lNiS-inl —1 2rt
FISSION PRODUCT RELEASE FROM
DEFECTED NUCLEAR REACTOR
FUEL FXJIWINTS
Ph.D. Thesis
8,3. LEWIS
1983 FISSION PRODUCT RELEASE FROM
DEFECTED NUCLEAR REACTOR
FUEL LCEMENTS
by
B..7. Lewis
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy in the University of Toronto
Department of Chemical Engineering and Applied Chemistry
University of Toronto
B.3. Lewis, 1983 ABSTRACT
The release of gaseous (krypton and xenon) arid iodine radioactive fission
products from defective fuel elements is described with a semi-empirical model.
The model assirrn;s pr"ecursor-_orr'.-cted "Booth diffusions! release" in the UO^
and subsequent holdup in the fuol-to-sheath j;ap. Transport in the ^ip is
separately modelled with a phenoinenoloj'ical rate constant (assuming ,• please
from the gap is a first order rate process), and a diffusivity constant (assuming
transport in the gap is dominated by a diffusional process).
Measured release data from elements possessing various states of defection are used in this analysis. One element (irradiated in an earlier experiment by
MacDonald) was defected with a small dril'ed hole. A second element was machined with ?'i slits while a third element (fabricated with a porous end plug) displayed through-wall sheath hydriding. Co np.inson of measured release data with calculated values from th" model yields estimates of empirical diffusion -10 -9 coefficients for the radioactive species in the l!.'.\, (1.56 x 10 to 7.30 x 10 s ), as well as escape rate constants (7.S5 x 10 to 3.*»4 x 10 s ) and diffusion coefficients (3.39 x 10" to 0-.88 x 10" cm'Vs) for these species in the fuel-to-sheath gap. Analyses al.'.o enable identification of the various rate- controlling processes operative in each element. For the noble gas and iodine species, the rate-determining process in the multi-slit element is "Booth diffusion"; however, for the hydrided element an additional delay results from diffusional transport in the fuel-to-sheath gap. Furthermore, the iodine species exhibit an additional holdup in the drilled element because of significant trapping on the fuel and/or sheath surfaces. Using experimental release data and applying the theoretical results of this wori<, a systematic procedure is proposed to characterize fuel failures in commercial power reactors (i.e., the number of fuel failures and average leak size). ACKNOWLEDGEMENTS
This thesis ,va-, carried of T) and M.7.F. Motley (GkNL) whose advice and support are gratefully acknowledged. Tiie author would like to especially thank Professors D.G. Andrews, R.A. Bonalumi and R.E. Jervis for their continuing nelp and guidance. The drilled defect experiment (FOO-&SI) was carried out by R.D. MacDonald at CRNL. Although the hydrided defect experiment (PFO-102-2) and the muiti-siit defect experiment (FFO-103) were carried out under my direct control and supervision, I would like to acknowledge the following assistance at CRNL. I wish to thank D.G. Hardy and D.R. McCracken for their helpful suggestions and assistance, and Y.H. Kang of the Korea Advanced Energy Research Institute for assistance with the preliminary data analysis. Thanks are also due to E.P. Penswick, D.D. Semenkik, D.F. Shields and various members of the Reactor Loops Branch l^r iheir conscientious data acquisitioning and processing, and to 3. Blair, M. Milgrom and R.L. da Silva for their invaluable help with the computer codes (see Appendix A). ! would aJso (ike to express my gratitude to R.l. Chenier, A.f:. Hut ton, !. Lu-I< and R.E. Moeller for their comprehensive rnetallographic examination, .I.E. Winegar for the X-ray diffra<;tion analysis and D.A. Leach for the neutron radiography examination. Special thanks are due to L. Blimkie and G.R. Phillips for their superb tracing work. Finally, ! would like to express my sincere thanks to my wife Patricia for her continuing help and support throughout this endeavour. Part of this study was funded by the Ontario Hydro - Atomic Energy of Canada Limited 3oint Programme. CONTENTS Pat-e 1. Introduction ' 2. Historical Review J 2.1 Previous Defect Models 5 2.2 Experimental Background 7 3. Experimental Detaiis '-> 3.1 Loop Monitoring Facililty 9 3.2 Experiment Description LI 3.2.1 Fuel Element Dpsign and Previous Irradiation History 11 3.2.2 Loop Operating Conditions li 3.2.3 Irradiation History J1 3.3 Post-Irradiation Examination 16 3.4 Discussion of Sheath and Fuel Degradation 22 4. Steady-State Fission Product Release 24 4.1 Results and Analyses 24 4.2 Discussion of Noble Gas and Iodine Behaviour 31 4.2.1 Chemical Nature of Iodine .31 4.2.2 Sweep Gas Experiments 33 4.2.3 De'L'Ct Experiments '34 4.3 Semi-rlmpirical Fission Product Release Model 37 4.3.1 Diifusion in the UO_ Fuel 37 4.3.2 Transport in die Fuel-to-Sheath Gap 42 4.3.3 Diffusion in i.!i<: Riel-to-Sheath Gap 48 4.4 Evaluation of Model Parameters 54 4.5 Discussion of Empirical Results 58 4.6 Comparison of Model with Previous Models 64 5. Transient Fission Product Release 67 5.1 Results 67 5.2 Discussion 70 6. Power Reactor Applications 72 7. Conclusions and Summary of Results 79 8. Recommendations 82 9. Nomenclature 83 10. References 85 IV Appendix A Computer Code Description 90 A.I The GRAAS Code 91 A.2 The SUMRT Code 9? A.3 The LATRIII' Code <,', ,\A The FISSPROD Code g7 A.5 The MLSQQ Code o8 Appendix ii The X-2 Loop Mode! 100 Appendix C Ftooth Diflusionj] Release Corrected for Precursor Diffusion 102 Appendix D Diffusion in the FueJ-to-Sheath Gap JD/J Appendix E Rare Gas Diffusion Coefficient from Kinetic Theory 1()a Appendix F Fuel Element Temperature Calculations -|11 Appendix G Thermodyjuriiir Calculations I [7 Appendix H Selected ENDF/1VV Decay Data no Appendix I Loop Design and Measurement 122 1.1 Description of the Loop 122 1.2 Spectrometer Design 123 1.3 Discussion of Error 124 LIST OF TABLES AND FIGURES Tables 3.1 Pre-Irradiation Fuel Element Design 1.! 3.2 Comparison of the X-2 Loop Coolant Conditions with the Specified Bruce NGS Primary Meat Transport System Conditions ] ;< 3.3 Average Element Power Ratings, Full Power Days and Ournups 13 3.4 Oxygen-to-Metai Ratios (O/U) for Elements A7E and A3N IS 3.5 Zirconium Oxide Thicknesses on the Sheath Surfaces -'1 4.1 Release Rate (R ), Birth Rate (i\) and Fractional Release (F) Values During Steady Reactor Power for Experiments FDO-6S1, FFO-102-2and FFO-103 ^6 4.2 Fractional Release Dependency on the Decay Constant of the Form a.\° 30 4.3 Comparison of the Slope on a Fractional Release Versus Decay Constant Plot for Various Defect Experiments 35 4.4 Correction Fa-.tor (H) ior Pr-.-rursor Diffusion '•, I 4.5 Evaluation of Empirical Par.n-'icters for FOO-6S1, FFO-102-2 and FFO-103 35 4.6 Experimental Gap Diffusiv', :ies for FOO-6S1 and FFO-102-2 56 4.7 Comparison of Measured and Calculated Fractional Releases 5 7 4.8 Comparison of Theoretical and Experimental Noble Gas Diffusivitics for FDO-W! and FFO-102-2 61. 4.9 Comparison of Calculated Fractional Releases (F) for Various Defect Models 64 6.1 Isotopic Release Rate Ratios for Experiments FDO-6S1, FFO-102-2 and FFO-103 and for a Recoil System 75 6.2 Release Rate Dependencies on the Decay Constant for Particular Reactor Core Conditions 76 6.3 1-131 Release Rates for Experiments FDO-681, FFO-102-2 and FFO-103 77 E.I Calculation of Rare Gas Diffusion Coefficients from Kinetic Theory 109 F.I Symbols Used in Temperature Calculation 113 G.I Calculation of Free Energies at 623 K (350 °C) for the Ionic Species 118 1.1 The X-2 Loop Design Parameters 122 1.2 Detector/Collimator Combination for Experiments FDO-681 FFO-102-2 and FFO-103 124 3.1 The X-2 Defect Loop !(l 3.2 Experiment FFO-102--22 Reactor Power History and Fission Product Concentratiomn and Release Rate Historvy for ! For over a decade fuel performance in the Canadian CANDU reactor system has been excellent. Remote instances of unsatisfactory performance were attributed to inadequate quality control procedures during fuel fabrication. Fuel elements containing manufacturing, porous end plug and faulty end weld defects (such that a small leak path is present between the primary coolant and the internal element atmosphere) have exhibited secondary sheath deterioration following irradiation. This deterioration was a result of hydriding of the Zircaloy sheath. Although no fuel handling problems have been encountered, fuel element deterioration and associated fission product releases may present economic penalties to power utilities from lost burnup and increased man-rem exposures of station personnel. To understand fuel defect performance and correlate fission product releases with sheath degradation, an irradiation program was established at the Chalk River Nuclear Laboratories (CRNL). This program was unique as both naturally and artificially defected elements were irradiated in an in-reactor test loop supplemented with on-line gamma-ray spectrometry. Following irradiation of the natural defect experiment, elements containing prifnary porous end plugs displayed secondary through-wall s'leath hydriding similar to that observed in power reactors; however, no such deterioration was observed following irradiation of the artificially defected elements (elements containing drilled holes or machined slits). The main objective of this thesis is to deduce the physical processes operative in defected nuclear fuel elements using experimental results of the CRNL Defect Program. Hence the physical parameters associated with release of the radioactive noble gases and iodines are quantitatively assessed in a semi- empirical fission product release mode! for quasi steady-state conditions. \ further objective of this investigation is the application of these experimental and theoretical results to defected fuel monitoring in commercial power reactors. Activity releases from the following CUNL defect ^••.f.n1'inenTs (representing a wide range of defect sizes) were analyzed in order to determine defected fuel behaviour. These experiments include: (i) Irradiation of an element containing a small (• • Im-n diameter) mid- element drilled hole in the sheath (experiment FDO-651) '; (ii) Re-irradiation of an element manufactured with a porous end plug and displaying through-wall secondary sheath hydriding from Lin earlier irradiation (experiment FFO-102-2) and; (iii) Irradiation of an element circumferentially machined with 23 slits along the sheath (experiment PFO-103). Analyses of these experiments indicated significant holdup of the fission gases and iodines in the fuel-to-sheath gap 'oelore release into the hot pressurized coolant. This effect was more predominant for the iodines. Such holdup and transport is modelled using two fundamentally different approaches. In one version an escape rate coefficient v is introduced representing the rate at which a fraction of the total number of atoms in the gap escape into the primary coolant. When this formalism is pursued, the release-to-birth rate ratio (R/B) or "fractional release" (for an isotope with decay constant ' ) is proportional to a factor ••/( \ + v)for the noble gases (and of similar form for the iodines), and arises because of the presence of the gap. As reported in the literature, ' a more fundamental approach may be used to model transport in the gap. In this version for CANDU fuel, the main transport process is identified as diffusion dominated by gas-gas collisions with a dilute species diffusing in a continuum steam medium. For this case, the fractional release is proportional to a "diffusion length" ( j>•/ \ I •' where • is a characteristic gap diffusivity. The two versions above depend on whether the rate controlling step for transport in the gap is chemical reaction (particularly for the iodines) or diffusion. Further, an additional delay occurs in the fuel pellet itself. Both treatments above assume that the fractional release is proportional to a constant source term arising from reJease (per unit time) lrorn the IJO^ fuel pellets into the gap. In CRNL sweep ;;as tests, the gap of an intact operating fuel element is swept with an inert carrier gas. These experiments indicate a diffusion- controlled release from the fuel ' i.e., both the noble gases and iodines diffuse through the UO~ with a *~ •• fractional release dependency on the decay constant. This dependence was originally predicted by Booth. Therefore, for highly- powered fuel (that is, for fuel temperatures above -v 1000 K) both versions above assume a diffusion-controlled source into the gap (corrected for precursor diffusion) with negligible contributions from recoi! and knockout. Consequently, for defected fuel, the phenomenological transport model predicts a release dependence of X ~ 2 to •<".' (depending on the relative magnitude of the rate constant and implicitly on the size of the defect) whereas the diffusion model predicts a release dependence of J i (assuming diffusion is the rate-determining process in the gap). In conclusion, the novelty of this work concerns a fission product release analysis of three deEect experiments. Subsequently a semi-empirical model is developed, and calculated activity releases are compared to measured releases for elements containing significantly different states of primary defection. In one particular experiment the model follows the progression of secondary sheath deterioration. This model is uniquely derived from a set of mass balance equations, assuming first order rate processes, as well as from a two-dimensional diffusion equation with chemical reaction. The source term in the gap assumes a "Booth diffusional release" trom the UO? as suggested by recent sweep gas experiments and the multi-slit defect experiment; however, this release is modified to allow for precursor diffusion effects. The various rate constants and fuel and gap diffusivities ere evaluated for each defect experiment and provide an insight into the different physical processes operative in each element for a particular defect state. Finally, with an understanding of the different rate- controlling processes, theoretical and experimental results are applied to defected fuel monitoring in the CANOU power reactor addressing such questions as: (i) What is the average size of the defect(s) present? (ii) How many defected elements are there? (iii) Is the activity in the pressurized heat transport system due to fuel failures or uranium contamination7 2. HISTORICAL REVIEW Many defect experiments ' ' ' have been performed to measure the rate of release of the fission product gases and iodines from operating fuel elernents where the sheath integrity has been breached. In the early experiments the sheath defect was generally a small artificially drilled hole. These early experiments were limited in scope since fuel element failures observed in power reactors have a comparatively different defect nature from drilled holes as a consequence of localized hydriding. Previous attempts to model fission product release behaviour were based on drilled element release data. Therefore, difficulties arise in applying these models to the power reactor where the release behaviour (as a function of the decay constant) is different. Several of the early defect models, used to predict the release behaviour for drilled elements, are described in Section 2.1. As discussed in this section these models have serious limitations. It is recognized that a more fundamental understanding cf the fission product release processes is needed. An irradiation program at CRNL was therefore established for fuel elements possessing various states of defection. A historical perspective of the experiments proposed in this program and used in this thesis is given in Section 2.2. 