss the development of data evaluation methodology for diversion detection in dynamic materials accounting, which is a key element in future safeguards systems, and the nonlinear curve fitting techniques that allow for both standards and measurement uncertainties. T h e key input-accountability measurement for nuclear fuel reprocessing plants will be at the accountability tank.

This measurement is

correlated with plant output measurements and with reactor operating data, and is discussed in Chapters Six and Seven. T h e next four chapters ix In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

describe some of the N D A instrumentation methods being investigated for on-line applications, while the final chapter (which was not presented at the symposium) describes an accountability system at an operating reprocessing plant. It includes a description of some of the measurement techniques and presents typical data that have been obtained. I want to express my thanks to the participants for their contributions toward making the symposium a success, and to Dr. Clemens Auerbach of Brookhaven National Laboratory fox chairing one of the sessions. Safeguards Systems Group Q-4

E . ARNOLD HAKKILA

Los Alamos Scientific Laboratory Los Alamos, N M June 20, 1978

χ In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1

Safeguards N e e d s in t h e M e a s u r e m e n t A r e a : t h e R e a l m of

Measurements

GLENN HAMMOND Office of Safeguards and Security, U.S. Department of Energy (DOE), Washington, DC 20545 CLEMENS AUERBACH Department of Nuclear Energy, Brookhaven National Laboratory, Upton, NY 11973 The ACS meeting an Analytical Chemical Technique a timely forum for permitting all of us from the various measurement areas in the nuclear field to participate and contribute to the v i t a l safeguards challenges. We wish to jointly share some of our ideas on measurements for safeguards, their evolution, and highlights and objectives of the emerging measurement advances. DOE's safeguards program relates to a l l its nuclear materials and f a c i l i t i e s , but concentrates on the more readily usable forms of f i s s i l e or special nuclear material (SNM) - plutonium, uranium enriched in 235 and 233 . I t supports the development of safeguards concepts for new power reactor designs and related fuel cycle f a c i l i t i e s . The general objective of the nation's safeguards program is to prevent successful malevolent acts involving special nuclear material and f a c i l i t i e s . The term "safeguards" then is used in a broad sense to include physical protection and materials control measures to deter and detect theft and to provide a monitoring and accountability capability for SNM flow streams, transactions and inventories. In addition, DOE considers U. S. national security to dictate that nuclear materials and f a c i l i t i e s wherever they appear in the world, should be protected against malevolent action as well as safeguarded internationally against nuclear proliferation. Reliable materials control and accountability include the need for (1) timely characterization of the material to determine the intensity of protection needed and quantitative determination of what, where and how much material is being protected (or requires protection) ; (2) rapid detection and localization of a loss and backup to physical protection; (3) effective means for investigation and, i f necessary, to i n i t i a t e actions for recovery, and (4) frequent testing for credible confirmatory assessment that the protection and control systems are working properly and have not been U

U

This chapter not subject to U.S. copyright. Published 1978 American Chemical Society In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2

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circumvented. The continuous monitoring of m a t e r i a l to meet these needs w i l l , i n a d d i t i o n , help meet plant r e q u i r e ­ ments f o r process and q u a l i t y c o n t r o l , materials management, c r i t i c a l i t y c o n t r o l and h e a l t h and s a f e t y . To give you a p i c t u r e of the important r o l e that measure­ ments play i n safeguards and the development necessary f o r s u c c e s s f u l implementation, we would l i k e to f i r s t review b r i e f l y the h i s t o r y of nuclear m a t e r i a l s measurements; second, the r a t i o n a l e f o r r e l i a b l e measurement i n m a t e r i a l s c o n t r o l and a c c o u n t a b i l i t y ; t h i r d , types of measurements of nuclear m a t e r i a l s i n c l u d i n g t r a d i t i o n a l chemical and i s o t o p i c analyses, and the newer non-destructive techniques; f o u r t h , a n a t i o n a l nuclear standards and measurement assurance program; and f i n a l l y , the challenges we see i n accomplishing the various tasks i n v o l v e d . BACKGROUN The c o n t r o l and measurements of nuclear m a t e r i a l s are not new. The nuclear m a t e r i a l s produced at Oak Ridge and Hanford i n the e a r l y 1940's were guarded c a r e f u l l y because of t h e i r extremely l i m i t e d q u a n t i t i e s and very s e n s i t i v e p o t e n t i a l m i l i t a r y a p p l i c a t i o n . The years just preceding World War II were marked by a dramatic e v o l u t i o n of a n a l y t i c a l chemistry of nuclear m a t e r i a l s as a science, drawing f r e e l y on developments i n p h y s i c a l chemistry and other r e l a t e d d i s ­ ciplines. Since U. S. s c i e n t i s t s were i n the f o r e f r o n t of some of these developments, the Manhattan Project was able, j u s t as i n a number of other areas, to p r o f i t not only from the new advances but a l s o from d i r e c t c o l l a b o r a t i o n with the key s c i e n t i s t s r e s p o n s i b l e f o r them. With the a i d of i n d i v i d u a l s l i k e Ν. H. Furman of Princeton U n i v e r s i t y , C. F. Metz of the then newly e s t a b l i s h e d Los Alamos S c i e n t i f i c Laboratory and many others, the a n a l y t i c a l procedures d e v e l ­ oped i n those days went f a r beyond s e r v i n g t h e i r immediate purpose. In c o n j u n c t i o n with new developments i n r a d i o chemistry, microchemistry and separation techniques, these procedures set a trend f o r a n a l y t i c a l techniques which has not been surpassed since, and indeed gave major impetus to the major advances i n a c t i n i d e chemistry. In s i m i l a r f a s h i o n , mass spectrometric techniques f o r measuring the i s o t o p i c composition of uranium were developed i n response to the demands of the Manhattan P r o j e c t , to a point where they could e v e n t u a l l y be adopted by the c i v i l i a n nuclear i n d u s t r y without much fundamental change. During the e a r l y years, the r e l a t i v e l y small p h y s i c a l i n v e n t o r i e s were d i f f i c u l t - t o - m e a s u r e however, using a v a i l ­ able manual techniques which were tedious and time-consuming. Methods and techniques f o r chemical and i s o t o p i c analyses were s t i l l being developed f o r the new m a t e r i a l s . There

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1.

H A M M O N D

AND

AUERBACH

Realm

of

Measurements

was v i r t u a l l y no instrumentation to reduce a n a l y s t s time, few standard reference m a t e r i a l s or standard methodology, and few l a b o r a t o r i e s for intercomparison of r e s u l t s . In f a c t , i n many cases, the a n a l y s i s was performed by the anal y s t who had just developed the method, and s t a f f who were f a m i l i a r with s t a t i s t i c a l methodology were not always a v a i l able to compare and review r e s u l t s . S h o r t l y a f t e r the war, the Atomic Energy Act placed r e s p o n s i b i l i t y for t h i s new energy source i n the hands of a c i v i l i a n agency. The nuclear m a t e r i a l processes and operations were s t i l l being developed and lacked e f f i c i e n c y . The m a t e r i a l was expensive to produce, and emphasis was placed on f i n a n c i a l r e s p o n s i b i l i t y for c o n t r o l . In subsequent years, p r i o r i t i e s — t e c h n i c a l , economic, and p o l i t i c a l — r e l a t e d to nuclear energy changed. L e g i s l a t i o n , the 1954 r e v i s i o f th Atomi t d th P r i v a t e Ownership Act o expansion of the use o energy Two years l a t e r i n 1966, f e d e r a l r e g u l a t i o n s were adopted which placed a s p e c i f i c o b l i g a t i o n on the domestic p r i v a t e i n d u s t r i a l sector to safeguard SNM. When i n t e r n a t i o n a l t e r r o r i s m e s c a l a t e d i n the e a r l y 1970's, nuclear m a t e r i a l s and r e l a t e d f a c i l i t i e s , at home and abroad, were recognized as p o s s i b l e targets for t e r r o r i s t purposes because of the p o t e n t i a l f o r extensive malevolent use and the growing a n t i nuclear i n t e r e s t s . The concept of balanced and i n t e g r a t e d systems was recognized as a means to improve e f f e c t i v e n e s s of safeguards. These developments led t o , among other t h i n g s , e v o l u t i o n a r y changes i n chemical and i s o t o p i c measurement methods along the l i n e s of i n c r e a s i n g r e l i a b i l i t y and speed u s i n g standards and automation. The AEC and i t s successor organi z a t i o n s (ERDA, NRC, DOE) have c o n s i s t e n t l y played a major r o l e i n supporting these a c t i v i t i e s , with the r e s u l t that measurement techniques at the U. S. Government-owned l a b o r a t o r i e s have become unique i n terms of s i z e , v e r s a t i l i t y and s o p h i s t i c a t i o n . I n t e r n a t i o n a l safeguards, as c a r r i e d out by the I n t e r n a t i o n a l Atomic Energy Agency (IAEA), places r e l i a n c e on m a t e r i a l s measurements i n a c c o u n t a b i l i t y systems. Signif cance i s attached to q u a n t i t i e s of nuclear m a t e r i a l s that could be used by a country as part of a nuclear e x p l o s i v e device. DOE, i n cooperation with other U. S. Government agencies, i n c l u d i n g the State Department, the Arms C o n t r o l and Disarmament Agency (ACDA), and the Nuclear Regulatory Commission (NRC) provides both safeguards experts and equipment to a s s i s t the IAEA. Implementation includes d i r e c t i n g a technology base towards answering t e c h n i c a l questions posed by U. S. n o n - p r o l i f e r a t i o n i n i t i a t i v e s and by U. S. p a r t i c i p a t i o n i n the I n t e r n a t i o n a l Nuclear Fuel Cycle

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

NUCLEAR

4

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ANALYSIS

E v a l u a t i o n (INFCE) program being conducted by the IAEA. Today, n a t i o n a l and i n t e r n a t i o n a l safeguards concerns are being addressed i n the development of concepts and supporting measurement technology for safeguard systems f o r spent f u e l storage, uranium enrichment, chemical reprocessing or coprocessing and p r o l i f e r a t i o n - r e s i s t a n t a l t e r n a t i v e f u e l c y c l e s . These e f f o r t s include major support to a n a t i o n a l N o n p r o l i f e r a t i o n A l t e r n a t i v e Systems Assessment Program (NASAP). Today, f u e l c y c l e a l t e r n a t i v e requires a comprehensive study and e v a l u a t i o n of measurement methods and instruments for the range of m a t e r i a l forms and compositions which are c h a r a c t e r i s t i c of the r e l a t e d processes. Accuracy, p r e c i s i o n and o p e r a t i o n a l features are required for o n - l i n e and a t - l i n e instrumentation to optimize m a t e r i a l s management, c o n t r o l and accounting systems RATIONALE FOR

AN EFFECTIV

Measurements and measurement q u a l i t y assurance programs are v i t a l to m a t e r i a l s c o n t r o l and a c c o u n t a b i l t y safeguards systems. M a t e r i a l balance accounting i s drawn around a plant and several major portions of the plant processes by adding a l l measured r e c e i p t s to the i n i t i a l measured inventory and s u b t r a c t i n g a l l measured removals from the f i n a l measured inventory. Measurements e s t a b l i s h the q u a n t i t i e s of nuclear m a t e r i a l i n each c u s t o d i a l area and a f a c i l i t y as a whole as one of a number of safeguards subsystems c o n t r i b u t i n g to the d e s i r e d c a p a b i l i t y to l o c a l i z e losses and i n generating and assessing safeguard alarms. Of course, appropriate checks and balances are required to detect mistakes and protect the m a t e r i a l accounting system from fradulent source data; and a s t r i c t measurement q u a l i t y assurance program i s necessary to ensure the accurate c a l i b r a t i o n of the measurement systems and the r e p r o d u c i b i l i t y of the measurements. As part of the safeguards system, nuclear f a c i l i t i e s are required to e s t a b l i s h and r e p o r t , on a regular b a s i s , m a t e r i a l balances based on these measured values. Regul a t i o n s to t h i s e f f e c t have been promulgated by DOE and NRC. These r e g u l a t i o n s center on the concept of inventory d i f f e r e n c e s (ID), p r e v i o u s l y known as M a t e r i a l Unaccounted For (MUF), and defined by the expression ID = BI + A where BI A EI

-EI

-R

beginning inventory a d d i t i o n s to inventory p h y s i c a l inventory ending inventory

since the

last

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1.

R

H A M M O N D

-

AND

AUERBACH

Realm

of

Measurements

removals from inventory since the l a s t p h y s i c a l inventory.

If a l l uncertainties, biases, t r a n s c r i p t i o n errors, process holdups, unmeasured l o s s e s , e t c . are properly accounted f o r , then i n the absence of t h e f t or d i v e r s i o n ID should be zero. The r e g u l a t i o n s s t i p u l a t e that ID s exceeding predetermined l i m i t s of e r r o r (LEID) s h a l l be viewed as the r e s u l t of p o s s i b l e t h e f t or d i v e r s i o n of nuclear m a t e r i a l and appropriate a c t i o n taken. L i m i t s on how large the measurement u n c e r t a i n t y may be, based e i t h e r on a f i x e d amount or on a r a t i o of throughput, are determined by s t a t i s t i c a l means. The s t a t i s t i c a l means and appropriate mathem a t i c a l modeling techniques have r e c e n t l y received a d d i t i o n a l i n t e r e s t s by DOE and some of i t s c o n t r a c t o r s . The goal i s to develop s t a t i s t i c a l propagatio methodolog which w i l l permit e v a l u a t i o n measurement c o n t r o l data goa grade approac whereby the LEID values w i l l r e f l e c t the s t r a t e g i c s i g n i f i cance of a given nuclear m a t e r i a l stream (flow or i n v e n t o r y ) . Much has been w r i t t e n on the use of mathematical s t a t i s t i c s i n e v a l u a t i n g the complex problems associated with safeguards systems. We note i n p a r t i c u l a r the work by John Jaech, " S t a t i s t i c a l Methods i n Nuclear M a t e r i a l C o n t r o l " Q ). 1

THE

REALM OF MEASUREMENTS

The realm of measurements for safeguards includes a v a r i e t y of techniques r e q u i r e d for c h a r a c t e r i z i n g and determining nuclear m a t e r i a l q u a n t i t i e s i n feed, process, product and waste streams; f o r standards and measurement c o n t r o l s , performance e v a l u a t i o n and system o p t i m i z a t i o n ; and f o r independent v e r i f i c a t i o n by a safeguards i n s p e c t o r ate . An e f f e c t i v e safeguards measurement system must combine the elements of v e r s a t i l i t y , r e l i a b i l i t y and t i m e l i n e s s . Streams to be measured include m a t e r i a l s ranging from essent i a l l y pure uranium and plutonium compounds, which are r e l a t i v e l y easy to sample and d i s s o l v e , to heterogeneous and i n t r a c t a b l e s o l i d waste generated i n the course of processing operations. This may include such d i v e r s e items as used c a s t i n g c r u c i b l e s , contaminated paper, rags, rubber gloves, f l o o r and hood sweepings, e t c . Each stream must be measured with an accuracy and p r e c i s i o n commensurate to the c o n t r i b u t i o n which the stream makes to the o v e r a l l nuclear m a t e r i a l balance. The guiding p r i n c i p l e i s the establishment of a f u l l y measured m a t e r i a l balance w i t h i n predetermined l i m i t s of e r r o r . To s a t i s f y these wide-ranging and sometimes c o n f l i c t i n g demands, a systematic and j u d i c i o u s choice must be made