2.1 Previous Defect Models An early and more successful model for drilled elements was proposed by Allison and Rae in 1965. In their model, the noble gases were assumed to originate in a hot central core. However, because of traps and radioactive decay, only a small fraction of the gases was postulated to move quickly into cracks in the cooler surrounding IJO-, by a first order rate process. Subsequently, axial movement occurs in the fuel-to-sheath gap with the fractional release for t'le noble gases expressed as a function of the product of the element length and decay constant. The iodines were modelled v/.t'n a somewhat different approach. It was assumed that they diffuse from the outer surface of the hot core into ,i porous region where ( onsiderable delay occurs through chemical trapping. Only a very small fraction was postulated to escape via cracks to the defect by a first order rate process. The long delay for iodine, as a result of chemical trapping in the porous region, results in an important source of xenon through radioactive decay. The Allison and Rae model yields a different fractional release expression for iodine compared with that for the noble gases. The release expression is independent of the fuel element length and varies as >. . \s discussed by Allison and Rae, however, the model is limited since it is derived explicitly to fit the experimental release data. The assumption that cracks exist at the boundary of the hot core disagrees with experimental observation. As stated by the authors, "there are difficulties in relating the model to the physical processes which are believed to be occurring in the fuel". A more fundamental model was derived by MacDonald and Lipsett in 1980. The model interfaced the fission gas release calculations of the ELFLSIM code (MOD 10 version) for the \.SO? fuel with the empirical equation of the Allison and Rae model for axial diffusion in the fuel-to-sheath gap. The ELESIM code assumes that the fission gases diffuse to the grain boundary by a Booth-type diffusional process or are collected by grain boundaries which sweep through the fuel. At the grain boundaries, the fission gases collect in bubbles which grow until they saturate and interlink to form boundary tunnels. The rate of release of the fission gases to the free volume of the fuel element is then equal to the amount of release (averaged over a steady-state period) which is in excess of that required to saturate bubbles on the grain boundary. The iodines are assumed to behave similarly to the fission gases. As shown in Section ^.6, the predictive ability of the MacDonald and Lipsett model is only fair compared to that of the Miison and Rae model. MacDonald and Lipsett suggest that the model may be improved by allowing for precursor diffusion and by modelling diffusion in the gap less empirically. Hence, the limitations of the MacDonald and Lipsett model is that the predictive ability of the model is only fair (compared to that of the less complicated Allison and Rae mode!) and it requires the use of the complex CLESIM code (the code requires the power history of the fuel element). From the discussion above, it is apparent that there is a need for a simple yet fundamental model which is capable of predicting the fractional release for a wide range of defect characteristics (as represented by the three defect experiments described in Section 2.2). The new model would require a more physical approach to treat the release of fission products in the fuel and transport of the fission products in the gap. Such approaches have been considered in the theoretical work? of Booth and Kidson for diffusion in the fuel and Helstrom and Beslu for transport in the gap. The development of a model based on the theoretical works of these authors as well as on the available experimental evidence is presented in Section (f. 2.2 Experimental Background The defect models described above have serious limitations r.ince they are based on limited experimental data for a small range of defect states. There was a need for further defect experimentation to cover a wider range of defect si^es and, in particular, to include a defect which is tyDical of that found in a power reactor. This need was recognized by MacDonald who proposed the following two irradiations: (i) Irradiation of elements containing porous end plug defects (experiment FFO-102) in an effort to promote sheath hydriding under experimental conditions and; (ii) Irradiation of an element machined with 23 slits (experiment FFO- 103) to rninimi/.e holdup and trapping of fission products in the fuel- to-sheath gap. Following irradiation of experiment FFO-102, elements containing primary porous end plug defects exhibited through-wall cracks and blisters from sheath hydriding. The sheath deterioration was typical of that observed in power reactors. At this point the experimental and theoretical aspects of this thesis begin. Experiment FFO-102-2 was proposed and designed for the thesis investigation to study the progression of secondary sheath deterioration and to correlate the deterioration with the fission product release. Experiments FFO- 102-2 and FFO-103 formed an integral part of the experimental work of the thesis. Raw release data from MacDonald's earlier drilled defect experiment FDO-681 (Phase 2) were re-analyzed to provide a more consistent set of fractional release values for comparison of the three representative defect experiments. The experimental details of the three defect experiments are given in Section 3. 3. EXPERIMENTAL DETAILS 3.1 Loop Monitoring Facility AJ] defect experiments were irradiated in the X-2 pressurized light water loop of the NRX research reactor. This loop is capable of operating at the coolant conditions specified for CANDU PHW reactors. A schematic diagram and simplified flow sheet of this facility is provided in Figure 3.1. The X-2 loop was modified to cope with high activity levels fro.n fission product release and UO^ loss through large defects. Full flow graphite filters were installed to prevent loop contamination from fuel debris and ion-exchange mixed bed resin columns were used to remove ionic fission products such as the radioiodines. Activity release in the loop was continually measured with on-line gamma-ray spectrometry at the inlet of the in-reactor test section for experiments FFO-102-2 and FFO-103, and at the outlet of the test section for experiment FDO-681. The measured activity consisted of the dissolved and gaseous fission products. The detector of the spectrometer was fabricated from a single piece of high parity germanium and was coupled to a collimator enabling optimum counting rates for fission product detection. The X-2 defect loop was supplemented with a sensitive BF, detector and a less sensitive fission counter detector for delayed neutron monitoring. These detectors respond principally to the shorter-lived delayed neutron precursors Br- 87 and 1-137 (half-lives of 54.5 s and 2UA s respectively). The design of the X-2 loop facility is described in more detail in Appendix I. Also included in this appendix are the design specifications for the on-line gamma-ray spectrometry equipment. ili fa) OllfCIOI 101 S*ICIIMCUI 101 Ml> uo COOIIU llirOUL CIICUIIS "« ttCMtmiKVioK IISIIK (b) Figure 3.1 The X-2 Defect Loop (Courtesy of Atomic Energy of Canada Limited) (a) Schematic Diagram (b) Simplified Flow Sheet n 3.2 Experiment Description 3.2.1 Fuel Element Design arid Previous Irradiation History All three defected fuel elements were sheathed in Zircaloy-4 tubing and contained sintered UOy pellets. Pre-irradiation fuel element design details are listed in Table 3.1. Element A7E was of a standard element design for a CANDU 37-element bundle modified with end fittings for use in a trefoil carriage. One end plug was manufactured from porous bar stock and had an equivalent pin-hole diameter of (?) 'i* I .1 (im as estimated with helium leak testing for a Hagen-Poiseuille flow. Metallographic examination of a typical unirradiated porous end plug revealed a large, axially-oriented, porous inclusion (<100ijm in diameter) almost completely filled with zirconium oxide. The multi-slit element A3N was of a similar design to A7E although it was fabricated with different end plugs and, consequently, had a slightly smaller fuel stack length. This element contained 23 slits, located circumferentially along the sheath, to minimize holdup and trapping of fission products in the fuel-to-sheath gap (yielding a total UO_ exposed area of 2.7 2 cm ). Element LFZ had a considerably shorter length, and larger sheath d/ameter and thickness than the other two elements. It was drilled with a 1.20 mm diameter hole at about the middle of the fuel stack length. Element A7E was irradiated in an earlier experiment and was chosen for re-irradiation in experiment FFO-102-2 because it had exhibited moderate sheath degradation (through-wall cracks and blisters - see Section 3.3). In the previojs experiment, the element had operated at a high linear power of 63.8 kW/m and had accumulated a midplanf burnup of 36.9 MWh/kg U. Both elements LFZ and A3N were unirradiated prior to experiments FDO-681 and FFO-103. Table 3.1 ?re Irradiation Fuel Element Design Experiment FDO-681 FFO-102-2 FFO-103 1. Fuel Element Identification Element Identity LFZ A7E A3N Primary Defect Drilled hole (mid-element) Porous end cap Machined slits (23) and Size 1.20 mm diameter 1.4 urn equivalent diam. 3.57 cm x .T*3 CTI for each slit 2. Fuel Parameters Fuel Enrichment (wt % U-235 in U) it. 52 5.02 5.02 Pellet Density (Mg/m ) 10.72 10.71 10.71 Pellet Outside Diameter (mm) 13.61 12.14 12.15 Pellet Length (mm) 13.0 16.46 16.48 Pellet End Dishing one end both ends both ends land width (mm) 0.56 0.46 0.46 depth (mm) 0.64 0.23 0.23 Pellet Stack Length (mm) 168.4 477.1 469.7 Total UO-, Weight (g) 257.1 580.6 561.5 3. Sheath Parameters Sheath Outside Diameter (mm) 15.16 13.11 13.11 Sheath Thickness (mm) 0.71 0.43 0.43 Can Length (mm) 1S4.5 485.0 485.0 Clearances diametral (mm) 0.11 0.10 0.10 axial (mm) 1.07 2.2 2.2 Fuel-to-Clad Interface Graphite CANLUB (DAG-154) on the inside surfaces of the three sheaths. 3.2.2 Loop Operating Conditions A comparison of the average X-2 loop coolant conditions prevalent during the three defe^ i experiments with those specified for the Bruce Nuclear Generating Stas m (BNG5) are shown in Tnble 3.2. Table 3.2 Comparison of the X-2 Loop CooJant Conditions with the Specified Bruce NGS Primary Heat Transport System Conditions X-2 Loop Experiment BNGS(1) F0O-6S1 FFO-102-2 FFO-103 H Coolant H2O 2° H2O D2O Inlet Temperature CO 237 247 250 252/256* Inlet Pressure (MPa) 7.65 10.3 10.5 9.3 Mass Flow (kg/s) 0.64 1.11 0.99 23.8** Coolant pH , 9.8-10.3 10.5 — 10.3-10.7 Hydrogen Content (cm /kg) .. S.2-30 6.4 _.. 3-7 Operating Coolant Volume (in ) 0.074 0.150 0.150 269.8 Coolant Recirculation Time (s) 105 105 105 26/22* Coolant Transport Time (s) 23 97 97 __ (from the fuel to the spectrometer) (1) A.M. Manner, AECL-'.Engineering Company, private communication. * Inner zone/Outer zone ** Maximum mass flow/channel The pH in the X-2 loop was controlled with LiOH. Chemical analysis to assess the coolant pH and hydrogen content was not performed during the FFO-103 experiment because of high activity levels in the loop. 3.2.3 Irradiation History The linear heat output histories of the three elements and reactor power histories are reported in References 3, k and •>. As typically shown for FFO-102- 2 in Figure 3.2, the reactor power history is plotted on the same time base with the fission product release history (loop activity concentrations (ftq/m ) and release rates (atoms/s) versus time) for Kr-85m. Data sampling periods for later reference are also included in this figure. ,m> 102-2 t KRSsm ]5Q,.g Figure 3.2 Experiment FFO-102-2 Reactor Power History and Fission Product Concentration and Release Rate History for Kr-85m Average heat ratings, .uruiuulated burnups and effective full power days (cfpii) of irradiation for the three elements are listed in Table 3.3. Al! element power data are based on loop caloriinetric measurements, accurate to approximately *S%. Table 3.3 Average Element Power Ratings, Full Power Days and Burnups Element LFZ A7E A3N 1. Average Element Power Ratings Heat Output (kW) S.I 31.5 22.3 Fission Rate* (fissions/s) 2.73 x 10U 1.06 x 1015 7.52 x 10 Midplane Linear Heat Output (kW/rn) 43.0 66.6 47.9 Midplane Surface Heat Flux*" (l 2. Days of Irradiation Effectiv:? Full Power Oavs (efpd) 24.1 1 S.6 * * * 14.6 3. Accumulated IVirnup Initial Midplane Burnup (MWh/kg U) 0.0 36.9 0.0 Final Midplane fturnup (MWh/kg U) 20.0 67.4 17.5 * Based on (S3 MeV/fission ** Sheath-to-Coolant *** Calculated for the FFO-102-2 irradiation During the FFO-102-2 irradiation, element A7E was irradiated at a high average linear power of 67 l U to a final burnup of 67 MWh/kg U. Elements LFZ and A3N were irradiated at an intermediate linear power of 48 kW/m in defect tests FDO-6S1 and FFO-I03, and had accumulated low rnidplane burnups of 20 and 18 MWh/kg U respectively. 3.3 Post-Irradiation Examination A visual examination of element A7E revealed a progression of sheath degradation during the FFO-102-2 irradiation (compare Figures 3.3 A and R). The larger cracked blister (11 mm in area) adjacent to the bottom (high- powered end) bearing pad in Figure 3.3 A had extended and opened up during re- irradiation (r^2 c:n of (JO., exposure), revealing wide cracks in the UO^ pellet, the sides of which exhibited a columnar structure (Figure 3.3 li-a). The original, smaller defect above the bearing pad in Figure 3.3 A did not appear to have deteriorated any further although a crud deposit made this difficult to determine visually, the source of the spallod Mg(OH)_ crud layer was found to be MgO insulation from a failed auxiliary loop heater. Another defect ("- 1 cm ), which did not exist prior to the FFO-102-2 irradiation, was observed on the surface of the sheath facing the trefoil carriage just above the main defect area shown in Figure 3.3 B-c. Here the fuel had been flattened from contact with the carriage wall and it could not be determined whether this defect occurred before or after contact with the carriage. The primary porous end plug defect, located at the high-powered end, appeared to be totally plugged with a white oxide. Neutron radiography revealed more extensive sheath hydriding following re-irradiation aroui^ the main defect area. *\ polished cross-section through the lower main defect of element A7E (see Figure 3.3 B-b) shows columnar and equiaxed grain growth in the UO- and central melting. Near the surface of the exposed fuel, long narrow columnar grains developed parallel to the exposed surface. A transverse section through the upper defect, which developed at a later time opposite the carriage wall, revealed much less distortion of the regions of central melting and grain growth in the UO^ (see Figure 3.3 B-d). (A) H) Figure 3.3 Visual and Metallographic Examinations of Element A7E (Courtesy of Atomic Energy of Canada Limited) (A)Pre FFO-102-2 Visual Examination (B) Post FFO-102-2 Visual (a,c) and Metallographic (b,d) In contrast, no sheath deterioration from massive hydriding was observed for artificially defected elements LFZ and A3N. The drilled hole in element LFZ remained unchanged during irradiation. However, the slits of element A3N opened up. As seen in Figure 3.4 a, and by comparing the three metallographk: photomacrographs (Figures 3.4 b, c and d), slits at the lower-powered (upstream) end had opened wider than those at the opposite end. A small amount of Mg(OM)2 crud contamination was also identified on the bottom third of element A3N. Oxygen-to-metal ratios (O/U) for elements A7E and A3N were deternr T-ed by gravimetric analysis and are listed in Table 3.4. Table 3.4 Oxygen-to-Metal Ratios (O/U) for Elements A7E and A3N Metallographic Distance From Bottom O/U Ratio Sample (High-powered) End Location (mm) A7E A3N Lower Plane Section* 43-63 2.15 N/A»* Middle Plane Section 195- 215 2.11 2.28 Upper Plane Section 365 -275 2.16 N/A** * This sample was located between the two large secondary defects. ** Not Available. Each ratio represents an average value for a single pellet sample. The ratios for element A7E were relatively constant and therefore did not reflect a significant axial oxidation gradient. Metallography of this element revealed a structure, predominantly in the finer columnar grain region of the main defect (Figure 3.3 B-b), which was tentatively identified as U. O? Oxidation of the fuel pellet periphery (near the main defect) can be seen in Figure 3.5 and is indicated by grain boundary separation. I. ,>-.trva:n (lowr-powered) end il, Ic V**! t Figure ?>M Post-Irradiation Visual and MetalloRraphic Examinations of Element A3N from FFO-103 (Courtesy of Atomic Energy of Canada Limited) (a) Visual Examination (b,c,d) Metallographic Examination • Figure 3.5 Grain Boundary Separation Indicating Oxidation of the Fuel Surface at the Main Defect Site (or Element A7E (Courtesy of Atomic Energy of Canada Limited) The single O/U ratio for the multi-slit element was notably greater. This result was corroborated with metallographic examination (Figures 3.4 b, c and d) which showed numerous unknown oxidation states of uranium, presumably between Up<) and U,Og i.e., the existence of the higher oxide UO^ in a steam and water environment can be ruled out on thernodynamic grounds. '' These higher oxide phases were observed in the fuel matrix and on pellet peripheries, principally in the top-half (upstream end) of the element. UO-, loss from the drilled element was considerably less than from the secondary-hydrided and multi-slit elements. Element LFZ had an estimated loss of •;.! &. Loss a: ''ie main oei'ect •:>*. dement '-sTc (estrndiea as •« 3 g) '.vas substantially greater than that at the second defect (estimated as ^.5 g) as seen in Figure 3.3 b and d. In comparison, the multi-slit element A3N exhibited the greatest fuel loss, calculated as -v60 g (or 11% of the total UO_ weight). As indicated in the metallographic examination (Figures 3A b, c and d), fuel loss was -•1 greater at the top of the element, where the slits were opened wider and where there was a greater degree of fuel oxidation, than at the opposite end. All values above represent upper limits as inevitably some fuel loss occurred during post-discharge handling. The three elements were covered with a continuous zirconium oxide film on both the outside and inside surfaces of the Zircaloy sheath (see Table 3.5). HowevT, graphite CANLUB interlayers could not be found in any of the fuei-to- sheath gaps after irradiation. Table 3.5 Zirconium Oxide Thicknesses on the Sheath Surfaces Element Distance from Bottom Zirconium Oxide Thickness on Sheath (High-Powered) End (v m) (mm) Inside Surface Outside Surface LFZ 92 6 to 56 .5 to 2 125 Primary Defect 4 to 30 .5 to 2 4 to 64 .5 to 2 A7E 8-38 Secondary Defect up to 30 (remote from defect) up to 36 ^100 (at defect) 63-8S Secondary Defect same as above up to 76 235 1 to 4 (oxide pockets 1 to 4 up to 7 0) (oxide pockets up to 26) 390 1 1 A3N 0-485 5 to 12 (remote from slits) 2 to 4 2 to 8 (at machined slits - maximum thickness near bottom (downstream) end of element) 3.* Discussion of Sheath and Fuel Degradation Increased deterioration of element A7II at the main defect resulted from localized sheath stresses during power reactor transients, and from swelling caused by fuel oxidation. This conclusion was drawn from stepped, steady--.tate increases in coolant fission product concentration levels following each successive transient (see for example Figure 3.2). Extensive cracking of the hydrided sheath may have occurred during transient reactor operation due to mechanical stresses imposed on the sheath by thermal expansion and contraction of the underlying fuel. The occurrence of a second defect at a later time was indicated by a sudden steady-state fission product release increase approximately V/i days before the end of the irradiation, and from the metallographic examination i.e., there was significantly less UO^ loss and grain growth distortion relative to that at the main defect. Since the fuel was flattened against the carriage wall, the second defect probably occurred from localized bulging and element bowing, and subsequent contact with the carriage. Slits at the top of element A3N were opened wider than those at the bottom because of more extensive fuel swelling caused by UO_ oxidation; increased oxidation at the top of the clement may have resulted from greater communication between the coolant and the upstream end. Fuel loss from the elements depended on the amount of time the fuel was exposed to the coolant and particularly, on the nature of the defect (the size and location) and the degree of fuel oxidation. UO_ loss was probably gradual resulting from coolant erosion after individual grains had been loosened by grain boundary oxidation (see Figure 3.5). No sheath degradation as a result of hydriding was observed for elements LFZ and A3N. Both of these elements had contained large primary defects (a drilled hole and machined slits). However, in experiment FFO-102 (the 2 i experiment prior to FFO-102-2) elements manufactured with porous end plugs (with effective pin-hole diameters of ^ L -,i m) exhibited secondary sheath liydriding and deterioration, similar to that observed in CANDU power reactors. As suggested by Davies, this result may be attributed to a critical H»:O_ r.itio in the internal atmosphere of a defected element. In elements with very small defects water ingress is limited, not only by the small hole si^e, but also because the hole may eventually plug up with zirconium oxide (see Section 3.3) or with fission products. Consequently, as oxygen reacts with the UOj and the Zircaloy sheath (as evidenced iy the thick zirconium oxide layer on the inside surface of the sheath - Table 3.5), the hydrogen partial pressure may increase, thereby favouring hydrogen pickup by the sheath. With large holes however, a critical H_:O_ ratio is never reached with a continuing supply of water and stearn and therefore the hydriding process cannot proceed. An out-of-reactor experiment has provided evidence that fission products may promote sheath hydriding; therefore, with a large defect fission products may escape from the gap before hydriding of the sheath can occur. Interestingly, hydriding progressed in the FFO-102-2 experiment even though a "large" secondary hydrided defect was present at the beginning of the irradiation (Figure 3.3 A). It may be argued that, once hydriding is initiated, the presence of massive hydride in the sheath may attract further hydrogen pickup. Since the hydride concentration increased in the principal defect region, the hydrogen partial pressure no longer appeared to be a controlling factor. In summary, the mechanisms responsible for the progression of sheath hydriding in the highly rated element A7E are not clearly understood, but are probably related to effects of higher temperatures and radiation. it. STEADY-STATE FISSION PRODUCT RELEASE *f.I Results and Analyses Fission products released into the loop coolant were continually monitored with a high resolution gamma-ray spectrometer previously described in Section 3.1. Data from the spectrometer were continually processed with H multi- channel pulse height analyzer and stored on magnetic tape. Each spectrum was collected over a M000 second counting interval during steady reactor operation and over a ^200 second counting interval during transient reactor operation. The computer code GRAAS (see Appendix A.I) used as input the mass storage file of the collected spectra. Gamma-ray photopeaks were identified by a smoothed second derivative test. For each significant peak, the area and its variance was calculated by fitting a Gaussian distribution on a straight line background. The count rate (c/s) was evaluated by dividing the total peak area by the counting period. An automatic calibration was used to convert the channel number of each peak into an energy. The computer program SUMRT (see Appendix A.2) used the output of the GRAAS code to calculate loop activity concentrations (Bq/m ) and release rates (atoms/s) versus time for the individual gaseous and dissolved fission products. These quantities are plotted on a common time base plot (typically shown for experiment FFO-102-2) in Figure 3.2 for Kr-85m. The mathematical model used by the SUMRT code to calculate fission product release rates is based on a mass balance in the loop and is reproduced in Appendix B. Steady-state fission product release rates were determined by averaging over a minimum of 7 spectra (representing a period of about 6 hours), remote from any reactor transients where all fission products displayed a relatively constant release rate at full reactor power (see for example, Figure 3.2 for data sampling periods for experiment FFO-102-2). Release rates of the xenon isotopes were corrected for iodine decay in the loop coolant. The instantaneous birth rate for each nuclide was evaluated by multiplying the fission rate by the cumulative chain yield' at time t. An average fission rate was calculated from loop calorirnetry measurements assuming 135 MeV per fission (see Table 3.3). The chain yield was calculated using the reactor lattice code LATREP (see Appendix A.3), and the fission product accumulation program FISSPROD-3 (see Appendix /\A). For each individual isotope, the observed release rate R was divided by the birth rate B yielding the conventional "(R/B) ratio" or fractional release F as shown in Table 't.l. Due to the high neutron absorption cross-section of Xe-135, an effective decay constant f was defined for this isotope i.e., f, = X + u £ for the fuel and f> A + fCTK,ij>u, as used in the SUMRT code for the coolant. Here 7 is the Westcott microscopic absorption coefficient, Westcott flux (fuel or coolant) and f is the ratio of the in-pile to total loop volume (f - 3.21/1 500. The Westcott cross-section and flux were evaluated with the LATREP physics code. For the following fractional release analyses, the effective decay constant for each experiment is given as, Experiment r, (fuel) (s *) FDO-681 3.23 x I0"5 FFO-102-2 1.20 x 10" FFO-103 9.89 x 10 Errors quoted in Table 4.1 are derived from a standard deviation about a mean value for measured release rates and fission rates (see Section 1.3 of Appendix I). The inverse of the variance of each fractional release value is used as a weight in a non-linear least squares fitting program in Section kA. * A The cumulative chain yield of an isotope ZM is defined as the sum of the direct (independent) yields of all members of the mass chain up to and including the isotope with atomic number z. Table ».l Release Rate (Rp)> Birth Rate (B) and Fractional Release (F) Values During Steady Reactor Power For Experiments FDO-681, FFO-102-2 and FFO-103 A. Krypton Experiment Data Sample Accumulated Parameter Isotope Kr-85m Kr-87 Kr-&8 Date and Time, t K-ray (keV) 131 •03 196 1 Time (s) Ms" ) ».3O x 10'5 1.52 x 10"* 6.78 x 10"5 5 9 9 9 FDO-681 1975 September 4.75 x 1Q Ro(a/s) 5.08 x.O 2.b5 x 10 9.55 x 10 12 03, 01:43 B (a/s) 3.57 x 10IZ 6.89 x 10 9.71 x 1012 - 03, 09:22 F i.42 x 10"3 3.34 x lO"1* 9.84 x 10'1* 5 9 9 10 1975 September 7.52 x 10 RQ(a/s) 8.94 x 10 4.0S x JO 1.1* xlO 12 12 06, 01:28 B (a/s) 3.57 xlO12 6.89 x 10 9.71 x 10 - 06, 10:29 F 2.51 x 10'3 5.92 x 10** 1.17 x 10"3 Average F 1.97 +. 12) x 1Q"3 (4.88 + .31) x 10'* (1.08 :.06)x 10"3 5 10 l0 10 FFO-102-2 1981 March 6.22 x 10 Ro(a/s) 4.00 x 10 1.6S x 10 4.49 x 10 13 24, 21:47 B (a/s) 1.39 xlO13 2.68 x 10 3.77 x 1013 - 25, 03:05 F (2.S8+.,14) x 10"3 (6.26 +.30) x 10"" (1.19 + .06)x 10"3 6 10 10 10 1981 March 1.06 x 10 Ro(a/s) 6.44 x!0 2.76 xlO h.SS x 10 13 13 29, 21:56 B (a/s) 1.39 xlO13 2.68 x 10 3.77 x 10 - 30, 04:12 F (4.65 +,.23) x 10*3 (1.C3 +.05) x 10"3 (1.82 + .09)x 10"3 5 11 1! U FFO-103 1981 June 5.18 x 10 R0(a/s) 2.14 xlO 1.79 x 10 3.69 x 10 06, 13:22 B (a/s) 1.00 xlO13 1.9 3 x 10 l3 2.72 x 1013 - 06, 22:44 F (2.14 + .14) x 10"2 (9.2(> 16.59)xlO"3 (1.36 +.09) x 10"2 Table *.l continued B. Xenon Experiment Data Sample Accumulated Parameter Isotope Xe-133 Xe-133m Date and Time, t Xe-135 Xe-138 1 -ray (keV) 81 233 249 1 Time (s) Ms" ) 1.53 xlO"* 6 5 3.66 x 10" 2.12 x 1 1 5 FDO-681 ' 1975 September 4.75 x 10 R (a/s) 1.71 11 9 9 o xlO 5.23 x 10 8.84 x 10 8.06 x 108 03, 01:43 B (a/s) 7.57 xlO12 13 3.81 x !0" 1.79 x 10 1.76 x 1013 03, 09:22 F 2.30 x \0~2 2 1 1.37 x 10" 4.95 x lO"" 4.59 x !0"5 1975 5 September 7.52 x I0 Ro(a/s) 5.35 xlO" 10 10 1.37x tO 1.95 x 10 8.84 x 10* 06, 01:28 B (a/s) 1.12 xlO13 11 13 4.76 x 10 1.79 x 10 1.76 x 1013 06, 2 2 3 10:29 F 4.77 x 10" 5 2.87 x 10" 1.09 x 10" 5.04 x .O" 2 2 Average F (3. 54 ±.58) x 10" 5 (2.12 ±.78) x 10" (7.92 ±.63) x 10"" (4.81 ±.37•)x 10" 5 FFO-102-2 1981 March 6.22 x 10 12 11 Ro(a/s) 2.354 xlO 1.88 x IO 24, 21:47 13 B (a/s) 3.76 xlO 6.94 x 1013 25, 03:05 2 3 F (6. 32 ±. 31) x 10" - (2.71 ±.25) x 10" 6 1981 March 1.06 x 10 12 R0(a/s) 6.73 x,0 3.70 x 10U 29, 21:56 13 B (a/s) 5.3S xlO 6.9i> x 1013 30, 04:12 3 F (1. 25±. ll)x 10"' — (5.33 ±.62) x 10" FFO-103 5 1981 3une 5.18 x 10 12 1 RQ(a/s) 2.68 xlO 3.8t x 10 ' 06, 13:22 3 B (a/s) 2.31 <10> 5.C1 x 1013 - 06, 22:4* 3 F (1..16 • 21) x 10"' (7.66 +1.1X) i in" Table 4.1 continued C. Iodine Experiment Data Sample Accumulated Parameter Isotope 1-131 1-132 1-133 1-13* 1-135 Date and Time, t way(keV) 364 668 530 S84 1261 1 7 5 Time (s) Mi' ) 9.98 x \0~ 8.37 x 10" 9.26 x 10"* 2.20 x 10"* 2.91 x 10"5 (ii FDO-681 1975 September 4.75 x io' R (a/s) 6.53 x I1)' 2.SS x 109 13, 01:43 B (a/s) 3.S5 x IQ12 1.81 x lo" __ ._ u - 'J3, 09:22 F Z.w-.f' 1.65 x 10 -- 5 [r> 1975 September 7.52 x 10 RoU/s) 1.06 x \i) 2.70 x 109 _ Ob, 01:28 B (a/s) 4.06 x I012 — I.Six 10IJ 1 - 06, 10:29 F 2.6? x to' - I.4S x IT* - - ^verage (2.46 J.76) x n"' _£ -- i.i.% ;.ss)x IO - - 5 11 FFO-102-2 1981 March 6.22 x 10 Ro(a/d 3.27 x IS 9.42 X 1010 24, 21:47 B(a/s) 1.37 x lo" .. 7.OT x I'i" 2 1 - 25, 03:05 F (2.18 !.24)x IT (1.35 :.16) x IT - - 6 11 to 1981 March 1.06 x 10 R la/s) 9.78 x lO o S.61 x 10 2.Wx lo" 29, 21:56 B (a/s) 1.97 x in" 4.22 x 10 7.11, 10" 2 - 30, 04:12 F ('..%_• .24) x IT n.O4:.n)xio"' (3.56 i.17) x 10"' - - 5 U 12 z 12 FFO-103 1981 5.18 x 10 R0(a/s) 3.90 x \0 L59XI1 i.s; x io' 5.57 xlO11 1.84 x 10 11 1 06, 13:22 B (a/s) 1 .19x 10 2.15 x n" i.O ) v in" 5.92 x I013 4.S? x lO13 1 2 - 06, 22:44 F !3.29 :.22) x I )"' !'.i;.- .f)) x IO" ('1.41 : .61) x 11"' (3.S2 _' .2M x IT2 (0 Dat 1 for experiment FDO-681 taken fro.n Reference 3. The stcjdy-stdte fractional release behaviour of the iodines and noble gases for the three experiments have been analyzed in a fractional release (F) versus decay constant ( >.) (double logarithmic) plot, shown in Figures 4.1 a and b respectively. \ DECAY CC*iS*fiNT *> (a) (b) Figure Fractional Release Versus Decay Constant Plots for FDO-681, FFO-102-2 and FFO-103 ?al Iodines (b) Noble Gases In this figure, the average fractional release value (of the two data samples) was plotted for experiment FDO-681 since the drilled hole had not changed in size during irradiation; however, both data samples were individually plotted for experiment FFO-102-2 as sheath deterioration had progressed during these sampling periods. The fission products were divided into three groups for direct comparison between the experiments, and include: (i) Iodines: 1-131, 1-133 and 1-135, (ii) Kryptons: Kr-85m, Kr-87 and Kr-88, and (iii) Xenons with long-lived precursors: Xe-133, Xe-133m and Xe-135. The dependency of the fractional release on the decay constant for the three groups of radionuclides is shown in Figures 4.1 a and b, and is listed in Table 4.2 assuming a dependency of the form a X1' where a and b are constants. Table *.2 Fractional Release Dependency on the Decay Constant of the Form a A Experiment Data Iodines* Kryptons Xenons Sample a b a b a b FDO-681 Avg.of 9.31 xlO"11 -1.24 3.24 x 10~8 -1.09 8.17 x 10"8 -0.9S 1 and 2 FFO-102-2 1 3.99 xlO"10 -1.30 2.07 x 10"8 -1.16 4.01 x 10~6 -0.72 2 2.77 x 10"9 -1.21 4.23 xlO"8 -1.14 7.76 x 10"6 -0.72 FFO-103 I 4.61 x 10" 5 -0.64 3.10 x 10"5 -0.64 1.87 x 10'5 -0.65 * Both J-132 and 1-134 have been neglected in this analysis due to precursor diffusion effects (see Section 4.3.1). The slopes (b values) indicate a slower release mechanism than predicted for diffusion (see Section 4.3.1) with instantaneous escape from the fuel element, which would be represented by a slope of -0.5. Interpretation and comparison of these results with other experiments is presented in the next section. 