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

6

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SAFEGUARDS

ANALYSIS

between methods which may be considered i n three i n t e r r e l a t e d areas: (1) bulk measurements which are d i r e c t e d to t o t a l volume and flow r a t e , gross and net weights, and t o t a l piece count; (2) sampling which i s d i r e c t e d to obt a i n i n g a r e p r e s e n t a t i v e and t r a c t a b l e p o r t i o n of a t o t a l batch under c o n s i d e r a t i o n ; and (3) a n a l y t i c a l determinations which are d i r e c t e d to s p e c i f i c c h a r a c t e r i s t i c s (chemical, p h y s i c a l , nuclear) of the m a t e r i a l under c o n s i d e r a t i o n . A n a l y t i c a l measurements then may be categorized broadly i n t o chemical and nondestructive methods. Chemical methods, i n the present context, are based on sampling followed by laboratory measurements of e i t h e r c o n c e n t r a t i o n or i s o t o p i c composition of SNM. Combined with appropriate bulk measurements these methods y i e l d the t o t a l quantity of SNM i n a given flow stream or inventory stratum. Nondestructive a n a l y s i s (NDA) i s based on the nuclear p r o p e r t i e s of uranium and plutonium; these p r o p e r t i e SNM content of m a t e r i a s e n t a t i v e fashion or which does not e a s i l y y i e l d to d i s solution . It i s now recognized that a t r u l y e f f e c t i v e safeguards measurement system must make concerted use of both chemical and nondestructive methods. A c c o r d i n g l y , the thrust of recent DOE-sponsored research and development has been towards p o t e n t i a l s o l u t i o n s which incorporate the most d e s i r a b l e aspects of both approaches. Work at Los Alamos S c i e n t i f i c Laboratory, Lawrence Livermore Laboratory, New Brunswick Laboratory (now l o c a t e d at Argonne, I l l i n o i s ) and at other l a b o r a t o r i e s and f a c i l i t i e s , i s d i r e c t e d at making chemical methods both more t i m e l y by way of automation, and more responsive to non-homogeneous or otherwise i n t r a c t able m a t e r i a l s , even to the extent of i n c o r p o r a t i n g some aspects of NDA methodology. At the same time, advances i n e l e c t r o n i c s and detector c a p a b i l i t y combine to make p o s s i b l e i n c r e a s i n g l y s o p h i s t i c a t e d NDA approaches, i n terms of both v e r s a t i l i t y and accuracy. A s i g n i f i c a n t aspect of these developments i s the c l o s e c o l l a b o r a t i o n between DOE cont r a c t o r l a b o r a t o r i e s and f a c i l i t i e s abroad, notably i n the Federal Republic of Germany and other members of the European community and the I n t e r n a t i o n a l Atomic Energy Agency (IAEA). Some of these developments w i l l be covered i n d e t a i l by other p a r t i c i p a n t s i n t h i s Symposium. Other than a few exceptions, chemical methods i n use today are based i n essence on developments which took place during the Manhattan Project and have not changed s i g n i f i c a n t l y i n terms of the general p r i n c i p l e s i n v o l v e d . In 1963, the AEC with the a s s i s t a n c e of an Advisory Committee f o r Standard Reference M a t e r i a l s and Methods of Measurement reviewed, evaluated, and published "Selected Measurement Methods for Plutonium and Uranium i n the Nuclear

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1.

H A M M O N D

AND

AUERBACH

Realm

of

Measurements

Fuel C y c l e " (j2). The p u b l i c a t i o n was r e v i s e d i n 1972 to recognize i n t e r v e n i n g improvements (3). These wet a n a l y t i c a l methods are i n existence at nuclear f a c i l i t i e s to measure uranium and plutonium i n a v a r i e t y of m a t e r i a l s — metal, a l l o y s , s a l t s and oxides. Much of DOE's work r e l a t e d to the improvement and automation of a n a l y t i c l methods to reduce u n c e r t a i n t i e s i n i n v e n t o r i e s or m a t e r i a l s balance c o n t r o l i s being c a r r i e d out at the New Brunswick Laboratory (NBL) and the Lawrence Livermore Laboratory (LLL); and at the Los Alamos S c i e n t i f i c Laboratory (LASL) r e l a t e d to fast d i s s o l u t i o n methods f o r r e f r a c t o r y nuclear m a t e r i a l s , and the t e s t i n g of an inexpensive mass spectrometer f o r i n - p l a n t i n s p e c t i o n use. The Davies-Gray method which i s used f o r determining uranium has been the subject of extensive development work both at NBL and LLL. Th o r i g i n a l method i based th r e d u c t i o n of U(VI) to U(IV followed by o x i d a t i o n o Fe(ll) presence of a Mo(Vl) c a t a l y s t and t i t r a t i o n with I^C^Oy to a c o l o r i m e t r i c ( v i s u a l ) end p o i n t . The method was improved and r e f i n e d at NBL by the a d d i t i o n of V(IV) to the s o l u t i o n to markedly speed up the attainment of e q u i l i b r i u m , which allowed the use of potentiometic end-point d e t e c t i o n . These e f f o r t s have r e s u l t e d i n a f u l l y automatic uranium t i t r a t i o n system, developed by LLL and d e l i v e r e d to the new NBL s i t e at Argonne N a t i o n a l Laboratory (ANL) i n 1976. This system i s being tested c u r r e n t l y f o r n o n - i r r a d i a t e d uranium, i n c l u d i n g uranium a l l o y s and scrap. Some 44 samples can be analyzed i n an 8 hour day with a r e l a t i v e standard d e v i a t i o n of about 0.1%, using 20-150 mg samples. Complete f a u l t and malfunction d e t e c t i o n hardware and software are used to permit unattended operation. An a t t r a c t i v e feature of t h i s system i s that i t a u t o m a t i c a l l y shuts down should data not match standard uranium values. A n a l y t i c a l r e s u l t s are c a l c u l a t e d and p r i n t e d on a hard copy minicomputer. The A n a l y t i c a l Chemistry Group at LASL has been r e s p o n s i ble f o r a large number of important developments i n the s a f e guards measurement area. One of the more i n t e r e s t i n g ones concerns an o v e r a l l a n a l y t i c a l system f o r scrap and other h a r d - t o - d i s s o l v e m a t e r i a l . The system i s depicted schemati c a l l y i n Figure 1, which demonstrates how an o v e r a l l e r r o r of l e s s than 1.5% may be a t t a i n e d even though about 10% of the sample cannot be d i s s o l v e d . A high pressure d i s s o l u t i o n technique i s employed, and subsequent automated chemical a n a l y s i s i s performed by a spectrophotometer system which was developed at LASL and has since been r e f i n e d . The instrument incorporates a solvent e x t r a c t i o n system and dual f i l t e r s which enable s e q u e n t i a l a n a l y s i s of U and Pu i n the same s o l u t i o n . The instrument can accommodate samples i n the m i l l i g r a m to submilligram range.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7

8

NUCLEAR

SAFEGUARDS

ANALYSIS

D i s s o l u t ion >90%

dissolved

Automated Chemical RSD* + 1 %

+ Σ I

V

( i ) T

( 1 5 )

»

i=0 where V j ( - ) and νχ( · ) ar urement e r r o r v a r i a n c e s i n t e r e s t i n g , even i f the m a t e r i a l - b a l a n c e e r r o r variances are not constant, because i t i s an estimate of the t o t a l amount of missing m a t e r i a l at any time during the p e r i o d o f i n t e r e s t . It i s g e n e r a l l y not optimal i n any sense, but i t has a u s e f u l p h y s i c a l i n t e r p r e t a t i o n and has become q u i t e common. A development analogous to that f o r the one-state Kalman f i l t e r y i e l d s the f o l l o w i n g SPRT: < - / 2 I In T I

, accept H

> + /2|ln Τ J

, accept Η

Q

I f

CUSUM (k)

Q

χ

, ,

(16)

otherwise, take another observation, which i s the same form as Eq. 12 i n that an s i o n i s compared to i t s standard d e v i a t i o n .

The Two-State Kalman F i l t e r

estimate

of

diver­

Statistic

I f the assumption that the inventory measurement e r r o r s are small compared to the t r a n s f e r measurement e r r o r s i s not v a l i d , then an approach devised by Pike and h i s coworkers (22,23,24,25) w i l l y i e l d a m a t e r i a l balance estimate having smaller v a r i a n c e than the one-state f i l t e r . The technique i s to estimate both the m a t e r i a l balance and the inventory, which means that the f i l t e r now has two s t a t e v a r i a b l e s r a t h e r than one. In r e c u r ­ sive form, the f i l t e r equations are

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

Decision

SHIPLEY

Analysis

47

I(k) = l ( k | k - l ) + B ( k ) [ l ( k ) - l ( k | k - l ) ]

,

1

M(k)

= M(k-l) + B ( k ) [ l ( k ) - l ( k | k - l ) ]

,

2

î(klk-l) = î(k-l) + T ( k - l ) - M(k-l)

(17)

,

and I(k) and M(k) are the inventory and material-balance estimates, r e s p e c t i v e l y , at time k based on a l l information through time k. The f i l t e r gains B^(k) and B (k) are given by 2

Vk) V

k

)

V (lc) flGr

v 7 k T

=

·

V

k

)

=

v

7

k

T

(

1

8

)

where Vj(k) and Vfg(k) respectively y mate e r r o r v a r i a n c e and the c^variance between the inventory and material-balance estimate ert*yrs. They are given r e c u r s i v e l y by Vj(k|k-l)V (k) I

V

î

(

k

)

=

Vj(k|k-l) +

v (k) x

(19) V-(k|k-l)V_(k) V

ÎM

( k )

" Vj(k|k-l) + V (k) x

'

with

Vj(k|k-1) = V j ( k - l ) - 2 V

îfi[

( k - l ) + V (k-1) + V ( k - l ) ft

T

:

(20) Vj (k|k-1) = V ft

îft

( k - 1 ) - V (k-1)

.

ft

The material-balance e r r o r variance at time k i s

2

V (k|k-1) f t i ) + v (k) fft

tyk) = v (k-D ft

The M(0)

V î ( k

( 2 1 )

x

filter is initiated with 1(0) = 1(0), Vj(0) = ν ( 0 ) , = 0, V ( 0 ) = oo, before. By a development s i m i l a r to that f o r the one-state filter, the SPRT can be shown to reduce to χ

M

a s

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

NUCLEAR

48

If

fi(k)

v^kl

< - /2 |ln TQ I

, accept H

Q

> + /2 |ln Ί

, accept H

1

χ

I

SAFEGUARDS

ANALYSIS

, ,

(22)

otherwise, take another o b s e r v a t i o n . G e n e r a l l y , t h i s t e s t w i l l be more s e n s i t i v e than Eq. 12 because the estimate e r r o r v a r i a n c e i s smaller. This formulation has two other advantages. First, i t pro­ v i d e s a b e t t e r estimate of the inventory. Second, the effects of c o r r e l a t e d m a t e r i a l balances caused by the common inventory measurement have disappeared as a r e s u l t of the f i l t e r s t r u c t u r e . However, we have bought these advantages at the expense of com­ p l e x i t y and information requirements.

A l l t e s t s such as those j u s t discussed are c a l l e d parametric because they depend upon knowledge of the s t a t i s t i c s of the measurement e r r o r s . They a l s o happen to work best when the measurement e r r o r s are Gaussian, a q u i t e common but by no means all-inclusive situation. I f the measurement e r r o r statistics are unknown or non-Gaussian, then nonparametric sufficient sta­ t i s t i c s ( 2 6 - 3 2 ) may give b e t t e r test results. In a d d i t i o n , nonparametric t e s t s can provide independent support f o r the r e s u l t s of parametric t e s t s even though nonparametric tests are g e n e r a l l y l e s s powerful than parametric ones under conditions for which the l a t t e r are designed. The two most common nonparametric t e s t s are the s i g n test and the Wilcoxon rank sum t e s t . The sufficient s t a t i s t i c for the sign test i s the t o t a l number of positive material balances. That f o r the Wilcoxon t e s t i s the sum of the ranks of the m a t e r i a l balances. The rank of a m a t e r i a l balance i s i t s r e l a t i v e p o s i t i o n index under a r e o r d e r i n g of the m a t e r i a l bal­ ances according to magnitude. Other, p o s s i b l y more e f f e c t i v e nonparametric t e s t s are being i n v e s t i g a t e d . Further discussion of nonparametric t e s t s i s beyond the scope of t h i s paper.

CORRELATIONS Consider f i r s t the problem of c o r r e l a t e d measurements, i n particular, correlated t r a n s f e r measurements. The following s i m p l i f i e d treatment i s due p r i m a r i l y to F r i e d l a n d (33,34,35). Let the a c t u a l net t r a n s f e r T ( k ) be represented by a

a

T ( k ) = T(k) - v(k) - w(k)

,

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

(23)

4.

SHIPLEY

Decision

Analysis

49

where T(k) i s the t r a n s f e r measurement, v(k) i s the random meas­ urement e r r o r ( i . e . , E[v(k)v(k+j) ] = 0 f o r a l l j ψ 0, and Ε [·] i s the expectation o p e r a t o r ) , and w(k) i s the s o - c a l l e d "systema­ t i c e r r o r . " L e t us assume that w(k) i s a b i a s that a r i s e s from instrument m i s c a l i b r a t i o n , say, and thus i s constant between c a l i b r a t i o n s . Further assume that the (constant) w(k) resulting from any c a l i b r a t i o n i s a Gaussian random v a r i a b l e w i t h mean zero and v a r i a n c e V . Then w(k) can be represented r e c u r ­ s i v e l y by the d i f f e r e n c e equation w

w(k) = a w(k-l) + ( l - a ) u ( k ) ,

k = 1,2,...,

0

i f a c a l i b r a t i o n j u s t occurred,

1

i f a c a l i b r a t i o n has not j u s t o c c u r r e d ,

(24)

where

and u(k) i s a Gaussian rando ance V equal to the covariance between t r a n s f e r measure ments. Equation 24 can be appended to the state equations f o r e i t h e r the one- or two-state Kalman f i l t e r , which w i l l then y i e l d an estimate of the b i a s w(k). Any systematic e r r o r can be t r e a t e d i n t h i s fashion merely by i n c r e a s i n g the order of the f i l t e r , but knowledge of the systematic e r r o r statistics is required. One of F r i e d l a n d s major r e s u l t s (33) i s that the optimum m a t e r i a l balance estimate can be expressed as w

!