4.2 Discussion of Noble Gas and Iodine Behaviour With reference to Table k.2 the radioiodines are delayed more than the noble gases, as generally indicated by the largei negative slopes of the iodines. This is due to the differing chemical natures of the two species. To understand this behaviour, a brief discussion on internal fuel chemistry for iodine is given in Section ^.2.1. A review of noble gas and iodine behaviour in operating UO_ fuel elements is provided in Section 4.2.2 (based on results of several CKNL sweep gas experiments). Finally in Section ^.2.3, the discussion is focused on the three defect experiments and on several other CRNL experiments with multi-drilled elements. The chemical nature of the fission product iodine has been investigated by (22) many experimenters. Peehs has suggested that fission product iodine is born in an elementary form, existing in the UO_-lattice as 1° and undergoing chemical reactions in the UO- pores or on free surfaces. The most convincing experimental evidence for Csl formation in the gap was reported by Lorenz et (23) al. in high temperature gap purge tests of highly-irradiated commercial LWR fuel. In these experiments at temperatures between i 100 and 1200 C most of the volatile cesium and iodine species, which were swept out of the fuel rod by a helium purge, deposited on a gold foil-lined tube at temperatures well above the sublimation temperature of L. These tests indicated that iodine was released as a metal iodide, probably as Csl. As discussed by Campbell et al., further evidence supporting Csl formation includes: CO similar iodine and cesium spiking behaviour during normal transient reactor operation (see Section 5), (ii) identification of Csl deposits on internal LWR cladding surfaces, and (iii) thermodynamic calculations indicating the relative stability of Csl to other iodide compounds. For example, in a thermodynamic and kinetic study, Torgerson et al. considered the following chemical forms of iodine for an iodine/cesium/steam system: Csl, (Csl)2, HI, I, HOI, \O and l^ The thermodynamic study (sec Figure 4.2) indicated that Csl is the most predominant species for both reducing and oxidizing conditions (particularly at the normal operating fuel temperatures in the gap - see Appendix F) while the kinetic study suggested a very rapid formation of this species under most conditions. (a) (b) Figure h.2 Iodine Species Distribution Diagrams Uake(taken frotrom Reference 21) (a) ReducinRdcigg conditionditi s ((hydrogeh n 2 mol) (b) Oxidizing conditions (oxygen 0.5 mol) The system contains steam (^ mol), iodine (10" mol) and cesium (Cs/I = 10) at a total pressure of 1.2 MPa. All species are gases except for Cs (s, 1) which refers to the solid or liquid state. Re-distribution studies of fuel artificially doped with cesium and iodine did not (26) support Csl formation under oxidizing conditions However, evidence for Csl is strong if circumstantial. ', j Thus available experimental and thermodynamic information indicates that fission product iodine behaves as a fission gas in the UC-lattice but undergoes chemical reactions, as prescribed by the surrounding fuel condition1:. Fission product iodine is probably found as an involatile iodide at free fuel surfaces and on the internal sheath surface during normal operation. The composition of this iodide is not positively known but indications are it is the water soluble salt Csl. 4.2.2 Sweep Gas Experiments In CRNL sweep gas tests under normal operation, no iodine was transported in the helium carrier gas and it was concluded that the iodine inventory was adsorbed on the fuel and/or sheath surfaces. (S) This result is consistent with the chemistry for Csl (see Section 4.2.1), as this compound would be involatile (see for example Figure 4.2) at the typical temperatures present in the fuel- to-sheath gap of an operating IIO^ fuel element (see Appendix F). An iodine release dependency of X~ " was deduced from the shutdown decay behaviour of the xenon daughter fission gases. This same X~ ' release (9) dependency was observed for the noble gases and is in agreement with Peehs results, suggesting that fission product iodine behaves like a fission gas in the UO~ (Section 4.2.1). Also, this release behaviour implies that the rate- controlling process for release of the rare gases and iodines in the UO~ is Booth diffusion (Section 4.3.1). The effect of steam and/or water in the gap on iodine transport was quantitatively analyzed when two sweep gas experiment:; defected allowing hot pressurized coolant to enter the sweep gas system. After defection iodine was observed at the detector. Transport of the iodine with liquid water in the gap was estimated to be 10 greater than with steam present (similar behaviour was observed in Section 5 for transient reactor operation). This result suggests that fission product iodine trapped on the UO_/sheath surface is water soluble, whereas it has a low volatility in steam. 4.2.3 Defect Experiments The fractionaJ release dependency on the decay constant A f A experiments FDO-681, FFO-102-2 and FFO-103 is compared in Table 4.3 with similar values from other defect tests involving multi-drilled elements. In this comparison, all three phases of experiment FDO-6&1 have been included as well as the three phases of experiment FDO-687. Each phase of the two experiments .ire briefly described in the table. For comparative purposes, fission products have been divided into the following three groups, accounting for the relative half- lives of the noble gas precursors: Group 1 -Radioiodines: [-131, 1-133, 1-134 and 1-135 Group II -Noble gases with short-lived precursors: Kr-85m, Kr-87, Kr-88 and Xe-138 Group III -Noble gases with long-lived precursors: Xe-133, Xe-133m and Xe-135 The slopes for phase 2 (element LFZ) of experiment FDO-681 were previously reported in the literature and are derived from an average of 9 sampling periods. Several important conclusions regarding fission product release mechanisms can be drawn from these data. The multi-slit experiment FFO-103 was designed to minimize holdup and trapping of fission products in the fuel-to- sheath gap and generally showed the smallest negative slopes. These slopes are approaching the slopes seen in the sweep gas experiments for a diffusion- controlled release in the WO-. Conversely, all other experiments yielded slopes Table *K3 Comparison of the Slope on a Fractional Release Versus Decay Constant Plot for Various Defect Experiments Experiment: FDO-681 * FDO-6S7 •" FFO-102-2 FFO-103 Defect Single Drilled Hole: Single Drilled Hole: Primary Porous End Cap Defect, 23 Longitudinal Slits Circumferen- Classification: - Phase 1 (Element RPL) - Phase 1 (Element RPR) and Secondary Through-*'all tially Located along Element - Phase 2 (Element LFZ) Longitudinal .Slit: Sheath Hydriding Length Two Drilled Holes: - Phase 2 (Element N5Z) - (Element A7E) - (Element A3N) - Phase 3 (Element RPP) Three Equidistant Holes: - Phase 3 (Element RPR) Remarks: Elements RPL and RPP were Element RPR was irradiated in- Sheath hydriding and detrior- Slits, particularly at the top of the previously irradiated intact to tact to a burnup of <*3 MWh/kg V ation progressed during element, enlarged during irradi- a burnup of 140 MWh/kg U. prior to phase I. For phase 3 irradiation. ation. No (.Tiassive) sheath Element LFZ was defected during this same element was drilled hydriding was observed. fabrication. No sheath degra- with two additional equidistant dation was observed following holes. Element NSZ was defected irradiation. during fabrication. No sheath degradation was observed following irradiation. Linear Power: 55 kw/m »8 kW/m 67 kW/m Fission Phase Phase Data Sample Data Sample Products 1 2 3 1 2 3 1 2 I Group I -1.83 -1.53 -0.90 -1.23 -1.29 -1.15 -1.30 -1.21 -0.64 (Iodines) Group 11 -0.96 -1.13 -0.87 -1.07 -0.95 -0.79 -1.16 -0.64 (Kryptons and Xe-138) Group III -0.77 -0.99 -0.59 -0.70 -0.7S -0.6S -0.72 -0.72 -0.65 (Xenons) (1) Reported in Reference 3. (2) Reported in Reference 11. much greater than -0.5 and these greater slopes are attributed to a holdup of fission products in the gap which is more predominant for singly-drilled elements. The iodines are delayed more than the noble gases, especially for elements containing smaller defecfs. As sheath degradation progressed in element A7E, the iodines reflected the greatest change in terms of decreased holdup. The slopes of the iodines and kryptons are similar for an element containing two closely-spaced holes (FDO-6S! Phase 3),however, this result was not evident for an element containing three widely-spaced holes (FDO-687 Phase 3). MacDonald suggested the similar iodine and krypton slopes may be due to wash-through of the coolant between the two closely-spaced holes. The differing behaviour of iodine compared to that of the noble gases in these defect experiments indicates iodine transport is strongly dependent on the environment in the gap. The dependence of iodine transport on the gap environment was also observed in defected sweep gas experiments (Section 4.2.2). In view of the discussion on the chemical nature of iodine, only those iodides deposited on the fuel and/or sheath surfaces at or near the defect are dissolved in the mixture of water and/or wet steam. For example, since Csl will not be present in the gas phase below ' 750 K (see Figure 4.2), transport will presumably occur for this species in defected fuel elements by dissolution in water and/or wet steam, dissociating into the non-volatile ions Cs and I" near the defect. Away from the defect, steam in the gap is superheated and dry and is not effective in iodine transport (as suggested by defected sweep gas experiments). This scenario of "localized iodine release" is supported by multi- drilled element results and is shown to occur in Section 4.5 with the calculation of diffusion lengths for 1-131 and Xe-133 (the diffusion length of 1-131 is considerably shorter than that for Xe-133). *>.3 Semi-Empirical Fission Product Release Model A steady-state fission product release model for defected fuel elements is developed in the following sections based on previous experimental observations. Evidence from the multi-slit and sweep gas experiments indicates that release from the fuel pellei is diffusion-controlled (for both the noble gases and iodines). This release represents a source in the gap. Subsequent fission product transport in the gap is modelled from a set of kinetic mass balance equations by: (i) defining a phenomenologica! g.ip escape rate coefficient, and (ii) identifying the transport process as diffusion. 4.3.1 Diffusion in the UO Fuel An idealized mathematical model was introduced by Booth to describe the diffusive release from the fuel of the stable and radioactive fission gases. The Booth model has proved to be an effective analytical tool in describing the release of the radioactive noble gases and iodines from operating fuel elements in recent sweep gas experiments at CRNL. ' These experiments at CRNL _y2 have shown that radioactive rare gas and iodine release rates obey a * dependence on the decay constant A. This functional dependency was originally predicted by Booth by applying classical diffusion theory to an equivalent UO_ grain sphere of radius a. An effective diffusivity D was introduced which incorporated the effects of radiation damage, trapping and resolution of the diffusing atoms. The original radioactive Booth model is derived below. The diffusion equation for a radioactive species, produced at a rate per chain yield Y), which has reached a steady-state concentration C is given by On solving this equation for the boundary conditions •;:'• (2a) C(a)=O (2b) the steady-state concentration profile is , ., j; (3) Using Fick's law to evaluate the flux of atoms passing the grain boundary surface r-n and defining the fractional release F as the release-to-birth rate ratio (R/B) where B " 4 ^" (5) the fractional release is given by SO (6) ' >. a' Generally for most nuclides of interest &>>1 and equation (6) reduces to (7) yielding the experimentally observed \~ 2 dependency. This derivation however neglects diffusion of the halogen and tellerium precursors in the UC>2 grain. When this diffusion is taken into account the fractional releases are enhanced more than that predicted by equation (7) as discussed below. Considerable theoretical efforts have been made to extend the simple model since its introduction in 1957. Recently, Kidson derived a general expression for the cumulative fractional release of the m™ member of a radioactive chain up to time t for k cycles of reactor operation. In this complete work, Kidson showed that earlier theoretical studies were simply special cases of his more general expression which included: (i) the time-dependent release of a single radioactive species during a (28) single cycle of operation described by Reck ; (ii) the cumulative release of a single stable isotope over several cycles of operation discussed by Noble and Rim et a!. and; (iii) the cumulative release of the mtn member of a radioactive chain during a single cycle of operation considered by Frir.kney and Speight.(31) In the latter analysis, only the first member of the radioactive chain was assumed to be produced by fission while' all remaining chain members were assumed to be produced only by radioactive decay. For the evaluation ot the diffusion coefficients of the halogens and rare gases, Turnbull et al. used the analysis of Friskney and Speight to resolve precursor effects. Kidson did not consider, however, the particular case of the cumulative release of a daughter species accounting for diffusion of the parent species during a single cycle of operation. This special case is derived in this thesis in Appendix C from Kidson's general solution. For instance, since early isotopic chain members exhibit relatively short half-lives, these members With reference to Appendix C, the two coupled, time-independent differential equations for the parent (p) and daughter (d) species are: [V:>(: -' <: 'I' =o P P P !' p (S) d il (1 (I p p il 40 The production term I' for the parent isotope includes the cumulative production irom earlier chain members. Here f; is a loss rate constant (s ) from radioactive decay and transmutation by neutron absorption (loss by neutron absorption is only important for Xe-135 as a consesquence of its high absorption cross section). The Laplacian operator reduces to a radial term for the idealized spherical grain geometry (see equation (1)). On solving these coupled equations for the boundary conditions given in equations (2a) and (2b) for both parent and daughter species and using Kidson's formalism (see Appendix C), the fractional release of the daughter species (accounting for diffusion of the parent in the equivalent grain sphere) i:; f>iven by (9) and H = The parameter Y is the cumulative fission yield of tl " parent isotope (accounting for production by decay of the earlier chain members), whereas Y , is the direct fission yield of the daughter isotope. Equation (9) is the simple idealized diffusion model introduced by Booth, multiplied by a correction factor H. (sotopic branching in each mass chain, particularly for the longer-lived isoineric precursors, can be included within the framework of equations (8) and (9). Using FISSPROD-3 and its ENDF/B-V decay data library and experimentally determined parent-to-daughter diffusion coefficient ratios, H correction factors have been evaluated for isotopes and isomers listed in Table 4.4. The diffusion coefficient ratios were assumed to be independent of temperature (ser Reference 32) with chosen values of DBr / D, Table kA Correction Factor (H) for Precursor Diffusion Isotope Kryptons Xenons Iodines 85m S7 88 133 133m 135 138 131 132 133 134 135 138 H Factor 1.87 1.74 1.11 1.21 1.41 3.01 1.00 1.02 11.70 1.05 2.07 1.00 1.02 Equation (9) may be applied to an entire fuel element, as discussed by Booth and Olander, by integratininte g the fractional release over the fuel element radius and length yielding where I) j is the volurnetrically-averaged empirical diffusion coefficient, including the unknown grain sphere radius also support this formalism for the iodine equations. For instance, these experiments indicate that iodine occurs in a non-volatile but water-soluble form (consistent with the chemical behaviour of Csl or a similar water-soluble species). It must be made clear that no experimental reaction rate constants are used in the model. Furthermore the model may still be used if at a later date more direct experimental evidence demonstrates the presence of an iodine species other than Csl. In fact both approaches above yield analogous mass balance equations for iodine. This result is to be expected as, for example, the Langtnuir adsorption isotherm is based on a kinetic equilibrium between the rates of adsorption and evaporation, analogous to that proposed for the iodine equations in this thesis i.e., it has be :n suggested by Glasstone ' that a single layer of solute molecules may form on the surface of a solid similar to that for chemisorption of a gas. However, for the xenon species, the two models differ significantly since the thesis model accounts for the additional source of xenon in the gap from decay of the iodines deposited on the surfaces and from decay of the iodines present in the gap (by comparison, in the Allison and Rae model, xenon is assumed to be produced by decay of iodine in the cool fuel surrounding the hot central core). Finally, the thesis mode) recognizes the source term in the gap as "Booth diffusional release" which yields the experimentally observed release rate dependencies on the decay constant for sweep gas experiments as well as for the multi-slit defect experiment (where gap holdup has been minimized). As discussed above and in the previous section, the source term in the gap foi both the radioactive rare gases and iodines is Booth diffusional release corrected for precursor diffusion (see equation (10)), and is given by It should be noted that IV in equation (11) is an empirical parameter applied to an entire fuel element and incorporates heterogeneous trapping effects which may impede atom migration through the UO-, pellet. As discussed by Turnbull et al., ' in the fuel mirrostructure only 3 fraction of the total grain boundary area is covered by edge porosity and, subsequently, only a fraction of these grain edge tunnels are instantaneously connected to the fuel surface. Hence, only a small fraction of the atoms released from the grain finds its way to the fuel surface. In summary, the following model is phenomenological and is based on experimentally observed fission product release characteristics, with the implicit assumption that both the rare gases and iodines diffuse through the UO., with individual diffusion coefficients as prescribed by equation (11). (i) Kryptons The condition of continuity for the concentr,. .ion of krypton atoms in the gap Nj, (a/cm') is given by the following source and loss terms, /production rate) (, !n«ntnH,,ntn i lo rdt e due l dNR I [, release ( ) tost rate due- to f u° dt I from the I JO if radlo;'Ctive decay release into the J. (irom tnein^ j ^ primary coolant j or mathematically, ..'.-£ = K,. ->.N -••- N (12b) u t 1 6 K s where U, (a/cirr- s) is the rate of escape of atoms to the gap from the fuel. The release rate of the nuclide through the defect into the coolant :N Ui/'.' M *s) is assu Mod to be a iirst order rate process i.e.. t'ie ra'.-.' •* directly proportional to the concentration in the gap: The proportionality constant v is defined as the gap escape rate coefficient. For steady-state conditions equation (12) gives ' 8 ~ * + v The release from the oxide is Booth diffusional release; therefore, using equations (11), (13) and (14), the observed fractional release into the coolant is (n) (ii) Iodines For the iodines there are two governing kinetic equations which account for iodine trapping onto the surfaces and transport in the gap. As previously discussed, experimental evidence suggests fission iodine diffuses through the UO_ grain as a fission gas but deposits on the cooler surfaces (in the fuel microstructure and on the sheath) probably as a solid metal iodide. Mass balance equations, describing the rate of change of the iodine concentration trapped on the UO-,/sheath surfaces Ns (a/cm ) and the concentration capable of transport in the gap Ng (a/cm ), are given by: for the free surfaces, production production rate by rate due to loss rate due loss rate due release from + deposition to dissolution + t0 radio. "dF (16a) the U(X, onto the into the gap active decay surfaces and in the gap, production loss rate due rate due to loss rate due loss rate due , to deposition tQ re ease dissolution to radio- + jnto the pd_ (17a) dt from the onto the sur- active decay surfaces faces mary coolant Alternatively, the above two equations may be written mathematically as, dN ,, 1 R + TIT = fs (sH.]Ng-k1Ns-ANs (l6b) V* " ^'k-,N« (18) the following equation is obtained d f 1 + k / k ) N l ------~t ~L-* = K^-tv + ACl+k^/k^)^ (19) In the above equation, the simple relation R, = (S/V) R, is used. Therefore, at steady-state, equation (19) becomes N = _!!.[£ (20) ' & v +• A (l + k / k ) - 1 1 Similarly, if the release from the oxide is Booth diffusional release then the observed fractional release into the coolant is where k is defined as, * = r+I 71"" (22) - ] 1 The form of the fractional release equation for iodine is identical to that for krypton. The iodine gap escape rate coefficient k is equal to the noble gas gap escape rate coefficient v reduced by the factor (1 + k /k ) . Therefore, for a large defect, there should be sufficient water or wet steam in the gap such that k. >> k . (more iodine will be dissolved into the gap than that redeposited onto surfaces) and k should approach v. (iii) Xenons For the mass balance equation of xenon, an additional source term must be included to account for decay of the iodine precursor in the gap and on the free surfaces: production rate production rate production rate due to release due to radio- due to radio- dNg from the UO2 + active decay of + active decay of dt iodine in the gap iodine on the surfaces (23a) loss rate due to radio- loss rate due to release active decay and neutron + into the primary coolant transmutation Hence, the above equation is described by dN g (23b) •TT The "*" refers to the iodine precursor and f is the isotopic branching fraction for the particular decay scheme (for Xe-133 and Xe-135, f can be taken as unity to include contributions from decay of the respective short-lived isomers). At steady-state, and using equations (18), (20) and (23) f.\*(l+k /k ) v + A * (1 + k _ / k ) . I A - Similarly, with the aid of equations (11), (13) and (22) the observed steady- state xenon fractional release into the pressurized coolant is given by, *?1 (25) Loss by neutron absorption is only significant for Xe-135 and therefore £ can be replaced by > for all otlwr xenon isotopes. By definition, the ratio •'.« of the iodine to xenon birth rate is equivalent to the ratio of the respective cumulative yields. Equation (2.5) is identical in form to that for the kryptons and iodines however it contains additional source terms (for involtatile precursor decay on free surfaces and precursor decay in the gap). Consider the two limiting cases of (i) a large defect and (ii) a small defect for the above fractional release equations. For a large defect there is little holdup in the gap ( instantaneous release into the coolant) implying that y (as well as k) are much greater than >. Hence, the gap presence factors (^+77) at)d 2 (J-JTJ:) tend to unity yielding a fractional release dependency of A . This dependence is consistent with CRNL sweep gas results where there is no holdup in the gap. Now, for the second limiting case, v (and especially k) are much less -3/2 than X for a small defect yielding a A dependence. This functional dependence was observed for the radioactive iodines in CRNL drilled defect experiments. 4.3.3 Diffusion in the Fuel-to-Sheath Gap The effect of different types of defects on the release to the coolant was originally described by Helstrom in 1956 for a diffusion process. In a more (39) accessible publication Lustman summarized the theoretical results of Helstrom for the case of a long slit and a small circular hole in a plane and cylindrical surface. A release expression for each case was obtained by the solution of a one-dimensional diffusion equation (for a particular defect geometry) .vith radioactive decay and with a constant source due to release from the fuel. A more recent and elaborate treatment by Kalfsbeek for defective Boiling Water Reactor (BWR) fuel pins considered transport in the gap by competing diffusion and convection processes. In this study Kalfsbeek postulated a "flowing and fluctuating" steam environment in the gap, through which fission products diffused in a one-dimensional manner towards a cylindrical hole in the sheath. The defining transport equation was of the same form as that reported by Helstrom except that an additional term was included (the gr.idk.-nt of the product of the atomic density and convection velocity) to account for a fluctuating bulk steam flow in the gap. The source term from the fuel assumed an empirical release fraction proportional to A. ' " and was based >n the experimental results of Appelhans and McDonald.(to) Transport in the gap for CANOU fuel can also be modelled b- assuming a diffusion phenomenon. f\y comparison, in the thesis model, a two-dimensional diffusion model (describing axial and azimuthal diffusion) is proposed for the case of a rectangular defect in a cylindrical fuel element. The competing convection process is neglected for CANHU fuel since, in the CANDU design, the thin sheath (which is covered with a graphite interlayer) creeps down onto the fuel and net bulk mass move nent is limited. The diffusion ^quation for the iodine species also accounts for chemical trapping effects as previously derived in the phenornenological transport model. In comparison the models of Helstrom and Kalfsbeek only treat the gaseous fission products, particularly, the inert noble gases. The diffusion equation for the venon species includes the additional source of xenon from decay of the iodines deposited on the surfaces and from decay of the iodines present in the gap. Once again a diffusional release from the fuel is assumed for both the noble gas and iodine species, corresponding to a release fraction from the fuel proportional to K ' . The diffusion model is mathematically derived below. The diffusion process is governed by a two-dimensional diffusion equation for an irreversible reaction (radioactive decay) and constant source (Booth diffusional release) (see Appendix 0) given by, J5v W -AN +K =o (26) The diffusion equation is defined for a cylindrical fuel element geometry and reduces to a two-dimensional problem since the gap thickness is much less than the di/fusion length L where, L=»£7A (27) and •!) is the gap diffusion coefficient. At the surface of the defect, fission products are swept away by the coolant. Therefore, the concentration Vp is zero at the defect surface and nearly zero everywhere beneath the opening. Far dway from the defect the concentration is finite and equal to the equilibrium value R.- ,M. For these boundary conditions, assuming the width w and length ?• of the defect are much less than L and neglecting fuel element end effects, the solution of the diffusion equation is 1'1" where y = T~/r^r?W 's" ~ 7—--1--:-./- and ° >s tne pellet radius. The flux of atoms ./ leaving the defect is evaluated from Pick's diffusion law, ;; -., _^VN t I at the sides •'• of the ili'frct Integration of this flux over the normal surface area of each side of the defect yields the release rate R. (atoms/s) into the coolant where R is the IVioth diffusional release rate (atoms/s) in equation (11), ,.!0 = (•J'+S.'-)* js the effective defect diameter and 1. . is the fuel stack length. Hence, the fractional release is given by Equation (26) is only valid for krypton and hence (31) does not apply to iodine or xenon release. The diffusion equation must account for iodine trapping on free surfaces as this influences both the iodine and xenon transport equations (see Section 4.3.2). Fractional releases for these species are derived in an analogous manner below. (i) Kryptons As mentioned above, the fractional release equation for krypton can be immediately written as, where the diffusion coefficients for the gap J&^ (cm2/s) and fuel l\(s ) are representative of all noble gases. (ii) Iodines Iodine trapping onto the surfaces and transport in the gap can be regarded as a problem involving simultaneous diffusion and chemical reaction and is described by the following differential equations (see for example Reference 41): + 1 in "T ' j. ' .u -1 K 'V' -I s (33) S ( v •v . Y\~ "" NV'S1 -I 8 is s These equations are identical to equations (16) and (17) except that a diffusion term has replaced a phenomenological loss term. Proceeding in an analogous fashion (assuming steady-state and a fast equilibrium between the forward and back reactions) the above equations reduce to the simple diffusion equation ? l •V Y*(i+k_i/k])Y V,> 05) This equation is identical in form to equation (26) and it is possible to write rW (36) where ,1); is defined as an effective iodine diffusivity i^., The form of the iodine fractional release is again identical to that for krypton. If the diffusivity of iodine dissolved in the wet steam (,!'* ) is approximately equal to that for the noble gases (,r> )then the effective %,\[> iodine diffusivity (;O is equal to the noble gas diffusivity reduced by a factor (1 + k_j/ki) (this was the equivalent definition for k in the previous transport model in Section 4.3.2). (iii) Xenons Similarly, the kinetic equation for xenon accounting for production in the gap from precursor iodine decay is given by JL -. }) v'.\ -t\\ +n> (N' + I^IN'I+K.. (3S) •) t \ >> a - i; \ s i R Neglecting precursor diffusion in the gap and using equations (IS), (31)) and (38), the steady-state diffusion equation becomes Thus the fractionat release is given by, (VO) [n equati.)ns (25) and (40) the source terms in the square brackets are identical except for a factor {—-)• Results of Section b.h indicate that this factor is approximately unity for moderate and smaller-sized defects ( k< Interestingly, the fractional release of each species is proportional to the defect size and inversely proportional to the fuel element length. Further, release is also proportional to the diffusion length L i.e., for the shorter-lived isotopes such as the delayed neutron emitters emission primarily occurs in the vicinity of the defect whereas, for those isotopes with longer half-lives, emission occurs from the bulk of the fuel element. (*f2) Experimenters have found that fractional release decreases with the length of the element. ' Lipsett dud MacDonald (4-3) observed a functional dependence on length for the shorter-lived radioactive noble gases; however, no such dependence was seen for the longer- lived isotope Xe-133. This length effect is a direct consequence of the ratio of the isotopic diffusion length L to the fuel ele/nent length L (see Section 't.')). Finally, the fractional releases tor krypton and iodine exhibit a X dependence -''2 - 1 on the decay constant (for xenon the dependence is between A and \ depending on the precursor decay term). This ?•" functional dependence '.vas observed in experiments FDO-681, FDO-687 and FFO-102-2 for both the iodines (for the larger defects where less trapping occurs) and the kryptons and Xe-13S (Group II isotopes) (see Table In experiment FFO-103, for the purpose of modelling, the 23 short slits may be replaced by a single siit of equivalent area extending over the entire length of the element since the circumference of the element b is much less than the diffusion length L (see .Section *iA). The diffusion equation (26) for this geometrical arrangement has been solved by Helstro n who obtained an expression for the release rate Ro (per unit length of slit) = 2 R, Lh tanh(b/2L). Here R, is a constant source (per unit volume) from the fuel. If b <•- 2L then the release rate Ro (atom/s) becomes R. bhLs = R where R is described by the diffusional release equation (11). Hence, the fractional release (for most species) is given by equation (10) and does not depend on the diffusion length i.e., diffusion in the gap is no longer a rate-determining process for this case. Moreover, the fractional release exhibits a X ~2 dependence on the decay constant which has been experimentally verified for the multi-slit element (see Table ^.3). (In Helstrom's published work an extra factor of 2 is incorrectly given in the above equation for the limiting case b << 2L.) *.