M(k) = M(k) + Dw(k)

(25)

where M(k) i s the b i a s - f r e e estimate, computed as i f there were no b i a s , and D i s r e l a t e d to the r a t i o of the covariance o f M(k) and w(k) to the variance of w(k) . Thus, c a l c u l a t i o n o f M(k) can be decoupled from the b i a s estimate u n t i l the f i n a l s t e p . This k i n d of systmatic e r r o r i s an example o f a p o s i t i v e c o r r e l a t i o n , and f a i l u r e to account f o r i t has two d e l e t e r i o u s e f f e c t s . F i r s t , the m a t e r i a l - b a l a n c e estimate i s b i a s e d , pos­ s i b l y g i v i n g a biased d e c i s i o n . Second, the v a r i a n c e o f the material-balance estimate e r r o r appears to be s m a l l e r than i s a c t u a l l y the case. This may r e s u l t i n a d e c i s i o n that seems to be b e t t e r than i t i s . Now consider m a t e r i a l balances that are c o r r e l a t e d (nega­ t i v e l y ) through the common inventory measurement, as f o r the one-state Kalman f i l t e r . Write the k t h m a t e r i a l balance as a

a

M(k) = - I ( k ) + I ( k - 1 ) - v_(k) + v ( k - l ) + T ( k ) , T

a

(26)

where I ( k ) i s the k t h a c t u a l inventory and v j ( k ) i s the k t h inventory measurement e r r o r with variance V-j-(k) . Define

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

50

NUCLEAR

v^k) = + v ( k - l ) ,

v (k) = -v^k)

I

In

2

SAFEGUARDS

ANALYSIS

.

(27)

,

(28)

r e c u r s i v e form, these equations are

v (k) = - v ( k - l ) , x

v (k) = -v^k)

2

2

where v^ and V2 are now considered as s t a t e v a r i a b l e s just as i s the m a t e r i a l balance i n the one-state f i l t e r . In analogy to the treatment of p o s i t i v e c o r r e l a t i o n s , Eq. 28 can be appended to the state equations f o r the one-state f i l t e r ( f o r the twos t a t e f i l t e r there i s no need), which then gives estimates, νχ and v , of the inventory measurement e r r o r s . That i s , this method of t r e a t i n g the negative c o r r e l a t i o n s also generates improved inventory estimates which give b 2

I(k-l|k) = K k - l ) -

x

(k|k)

, (29)

I(k|k) = I(k) + v (k|k) 2

.

Notice that l(k|k) i s the f i l t e r e d estimate of the inventory at time k and i s based on the f i r s t k inventory measurements. The estimate l(k-l|k) a l s o uses the f i r s t k inventory measurements, but i t i s the lag-one, smoothed estimate of the inventory at time k-1. A negative c o r r e l a t i o n such as t h i s , contrasted to the p o s i ­ t i v e ones treated above, causes no b i a s i n the m a t e r i a l balance estimate. However, i t does r e s u l t i n a m a t e r i a l balance error v a r i a n c e that appears l a r g e r than a c t u a l i f the c o r r e l a t i o n i s ignored. The s e n s i t i v i t y of the corresponding d e c i s i o n test would, t h e r e f o r e , be degraded.

TEST APPLICATION Procedure As d i s c u s s e d above, we seldom w i l l know beforehand when d i v e r s i o n has s t a r t e d or how long i t w i l l l a s t . Therefore, the d e c i s i o n t e s t s must examine a l l p o s s i b l e , contiguous subsequences of the a v a i l a b l e m a t e r i a l s accounting data (1,2,3,18). That i s , i f at some time we have Ν m a t e r i a l balances, then there are Ν s t a r t i n g points f o r Ν p o s s i b l e sequences, a l l ending at the Nth, or c u r r e n t , m a t e r i a l balance, and the sequence lengths range from Ν to 1. Because of the s e q u e n t i a l a p p l i c a t i o n of the t e s t s , sequences with ending p o i n t s less than Ν have already been tested; those with ending p o i n t s g r e a t e r than Ν w i l l be done i f the t e s t s do not terminate before then.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

Decision

SHIPLEY

51

Analysis

Another procedure that helps i n i n t e r p r e t i n g the r e s u l t s of tests i s to do the t e s t i n g at several significance levels, or f a l s e - a l a r m p r o b a b i l i t i e s . This i s so because, i n p r a c t i c e , the test thresholds are never e x a c t l y met; thus, the true signifi­ cance of the data i s obscured. Several thresholds corresponding to d i f f e r e n t f a l s e - a l a r m p r o b a b i l i t i e s give at l e a s t a rough idea of the a c t u a l p r o b a b i l i t y of a f a l s e alarm.

D i s p l a y i n g the

Results

Of course, one of the r e s u l t s of most i n t e r e s t i s the suffi­ cient s t a t i s t i c . Common p r a c t i c e i s to p l o t the s u f f i c i e n t sta­ t i s t i c , with symmetric e r r o r bars of length twice the square root of i t s v a r i a n c e , vs the m a t e r i a l balance number. The ini­ t i a l m a t e r i a l balance an are chosen a r b i t r a r i l y campaign s t r u c t u r e of the process. For example, i f balances are drawn hourly, and a day c o n s i s t s of three s h i f t s , then the ini­ t i a l m a t e r i a l balance might be chosen as the f i r s t of the day, and the t o t a l number of m a t e r i a l balances might be 24, covering three s h i f t s . Remember, however, that t h i s choice is for dis­ play purposes only; the actual t e s t i n g procedure s e l e c t s a l l p o s s i b l e i n i t i a l p o i n t s and sequence lengths, and any sufficient s t a t i s t i c may be d i layed as seems appropriate. The other important r e s u l t s are the outcomes of the tests, performed at the s e v e r a l s i g n i f i c a n c e l e v e l s . A new t o o l , c a l l e d the alarm-sequence chart (1,2,3,18), has been developed to dis­ play these r e s u l t s i n compact and readable form. To generate the alarm-sequence c h a r t , each sequence causing an alarm i s assigned (1) a d e s c r i p t o r that c l a s s i f i e s the alarm according to its f a l s e - a l a r m p r o b a b i l i t y , and (2) a pair of integers ^ l > 2 ^ that are, r e s p e c t i v e l y , the indexes of the initial and f i n a l m a t e r i a l balance numbers i n the sequence. I t i s a l s o p o s s i b l e to d e f i n e ( r ^ , ^ ) as the sequence length and the f i n a l m a t e r i a l balance number of the sequence. The two defini­ tions are e q u i v a l e n t . The alarm-sequence chart i s a point plot of r ^ vs r f o r each sequence that caused an alarm, with the s i g n i f i c a n c e range of each point i n d i c a t e d by the p l o t t i n g sym­ bol. One p o s s i b l e correspondence of p l o t t i n g symbol to signifi­ cance i s given i n Table I. The symbol Τ denotes sequences of such low s i g n i f i c a n c e that i t would be fruitless to examine extensions of them; the l e t t e r Τ indicates their termination points. I t i s always true that r\ £ r so that a l l symbols l i e to the r i g h t of the line r^ = r through the origin. Examples of these charts are shown i n the s e c t i o n on r e s u l t s . r

r

2

2

2

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

52

NUCLEAR

SAFEGUARDS

ANALYSIS

TABLE I ALARM CLASSIFICATION FOR

Classification ( P l o t t i n g Symbol)

THE ALARM-SEQUENCE CHART

False-Alarm P r o b a b i l i t y ΙΟ"

A Β

5 χ

ίο"

to 5

3

to

3

to 5

ίο"

C

2

X

ίο" ίο"

X

ίο"

D

5 χ ΙΟ"

4

to

ίο"

Ε

ΙΟ"

4

to

ίο"

3

3

4

4

5

F 0.5

Τ

AN EXAMPLE The

Process

To demonstrate the a p p l i c a t i o n of d e c i s i o n a n a l y s i s , we present r e s u l t s from a study (2) of m a t e r i a l s accounting in a nuclear f u e l r e p r o c e s s i n g p l a n t s i m i l a r to the A l l i e d - G e n e r a l Nuclear S e r v i c e s (AGNS) chemical separations facility at Barnwell, South C a r o l i n a (BNFP). The BNFP (36) i s designed to use the Purex process to recover uranium and plutonium from power-reactor spent fuels c o n t a i n i n g e i t h e r enriched uranium oxide or mixed uranium-plutonium oxide. Nominal c a p a c i t y i s 1500 MT/yr of spent f u e l , which i s approximately equivalent to 50 kg/day of plutonium. For a p l a n t such as BNFP, the most d e s i r a b l e areas f o r mate­ r i a l s accounting would be those c o n t a i n i n g the l a r g e s t amounts of plutonium i n a form most a t t r a c t i v e to the d i v e r t o r . The plutonium at the head end of the process i s not a t t r a c t i v e be­ cause i t c o n t a i n s l e t h a l concentrations of f i s s i o n products and i s d i l u t e d approximately 100-fold with uranium. However, a f t e r the IB column, the bulk of the f i s s i o n products have been removed and the uranium/plutonium r a t i o has been reduced to 2/1. From t h i s p o i n t the plutonium becomes i n c r e a s i n g l y a t t r a c t i v e as i t proceeds through the process to the plutonium-nitrate storage tanks. Hence, t h i s area, the plutonium purification process (PPP), was s e l e c t e d f o r design of a dynamic m a t e r i a l s accounting system. A b l o c k diagram of the PPP i s shown i n F i g . 2. Typical values f o r c o n c e n t r a t i o n s and flow r a t e s are given i n Table I I , and Table I I I l i s t s nominal in-process i n v e n t o r i e s .

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

SHIPLEY

Decision

Analysis

Figure 2. Block diagram of the plutonium purification process

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

54

NUCLEAR

SAFEGUARDS

ANALYSIS

TABLE I I CONCENTRATIONS AND FLOW RATES IN THE PPP

Stream

Plutonium Concentration (g/L)

Flow (L/h)

IBP 3PCP

400

5

8

250

2AW

500

trace

3AW

215

0.1

3PD

32

trace

2BW 3BW

TABLE I I I IN-PROCESS HOLDUP IN TANKS AND VESSELS OF THE PPP

Identification^

Volume (L)

Plutonium Concentration

(g/D

a

Plutonium Holdup (kg)

4.942

7.4

IBP Tank

1500

2A Column

700

c

4.6

2B Column

500

c

2.8

3A Column

600

c

5.4

c

4.8

58.70

1.2

3Β Column

440

3PS Wash Column

20

3P Concentrator

60

250.

15.

a

These values are not flowsheet values of any existing reprocessing f a c i l i t y but represent t y p i c a l values w i t h i n r e a ­ sonable ranges of a workable flowsheet.

b

See F i g . 2.

c

A model of the c o n c e n t r a t i o n p r o f i l e s and the holdup i n the pulse columns i s described i n Ref. (2^).

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

Decision

SHIPLEY

55

Analysis

The M a t e r i a l s Accounting

System

To i s o l a t e the PPP as a u n i t process r e q u i r e s flow and con­ c e n t r a t i o n measurements at the IBP tank (input) and 3P concen­ t r a t o r (output). In a d d i t i o n , a c i d r e c y l e s (2AW, 3AW, 3PD) and organic r e c y c l e (2BW, 3BW) must be monitored f o r flow and con­ c e n t r a t i o n , and an estimate o f the in-process inventory must be obtained. Table IV gives the required measurements and some p o s s i b l e measurement methods and a s s o c i a t e d u n c e r t a i n t i e s . The r e l a t i v e p r e c i s i o n o f dynamic volume measurements i s estimated to be 3% (1σ) f o r the IBP tank, t h r e e f o l d more than f o r a conventional p h y s i c a l - i n v e n t o r y measurement because liquid is continuously flowing i n t o and out o f the tank during process­ i n g . Dynamic estimates o f plutonium c o n c e n t r a t i o n i n the IBP and 3P concentrator tanks can be obtained from d i r e c t , in-line measurements (by absorption-edg from combinations o f adjacen measurements.

TABLE IV MATERIALS ACCOUNTING MEASUREMENTS FOR THE PPP

Instrument Precision (1σ, %)

Calibration Error (1σ, %)

Measurement Point

Measurement Type

IBP, 3PCP streams

Flow meter Absorption-edge densitometry

1

0.5

1

0.3

Volume Absorption-edge densitometry

3

2A,2B,3A,3B columns

See text

5-20

2AW,2BW,3AW, 3BW, 3PD streams

Flow meter NDA

IBP surge tank

3

5 10

3PS column

See text

5-20

3P concentrator

Volume (constant) Absorption-edge densitometry

1.5

H i g h - q u a l i t y measurements o f the in-process plutonium tory i n the columns are the most d i f f i c u l t to make.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

inven­ In the

NUCLEAR

56

SAFEGUARDS

ANALYSIS

reference design, the columns are f u l l y instrumented f o r process control, i n c l u d i n g measurements o f the position o f the aqueous-organic i n t e r f a c e and o f the l e v e l and d e n s i t y o f l i q u i d i n the product-disengagement volume. Much of the column holdup i s i n the product-disengagement volume, and a good measurement of t h i s volume i s a v a i l a b l e . However, only a crude estimate of plutonium c o n c e n t r a t i o n can be made without additional instru­ mentation. R e l a t i v e p r e c i s i o n f o r column-holdup measurements i s estimated to be i n the range o f 5-20% (1σ). The 20% l i m i t appears to be conservative i n terms o f d i s c u s s i o n s with industry and DOE personnel. A p r e c i s i o n o f 10% should be p r a c t i c a b l e using the current p r o c e s s - c o n t r o l instrumentation. Improvements toward the 5% f i g u r e (or b e t t e r ) w i l l require a d d i t i o n a l research and development to i d e n t i f y optimum combinations of a d d i t i o n a l o n - l i n e instrumentation and improved models of column behavior. Waste and r e c y c l e stream fro th column d th t r a t o r i n the PPP are and NDA-alpha detector plutoniu alph monitors are already used f o r process c o n t r o l i n the reference design and r e q u i r e only modest upgrading (primarily calibration and s e n s i t i v i t y s t u d i e s ) to be used f o r a c c o u n t a b i l i t y as w e l l . Flow measurements i n the waste and r e c y c l e streams can be simple and r e l a t i v e l y crude (5-10%) because the amount o f plutonium i s small. A rough c a l i b r a t i o n o f the a i r l i f t s f o r l i q u i d flow may s u f f i c e , or continuous l e v e l monitors i n the appropriate headpots could provide the r e q u i r e d data. Several measurement s t r a t e g i e s have been i n v e s t i g a t e d , i n ­ c l u d i n g one i n which m a t e r i a l balances are drawn every hour, column inventory measurement p r e c i s i o n i s taken as 5%, and flow meters are r e c a l i b r a t e d every 24 hours. This i s the best o f the s t r a t e g i e s considered and i s the one on which the f o l l o w i n g r e s u l t s are based.