* Evaluation of Model Parameters For each experiment, the fractional release parameters are evaluated using the weighted non-linear least squares fitting routine MLSQQ (see Appendix A.5). Weights are defined as the inverse of the variance of the measured fractional release values (the inverse of the square of the errors reported in Table 4.1). The phenornenological gap escape rate coefficient -.> was assumed to be the same for krypton and xenon s:nce both species are chemically inert. Similarly, the empirical diffusion coefficient D., was also considered identical for both species. The contrasting chemical nature of iodine necessitated a unique set of iodine parameters: the rate constant k and empirical diffusion coefficient D. were evaluated from both iodine and xenon release data. All parameters above were evaluated for the three defect experiments (covering a wide range of defeat si/.es) and are shown in Table 4.5. Because of large errors in the iodine release data for experiment FDO-681 (see Table 4.1), iodine parameters were only estimated for this experiment and were not calculated witli the least-squares program because of convergence problems. The diffusion transport model is only applicable for elements containing moderate and smaller si/.ed defects, where diffusion is significant. Of the three defected elements, only elements LFZ and A7E exhibited release dependencies of X (see Table 4.2). Further, for element A3N, the defect size (23 slits) was greater than the isotopic diffusion length, in violation of the previous assumption. Gap diffusivities are therefore only calculated for experiments FDO-6S1 and FFO-102-2 (sample 2). In the calculation, empirical UO2 diffusivities listed in Table 4.5 and fuel stacks lengths and pellet radii in Table 3.1 are entered into the fitting routine for each element. The main defect of element A7E did not appreciably deteriorate following the reactor trip (as indicated by steady-state fission product release levels). Figure 3.3 B-a thus provided a reasonable assessment of the defect size for the second sampling Table 4.5 Evaluation of Empirical Parameters for FDO-681, FFO-LQ2-2 and FFQ-IQ3 Parameter Experiment Gap Escape Rate Coefficient Empirical Diffusion Coefficient Noble Gases Iodines Noble Gases Iodines v (s~l) k (s"1) FDO-681 (7.14 +1.36)x 10-6 (2.55 + 1.41) x 10"10 (Drilled Element LFZ) -5 FFO-102-2 (2.02 +.25) x 10 (7.S5 + 1.22) x 10-7 (1.56 +.61) x 10"10 (3.10+.83) x 10'10 -5 -10 (Hydrided Element A7E) (2.28 +.40) x 10 (1.25 +.14) x (3.06 + 1.26)x lO'10 (9.27 + 1.S9) x 10 FFO-103 (2.38 +.38) x 10"5 (3.44 +.37) x 10'5 (3.58 + .90) x 10~9 (7.30 + .92 ) x 10""9 (.Multi-Slit Element A3N) These parameters were estimated as k = 5.07 x 10~ s' and D'j - 2.68 x 10" s~ for use in the xenon equation. period (ilc - 1A cm). For element LFZ, the defect did not change during the irradiation and therefore the equivalent defect diameter Je was equal to the original drilled-hole diameter (0.12 cm). The rare gas diffusion coefficients (cP> N) and the effective iodine diffusion coefficient ( Table 4.6 Experimental Gap Diffusivittes for FDO-681 and FFO-102-2 Empirical Gap Diffusion Coefficients Noble Gases Iodines Experiment <&"., (cnr>/s) o& (cm2/s} N 1 FDO-631 (-V.88 + .30) x 10"2 (Drilled Element LFZ) FFO-102-2 (Sample 2) (2.CS *.!'•») x 10"3 (3.39 + .22) x 10"5 (Hydrided Element A7E) A comparison of the calculated fractional release values with the experimentally measured values (Table 4A) can be made by substituting parametric values in Tables '4.5 and These results are shown in Table '4.1. The agreement between theory and experiment is very good for most nuclides, suggesting that the phenomenoiogical transport mode! is applicable to a wide range of defect sizes and characteristics. On the other hand, the diffusion transport model is only applicable Eor moderate and smaller-sized defects where transport is diffusion-controlled (i.e., indicative of a release dependence of X ). For small defects ( ^ 2 mm), diffusion is only important for the noble gases. The predominant rate process for iodine is the dissolution of trapped iodine on free surfaces (indicative of a release dependencdependen e of A ' ) and therefore, for this species, the diffusion model is no longer valid. Table 4.7 Comparison of Measured and Calculated Fractional Releases A. Rienomenological Transport Model FDO-681 FFO-102-2 FFO-103 Data iample 1 Data Sample 2 Nuclide Measured Calculated Measured Calculated Measured Calculated Measured Calculated Kr - 85rn .0020 .0019 .0029 .003* .00*7 .0052 .021 .018 Kr - 87 .000*9 .000^0 .00063 .00062 .0010 .0010 .0093 .003* Kr - 88 .0011 .0006 .0012 .0012 .0018 .0018 .01* .006 Xe- 133 .035 .0*1 .063 .06* .13 .OS .12 .20 Xe - 133m .021 .025 -. -- .- -- Xe- 135 .0008 .0013 .0027 .002S .0053 -OCS .oos .013 Xe - 13S .0000*S .000015 ------1 - 131 .. .02* .02* .050 .052 .33 .26 I - 132 __ -_ .0020 .0017 .068 .096 I - 133 __ .0013 .001* .001* .003S .075 .070 I - 13V __ __ -- .009* .00*S I - 135 — ------.038 .026 B. Diffusion Transport Model FDO-681 FFO-102-2 Data Sample 2 Nuclide Measured Calculated Measured Calculated Kr -85m .0020 .001) .00U7 .00*3 Kr - 87 .000*9 .000*0 .0010 .0011 Kr - 88 .0011 .0006 .'MIS .0016 Xe- 133 .035 .030 .13 .1* Xe - 133m .021 .OR -- -- Xe - 135 .0008 .001'* .0053 .0053 Xe - 138 .0000*8 .00004 3 -- -- 1-131 .. .050 .020 1-132 _- .0020 r> r, •) -» 1-133 __ .0034 .0022 4.5 Discussion of Empirical Results With reference to Table 4.5, the empirical diffusion coefficients generally increased with the defect size (the only exception was for FDO-6S1, although a large error was associated with this coefficient). This result may be attributed to increased oxidation of \)Oj fuel by steam (element A3N had an O/U ratio of 2.28 compared with a smaller average ratio of 2.14 for element A7E). Previous experiments ' have shown that gas mobility is substantially increased in hyper-stoichiometric UO? (see Figure 4.3) and defected fuel pins in water reactors have also shown an enhanced release. D The latter result is also attributed to indirect temperature effects of oxidation i.e., oxidation causes a reduction in the UO_ thermal conductivity resulting in an average fuel element temperature increase and hence an increase in the average empirical diffusivity. For the defect experiments, this secondary effect was probably not as significant — T(°C) 2000 1200 800 600 2000 1200 800 600 4 6 8 10 12 4 6 8 10 12 104/T ( K-1) — Figure 4.3 Rare Gas Diffusion Coefficient as a Function of Temperature and Stoichiometry (a) Miekeley and Felix (Reference 44) (b) Lindner and Matzke (Reference 45) "l't as that for direct enhanced mobility since element A7E had operated at a higher linear power (67 kW/m) than element A3N (48 kW/rn). According to a review by (47) Lawrence, the mechanisms of rare gas diffusion are not well understood. It is known, however, that rare gas diffusion is highly dependent on stoichiometry; an O/U ratio of 2.12 yields an enhanced rare gas diffusion coefficient approximately 40 times larger than that for stoichiometric UO_. The diffusivity of A3N was enhanced by a factor of MO from that for A7E (Sample 2), in reasonable agreement with Figure 4,3 b. Further, the noble gas empirical diffusion coefficients in Table 4.5 were within an order of magnitude of those values reported by Schuster for low-power PWR defective luel rods (see Figure 4.4). For experiments FFO-102-2 and FFO-103, empirical diffusion coefficient ratios ",/iL were approximately 2-3; a similar result was reported by Turnbull for diffusion ratios |) /[) for stoichiometric single and polycrystalline I \< uo . 2 -9 Defective Rods 10 a * Kr.85m o "• Xe-135 Q6PWR J2 -10 a -~ 10 • A BWR -11 -Intact Rods 10 -I • o» Stable Gases o PWR • BWR -12 10 o* -13 10 H -14 10 12 14 16 18 20 22 24 26 Linear Heat Rating (kW/m) —•- Figure UA Correlation of Empirical Diffusion Coefficients Versus Linear Heat Rating for Intact and Defective German BWR and PWR Fuel Rods (Reference 46} In experiment FFO-102-2, the empirical diffusion constant for both species increased with irradiation time (with each successive sample period). This effect may be principally attributed to venting of previously closed tunnel networks to the pellet surface through stress-induced cracking of the UCX (following successive reactor transients). During steady power these cracks may heal; however, if this healing process is relatively slow, one would expect greater release from the fuel microstructure at each successive transient. Since steady- state releases were relatively constant, any reduction of fission product release from crack healing was presumably offset by continued grain boundary interlinkage trom equilibrium grain boundary bubble growth and subsequent tunnel formation, and continued fuel oxidation. Both noble gas and iodine escape rate coefficients increased with the defect size. The iodine rate constant k was more sensitive to changes in defect size than the noble gas rate constant v. For smaller defects, v was about 20 times larger than k reflecting greater iodine holdup and trapping in the fuel-to- sheath gap. However for the multi-slit element, v and k were of the same order indicating that more iodine was dissolved into the gap than redeposited onto surfaces (i.e., !<[ r>> k_j - see Section 4.3.2 (ii)). This result was a direct consequence of the greater qmntity of water and/or '.vet .steam in the gap. Further, for the hydrided element A7E, v (and especially k) increased in the second sample period indicating an increased defect size. The increased defect size presumably resulted from the breakage of brittle areas of the sheath from stresses imposed on it by thermal expansion and contraction of the underlying fuel (during the previous reactor trip). Empirical rare gas diffusion constants for the gap (see Table 4.6) can be compared to thov. predicted by kinetic theory (for particular gap temperatures and pressures) - see Appendix E. Using Chapman-Enskog kinetic theory, the diffusion coefficient for a binary gaseous mixture at low density is I :• 1 .' where for the case of diffusion in the gap, ^\2 ~ bLnarY diffusion coefficient for a non-polar (noble gas) and polar (hLO) gas pair (cmVs) I = gap temperature («) Mj , M, = molecular weights of noble gas (Kr, Xe) and H?O molecules P = gap pressure (aim) cr ^ -, = collision diameter f A") ^! = collision integral (dirnensionless function of temperature and the intermodular potential field). In this calculation a nominal gap temperature of 'WOO K has been assumed for experiments FDO-6.S1 and FFO-102-2 (see Appendix F). At high pressure lr is no longer inversely proportional to pressure. As suggested by Bird however, the high pressure diffusion coefficient can be estimated from the low density formula (equation (•'+1)) and corrected to high pressure by a correction factor derived from self-diffusion studies (see Appendix E). The gap pressures were assumed to equal experimental coolant pressures for equilibrium conditions. The theoretical noble gas diffusivities (derived in Appendix E) are compared with the empirical values (Table 4.6) for experiments FDO-681 and FFO-102-2 in the table below. Table ^.8 Comparison of Theoretical and Experimental Nobie Gas Diffusivities for FDO-681 and FFO-102-2 Experiment Noble Gas Gap Diffusion Coefficient h ( c m 2 / s) N Kinetic Theory Empirical Value FDO-681 9.08 x 10"3 4.S8 x 10"2 (Drilled Element LFZ) FFO-102-2 (Sample 2) 6.26 x 10"3 2.68 x 10"3 (Hydrided Element A7E) The gap diffusivity for the noble gases is predicted within a factor -, 5 indicating good agreement between theory and experiment. As expected, noble gas diffusivity for FFO-102-2 is much greater than effective iodine diffusivity (from Table 4.6 fV,/^! - 79) implying a slower diffusion process for iodine and hence a smaller diffusion length for a given decay constant. Therefore, iodine release is very "localised" compared to noble gas release. For example, the longer-lived nuclides 1-131 and Xe-133 have experimental diffusion lengths of 6 and 42 cm respectively (in contrast: with xenon, only those iodine atoms released from the fuel within a short distance from the defect will eventually reach the coolant before decay). Furthermore, Xe-133 has a diffusion length much longer than the length of element L\'-'Z (!9 cm); in comparison, the kryptons (and Xe- 138) have diffusion lengths approximately equal to or shorter than the element length. This situation would account for the apparent inconsistent release dependence on length for the longer and shorter-lived isotopes reported by Lipsettand MacDonald (see Section 4.3.3). If one assumes similar noble gas and iodine diffusivities (..'>• = 0.013, where Keq is the equilibrium reaction constant. This ratio can also be estimated from the ratio of the phenomenoiogical rate constants v and k yielding a value of 0.059 (larger by a factor 4.6 but in reasonable agreement). In comparison, the rate constant ratio (ki/k_j) is much greater than unity for the multi-slit element where there is a continuing supply of "wet steam" in the gap. The latter result can be predicted from thermodynamics (see Appendix G). For example, for the multi-slit element, consider that the system can be described by an ideal equilibrium reaction for the dissolution of solid Csl (melting point of 621 C) in the gap with "wet steam" or effectively water: Csl(s) ;• Cs (aq) + I (a",) Fryin tne stancLi/o Gibbs free energies of formation for each species at a nominal inside sheath temperature of 623 K (3.50 /, the Gibbs energy of reaction .\G|^ -- -16.7 kJ/inoIe (see Appendix G). (Gibbs energy values for the ionic species are extrapolated using a semi-empirical Criss-Cobble treatment employing a linear entropy correlation. Entropy predictions a: •_• in agreement with limited experimental data at 200 "C; however, the valid.cy of extrapolation to higher temperatures is uncertain. The Gibbs energy value for Csl is evaluated using a fitted energy function described in Reference 52. Vhermodynamic values used in these calculations at 298 K. generally agree within V per cent of other published values also at 29S K.) Since the equilibrium constant Keq is related to ,'G^ by AG^ - -RT In Keq, the ratio of the rate constants k^/k_| = Keq - 2 5. This ratio is in agreement with the above empirical result. Furthermore, around a Mtialler-sized defect steam in the gap is mucn drier as a consequence of a smaller area of transition from pressurized water to steam (and therefore less i-flcctive in Csl dissolution) and the above reaction will shift to the left os indicated b;, the experimental ratio for the hydrided element. The experimental ratio of k\fk_[ for the hydrided element results in an estimate of the iodine loading on the free surfaces which is greater than 100 monolayers. The experimentally measured activity of iodine in the loop coolant also indicates the presence of a large surface loading. The presence of a thick deposit supports the proposed kinetic model but is at variance with the adsorption model of beslu (even though both models are mathematically equivalent - see Section 4.3.2) since chemical and physical adsorption processes generally pertain to surface thicknesses of a few monolayers. In conclusion, parameters from ooth transport models are identified with real physical constants and thereby provide information on rate determining processes operative in delected fuel elements. The diffusion transport model is fl'l only applicable for those species which exhibit a \~ dependence (where diffusion is the dominant transport process). However, the phenomenological transp >rt model can be applied to a wide range of defect sizes and characteristics. it.6 Comparison ot Model with Previous Models A comparison of the phenoinenologicai transport and diffusion models {see Table 4.7) with the previous defect models proposed by Allison and Rae and WacDonald and Lipsett (as reported in Reference 3) is shown below. Table 4.9 displays the measured and calculated fractional release values (F) of the noble gases for the drilled element LFZ. Table 4.9 Comparison of Calculated Fractional Releases (F) for Various Defect Models Thesis Model Calculated (F) from Model Nuclide Measured (F) Transport Diffusion Kr - 8.5m .0020 .0019 .0015 Kr - 87 .00049 .00030 .00040 Kr - 88 .0011 .0006 .0006 Xe- 133 .035 .041 .030 Xe- 133m .021 .025 .014 Xe- 135 .0008 .0013 .0014 Xe- 138 .000048 .000015 .000043 B. CRNL Defect Models Calculated (F) from Model Nuclide Measured (F)* Allison and Rae MacDonaJd and Lipsett Kr - 85m .0021 .0016 .0005 Kr - 87 .00053 .0007! .0002 Kr - 88 .0009 .0012 .0004 Xe- 133 .030 .005 .014 Xe- 133m .037 .004 Xe- 135 .0017 .0010 .0011 Xe- 138 .00007 .00020 .000009 Average of 9 sampling periods.