Results D e c i s i o n a n a l y s i s techniques have been used to evaluate the d i v e r s i o n s e n s i t i v i t y o f t h i s m a t e r i a l s accounting s t r a t e g y and others (2^). Part o f the e v a l u a t i o n c o n s i s t s of examining test r e s u l t s , i n the form o f estimate (sufficient s t a t i s t i c ) and alarm-sequence c h a r t s , f o r v a r i o u s time i n t e r v a l s . Examples of t y p i c a l one-day charts f o r the CUSUM and two-state Kalman f i l t e r , both with and without d i v e r s i o n , are given i n F i g s . 3 and 5; the h o r i z o n t a l marks i n d i c a t e the values o f the estimates, and the v e r t i c a l l i n e s are + 1σ e r r o r bars about those estimates. The corresponding alarm-sequence charts are shown i n F i g s 4 and 6. The d i v e r s i o n l e v e l f o r the lower charts i s 0.073 kg Pu/balance p e r i o d , which i s about 0.1 standard d e v i a t i o n o f a s i n g l e mate­ r i a l balance. Results o f a l a r g e number of t e s t s show that the

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Decision

SHIPLEY

Analysis

cn ZD CJ

5

10

15

20

25

MRTERIRL BRLRNCE NUMBER

Q_

2 +

CD

=3

CO

3

0-

"+-

—I— 15

MRTERIRL BRLRNCE NUMBER

Figure 3.

CUSUM

charts without diversion (upper) and with diversion (lower)

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

NUCLEAR

ι

1

1

SAFEGUARDS

r

20 +

•

15 +

Q_

az £ 10 4-

1 0

5

1 10

FINRL

5

10

1 15

1 20

25

POINT

15

20

F I N R L POINT

Figure 4. Alarm-sequence charts for the of Figure 3

CUSUMs

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ANALYSIS

SHIPLEY

Decision

Analysis

1

1

1

-

ι 1 1 1 1 1 1 1 ι . . . ι

)t'

-

1 0

li

5

1

1

1

10

15

20

25

MRTERIRL BRLRNCE NUMBER

1

1

!

--

I | t l t n m

m

r

1 -

— h

1

1

10

1 —

15

1

MRTERIRL BRLRNCE NUMBER

Figure 5. Kalman filter estimates of average missing material with­ out diversion (upper) and with diversion (lower)

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

NUCLEAR

60

SAFEGUARDS

Q_ _J CE

25

π

1

1—"

r

20 +

15 + CE

^

10 +

fl R BCDEDCDDCCBflflflC

1 0

5

1 10

FINRL

1 15

1 20

25

POINT

Figure 6. Alarm-sequence charts for the Kalmanfilter estimates of Figure 5

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ANALYSIS

4.

SHIPLEY

Decision

Analysis

61

two-state Kalman f i l t e r gives somewhat b e t t e r r e s u l t s than the CUSUM, as expected. In the course of e v a l u a t i o n , many such sets of charts are examined so that the random e f f e c t s of measurement e r r o r s and normal process v a r i a b i l i t y can be assessed; that i s , we perform a Monte Carlo study to estimate the sensitivity to d i v e r s i o n . In applying d e c i s i o n a n a l y s i s to data from a f a c i l i t y operating under a c t u a l c o n d i t i o n s , only one set of data w i l l be a v a i l a b l e f o r making d e c i s i o n s , r a t h e r than the m u l t i p l e data streams gen­ erated from a s i m u l a t i o n . In p a r t i c u l a r , direct comparison of charts with and without d i v e r s i o n , as shown here, w i l l be impos­ s i b l e . The decision-maker w i l l have to e x t r a p o l a t e from h i s t o r ­ i c a l information and from c a r e f u l process and measurement analy­ s i s to determine whether d i v e r s i o n has occurred. The r e s u l t s of the e v a l u a t i o n are given i n Table V. By com­ p a r i s o n , current r e g u l a t i o n u n c e r t a i n t y be l e s s tha accounting p e r i o d , which corresponds to 75 kg of plutonium f o r t h i s process. Such l a r g e improvement in diversion sensitivity i s p o s s i b l e through the combination of timely measurements with the powerful s t a t i s t i c a l methods of d e c i s i o n a n a l y s i s .

TABLE V DIVERSION SENSITIVITY FOR

Average D i v e r s i o n per Balance (kg Pu) 2.6

Detection Time (h)

THE

PPP

T o t a l at Time of Detection (kg

1

2.6

0.075

24

1.8

0.025

168

(1 week)

Pu)

4.2

LITERATURE CITED

1.

Shipley, J . P., Cobb, D. D., Dietz, R. J., Evans, M. L . , Schelonka, E. P., Smith, D. B . , and Walton, R. B., "Coordinated Safeguards for Materials Management in a Mixed-Oxide Fuel Facility," Los Alamos Scientific Laboratory report LA-6536 (February 1977).

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

62

NUCLEAR SAFEGUARDS ANALYSIS

2.

Hakkila, Ε. Α . , Cobb, D. D . , Dayem, Η. Α . , Dietz, R. J., Kern, Ε. Α . , Schelonka, E . P . , Shipley, J . P . , Smith, D. B . , Augustson, R. H . , and Barnes, J . W., "Coordinated Safeguards for Materials Management in a Fuel Reprocessing Plant," Los Alamos Scientific Laboratory report LA-6881 (September 1977).

3.

Dayem, Η. Α . , Cobb, D. D., Dietz, R. J., Hakkila, Ε. Α . , Kern, Ε. Α . , Shipley, J . P . , Smith, D. B . , and Bowersox, D. F., "Coordinated Safeguards for Materials Management in a Nitrate-to-Oxide Conversion Facility," Los Alamos Scientific Laboratory report LA-7011 (to be published).

4.

Keepin, G. R., and Maraman, W. J., "Nondestructive Assay Technology and In-Plant Dynamic Materials Control--DYMAC," in Safeguarding Nuclea Materials Proc Symp. Vienna Oct. 20-24, 197 Vienna, 1976), Pape , , pp

5.

Augustson, R. H . , "Development of In-Plant Real-Time Materials Control: The DYMAC Program," Proc. 17th Annual Meeting of the Institute of Nuclear Materials Management, Seattle, Washington, June 22-24, 1976.

6.

Howard, R. Α . , "Decision Analysis: Pespectives on Inference, Decision, and Experimentation," Proc. IEEE, Special Issue on Detection Theory and Applications 58, No. 5, 632-643 (1970).

7.

Ref. (2), Vol. II, App. E .

8.

Shipley, J . P . , "Decision Analysis in Safeguarding Special Nuclear Material," Invited paper, Trans. Am. Nucl. Soc. 27, 178 (1977).

9.

Shipley, J. P . , "Decision Analysis for Dynamic Accounting of Nuclear Material," paper presented at the American Nuclear Society Topical Meeting, Williamsburg, V i r g i n i a , May 15-17, 1978.

10.

Sage, A. P. and Melsa, J . L., Estimation Theory with Applications to Communications and Control (McGraw-Hill, 1971).

11.

Lehmann, Testing S t a t i s t i c a l Sons, Inc., 1959).

12.

Blackwell and Girshick, Μ. Α . , Theory S t a t i s t i c a l Decisions (Wiley, 1954).

Hypotheses

(John of

Wiley Games

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

and and

4. SHIPLEY

63

Decision Analysis

13.

Wald, Α . , Sequential Analysis (John Wiley 1947).

14.

Kalman, R. E., "A New Approach to Linear F i l t e r i n g and Prediction Problems," Trans. ASME J. Basic Eng. 82D, 34-45 (March 1960).

15.

Kalman, R. E . and Bucy, R. S., "New Results in Linear Filtering and Prediction Theory," Trans. ASME J. Basic Eng. 83D, 95-108 (March 1961).

16.

Meditch, J. S., Stochastic Optimal Control (McGraw-Hill, 1969).

17.

Jazwinski, Α. Η . , Stochastic Processes and F i l t e r i n g (Academic Press, 1970)

18.

Cobb, D. D . , Smith, D. B . , and Shipley, J . P . , Sum Charts in Safeguarding Special Nuclear submitted to Technometrics (December 1976).

19.

Duncan, A. J., Quality Control (R. D. Irwin, Inc., 1965).

20.

Page, E . S., "Cumulative Sum Charts," Technometrics 1, 1-9 (February 1961).

21.

Evans, W. D . , "When and How to Use Cu-Sum Technometrics 5, No. 1, 1-22 (February 1963).

22.

Pike, D. Η . , Morrison, G. W., and Holland, C. W., "Linear F i l t e r i n g Applied to Safeguards of Nuclear Material," Trans. Amer. Nucl. Soc. 22, 143-144 (1975).

23.

Pike, D. Η . , Morrison, G. W., and Holland, C. W., "A Comparison of Several Kalman F i l t e r Models for Establishing MUF," Trans. Amer. Nucl. Soc. 23, 267-268 (1976).

24.

Pike, D. H. and Morrison, G. W., "A New Approach to Safeguards Accounting," Oak Ridge National Laboratory report ORNL/CSD/TM-25 (March 1977).

25.

Pike, D. H. and Morrison, G. W., "A New Approach Safeguards Accounting," Nucl. Mater. Manage. VI, No. 641-658 (1977).

26.

Thomas, J . B . , "Nonparametric Detection," Proc. IEEE, Special Issue on Detection Theory and Applications 58, No. 5, 623-631 (May 1970).

Linear

and Sons,

Inc.,

Estimation

and

Theory

"Cumulative Materials,"

and Industrial

Statistics

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3,

No.

Charts,"

to 3,

NUCLEAR SAFEGUARDS

64

Z.,

Theory

27.

Hajek, J. and Sidak, Press, 1967).

28.

Carlyle, J. W. and Thomas, J. B . , "On Nonparametric Signal Detectors," IEEE Trans. Info. Theory IT-10, No. 2, 146-152 (1964).

29.

Tantaratana, S. and Thomas, J . B . , Detection of a Constant Signal," IEEE IT-23, No. 3, 304-315 (May 1977).

30.

Capon, J., "A Nonparametric Technique for the Detection of a Constant Signal in Additive Noise," 1959 IRE WESCON Convention Record, Part 4, San Francisco, August 1959.

31.

Gibson, J . D. and Melsa Nonparametric Detectio 1975).

32.

Puri, M. L . and Sen, P. Κ., Nonparametric Multivariate Analysis (Wiley, 1971).

33.

Friedland, B . , "Treatment of Bias in Recursive F i l t e r i n g , " IEEE Trans. Autom. Contr. AC-14, No. 4, 359-367 (1969).

34.

Friedland, B . , "Recursive F i l t e r i n g in the Presence of Biases with Irreducible Uncertainty," IEEE Trans. Autom. Contr. AC-21, No. 5, 789-790 (1976).

35.

Friedland, B . , "On the Calibration Problem," Autom. Contr. AC-22, No. 6, 899-905 (1977).

36.

"Barnwell Nuclear Fuel Plant-Separation F a c i l i t y Final Safety Analysis Report," A l l i e d General Nuclear Services, Barnwell, South Carolina (October 1975).

J

of

Rank

Tests

ANALYSIS

(Academic

"On Sequential Sign Trans. Info. Theory

L.

Introductio

t

Methods

IEEE

RECEIVED JUNE 9, 1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

in

Trans.

5

A Nonlinear

Method

for I n c l u d i n g the Mass U n c e r t a i n t y

of S t a n d a r d s a n d t h e S y s t e m M e a s u r e m e n t E r r o r s in t h e F i t t i n g of C a l i b r a t i o n C u r v e s

1

W. L. PICKLES, J. W. McCLURE, and R. H. HOWELL Lawrence Livermore Laboratory, Livermore, CA 94550 The goal of the wor highly accurate (0.1 to assay instruments where the accuracy of the standards available is the limiting factor, or at least a major source of calibration error. In reaching the ultimate accuracies possible for a particular NDA measurement system the instrument long-term precision is often not the limiting factor. The v a r i a b i l i t y of sample preparation and the accuracy and applicability of the standards used for c a l i bration of the instrument usually create the greatest source of uncertainty (1). We have developed a mathematical method of dealing with these types of errors in a s t a t i s t i c a l l y correct way. Our f i r s t test of this method was with standards accuracy for x-ray fluorescense analysis of freeze-dried (2) UNO . The method can also be used to evaluate the importance of sample v a r i a b i l i t y errors. The type of computer code we have used in this method is commercially available from several sources ( 3 , 4 ) as a package which requires only a small amount of input-output user generated software. 3

Method Our LLL XRFA system (5) has a repeatable precision which has been measured to be 0.1% (two standard deviations). In attempting to u t i l i z e this system for accountability measurements in the nuclear fuel cycle, we were continually frustrated by the lack of high accuracy solid samples in the mass range from 10 to 1000 yg. We were f i n a l l y able to produce UNO3 standards by a freeze-drying method with an NBS traceable accuracy of 0.2% (one standard deviation) (1). These samples were thought to have particle size absorption, but because of the uniform fibrous nature (1) of the freeze-dried samples i t was expected that these absorption effects would be calculable to high accuracy. We have used 100 of these standards to calibrate our XRFA instrument. Since the mass accuracy error of the standards was estimated to be twice as large as the instrument precision errors, we f e l t This chapter not subject to U.S. copyright. Published 1978 American Chemical Society In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

66

NUCLEAR

SAFEGUARDS

ANALYSIS

i t was p a r t i c u l a r l y important t o i n c l u d e the mass u n c e r t a i n t y i n the c a l i b r a t i o n procedure. Our approach was to t r e a t the mass values of the standards i n e x a c t l y the same way as we normally t r e a t the instrument's response t o those standards. That i s , the mass v a l u e of each standard i s a g r a v i m e t r i c a l l y measured q u a n t i t y . The g r a v i m e t r i c a l mass v a l u e , M-^, i s not the "true mass" o f the standard. I t d i f f e r s from the t r u e mass i n a normal way. The g r a v i m e t r i c a l l y measured mass, M-^, has a 67% p r o b a b i l i t y of d e v i a t i n g from the t r u e mass value by l e s s than 0.2%. We t h e r e f o r e created a s e t o f parameters which represent the t r u e mass values,

M There i s one X i , or t r u e mass, f o r each standard. I t i s now p o s s i b l e to use these new parameters i n expressing the instrument response c a l i b r a t i o n curv YFUN = G(A,B,C,y ,y ,X ) 1

2

i

The t r u e mass X^ of the standard i s one o f the v a r i a b l e s i n the c a l i b r a t i o n f u n c t i o n i n s t e a d o f being a f i x e d constant. Consequently, the t r u e mass, X i , may be f i t along with A,B,C,yi and y2, the " u s u a l " c a l i b r a t i o n curve f i t parameters. The r e s u l t of t h i s technique i s t o s t a r t from a s e t o f g r a v i m e t r i c a l l y measured S t a n d a r d mass values and measured XRFA i n s t r u ment responses t o those standards and a r r i v e at both the most probable, or t r u e mass, of the standard, and the most probable response v a l u e . T h i s i s diagrammed s c h e m a t i c a l l y i n F i g u r e 1. The f i t t i n g procedure i s accomplished by a commercially a v a i l a b l e (2), n o n - l i n e a r , unconstrained minimization, computer program. The program minimizes the q u a n t i t y chi-squared. Our chi-squared not only i n v o l v e s the d e v i a t i o n s i n the instrument response from the c a l i b r a t i o n curve as i s u s u a l , but must a l s o i n c l u d e the d e v i a t i o n s o f the g r a v i m e t r i c mass values from the t r u e mass. The value of chi-squared per degree of freedom i s a measure of the "goodness" of f i t of the c a l i b r a t i o n curve and true masses t o a l l the experimental data. Our chi-squared i s def i n e d i n F i g u r e 2. The expression f o r chi-squared has two sums of weighted, squared d e v i a t i o n s . The f i r s t of these terms i s past. I t i s d i f f e r e n t i n that the t r u e mass, X i , i s used i n p l a c e of the g r a v i m e t r i c a l l y measured mass, Mi- The second term i s new, and i s the sum of the squares of the d e v i a t i o n s of the measured s from the t r u e mass, weighted by the g r a v i m e t r i c e r r o r s . The cual c a l i b r a t i o n curve f u n c t i o n , YFUN, which we used i n t h i s j r k i s shown i n F i g u r e 3. The f u n c t i o n contains t h r e e terms; the f i r s t term i s a constant, the second i s a term that represents simple mass a b s o r p t i o n , and the t h i r d term allows f o r a b s o r p t i o n i n the long t h i n f i b e r s of UNO3 o r i e n t e d perpendicular to the plane of the sample. The f a c t that the f r e e parameters i n t h i s

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5.