(3) The predictive ability of the transport and diffusion models is comparable to that of the Allison and Rae model; for most isotopes the fractional releases are calculated within a factor of 2 (although the calculation is poor for Xe - 133 in The Allison and Rae model). In the MacDonald and Lipsett model agreement between theory and experiment is only fair (the calculated values are systematically law by a factor of -3 from the measured values for the noble -ases). As evident above and with reference to Table 4.3, the Allison and Pae model is successful in describing t'ie fractional release behaviour for elements with small drilled holes. However, for the iodine species the model t tils to describe the release bohaviour for elements * with larger-si/.ed defects (as typically found in the power reactor). For example, a fr^.tional release -3/2 dependence of J is theoretically predicted for iodine but this dependence is only observed in defect experiments for small drilled holes (see Table 4.3). On the other hand, the transport riodel convincingly predicts all observed release -3/2 dependencies for both the noble gas and iodine species, from a \ dependence (where significant chemical holdup occurs for the iodine species in the gap) to a \ 2 dependence (where there is no holdup for any species in the gap). The diffusion model predicts the experimentally observed .\ dependence for both species (for a dominant dif fusional process in the gap). A more complicated fractional release expression was derived by Helstrom for the release of fission products through a small hole in the sheath by a diffusion process; this expression did not agree with the experimentally observed \ dependence. The success of the transport and diffusion models, as indicated by the excellent agreement between the calculated and measured fractional release values in Table k.7, is attributed to the fact that these models reflect a better understanding oC the physical processes occurring in the fuel element. As (•>?> ed by experiment, the node's assume that the noble gas and iodine species diffuse in the same mariner in the UO~ but have J significantly different behaviour in the gap (since iodine transport is strongly dependent on the chemistry there). In contrast, the Allison and Rae model assumes that the iodines behave quite differently from the noble gases in the fuel in the intermediate region surrounding the hot central core (see Section 2.1). This assumption is in disagreement with present experimental evidence and in fact the authors themselves suggest there are difficulties in relating the 'node! to the actual physical processes occurring in the fuel. Also, in the diffusion model proposed by Helstrom, the constant source term in the gap is not identified with any physical release process for the fuel (such as Booth-type diffusion in the present model). In summary, both the transport and diffusion models developed in this thesis reproduce the measured fractional release data exceptionally well for a wide range of defect states. The present models have the distinct advantage of being simpler y>t more lund.jmoital compared with the earlier models. Because the; present models ire base;;! in physical principles, the empirical fitting parameters can be identified with appropriate physical quantities as exemplified by the characteristic "gap diffusion coefficient" i.e., for the first time the noble gas diffusivity in the gap is derived from experiment and compared to kinetic theory for defected fuel. A characteristic gap diffusivity for iodine is also evaluated from experiment. Evaluation of the "gap escape rate coefficients1' for tht noble gases and iodines leads to a better understanding of the holdup process in the gap. Knowledge of the holdup process in the gap is applied in Section 6 with the result that more appropriate isotopic release rate ratios are suggested to better characterize fuel failures in commercial power reactors. f,7 5. TRANSIENT FISSION PRODUCT RELEASE 5,1 Results During these experiments, several types of reactor power transients occurred. As shown in a typical irradiation history plot for experiment FFO-102- 2 (Figure 3.2), three significant transients are present: (i) A reactor trip when the reactor power was reduced from full povver (fp) to zero power very quickly and remained shutdown for Jess than a half hour. The subsequent reactor startup was quite rapid, (ii) A reduction in power when the reactor power was lowered to 2C->% fp (6 M\V) for about 15 in before being rapidly returned to full power, (iii) A scheduled reactor shutdown at the end el the irradiation when the reactor power was reduced to I 5% fp over approximately two minutes and then tripped to zero power. The loop coolant temperature and pressure were reduced within a few hours after shutdown. To investigate fission product transient release behaviour, concentrations oi several isotopes were plotted for the FFO-102-2 reactor trip arid scheduled shutdown (insufficient data were available for the power reduction). Coolant temperatures and pressures were also plotted on the same time base Eor the reactor shutdown. These plots were typical of FDO-681 transient behaviour. No transient analysis was carried out for experiment FFO-103 as no reactor trips or significant power reductions occurred. Further, immediately after the FFO-103 reactor shutdown, the ion-exchange purification loop was valved in (as the X-2 I- 131 activity limit had been reached) and therefore no radioiodine data was available. Figures 5.1 a and b show several iodine and noble gas activity concentrations for the reactor trip on March 25. The upper figure displays the transient behaviour of the longer-lived iodines (1-131 and 133), xenons (Xe-133 Hnd~L35) and krypton (Kr-85m). The lower figure shows the transient behaviour for the shorter-lived iodine (I-13't) and kryptons (Kr-S7 and-88). Also plotted on this latter figure is the delayed neutron signal (BF3 detector). Following the vrip, iodine activity concentrations increased whereas noble gas activity concentrations generally remained constant or decreased slightly (except for Kr- 37). On the subsequent reactor startup all isotope concentrations increased dramatically; isotope concentration increases were strongly dependent on the decay constant with the greatest increases occurring for the shorter-lived isotopes. As observed in experiment FOO-681 (see Reference 3), most of the peak iodine concentrations occurred when the reactor was still at low power power ( 'v 3.VUV) while the krypton and xenon concentrations appeared to peak several minutes later when the reactor power was greater than 15 \1W. The delayed neutron peak occurred when the reactor was still at low power, at roughly the same time as the iodine peak, in agreement with the observation of the French/54' Immediately after the scheduled reactor shutdown (see Figure 5.2) alJ isotope concentrations increased, with the iodines exhibiting the greatest change from their previous steady-state values (increasing by a factor of 9.1 for 1-134 compared with factors of 2.3 and \A for Kr-85m and Xe-135 respectively). Generally, transient releases were again dependent on individual isotope half- lives with the shortest-lived isotopes of each species exhibiting the greatest release. Spiking behaviour of Cs-138 (32.2 m half-life) was similar to that for the shortest-lived iodine, I-13 1133 ••= Xe I 35 Kr85m 1131 MW 15 1300 1400 1500 1600 1700 1800 1900h I 98 I MARCH 25 TIME (h) ,14c- 1300 1400 1500 1600 1700 1800 1900 1931 MARCH 25 TIME (h) Figure 5.1 Fission Product Activity Concentrations During a Reactor Trip for FFO-102-2 (a) Longer-Lived Iodine, Xenon and Krypton Concentrations (b) Shorter-Lived Iodine and Krypton Concentrations and Delayed Neutron (D.N.) Signal REACTOR SHUTDOWN (1400 h) STEADY-STATE REACTOR OPERATION 123 MW) MPa 1300" 1400 1500 1600 I 98 I APRIL 05 TIME (h) Figure 5.2 Iodine, Xenon, Krypton and Cesium Concentrations During a Scheduled Reactor Shutdown for FFO-102-2 5.2 Discussion The transient iodine behaviour described in the previous section was similar to that reported by other investigators. ' The iodines appear to be trapped on the UO_ or sheath surfaces, probably as a water-soluble deposit - poauibly Csl (see Section ^.2.1). Since the temperature in the gap of element A7E ( ^460 C from Appendix F) was above the saturation temperature ( '\.314 °C) during full power operation, only steam couid have existed in the gap especially away from the defect, and transport of iodine would have been exceedingly slow. During a reactor shutdown, the gap temperature is reduced so water can exist in the gap as 71 a liquid. The presence of a liquid water phase enables iodine, previously trapped on internal Moment surfaces at and below the defect location, to be dissolved and transported along the gap, through the defect and into the Joop coolant. This mechanism would account for increased iodine activity concentration immediately following a reactor shutdown. During a subsequent startup, iodine- rich water would be expelled from the defected element at low power resulting in another, and larger, "iodine :;pi!.e". In the FFO-102-2 test transient Cs-13S behaviour was similar to th.it of 1-134, at least showing a close association between the two elements, if not evidence for the formation of Csl in the gap. The similar delayed neutron behaviour was attributed to dissolution of the delayed neutron precursor 1-137 during shutdown, and its rapid formation (2-V.-V s half-life) and expulsion following startup. The noble g.isos exhibit' .1 ,i comparatively different behaviour from the iodines; this behaviour was als> observed in drilled hole defect tests. ' IT is believed that during shutdown xenon and krypton are released from the fuel by thermal cracking. Since the. defect was located at the bottom of the element, only a small fraction of the gap inventory could be released from the element i.e., the pressurized water only replaced the gases below the defect in a vertically oriented loop. Only the shorter-lived Kr-37 revealed any substantial activity increase immediately following the reactor trip. Observed noble gas activity increases after the scheduled shutdown may be attributed to the presence of a second defect which occurred after the reactor trip (see Figure 3.3 B-c). MacDona'd pointed out that the noble gases can only be released after pressurized water inside the element has flashed to steam during the subsequent startup. Hence, expulsion of water from the gap early in the startup would explain w'ny iodine concentrations peaked at a reactor power of n-3 MW while noble gas concentrations did not peak until reactor power had reached 15 MW. 6. POWER REACTOR APPLICATIONS In this report it has been established that iodine release is very sensitive to the size the gap is strongly dependent on whether steam or water is present. These results may find direct application in defected fuel monitoring in CANIDU power reactors. In the CANDU system, delayed neutron (D.N.) monitoring is employed to locate defected fuel; generally, an individual channel D.N. signal is compared with a nominal background D.N. signal (discrimination ratio) and depending on this ratio, this may indicate the presence of defected fuel. As previously mentioned, the delayed neutron emitters primarily occur in the vicinity of the defect (owing to their characteristically small diffusion length) and are mainly present from fission recoil and knockout. However, during low power reactor operation, the diffusion length can be appreciably increased since water (which is now present in the gap) can dissolve the 1-137 delayed neutron precursor and thereby enhance the delayed neutron signal; in fact, this result was observed at 10% fp where the discrimination ratio was enhanced by a factor '^2 from that at (57) full power. Allison and Robertson have proposed that specific fission prouuet ratios are indicative of fuel element integrity, [f this is so in a power reactor, these ratios must distinguish between contaminated in-reactor surfaces (which are covered with tramp uranium) and defected fuel elements. Tramp uranium results from UO_ loss from fuel clement failures (presumably by grain boundary oxidation and coolant erosion - see Figure 3.5). Consequently, fission product release from uranium contamination is a low temperature process and the dominant release mechanism is direct recoil and or knockout. (58) Release rates n for recoil (R '*') and knockout (R °) can be written, . >' <•' <-" I r^S,'\ and, vT^;; >« where w f f - the range of the fission fragment ~ 10" cm for all fission products .S , -- the geometric area of the fuel S'j. := the total surface area of the fuel \ - the fuel volume II -- the knock-on ejection yield of uranium ~ 5 •^(l - the number of uranium atoms f the fission rate (fissions/s) I* - the instantaneous birth rate The >~ dependence for the knockout process is only valid for shorter half-lif^ isotopes (e,g. Kr-85m, 87 and SS) and is less strongly dependent upon the decay constant for longer-lived isotopes. Allison and Robertson have suggested that the dominant (low-temperature) release mechanism for uranium contamination is recoil. For example, in a contaminated loop (without defected fuel), measured Kr-8S/Xe-138 release rate ratios were between A and .7, in excellent agreement with the predicted ratio for recoil („''! = -Jf =-r>") but at variance by an order of magnitude with that calculated for knockout (—" | = r"* y'=b.7\'.' When defected fuel was present in the loop, these ratios were always greater than r,] and generally in the range 2 to 5. The larger ratio is due to a preponderance of the longer-lived nuclide (Kr-SS) caused by a delay from various diffusion processes in the fuel element. This and similar ratios have not been fully exploited in the CANDU power reactor system as operators (and researchers alike!) cannot interpret the relative significance of the measured values (Are the defects large or small? How much tramp uranium is there?) These ratios have generally generated (nore coiifusion. In n ler>]i system, 1:1 Ie birth race B = fY for both the recoil and I'noc-koiil: processes. The three defect experiments in this report,however, provide an excellent opportunity to relate isotopic ratios with a wide range of defect sizes {und-zi experimental coalitions where uranium contamination is minimal and wh-ve the si/.G of the defect can be estimated). Since the iodines ore more sensitive to the defect si/.a than are the noble gases (see Table 4.5;, an iodine/noble gas release- rate ratio would reflect the greatest change as a defect increases in si/.e. This can be seen in Table 6.1 by comparing the release rate ratios of mix^d (and chemically different) species with the traditional ratios I-131/I-133 and Xe- 133/Kr-88. The latter ratios are ratios of longer-lived to shorter-lived isotopes as suggested by Allison and Robertson. Release rates in Table 4.1 were corrected to equilibrium by multiplying by a factor 1/(1 - e ) where t is the accumulated time from the start of the irradiation. The defect area for each dlemfMt -.vas estimated from pro and post-irradiation visual examinations. Inspection of Table 6.1 reveals that only the proposed (iodine/noble gas) ratios yield a consistent set of values as a function of the UO_ exposure (or equivalently the defect size). Therefore, only these ratios are recommended for use in a power station. Important information about the status of the reactor core can also be obtained from a double logarithmic, Release Rate/Yield versus Decay Constant plot. Summarized in Table 6.2 are the pertinent release rate dependencies which should be observed for a particular core condition, based on previous theoretical and experimental analysis in this report. For Xe-138, the additional source term (from precursor iodine decay) in equation (25) is negligible and this isotope has the same functional form as that for krypton. On a double logarithmic scale, the equivalent "fractional release" (-^ or -^/\{) should exhibit a linear relationship Y Y with respect to the decay constant (A ); if the slope is zero then the core is contaminated whereas if it is between -0.5 to -1.5 then defected fuel is present. Table 6.1 Isotopic Release Rate Ratios for Experiments FDO-681, FFCM02-2 and FFO-1Q3 and for a Recoil System Isotopic Release Rate Experiment and Estimated UO? Exposure Recoil System Ratios FDO-681 FFO-102-2 FFO-103* (Equation 42) (1.1 mm2) (>12mm2) (<2cn2) (3-9 cm2) A. Proposed Ratios 1-133 0.0051 0.024 0.029 0.79 1.00 Xe-L33 1-133 0.27 2.1 3.5 10.4 1.89 Kr-88 1-131 0.033 0.18 0.1S 1.5 0.43 Xe-133 B. Traditional Ratios 1-131 6.5 7.5 6.3 1.9 0.43 1-133 Xe-133 53.5 86.4 122.0 13.3 1.89 Kr-88 * The 1-131 -.elease rate is corrected to equilibrium by the factor 1 / [ 1 —o 1 i>:'rre the average fuel element escape rate coefficient v='F/(1-F). ( ^ ' •'*) Table 6.2 Release Rate Dependencies on the Decay Constant tor Particular Reactor Core Conditions Species fractional Release Equation Limiting Form Core Description Definirw liquation B (for Logarithmic Plot) A. Iodines 2-. where, Y I n a (= constant) b (i) Defected Core (36) 0.5 Large Defects (> 10 cm2) 1.0 Moderate Defects ( ^ 2 cm2) I I ^p ],s 1.5 Small Defects (> 1 mm2) (12) — = c = constant where, (ii) Contaminated Core Y c = 'ii.ff (Sg/V)f B. Noble Gases (15) = i where, (Kryptons and Xe-1 38) X aU constant) b (i) Defected Core 2 (32) 0. 