PICKLES

E T A L .

Calibration

Curves

67

Most probable

standard value Figure 1. Overall result of nonlinear least squares fitting is a most probable system response value and a most probable standard mass value

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

NUCLEAR

SAFEGUARDS

ANALYSIS

System response R.-YFUN (A B ,M M ,C,[x]|2

Σ

r

.

2

r

2

A l m 0

s t normal

J CHISQUARED

[

Standards standard variations ,2

New contribution to CHISQUARED

Figure 2. New two-dimensional definition of chi-squared used in the nonlinear fitting technique. Note the use of true rather than gravimetric mass. To consistently use both types of errors chi-squared must include the standards mass errors.

Ι Ι ( Ι Ι Ι Ι I I I J Ι J I — ^ L - J l _ I L _ J L _ J I _ l L _ l l _ ,

Fibrous nature of standard creates particle size effects

Exciter YFUN = A + B [ 1 - e - i ] + M

m

C[1-e"V]

^Background ^Normal mass ^Rbrous particle absorption size absorption •

Thus the function becomes YFUN = A + B[1—β~ ι '] +C[1-e-/ 2 { ί } appear as products and that the expres­ s i o n f o r chi-squared contains X^'s which are f r e e parameters, d i c t a t e s the use of a n o n - l i n e a r f i t t i n g program. Results The f i n a l r e s u l t s of u s i n g t h i s technique i s a " b e s t - f i t " value f o r A,B,C,yi,y2* a l l the Xj/s as shown i n Figure 4 n u m e r i c a l l y and i n Figure 5 g r a p h i c a l l y . As can be seen i n F i g u r e 5, 40% of the under response i s due to simple mass absorption and 60% i s due t o p a r t i c l e s i z e a b s o r p t i o n . a

n

d

Errors A n o n - l i n e a r l e a s t squares f i t t i n g program does not use simple matrix i n v e r s i o n t o o b t a i n a unique best f i t value f o r each f r e e parameter and consequently does not produce a unique e r r o r matrix f o r the f r e e parameters estimate f th o v e r a l l e r r o r i s p o s s i b l e by tw ture of chi-squared spac para meter i s an i n d i c a t i o n of the s e n s i t i v i t y of the f i t t o that para­ meter. The second and more u s e f u l method i s to r e l a x the e r r o r s on the g r a v i m e t r i c masses and/or the instrument response p r e c i s i o n u n t i l a chi-squared per degree of freedom of approximately three i s obtained. A chi-squared per degree of freedom of three means the p r o b a b i l i t y that a l l the f i t parameters are w i t h i n one standard d e v i a t i o n of t h e i r " c o r r e c t " value i s 67%. We were able to o b t a i n a chi-squared per degree of freedom of three by r e l a x i n g the i n ­ strument response e r r o r s t o 0.2%. The c o n c l u s i o n we draw from t h i s i s we should accumulate counts on an unknown sample u n t i l the p r e c i s i o n of the response i s 0.1% and then the e r r o r we a s s i g n to the measurement of that sample w i l l be 0.2% (1 sigma). Summary We have found that n o n - l i n e a r f i t t i n g techniques as described here t o be a powerful method of c r e a t i n g r e a l i s t i c c a l i b r a t i o n curves f o r an NDA instrument and a p a r t i c u l a r standards s e t . The method uses both the g r a v i m e t r i c mass e r r o r s and the instrument response e r r o r s i n a s t a t i s t i c a l l y c o n s i s t e n t way. I t incorpo­ r a t e s the independent g r a v i m e t r i c measurement of the standards i n the c a l i b r a t i o n curve parameters thus e x t r a c t i n g a l l the e x p e r i ­ mental information a v a i l a b l e f o r the instrument response and the standards s e t . I t determines the a c t u a l most probable value of each standard mass. I t allows s e n s i t i v e s e l e c t i o n among the c a l i b r a t i o n curve models. I t e l i m i n a t e s the need t o cross measure standards, and i t allows a r e a l i s t i c a p p r a i s a l of the o v e r a l l accuracy e r r o r o f an NDA instrument and i t ' s standards.

Abstract At LLL we have used a sophisticated non-linear multiparameter f i t t i n g program to produce a best f i t calibration curve for the response of an x-ray fluorescence analyzer to uranium nitrate,

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

70

NUCLEAR SAFEGUARDS ANALYSIS

• A set of most probable model parameters Y F U N = 1.02 X 1 0 + 4 . 6 X 1 0 [ 1 - e " 6

s

2

1 x 1 0

~

4x

] + 5.6 X 1 0 [ 1 - e " - * s

7

3

1 0 _ 4 χ

]

i

i

!

Background

Normal

Fibrous particle

• A set of most probable standard values X DATA 4.454E+00 4.459E+00 9.521E+00

X FIT 4.294E+00 4.341E+00 9.594E+00

•

RES/SIGMA 1.599E+00 λ .186E+00 -7.339E-01

•

SIGMA 1.000E-01 1.000E-01 1.000E-01

•

Figure 4. Actual numerical results of our fitting method showing our best fit parameters

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

PICKLES

E T

A L .

Calibration

Curves

Mass of standard

Figure 5. Graphical representation of our best fit calibration curve showing the normal mass absorption (40%) and the fibrous particle-size absorption (60%) under responses from the linear. Particle size and mass absorption are approximately equal.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

72

NUCLEAR SAFEGUARDS ANALYSIS

freeze dried, 0.2% accurate, gravimetric standards. The program is based on unconstrained minimization subroutine, VA02A. The program considers the mass values of the gravimetric standards as parameters to be f i t along with the normal calibration curve parameters. The f i t t i n g procedure weights with the system errors and the mass errors in a consistent way. The resulting best f i t calibration curve parameters reflect the fact that the masses of the standard samples are measured quantities with a known error. Error estimates for the calibration curve parameters can be obtained from the curvature of the "Chi-Squared Matrix" or from error relaxation techniques. We have shown that non-dispersive XRFA of 0.1 to 1 mg freeze-dried UNO3 can have an accuracy of 0.2% in 1000 sec. x

Work performed under the auspices o f the U.S. Department of Energy by the Lawrence Livermor Laborator unde c o n t r a c t numbe W-7405-ENG-48. NOTICE "This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately-owned rights."

Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Department of Energy to the exclusion of others that may be suitable.

Literature Cited 1. Pietri, C. E., P u l l e r , J . S., Bingham, C. D., "The Chemical and I s o t o p i c A n a l y s i s o f Uranium, Plutonium, and Thorium i n Nuclear F u e l s , " Proceedings o f the ANS T o p i c a l Conference on A n a l y t i c a l Methods f o r Safeguard and A c c o u n t a b i l i t y Measurement o f S p e c i a l Nuclear M a t e r i a l , 1978. 2.

Wong, C. M., Cate, J . L., P i c k l e s , W. L., " P r e p a r a t i o n o f Uranium Standards f o r X-Ray Fluorescence A n a l y s i s , " Proceedings o f the ANS T o p i c a l Conference on A n a l y t i c a l Methods f o r Safeguard and A c c o u n t a b i l i t y Measurement o f S p e c i a l Nuclear M a t e r i a l , 1978.

3.

I n t e r n a t i o n a l Mathematic and Science L i b r a r y — X C S S Q

4.

N a t i o n a l Bureau o f Economic Research—NL2SOL Routine.

5.

P i c k l e s , W. L., Cate, J . L., " Q u a n t i t a t i v e Nondispersive X-Ray Fluorescence A n a l y s i s o f H i g h l y R a d i o a c t i v e Samples f o r Uranium and Plutonium C o n c e n t r a t i o n , " Advances in X-Ray A n a l y s i s V o l . 17, Plenum P u b l i s h i n g Corp., New York, 1973.

Routine.

RECEIVED JUNE 12, 1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

6 Progress in the Verification of Reprocessing Input Analysis for Nuclear Material Safeguards L.

KOCH

Commission of the European Communities, Joint Research Centre, Karlsruhe Establishment, European Institute for Transuranium Elements, Karlsruhe, West Germany Ε.

MAINKA

Institut für Radiochemie, Kernforschungszentrum Karlsruhe, Postfach 22 66, D-7500 Karlsruhe 1, West Germany

The reprocessing inpu nuclear fuel cycle no The fuel can be directly analysed for the f i r s t time since i t s fabrication. A material balance between initial, fissioned and remaining material is possible with high accuracy. In addition, the portion of the fuel converted into special nuclear material e.g. plutonium is measured before it i s purified for recycling. Three possible methods for an input analysis are in use, of which the f i r s t one is applied usually by the plant operators, therefore the two latter ones can be used as a redundant measure (1,2,3). The method of choice for most plants is the volume concen­ tration method by which the volume of the dissolved fuel and the concentration of uranium and plutonium in it are measured. The Pu/U-method needs only analysis of the ratio of these two elements in the spent fuel but requires information about the burn-up and the initial amount of the fuel. A recently developed isotope correlation technique uses correlations between an isotopic ratio (which can be easi­ ly and with high accuracy measured) and the uranium or plu­ tonium quantity. To obtain the input of the actinides the initial amount of the fuel has also to be known. The following describes the progress made recently in Karlsruhe to verify the reprocessing input by automatic direct analysis, or by balancing pre- and post- irradiation amounts of fuel or by the isotope correlation technique. AUTOMATES FOR DIRECT ANALYSIS The automatic x-ray fluorescence spectrometer described earlier (4,5,6) has been improved: An instrument with a seven-channel analyser has been installed in the reprocessing f a c i l i t y , WAK, where i t is manually operated under test. The automatic sample preparation stage has been completely redesigned. A more com­ pact sampling device has been fabricated which is controlled by a microprocessor. This part of the automat is now being ex0-8412-0449-7/78/47-079-073$05.00/0 © 1978 A m e r i c a n C h e m i c a l Society

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

74

NUCLEAR

SAFEGUARDS

ANALYSIS

t e n s i v e l y t e s t e d c o l d under r o u t i n e c o n d i t i o n s . A l a b o r a t o r y f o r automatic i s o t o p e d i l u t i o n a n a l y s i s , AIDA, i s i n r o u t i n e use f o r a n a l y s i n g samples taken by the EURATOM safeguard i n s p e c t o r s . T h i s l a b o r a t o r y comprises the f o l l o w i n g automates: - ion-exchange to c o n d i t i o n uranium and plutonium f o r the sub­ sequent isotope a n a l y s i s ( F i g . 1), - a balance to weigh the sample and s p i k e s o l u t i o n f o r the i s o ­ tope d i l u t i o n , - an α-spectrometer to determine Pu-238 and t r a n s p l u t o n i t e abundances, - an automatic mass-spectrometer a i d e d by a high-vacuum l o c k f o r continuous sample feeding ( F i g . 2) . The c o n d i t i o n i n g of the r e p r o c e s s i n g input s o l u t i o n sample i s done by s o r p t i o n o f the n i t r a t o complexes o f U and Pu on an anion-exchanger and subsequent e l u t i o n with d i l u t e n i t r i c a c i d (7) . The automat hold programmed i n d i v i d u a l l f o r y i e l d i n g up to four f r a c t i o n s w i t h v a r i a b l e volumes (8) . The a d d i t i o n of known amounts o f the spikes to a known a l i ­ quot of the sample s o l u t i o n i s achieved by means of an automatic balance which d i r e c t l y transmits the weights v i a a PDP 11/10 to a IBM-370 computer f o r the a n a l y s i s e v a l u a t i o n ( F i g . 3) (9). A l l operations of the ma s s- spec t r orne t e r necessary to ana­ l y s e the i s o t o p i c abundance of uranium and plutonium are con­ t r o l l e d by a dedicated computer. Continuous l o a d i n g of the samp­ l e s i s achieved by a three-chamber high-vacuum l o c k which speeds up the measurement by preheating the samples before they enter the i o n source of the instrument. From a thorough systematic a n a l y s i s of a l l operations used i n manual o p e r a t i o n mass spec­ trometry, elaborate software has been w r i t t e n f o r a dedicated process computer. S t a r t i n g from i n s e r t i o n o f the samples i n t o the l o c k , t h e computer c o n t r o l s a l l steps such as baking out the samples, heating up i n the ion source, f o c u s s i n g and r e f o c u s s i n g the instrument, scanning a t a p r e - s e l e c t e d i o n c u r r e n t with p o s s i b l e subsequent measurement o f uranium, plutonium and neodymium from a s i n g l e sample and r e d u c i n g the mass spectra to atom r a t i o s , averaged over ten scans (9.10,11). DATA PROCESSING The handling of the data from r o u t i n e r e p r o c e s s i n g a n a l y s i s , generated f o r a s i n g l e a n a l y s i s over a p e r i o d o f s e v e r a l days, j u s t i f i e s o n - l i n e data processing. The c o n f i d e n t i a l i t y and data s e c u r i t y r e q u i r e d by safeguards make i t mandatory. The system employed i n AIDA g i v e s none of the o p e r a t o r s d i r e c t access e i t h e r to the c h a r a c t e r i s t i c s of the sample o r t o the r e s u l t . For each a n a l y s i s the i d e n t i t y and c h a r a c t e r i s t i c s of the sample are f i l e d i n a s p e c i f i c matrix o f the computer, which p e r i o d i c a l l y c o l l e c t s information a v a i l a b l e a t the automates. The data are sorted out according t o the a n a l y s i s i n d e n t i t y and f i l e d i n t o the corresponding matrix. As soon as one matrix has

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

K O C H AND M A I N K A

Figure 1.

Input

Analysis

Automatic device for six parallel U and Pu separations for subsequent MS analysis

Figure 2. Automatic MS and a high-vacuum lock for continuous sample feeding

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

76

NUCLEAR

SAFEGUARDS

ANALYSIS

been completed the programme i s s e l e c t e d according to the type of data and the e v a l u a t i o n o f the a n a l y s i s s t a r t s (9). The a-spectrometer and balance are on l i n e t o a PDP-11 which reduces the source data and transmits them t o the IBM-370. The measurements of the mass spectrometer are converted to mass r a t i o s by the process computer and are then t r a n s f e r r e d v i a the PDP-11 to the IBM ( F i g . 4) (1_2) . ISOTOPE CORRELATION TECHNIQUE The r e s u l t s are f i l e d i n a DATABANK together with e a r l i e r ( h i s t o r i c a l ) data where they can be checked by u s i n g the r e c e n t l y developed i s o t o p e c o r r e l a t i o n technique. From a s e t o f h i s t o r i c a l data o f s i m i l a r o r i g i n , a p p r o p r i a t e c o r r e l a t i o n s are s e l e c t e d f o r different applications. The c o n s i s t e n c y of the new dataset i s checked to see i f the a n a l y s i s o f one of the i s o t o p e s i s f a u l t y . By comparing d i f f e r e n t c o r r e l a t i o n s a p o s s i b l e e r r o r during the course o f the a n a l y s i s can be spotted. The burn-up determinatio done e i t h e r by the c o s t l y Nd-148 a n a l y s i s (also by u s i n g AIDA) or by employing c o r r e l a t i o n s between e.g. plutonium i s o t o p e r a t i o s versus the burn-up (Tab. 1) (13,14,15,16). A more advanced a p p l i c a t i o n of the i s o t o p e c o r r e l a t i o n t e c h nique i s the p r e d i c t i o n of the f i s s i l e m a t e r i a l content d i r e c t l y from i s o t o p e c o r r e l a t i o n s . For t h i s purpose, c o r r e l a t i o n s are under study between the i s o t o p i c r a t i o w i t h i n an a c t i n i d e or f i s s i o n product and the f i s s i l e isotope content r e l a t e d to the i n i t i a l metal atoms o f the u n i r r a d i a t e d f u e l (IMA). From such a c o r r e l a t i o n the Pu-content could be deduced: Pu = Pu IMA · U with U the i n i t i a l amount o f f u e l and the Pu IMA c o r r e l a t i o n , Pu IMA = a · Pu i s o t o p e r a t i o + b (Table 1 ) . CONCLUSIONS The v a l u e of the automatic x-ray f l u o r e s c e n c e spectrometery l i e s i n i t s p o t e n t i a l f o r producing q u i c k l y a measurement of the chemical c o n c e n t r a t i o n of f i s s i l e m a t e r i a l , which i s needed during i n v e n t o r y t a k i n g i n the v a r i o u s hold-up v e s s e l s . At present, t e s t s are on the way to improve the accuracy by means of a m u l t i channel analyser (18). The developement of AIDA can be regarded as being completed. F u r t h e r automation would o n l y be j u s t i f i e d by l a r g e r sample throughputs i n order to reduce the a n a l y s i s c o s t . From the present experience i t can be concluded t h a t AIDA has increased the sample throughputs by f i v e times compared t o t h a t from the e a r l i e r manual o p e r a t i o n . The accuracy (1/7) i s not a f f e c t e d by the automation; on the c o n t r a r y , the automatic procedure r e j e c t s samples showing an odd behaviour i n the mass spectrometer,thus e l i m i n a t i n g p o t e n t i a l wrongly prepared m a t e r i a l . A comparison between the three above mentioned methods shows t h a t the volume c o n c e n t r a t i o n procedure r e q u i r e s the h i g h e s t number of measurements. However no a d d i t i o n a l i n f o r m a t i o n o f the f u e l h i s t o r y i s r e q u i r e d (Tab. 2). For the second procedure the volume and d e n s i t y measurement as w e l l as

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

KOCH

AND

MAINKA

Input

Analysis

Figure 3. Automatic balance for aliquotation used in isotope dilution analysis

Figure

4.

Scheme of on-line data handling between automates, process computers, and an IBM-370

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

m

F

Τ

m

Τ

F

14.3 (Pu-242/240)

=

- 0.436

- 4.11

- 5.98 E-4

Pu-242 = 1.89 E-3 (Pu-242/240)

2.84 (Xe-132/131)

- 9.29 E-3

Pu-242 = 5.24 E-4 (Xe-132/131)

=

+ 4.48 E-4

78

29

51

11

51

34

- 3.61 E-4

Pu-240 = 7.80 E-3 (Pu-242/240)

Pu-240 19

η

Pu-240 = 5.65 E-3 (Pu-240/239)

b

_ 2.97 E-3

+

.97

.98

.99

.99

.98

.98

.99

R

8.0

5.8

6.7

6.6

3.9

3.2

5.5

error %

all

all

PWR

PWR

GARIGLIANO

OBRIGHEIM

GARIGLIANO

OBRIGHEIM

TRINO VERCELLESE

reactor

s = error of prediction; R = correlation coefficient)

= a · (isotope r a t i o )

numbers o f p o i n t s ;

Isotope c o r r e l a t i o n s t o p r e d i c t burn-up (F ), Pu-240 IMA or Pu-242 IMA. 2 2 1 2 (Error: s = σ (1 + / η ) ; σ = sums o f squared d e v i a t i o n s / ( n - 2 ) ; η =

2.00 E-3 (Xe-132/131)

y

Table I :

6.

KOCH

A N D MAINKA

Input

Analysis

79

Table H: Comparison o f p o t e n t i a l e r r o r sources (+) f o r each o f the methods.

ERROR SOURCES

MEASUREMENTS

- ω &

η

U

C

j

Ρ)

Η

METHOD

3 Β en en

ρ· Χ

0

0

Hi

Ί) Η ^

e o n

Volume/concentration

+ + +

OTHERS

ADDITIONAL INFORMATION

> ο a » 3 fD ο Η, Ω 3 W π) ks

^ Η. Η·

Hi 3 fD vQ (D ft Ο & So ft PU Hi CO

+ + + +

148 Pu/U r a t i o

(

+ +

+ + +

+ + + +

+ +

+ +

+ + + +

Nd)

(Corr) Isotope C o r r e l a t i o n s (U,Pu) (Xe,Kr)

+ +

+ + + +

+ +

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

80

NUCLEAR SAFEGUARDS ANALYSIS

the aliquoting of the sample i s eliminated, but instead a burnup measurement i s needed, which can be done by isotope corre­ lations on actinide isotopic ratios thus avoiding the normally applied, costly Nd-148 analysis. Information on the i n i t i a l amount of uranium i s needed. The number of potential error sour­ ces i s reduced compared to the f i r s t method. For the third pro­ cedure only a simple isotope analysis i s required. However the need for additional information on the fuel i s increased. Be­ sides the i n i t i a l amount of uranium, h i s t o r i c a l data from which isotope correlations can be deduced have to be provided. The po­ tential error source of cross contamination during sampling i n ­ side the reprocessing plant i s eliminated by using the fission gas correlations, since a cross contamination from samples taken from the exhaust gasses i s unlikely. 1

2 3

4 5

6 7 8 9 10

11 12 13

Koch L., Bresesti M. Inst. of Nuclear Material Management, New Orleans, USA; Journal f th Institut f Nuclea Mat Manage ment, (1975) V o l . IV Koch L., Cottone G Reaktortagung , ruhe, (1973) Tagungsberichte S. 287 Koch L., Ahrens H.J., Baeckmann A . v . , Cricchio Α . , De Meester R., Romkowski Μ., van der Stijl E., Wilhelmi M. Intern. Atomic Energy Agency: Int. Symposium on Safeguarding of Nuclear Ma­ t e r i a l , Wien; Proceedings of the Symposium (1975) Baeckmann A . v . , Koch L., Berg R. 70. Meeting of Americ. Chem. Soc. Chicago (1975) Baeckmann A . v . , Küchle M . , Weitkamp C., Avenhaus R., Baumung K . , Beyrich W., Böhnel Κ., Klunker J., Mainka Ε., Matussek P . , Michaelis W., Neuber J., Wertenbach Η . , Wilhelmi Μ., Woda Η . , H i l l e F., Linder W., Schneider V.W., S t o l l W., Koch L., Eberle R., Stegmann D . , Zeller W., Krinninger Η . , Mausbeck Η . , Ruppert E. Intern. Atomica Agency, Genf (1971) Proceedings of 4. Confe­ rence "Peaceful uses of Atomic Energy" A/Conf. 49/A/809 Baeckmann A.v., Koch L., Neuber J., Wilhelmi M. Intern. Atomic Energy Agency, Wien (1972) Proceedings SM-149/42 Koch L., Radiochim. Acta (1969) 12, 160 Bol D . , Brandalise Β . , Bier Α . , De Rossi M . , Koch L . EUR-5141 (1974) Brandalise Β., Cottone G . , Cricchio Α . , Gerin F., Koch L . EUR5669 (1977) Koch L., Wilhelmi Μ., Brandalise B., Rijkeboer C., Romkowski M. Proc. of 7. Int. Mass Spectrometer Conf., Florence (1976) V o l . 7 Wilhelmi Μ., Brandalise Β., Koch L., Rijkeboer C . , Romkowski M. EUR 5504 d (1977) Koch L . V Convegno d i Spettrometria d i Massa, Catania (1977) Annali de Chimica to be published Ernstberger R . , Koch L., Wellum R. ESARDA Symp. on Isotopic Correlation and i t s Application to the Nuclear Fuel Cycle, Stresa, Italy, May 9-11 (1978)

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

6.

14 15 16 17 18

KOCH AND MAINKA

Input Analysis

Wellum R., De Meester R., Kammerichs Κ., Koch L . i b i d . Brandalise B . , Koch L., Rijkeboer C . , Romkowski D. i b i d . Schoof S., Steinert Η., Koch L . i b i d . Beyrich W., Drosselmeyer E . KFK-1905 (1975) Neuber I . , Flach S., Braun R., Stöckle D. in KFK-2465 P.3-8 (1977)

RECEIVED JUNE 12,

1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7

I s o t o p i c Safeguards

Techniques

1

C. L. TIMMERMAN Battelle, Pacific Northwest Laboratories, Richland, WA 99352 The purpose of this paper is to explain and illustrate the idea and uses of isotopic safeguards techniques. The paper maintains a generalized, simple approach to f a c i l i t a t e understanding of the techniques. Once understood, the application, demonstration, and implementatio becomes much easier. Introduction As uranium is burned in a nuclear reactor, plutonium is produced. Natural laws control this process, yielding simple relationships between the beginning and ending isotopic concentrations of the nuclear fuel. That i s , the amount of plutonium produced is related to the amount of uranium remaining. The concentrations of many of the isotopes of both elements (U and Pu) can also be used to form useful relationships. These relationships, called isotopic functions, have become a prime tool in developing a r e l i a b l e , straightforward method for verifying measurements of the total amount of plutonium and its isotopes produced in the nuclear fuel. The need to verify the amount of plutonium and other isotopics is illustrated by Figure 1. The fact that this technique would fill the material accounting safeguards gap in the fuel cycle between the fuel fabricator and the reprocessor is potentially its greatest asset. Isotopic safeguards has developed into a proven, reliable technique to verify the spent fuel content at the head end of a reprocessing f a c i l i t y . The fact that the aforementioned relationships exist has long been recognized. (1,2) Both burnup experiments and calculational burnup codes have been used to study the transmutation of uranium to plutonium. The transmutation of isotopes is p r i n c i pally governed by simple first-order differential equations. (3) However, the coefficients of these equations depend on numerous core details and on the reactor operating history. The A

This work is currently sponsored by the Department of Energy through the International Safeguards Project Office, Brookhaven National Laboratory, under Control EY-76-C-06-1830. Much of the work was originally sponsored by The Arms Control and Disarmament Agency. This chapter not subject to U.S. copyright. Published 1978 American Chemical Society In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

FABRICATION

uo 2

DISSOLVER

MEASUREMENTS

2

Figure 1. Why isotopic safeguards are important

2

MATERIAL . BALANCE

Pu0

VULNERABLE TO U N D E R S T A T E M E N T OF Pu C O N T E N T

NO ACCOUNTABILITY

REACTOR

2

U0 , Pu0

REPROCESSING

8

c*

Co «δ

ο "β Ci*

Ο

>

N U C L E A R SAFEGUARDS ANALYSIS

84

complexity of the core models, the cross sections of the isotopes, and the approximations needed to solve the equations has obscured the simplicity of the relationships. Similar relationships have been found in measurements of isotopic concentrations in batches of dissolved spent fuel at chemical reprocessing plants. These measurements represent random samples of large amounts of irradiated fuel forming batches as large as one tonne. Observations of these functional relationships provide the best accuracy obtainable because they represent actual spent fuel measurements coupled with predictions from the theory associated with burnup calculations. The isotopic functions have been investigated under programs principally funded by the U.S. Arms Control and Disarmament Agency in the past and currently by the Department of Energy through the International Safeguards Project Office which is managed by the Brookhave National Laboratory Th f the programs has been t Agency (IAEA) with a practical verification technique for safe guarding the amount of plutonium input to chemical reprocessing f a c i l i t i e s . The programs are known as Isotopic Safeguards Techniques. Isotopic Functions and Ratios An isotopic function is defined as a functional relationship between the measured isotopic concentrations of uranium and plutonium, or as the total elemental Pu/U mass ratio, for a given dissolution batch. Examples of such functions include Pu/U versus U, U versus U , and ( P u ) versus U. In each example the Pu/U, U , and ( P u ) are the dependent or y variables and the U is the independent or χ variable. The slope, or isotopic ratio, of two variables is defined as the ratio of the dependent variable's irradiated value minus its i n i t i a l value divided by the independent variable's irradiated value minus its i n i t i a l value. The following example is provided for i l l u s t r a t i o n : 2 3 5

2 3 6

2 3 5

2 3 9

2 3 6

2 3 9

2

2 3 5

2

2 3 5

Isotopic R

a

t

i

=

(236y)

(

0

235

irradiated - (

236

U ) irradiated - (

U) initial

235

U) initial

The above relationship is stated more simply as Δ υ/Δ U for nomenclature convenience. Because the term Δ υ is used so frequently i t has been further simplified to D to indicate the depletion of the U isotope. Obtaining a consistency for the slope of any function is of primary importance to isotopic safeguards techniques. By having a constant slope, the functions derived will be of a linear form. The linearity provides a functional consistency of the isotopic relationship over a large exposure or burnup range. This 2 3 6

2 3 5

2 3 5

2 3 5

2 3 5

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7.

TiMMERMAN

Isotopic

Safeguards

85

Techniques

functional consistency is necessary for an isotopic function to be of value to the technique and is a basic criterion for determining the merit of various isotopic functions. A graphical example of the linearity of the isotopic function U versus U is provided in Figure 2. This example illustrates the functional consistency for various enrichment groups of three different reactors. An isotopic ratio can be used as a consistency check for batch-to-batch measurements in a reprocessing campaign. That i s , the isotopic ratios formed from measurement data should be relatively constant for batches dissolved from the same reactor fuel lot. The ratio can also be used as a verification tool. Historical data from the same reactor, or a similar type reactor, can be used to form the isotopic ratio, which is compared (within accuracy limits) to incoming batch measurements from a present reprocessing campaign In this way previous data can be used to verify present data throug When historical dat highly characterize a particular f u e l , these values may be applied to future similar fuels from the same reactor (assuming of course that controlling irradiation conditions are the same). The use of historical data to check successive discharges from the same reactor is illustrated in Table I for the Yankee Rowe reactor. All the Yankee fuel in this example is stainless steel clad and the same design. Reactor lots processed (10-20 tonnes U) at the chemical plant d i f f e r only in the enrichment and exposure. Two features of the empirical correlations are illustrated in Table I. F i r s t is the constancy of Pu/U versus D for material of the same i n i t i a l enrichment and design for a PWR. Second is the empirically derived expression relating the term (Pu/U)/ D to the i n i t i a l enrichment. Each batch reported by the operator is tested by forming the ratio between Pu/U and D. If a l l data check within s t a t i s t i c a l limits of the historical values and within direct IAEA measurements of input and product samples, the Pu/U ratio of input to the campaign is verified. The case of no historical data but a high degree of consistency is illustrated by the data in Table 11.(4) In this case, advantage is taken of the consistency of the data over a wide range of exposure, e.g., the Pu/U varies widely but the isotopic ratio is nearly constant. The general verification procedure outlined above is used. Each batch reported by the operator is tested to see i f i t differs from the majority of the data. If no significant differences are found, the verification of specified isotopic functions has been shown to a given accuracy. 2 3 6

2 3 5

2 3 5

235

2 3 5

Pu/U Ratio Method(5) There are presently no adequate safeguards measures for checking the content of nuclear fuel from the fabrication f a c i l i t y through the reactor to input at a reprocessing plant.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

86

N U C L E A R SAFEGUARDS

ANALYSIS

i 3 to S

ο

1 I

t ED

(Ο Ci ©I

I

.se

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7.

TiMMERMAN

Isotopic Safeguards

87

Techniques

Table I , Comparison o f P l u t o n i u m R e s u l t s by E m p i r i c a l 235 U D e p l e t i o n Method t o Measured Values Yankee Rowe Fuel

No. o f Dissolver Batches

Uo Wt. %

235

Ί6

3.404

.7981

Tonne U 2Jb

2 3 5

D

D

5,727

%

Grams Pu Tonne U

Grams Pu Tonne U

4,571

4,530

0.91

Difference

14

3.406

1.0349

5,726

5,926

5,982

-0.94

11

4.101

1.5252

5,376

8,200

8,257

-0.69

4.101

1.4276

5,376

7,675

7,628

11

4.935

1.9820

4,957

9,824

9,899

12

4.935

2.1594

4,957

10,703

10,692

0.10

11

4.941

2.0536

4,954

10,173

10,099

0.73

7

0.62 -0.76

• O b t a i n e d by f o l l o w i n g e q u a t i o n : Grams Pu/Tonne U 235

.

l

m

.

5

Q

3

(

235

U o )

D

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

88

NUCLEAR SAFEGUARDS ANALYSIS

Table I I (4). Example Of Pu/U And I s t o p i c Consistency Yankee Rowe Core V Data

Raw Data

Plutonium I s o t o p i c s

Uranium I s o t o p i c s Input Batch #

Exposure MWd MTU

2 4 2

2 3 5

u Wt. %

2 3 6

u Wt. %

u Wt. %

Pu Wt. %

Pu Wt. %

Pu Wt. %

4,968

3.176

0.2209

85.05

10.29

4.01

0.36

Total Pu q/TU

2 3 9

2 4 0

2 4 1

1

9,700

20

13,900

10

15,800

7,930

2.675

0.3253

77.57

13.47

7.37

1.04

22

19,700

8,863

2.471

0.3589

75.14

14.54

8.29

1.34

18

21,400

9,794

2.254

0.3993

72.69

15.46

9.18

1.75

16

25,600

11,119

2.046

0.4454

69.31

16.34

10.85

2.50

I s o t o p i c Ratios

Exposure MWd MTU

Input Batch #

235

2 4 0

Pu/U

Pu/U Total Pu q/TU

D

% Dev.

A

2 3 6

U

% Dev.

2 3 9

Pu

P u (100 -

2 3 9

Pu)

% Dev.

1

9,700

4,968

5,371

-0.52

27,463

-0.01

7.748 E-3

2.76

20

13,900

7,104

5,448

0.91

27,334

-0.48

7.387 E-3

-2.04

10

15,800

7,930

5,417

0.33

27,516

0.19

7.486 E-3

-0.72

22

19,700

8,863

5,441

0.78

27,792

1.19

7.519 E-3

-0.28

18

21,400

9,794

5,306

-1.72

27,258

-0.75

7.535 E-3

-0.07

16

25,600

11,119

5,413

0.26

27,427

-0.14

7.567 E-3

0.35

Where:

3

X = 5,399

X = 27,465

X = 7.540 E-3

σ = 0.98%

σ = 0.67%

σ = 1.58%

3

" D = wt. % " U f i n a l Δ

2 3 6

υ = wt. %

2 3 6

U final

-

3

wt. % " U wt. %

2 3 6

U

initial initial

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7.

TiMMERMAN

Isotopic

Safeguards

Techniques

89

The need to verify the measured amount of plutonium in spent fuel at the input to a reprocessing plant is the basic reason for developing the isotopic safeguards concept. The plutonium-touranium ratio method is used to independently determine the plutonium content of a reprocessor s dissolver batch. The amount of plutonium at the input of the reprocessing plant is derived by the following equation: 1

Plutonium at Input = Pu/U ratio χ (Initial Uranium - Burnup). Measurements from three sources, two of them independent of chemical reprocessing, are used in the above equation. The i n i t i a l uranium measured at fabrication must be measured accurately for the technique to be valid. Data(6j have proven this accuracy to be true, for the data have shown the fabricator's measurements to have a 0.15% relativ precisio d 0.05% relative standard deviatio the i n i t i a l uranium for burnup introduces the second independent source of information, the amount of heat produced by the uranium during irradiation. This calculated burnup is generally ±5% of the true value on an assembly level. (7^) This error is not very large when one considers that only 2 to 5% of the i n i t i a l uranium, depending on the burnup, is burned during irradiation in a reactor core. The third source of information is the Pu/U ratio obtained from the reprocessing plant. The accuracy of the Pu/U ratio as shown by our s t a t i s t i c a l studies is within 2% or less depending on the reactor and enrichment group. Using this ratio in con­ junction with the final total uranium, obtained from the i n i t i a l uranium and predicted burnup, a value for the total plutonium can be derived as stated in the above equation. To obtain an independent value of the plutonium content using the Pu/U ratio method, i t must be shown independently that the Pu/U ratios measured by the reprocessing plant are correct. By applying past similar reprocessing data and consistency checks to the Pu/U ratio and other isotopic ratios and functions, isotopic safeguards can provide an important complement and supplement to independent verification of input reprocessing batches. It has been reported(8) that a l l of the observed differences are 1.0 to 1.5% or less for measured plutonium input compared to plutonium derived by isotopic safeguards methods. The 1.5% is considered a r e a l i s t i c upper limit, where larger differences on a batch level may require further sampling and investigation. As demonstration of the technique progresses, a definite practical upper limit can be determined. A main process condition required to use the Pu/U ratio or other isotopic functions is that the input dissolver measurements must come s t r i c t l y from the spent fuel from which they were derived. This is normally the case for head-end processes without recycle. If the acid which dissolves the spent fuel is recycled

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

90

N U C L E A R SAFEGUARDS ANALYSIS

from other sections of the reprocessing plant, corrections are required for such additions of recycle acid. Recycle of any nuclear material before measurement is made at the accountability tank must be taken into account. This procedure of measuring a l l recycle nuclear material holds for a l l verification procedures and is not just particular to isotopic safeguards. In general, verification procedures are easier to apply for the case of no recycle because only one actual measurement needs to be made per batch. Recent Developments A s t a t i s t i c a l package has been incorporated into the tech­ nique and is used to quantify the properties of various isotopic functions and their associated data. The use of these automated s t a t i s t i c a l procedures has provided many more meaningful results which can be derived fro The s t a t i s t i c a l tool analyz y the paired comparison and regression analysis. A paired compari­ son results when a sample from a reprocessor's measurement batch is analyzed by two different laboratories. These paired compari­ sons can be used to compare laboratories for bias, to estimate measurement variances, and to indicate the presence of outlier batch results. The second analysis tool, the linear regression, i n i t i a l l y involved the comparison of various linear regression approaches. After much study of these various approaches, a decision to use Deming's approach(9^) was reached. Deming's approach is a model in which errors in both variables (x and y) are considered. Both an intercept model, y = α + 3x, and an i n i t i a l point model, y - y = $(x - xo)> are utilized to provide the maximum statistical data from the regression analysis. For example, the i n i t i a l point model provides a stablizing l i n e f i t t i n g method for data having a small burnup range, while the intercept model supplies a more accurate f i t t i n g to larger ranged data. The decision to use this regression technique with errors in both the χ and y variables resulted when i t was shown(10) that the random variances for the χ and the y variable were approximately equal, or at least that the error variance of y was not substantially larger than the error variance of x. This fact illustrated that errors occurred in both variables. After choosing the appropriate s t a t i s t i c a l approach and corresponding models, these statistics are useful in defining the magnitude of the variance components along with identifying anomalous or outlier data. The regression analysis also provides a least squares type linear f i t t i n g of the data points grouped by enrichment. This f i t t i n g supplies a more accurate estimate of the slope and intercept than was previously possible. However, possibly the most important feature of the statistics is that they specify the accuracy basis for acceptable verification results for each isotopic function. 0

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

7.

TiMMERMAN

Isotopic

Safeguards

91

Techniques

Rough ideas had been used in the past to identify useful linear functions. Because of the large number of isotopic variables and functions possible, automated decision and identi­ fication techniques needed to be incorporated. The resultant program determines the isotopic variables, and eliminates any redundant functions that occur. The pairing of the variables u t i l i z e s the idea that the relative change in one variable's concentration over a sample burnup range should be approximately equal (within 0.1%) to the relative change in the other variable's concentration over the same burnup range in order to form a linear function. Computer calculations have greatly improved the efficiency and precision with which linear functions can now be found. The following are examples of beneficial, linear functions which have been studied by this method to date: 240p

u

2hlp

u

x

2351J 239p

u

239p 2 u

2 3 9

2k0p

u

x

x

240p 2 u

P u X (100 -

240p 2t0p

239p 2

vs

235u χ

vs

2"0p

u

vs

A

u

vs

A(

u

vs

2 3 9

vs

PU

X (100 -

239

Pu)

vs

39

)/235

2Hlp

u

u

(235lJ X 235

2 3 9

PU )

U )

P u X (100 -

(100 -

239

Pu)

vs

(100 -

239

Pu)

Pu/U

vs

235

D

236u

vs

235

υ

2 3 9

Pu/U

2

2

P U

U 2

2

2

239

Pu)

Data Base A substantial data base has been collected to date. A l i s t i n g of the data sets according to type, reactor, and quantity is provided in Table III. These data have increased the safe­ guards benefit of isotopic functions by providing a sufficiently large set of data from which to work. Calculated burnup data are included in the data base, which complement the empirical methods, and this has provided greater theoretical insight into the tech­ nique. The features of the isotopic functions observed for the measured data have also been observed for the calculated data, thus supplying a high level of confidence in the isotopic functions. An in-depth analysis of the data base using the s t a t i s t i c a l package and reactor operator and design information has led to a labeling index as to the qualities and properties of every data point in each data set. A l i s t of the markings used for this

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

N U C L E A R SAFEGUARDS ANALYSIS

92

Table

III»

Isotopic Safeguards

Reactors I.

Connecticut Yankee Diablo Canyon Fort Calhoun Indian Point 1 Point Beach 1 San Onofre 1 Saxton Sena T r i no Vver Yankee Rowe H. B. Robinson 2 Total

AGR Calder Hall Chapel Cross NPR Windscale AGR Total

Big Rock Point 1 Browns Ferry 1 Dodewaard Dresden 1 Garigliano Humboldt Bay KRB LaCrosse Nine Mile Point 1 Oyster Creek 1 VAK JPDR-1 Total

20

20 6 67

3 1

89

82

35 3

5

166

179

137

16

24 11 10 21

24

23 13 62 31 20 lb

20 29

3

4

10 30

167

77

71

9 3

9 6

6

12

15

6 18

13 18

16

Heavy Water 1. 2. 3. 4. 5.

NPD (Candu) Douglas Point Gentilly 1 Pickering NRU Total

V.

Number of Sets Calculated Data

B o i l i n g Water 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

IV.

Number Of Burnup Samples

Graphite Moderated 1. 2. 3. 4. 5.

III.

Number of Input Batches Measured Remeasured

Pressurized Water 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

II.

Data Base

24 30

Fast Reactor 1.

EBR-11

18 Total 35 Reactors

366

271

280

39

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Sets

7.

TiMMERMAN

Isotopic

Safeguards

Techniques

93

quality index is given in Table IV. It must be understood that most of the data f a l l s under the ordinary category, for this is basically an index for marking and labeling unusual and outlier points to provide a clearer understanding into their meaning. Our data base makes an effective safeguards tool in i t s e l f because of the isotopic functions now developed. Measurement histories of particular reactors and/or fuels become inherent as the data bank increases. Perhaps the most important aspect of the data base is that the isotopic functions determined from new reprocessing measurements should be consistent with past results and with properties defined by the data base for that type of reactor fuel. In this way the data base contributes in a positive way to the future analyses of reprocessing input measurement. Tabl

IV*

Property Normal data point Exposure averaging Enrichment averaging Exposure and enrichment averaging Fringe effects Exposure averaging and fringe effects Cladding differences Unirradiated assembly Uranium outlier Plutonium outlier

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

94

NUCLEAR

SAFEGUARDS

ANALYSIS

Acknowledgment I am indebted to Dean Christensen for his training and knowledge which has aided in my understanding of this technique. Kirk Stewart is also to be acknowledged for developing the sta­ t i s t i c s applicable to isotopic safeguards techniques. Literature Cited 1.

2.

3.

4.

5.

6. 7.

8.

9. 10.

Rider, B. F., Russel, Jr., J. L., Harris, D. W., Peter­ son, Jr., J. P., "The Determination of Uranium Burnup in MWd/Ton," GEAP-3373, Vallecitos Atomic Laboratory, General Electric Company, Pleasanton, CA, March 1960. Moeken, H. H. Ph. and Bokelund, H . , "Verification of the Uranium and Plutonium Measurements on a Batch of Dissolved Reactor Fuel," ETR-235 European Company for Chemical Pro cessing of Irradiate Available from NTIS Beets, C . , "Role of Measurements of Nuclear Materials in Safeguards," presented at Symposium on Practical Applications of Research and Development in the Field of Safeguards, Rome, March 7-8, 1974. Centre d'Etude de L'Energie Nucleaire, Belgium. Schneider, R. Α . , Stewart, Κ. Β . , and Christensen, D. Ε . , "The Use of Isotopic Correlations in Verification (Safe­ guards Application)," BNWL-SA-4251, presented at IAEA Working Groups on the Use of Isotopic Composition Data in Safeguards, Vienna, Austria, April 10-14, 1972, Battelle, Pacific Northwest Laboratories, Richland, WA 99352, February 1972. Stewart, Κ. B. and Schneider, R. Α . , "Properties of the Pu Estimate Based on Weighted Pu/U Values," IAEA SM-133/55, Safeguards Techniques, IAEA, Vienna, Austria, July 1970. Stephens, F. B . , et al., "Methods for the Accountability of Uranium Dioxide," NUREG-75/010, Lawrence Livermore Laboratory, June 1975. Reactor Burn-up Physics, Proceedings of a Panel on Reactor Burn-Up Physics Organized by the International Atomic Energy Agency, Vienna, Austria, July 12-16, 1971, February 1973. Christensen, D. E. and Schneider, R. Α . , "Summary of Experi­ ence with Heavy-Element Isotopic Correlations," Safeguard­ ing Nuclear Materials, Vol. II (p. 377), IAEA, Vienna, Austria, 1976. Deming, W. E., Statistical Adjustment of Data, Willey, New York, 1943. Timmerman, C. L., Christensen, D. E., and Stewart, Κ. B . , "Statistical Evaluation of Isotopic Safeguards Data," BNWL-SA-6371, presented at the 18th Annual Meeting of the Institute of Nuclear Materials Management, Washington, DC, July 1, 1976.

RECEIVED JUNE 6,

1978.

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

8 N u c l e a r Safeguards A p p l i c a t i o n s of E n e r g y - D i s p e r s i v e Absorption

Edge Densitometry

T. R. CANADA, D. G. LANGNER, and J. W. TAPE Los Alamos Scientific Laboratory of the University of California, P.O. Box 1663, Los Alamos, NM 87545 For a number of years absorption edge spectrometry tool of the analytical chemist (1-8). This reasonably matrix -independent technique, which requires the measurement of photon transmissions through a sample at two energies, one on each side of the elemental absorption edge of interest, has found in the past only limited application in the measurement of special nuclear materials (9,10,11). This is due primarily to the limited f l e x i b i l i t y of the wave length dispersive spectrometry approach and its associated complex measurement procedures. High-resolution energy-dispersive spectrometers have alleviated, to a large degree, these drawbacks while maintaining the at­ tractive matrix insensitivity feature of the technique. This paper reviews briefly the theory of energy-dispersive absorption edge densitometry, describes its recent applications to the measurement of special nuclear materials (SNM) and d i s ­ cusses some possible future adaptations that w i l l broaden its impact in the field of nuclear safeguards. Although the ex­ amples reviewed are concerned only with plutonium, uranium, and thorium, the extension of the technique to other elemental determinations is straightforward. I.

TECHNIQUE DESCRIPTION The basic experimental components of energy-dispersive photon transmission measurements are shown schematically in F i g . 1. The ratio of photon intensities from the transmission source measured at an energy Ε with and without the sample present determines the transmission T, where Τ = exp(-u p x) s

exp(-y p x).

s

m

m

χ is the sample thickness, μ and y are the mass attenuation coefficients at E , and p and ρ are the densities of the SNM of interest and the matrix materiaTs (everything else), respec­ tively. The collimation defines the detector-source geometry m

g

This chapter not subject to U.S. copyright. Published 1978 American Chemical Society In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

96

N U C L E A R SAFEGUARDS

ANALYSIS

and reduces the detector s e n s i t i v i t y to photons o r i g i n a t i n g w i t h i n the sample, whether due to gamma-ray decay or fluorescence. An absorption edge densitometry-based assay r e q u i r e s that photon transmission measurements be made through a sample at two photon energies (12^). The r a t i o of transmissions f o r two photon beams at energies E\j and E L through an SNM-bearing sample i s given by Ttj/TL = e x p ( - A y P x ) e x p i - Δ μ ^ χ ) g

u

(D

s

L

where Δμ. = μ. ι ι

- μ. . ι

Figure 2 i s a p l o t of μ versus photon energy f o r three m a t e r i a l s , water, t i n and uranium The uranium curve shows a sharp d i s c o n t i n u i t y a K-absorption edge. I that i s the b a s i c signature on which a b s o r p t i o n edge d e n s i ­ tometry i s based. The energy Ε at which a given elemental absorption edge appears i s i n general unique, and i n the immediate neighborhood of Ε the mass a b s o r p t i o n c o e f f i c i e n t s f o r a l l other elements are monotonically decreasing f u n c t i o n s of energy. I f Erj and E L of eq. (1) are picked to be Ε plus and minus a ΔΕ (where ΔΕ i s s m a l l ) , r e s p e c t i v e l y , then Δμ^ - 0, and p i s given by g

ρ

s

-

-in

R/Δμ

χ s

(2)

where R = TJJ/TL. As ΔΕ 0, approximation (2) approaches an e q u a l i t y , i . e . , the measurement i s s p e c i f i c to the SNM of i n t e r e s t and i s independent of the matrix p r o p e r t i e s . The s e n s i t i v i t y of t h i s technique i s determined by the product Δ μ χ and may be increased by having a l a r g e r sample thickness χ or p i c k i n g an a b s o r p t i o n edge f o r which Δ\ι^ i s l a r g e r . The uranium and plutonium Κ and L m absorption edges are at energies that make transmission measurements p r a c t i c a l . A l i s t of these and the corresponding Δμ values are given i n Table I. The r e l a t i v e p r e c i s i o n with which R must be measured to give a designated r e l a t i v e p r e c i s i o n i n ρ i s given by s dR dp (3) 3

—

=

(Δμ Ρ Χ) δ

3

Τ

The mean a r e a l SNM d e n s i t y , ρ χ i n g/cm , f o r which Δμ p x = 1, i s a u s e f u l parameter to i n d i c a t e the lower bounds of a p p l i c a b i l ­ i t y of a given absorption edge. At the uranium and plutonium 2

g

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CANADA

E T A L .

Figure

1.

Absorption

Edge

Densitometry

Basic experimental components of photon transmission

lO.Or 8.0 [

0.| I Ο

. 100

1

200

Ε

γ

Ι ­

300

(KeV)

Figure 2. Total mass absorption coefficients as a function of energy for H>0, Sn, and U

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

98

N U C L E A R SAFEGUARDS ANALYSIS

a n c

Table I.

^ I I I * ^ absorption edge energies f o r uranium ana plutonium.

Absorption Edge L

Edge Energy (keV)

Δμ (cm /gm)

18.05

51.90

U

115.60

3.65

Pu

121.76

3.39

Element

2

III Pu

κ

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

8.

CANADA

E T A L .

Absorption

Edge

99

Densitometry

2

Κ and L i n edges these are approximately 0.3 g/cm and 0.02 g/cm , r e s p e c t i v e l y . Note that the sample t h i c k n e s s , x, i s l i m i t e d by p r a c t i c a l l i m i t a t i o n s upon the transmission source intensity. In general, high-energy r e s o l u t i o n photon d e t e c t o r s , S i ( L i ) , G e L i ( L i ) , and Ge, are required to achieve the accuracy, matrix i n s e n s i t i v i t y , and v e r s a t i l i t y a v a i l a b l e i n the a p p l i c a t i o n o f t h i s technique. The choice of detector depends upon the transmission source used f o r a given problem. 2

I I . APPLICATIONS A v a r i e t y o f transmission photon sources are a v a i l a b l e that s a t i s f y the c r i t e r i o n that ΔΕ approach zero. These i n c l u d e x-ray generators, bremsstrahlung sources, and c e r t a i n gamma-ray emitting radioisotopes a number o f factors i n c l u d i n t a t i o n s , desired accuracy, and allowed assay time. The x-ray generator i s probably the most v e r s a t i l e source but a l s o the most expensive. I t s use has many advantages: (a) the brems­ strahlung energy and i n t e n s i t y are v a r i a b l e , (b) the energy displacement, ΔΕ, from the absorption edge i s l i m i t e d only by the detector r e s o l u t i o n , and (c) m u l t i p l e simultaneous elemental determinations, such as plutonium/uranium are p o s s i b l e . Bremsstrahlung sources share advantages (b) and (c) and are i n a d d i t i o n compact and inexpensive. R a d i o i s o t o p i c gamma-ray sources are only a p p l i c a b l e when t h e i r decay schemes i n c l u d e gamma rays near enough i n energy to the absorption edge o f i n t e r e s t . However, they are convenient and inexpensive when a v a i l a b l e with the c o r r e c t energies. A. R a d i o i s o t o p i c Sources SNM-bearing samples with p x £ 0.2 g/cm may be conveniently assayed at the K-absorption edge using gamma-ray e m i t t i n g r a d i o i s o t o p e s . Table I I summarizes a number o f source-gamma-ray combinations that bracket the uranium and plutonium K-edges. In the case of Pu, the S e and C o gamma rays at 121.12 keV and 122.06 keV, r e s p e c t i v e l y , bracket the Pu K-edge at 121.795 keV so c l o s e l y that, i n most cases, approximation (2) may be considered an e q u a l i t y (Γ3). F i g u r e 3 shows an example of a measured c a l i b r a t i o n curve using these sources and a set of 2-cm-thick plutonium-bearing s o l u t i o n s . I t a l s o shows a s i m i l a r curve f o r the two S e l i n e s at 121.12 keV and 136.00 keV, which, as a r e s u l t of a l a r g e r ΔΕ from the edge, e x h i b i t s a smaller slope and a l a r g e r matrix s e n s i t i v i t y , i . e . , a measured i n t e r c e p t > 1. To demonstrate the matrix s e n s i t i v i t y f o r these r a t i o s o f transmissions, measurements were made through a plutoniumbearing s o l u t i o n ( p p 67.5 g/&) and a v a r i e t y o f t i n t h i c k ­ nesses. The r e s u l t s are p l o t t e d i n F i g . 4 as R versus the 2

g

7 5

5 7

7 5

=

u

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

N U C L E A R SAFEGUARDS ANALYSIS

100

Table I I .

Convenient gamma rays f o r use i n K-edge densi­ tometry measurements of plutonium and uranium.

Plutonium = 121.8

Source

7 5

Se

Ey (keV)

2 Δμ ^(αιι /gm) ρ

121. 2.12 136.0

7 5

Se

121.1

5 7

Co

122.1

3.38

Uranium = 115.6 κ. 2 Source

1 6 9

Yb

Ey(keV)

Δμ ^(αη ρ

/gm)

109.8 2.20 130.5

169 Yb 5 7

Co

1 8 2

Ta

109.8

2.70

122.1 113.7 3.53 116.4

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

8.

CANADA E T A L .

0.4

h

0.3

h

0.2

h

Absorption

Edge

Densitometry

101

R =0.993 e - 6 - 0 6 / ° P

100

200

300

f>(g>'£) Figure 3. Calibration curves for the measurement of 2-cm thick Pu bearing solutions using the 121 keV and 122 keV gamma rays of Se and Co and using the 121 keV and 136 keV Se gamma rays 75

57

75

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

N U C L E A R SAFEGUARDS

Figure 4. Ratio of transmissions, R, as a function of Sn matrix density for a 67.5 g/L Pu solution and two transmission energy combinations (R is the (136/121 ) ratio corrected for matrix) c

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ANALYSIS

8.

CANADA ET AL.

Absorption

Edge

103

Densitometry

e f f e c t i v e t i n d e n s i t y had i t been d i s t r i b u t e d i n the s o l u t i o n . These data show the matrix s e n s i t i v i t y o f R(122/121) to be reasonably small whereas that at R(136/121) i s s i g n i f i c a n t . It i s p o s s i b l e to c o r r e c t the measured R value when matrix contaminants with Ζ > 50 are known or suspected to be present i n a sample. As shown i n F i g . 5 ( ] Λ ) , l o g (μ) versus the l o g (E) may be approximated as a s t r a i g h t l i n e over a l i m i t e d energy range. Figure 6 shows that the slope o f t h i s l i n e , m, i s approximately a constant f o r a l l elements with Ζ > 50. Trans­ missions measured near the K-edge may then be e x t r a p o l a t e d to that which would have been measured at the absorption edge g i v i n g (15)

where Δμ i s measured at the absorption edge energy, E, and m 2.55. Afso shown i n F i g . 4 i s the r a t i o obtained from the c o r r e c t e d transmission v a l u e s , R (136/121), which v a r i e s by only 1.5% with the a d d i t i o n of t i n equal to ^ 23 times the plutonium c o n c e n t r a t i o n . The 121 keV/122keV r a t i o i s p r e s e n t l y being incorporated i n t o a plutonium i s o t o p i c concentration spectrometer (16). The f e a s i b i l i t y experiments were conducted with 3.5-cm-thick s o l u t i o n s c o n t a i n i n g 130-360 g P u / T h e transmission measure­ ments were made simultaneously f o r both l i n e s with a mixed C o S e source and the r e s u l t i n g doublet computer f i t t e d . The r e ­ s u l t s showed an accuracy o f < 0.5% but i n d i c a t e d a n o n l i n e a r i t y i n the c a l i b r a t i o n curve at the extremes of the c o n c e n t r a t i o n range. The l a t t e r may be due to the imbalance i n the r e l a t i v e peak i n t e n s i t i e s at these concentrations and the corresponding d i f f i c u l t i e s i n f i t t i n g the doublet a c c u r a t e l y . No obvious gamma-ray l i n e s e x i s t that bracket the K-edge o f uranium as c l o s e l y as do the 121.1- and 122.1-keV gamma rays f o r that o f plutonium. F i g u r e 7 summarizes a s e r i e s of measurements made with 1-cm-thick s o l u t i o n s c o n t a i n i n g 50-400 g U / L These data have been normalized to a 1-cm-thick water sample (the uranium sample solvent) and thus do not r e f l e c t any matrix s e n s i t i v i t y . The peak-to-background r a t i o s f o r the Ta 116-keV and 113-keV and the Y b 118-keV gamma rays are too poor to be u s e f u l i n a p r a c t i c a l assay instrument. An optimum combination now appears to be a mixed C o (122 keV) and Y b (110 keV) source. The Y b 109.8-130.9 keV gamma rays are p r e s e n t l y used i n a Ge(Li) detector based s o l u t i o n measurement system ( F i g . 8) to 5 7

75

1 6 9

5 7

1 6 9

1 6 9

In Nuclear Safeguards Analysis; Hakkila, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

N U C L E A R SAFEGUARDS

104

Figure 5.

ANALYSIS

Measured mass absorption coefficient of Pu vs. energy plotted on a log-log scale

π

1

_l

I

1—r

I

I

Ί

TT

I

J

I I I

5

I

1

1

1—I

I

I

I

Γ

I

I I

10 ATOMIC

NUMBER

Ζ

Figure 6. Slope m of log μ(Ε) vs. log Ε between 100 and 150 keV vs. atomic number '