5 Large Defects ( > 10 cm ) 1..0 Moderate Defects (> 2 cm2) " ''' L s ^ 1..0 Small Defects ( > 1 mm2) R C - ' I "•! <»2> c = constant where, Gi) Contaminated Core Y 1 SK/V) f If Me slope exhibits a linear reJationship for the longer-lived isotopes but is generally independent of the decay constant for the shorter-lived ones, then boti conditions exist. Once the presence of defected fuel is established from ratios and fractional release plots (and the average defect size from Tables 6.1 and 6.2 - note one cannot differentiate, as a result of this study, between an element containing many small defects or one large defect), the number of fuel failures can be estimated. This is achieved by dividing the 1-131 power reactor release rate (obtained from the measured coolant activity concentration - see below) by the experimental release rate value in Table 6.3 (for a single element of a given defect size). Table 6.3 1-131 Release Rates for Experiments FDO-681, FFO-102-2 and FFO-103 Experiment FDO-681 FFO-102-2 FFO-103 Element LFZ A7E A3N Heat Rating (kW/m) 48 67 48 Fuel Stack Length (cm) 16.8 $7.7 W.O Sample 1 Sample 2 2 UO7 Exposure 1.1 mm2 > 12 mm2 < 2 cm2 3-9 cm 2 1-131 Equilibrium 1.87 x 1010 7.07 x lO'-l 1.50 x 1012 7.26 x 10' Release Rate (atoms/s) This procedure assumes a negligible contribution from in-core tramp uranium, which is generally true for 1-131 because of its relatively high fractional release value. No effort is made though, to account for power dependence effects or length effects (since iodine release is very localized) for release values quoted in Table 6.3 i.e., certain parameters in the above table are at variance with those parameters specified for CANDU fuel. However in Reference 13, a release value of 4.2 x 10 atoms/s was reported for the drilled (0.33 mm diam.) element 7 a CEX, in reasonable agreement with that reported for element LFZ i.e., this element was irradiated at a higher linear power (69 kW/rn) and had a considerably longer fuel stack length (45.7 cm) than element LFZ. Furthermore, an analysis of the 1-131 activity concentration in the primary coolant of a CANDU Reactor (containing defected fuel) and an extensive post-irradiation fuel examination yielded an average release rate per element of 6.2 x 10 atoms/s. Defected elements observed in this examination were similar in appearance to that seen in Figure 3.3 A (Sample ! of FFO-102-2) and hence, the agreement of this release rate value (per element) with that in Table 6.3 is excellent. Therefore, the above procedure is a reasonable tool for predicting the number of fuel failures in-core. In order to use the analysis in this section, isotopic release rates must be calculated from activity concentrations measured in the PHT System of the power reactor. Steady-state release rates R^(atoms/s) can be related to PHT activity concentrations Cm (yc.i /kg) by the formula (see Appendix B): 'v, = k ' ( ' -,- - ) V c C where k ' - 3.7 x 10* dps/iii: i (---—) - the correction factor for ion-exchange operation: a (s~ ) is the * station ion-exchange purification constant (a = 0 for the noble gases) V - PHT mass volume (kg) rtr = tne transPort time from the core to the sample location (s) Also, pertinent tsotopic decay data needed for this analysis are included in Appendix H (from the ENDF/B-V decay data library); the fission yield data do not include any contributions from Pu for high burnup fuel. In summary, several power reactor applications based on previous theoretical and experimental developments have been proposed. These applications may provide a more accurate description of a particular power reactor core condition. 79 7. CONCLUSIONS AND SUMMARY OF RESULTS A model describing the steady-state release of the radioactive noble gases and iodines has been presented. Non-linear least-square fits of the theoretical expressions to the measured data in Table 4.7 are excellent (generally within a factor of 2 for most isotopes) for a wide range of defect states. Parameters estimated in this analysis for the noble gases and iodines include: the empirical diffusion coefficient in the UO2 fuel (Table 4.5), and the diffusion coefficient (Table 4.6) and escape rate coefficients (Table 4.5) in the fuel-to-sheath gap. The absolute and relative magnitudes of the empirical UO_ diffusivities are generally consistent (within an order of magnitude) with those values reported in other studies. The noble gas gap diffusivity is in reasonable agreement (within a factor of ~5) with that predicted by kinetic theory. A comparison of the noble gas and iodine escape rate constants for each defected element indicates the greater sensitivity of the iodine constant to the defect size; consequently, the effect of iodine trapping in the fuel-to-sheath is quantitatively assessed in this study. Furthermore, the various rate-controlling processes operative in ~ach defected element (for a given defect size) are deduced from the data. The present analysis has been applied to the case of a power reactor and a procedure has been developed to determine a particular reactor core condition. Isotopic ratios currently used in the power stations have been shown to yield inconsistent results and more appropriate ratios have been recommended (Table 6.1). The general experiment.il and theoretical results of this study are summarized below: '-; •') 7.1 No massive sheath hydriding was observed for elements LFZ and A3N which originally contained large primary defects. In contrast, element A7E, which was fabricated with a porous end plug, exhibited through-wall cracks and blisters after an earlier irradiation. Following re-irradiation, sheath hydciding and degradation was more extensive. 7.2 During the FFO-102-2 irradiation (element A7E), both the noble gases and iodines (and delayed neutron transmitters) exhibited stepped release increases after each successive power transient, This increase vvis attributed to sheath degradation and pellet cracking as a result of transient operation; a relatively constant release during steady-state operation suggested that crack healing was offset by continued oxidation and grain boundary inter-linkage. \ sudden burst increase during steady-state operation near the end of the irradiation indicated the presence of a second defect. 7.3 Analyses of the defect experiments revealed that both the noble gases and iodines obeyed ftooth difhisional release in the UO,. when corrected for precursor diffusion; however, all isotopes are held up in the fuel-to-sheath gap. Fission gases were delayed as they diffused in the narrow gap but iodine holdup was greater because of iodine trapping on internal element free surfaces. 7.4 A fission product release model for defected fuel, developed from experimental observation, was in good agreement with measured release data. The model assumed Booth diffusional release the UO_ with transport in the gap. Gap transport was modelled with (0 a phenomenological rate constant, and (ii) a gap diffusivity. The phenomenological transport model was applicable for a wide range of defect sizes (for release dependencies of \~ to j ) whereas the diffusion model was only applicable for a smaller range of defect si/.es where transport was diffusion-controlled (for a release dependency of >" ). 7.5 Empirical parameters from both transport models were identified and compared with real physical constants (e.g. diffusivities in the UO^ fuel and in the gap). This analysis identified rate-controlling processes in the defected fuel elements (diffusion in the UO-, fuel and in the fuel-to-sheath gap and iodine trapping on the fuel and/or sheath surfaces) as a function of the defect size. 7.6 The iodines were released on both reactor startups and shutdowns, whereas the noble gases were only released in quantity on reactor startup. During startup, iodine release always preceded noble gas release and this was due to expulsion of water from the fuel-to-sheath gap. 7.7 Based on experimental and theoretical developments in this work, a method is proposed to assess power reactor core conditions (to distinguish between a uranium contaminated core and one which contains defected fuel, and to identify defect size and the number of fuel failures). 8. RECOMMENDATIONS It is recommended that fission product release data measured in the primary heat transport system of CANDU power reactors be used to test the procedure described in Section 6 (to identify the reactor core condition). For example, the number of fuel failures can be predicted from an analysis of release data from the Douglas Point NGS and then compared with the number of fuel failures previously identified by delayed neutron monitoring and a post-irradiation visual examination in which fuel bundles in channels exhibiting relatively high discrimination ratios were visually examined following discharge from the reactor. Further experimentation may include the irradiation of elements containing very small laser-drilled holes (diameters of -10 to 100 urn) to determine the critical sue of a defect necessary to promote sheath hydriding. This information is of importance to the fuel element fabricators in attempting to improve quality control procedures during leak testing operations. A load- following experiment with defected fuel is also recommended to investigate the effect of load-following on sheath degradation and fission product release for hydrided fuel. This experiment is necessary since the present study indicates that sheath deterioration (for high-powered fuel) occurs mainly during transient reactor operation. Furthermore, the present study also shows that iodine release is greatly enhanced when water is present in the liquid phase and therefore that "iodine spiking" may occur during transitions from high to low power cycles (and vice-versa), particularly for defective elements in lower-powered bundle positions. 9. NOMENCLATURE a radius of equivalent grain .sphere B birth rate C concentration in matrix (.•„, measured loop activity concentration elf effective defect diameter I) apparent diffusion coefficient in the fuel I) ' empirical diffusion coefficient in the fuel T: diffusion coefficient in the gap y> ' effective diffusion coefficient in the gap f ratio of in-pile to total loop volume; isotopic branching fraction f fission rate l; fractional release (ratio of release to birth rate for radioactive species) 11 precursor diffusion correction factor .1 flux of atoms to surface k iodine escape rate constant k ' conversion constant k | iodine forward reaction rate constant k _ j iodine backward reaction rate constant Keq iodine equilibrium reaction constant (- kj/k_i) I defect length \. diffusion length l,s fuel stack length M molecular weight N'g number density in the gap Ns number density on the free surfaces Ny number of uranium atoms P pressure r radial coordinate K release rate Rf g release rate per unit volume in the gap Hf s release rate per unit area on the free surfaces S surface area t time T temperature V volume Y fission yield z axial coordinate along fuel element length Greek Letters a knock-on ejection yield; purification constant o birth rate per unit volume Y, 5 separation constants A radioactive decay constant u range V escape rate constant f> effective decay constant P fuel pellet radius 0 collision diameter westcott absorption cross section for Xe -135 azimuthal coordinate westcott neutron flux (.:. defect width (-,,,< •) ft collision integral Subscripts and Superscripts d daughter species f f fission fragment g geometric I iodine species ko knockout N noble gas species 0 observed p parent species r recirculation i-cc recoil t r transport T total U uranium 1 , - trace and continuum species per unit volume cumulative fuel element average * iodine species •Vj 10. REFERENCES 1. D.G. Hardy, 1.C Wood and A.S. Bain, "CANDU Fuel Performance and Development", AECL-6213, 1978 December. 2. N.V. lvanoff and R.D. MacDonald, "Sheath Deterioration and Fission Product Escape from Fuel Elements Having End Cap Porosity Defects - An Interim Report on Experiment Exp-FFO-102", Exp-FFO-10209, 1980 December. 3. R.D. MacDonald and 1.1. Lipsett, "The Behaviour of Defected Zircaloy Clad UO2 Fuel Elements with Graphite Coatings Between Fuel and Sheath Irradiated at Linear Powers of 48 kW/m in Pressurized Water", AECL-67S7, 1980 .luly. •t. B.I. Lewis, "Behaviour of a Zircaloy-Sheathed UO2 Fuel Element Containing a Porous End Plug Defect and Exhibiting Secondary Sheath Hydrid'mg Irradiated in Pressurized Light Water at a Linear Power of 0>7 kW/m", CRNL-2473, 19S3 May. ">. D.D. Semeniuk, B..1. Lewis et a!., "Irradiation and Gamma-Ray Spectrometry Data for the Multi-Slit Defect Experiment", Exp-FFO-10 306, 1982 April. 6. C. Helstrorn, "Emission Rate of Fission Products from a Hole in the Cladding of a Reactor Fuel Element", AECU 3220, 1956 3uly. 7. H.W. Kalfsbeck, "The Abundance of Fission Gases in the Off Gas of a Boiling Water Reactor", Nucl. Technol. 62 (1983) 7. 8. 1.1. Lipsett, 1.1. Hastings and C.E.L. Hunt, "Behaviour of Short-Lived Iodines in Operating IJO2 i'uel Elements", presented at the CNS 3rd Annual Conference, Toronto, Ontario, ISSN 0227-0129, 1982 June 09. 9. LI. Hastings, C.E.L. Hunt and 1.1. Lipsett, "Behaviour of Short-Lived Fission Products Within Operating UO2 Fuel Elements", to be published in Res. Mechanica, 1983. 10. A.H. Booth, "A Suggested Method for Calculating the Diffusion of Radio- active Rare Gas Fission Products from UO2 Fuel Elements and a Discussion of Proposed In-Reactor Experiments that may be used to Test its Validity", AECL-700, 1957 September. 11. R.D. MacDonald et. al., "Purposely Defected UO2-Zircaloy Fuel Elements Irradiated in Pressurized Light Water at Linear Powers of 55 kW/m", to be published. 12. G.M. Allison and R.F.S. Robertson, "The Behaviour of Fission Products in Pressurized-Water Systems (A Review of Defect Tests on UO~ Fuel Elements at Chalk River)", AECL-1338, 1961 September. 13. CM. Allison and U.K. Rat', "The Release of Fission Gase 1'*. W.3.F. Motley, "ELF.SIM: A Computer Code for Predicting tn? Performance of Nuclear Fuel Clements", Nucl. Technol. W (1979) tU5. 1 5. G.V. Kidson, .1. Nucl. Mater. S8 (1980) 299. 16. P. Beslu, C. Leuthrot, G. Fresjaville, "PROF1P Code: A Model to Evaluate; the Release of Fission Product from a Defected Fuel in PWR," presented at the IAEA Specialists Meeting on Defected Ceramic Fuel, Chalk River, IWGFPT/6, 1979 September. 17. B.E. Schaner, "Metallogriphic Determination of the 1 IC^-U^Og Phase Diagram", 3. Nucl. Mat. 2 (1960) 110. IS. D.R. McCracken, CRNL, private communication. 19. D.T. liittci, L.H. Sjodahl and 3.R. White, 1. Am. Cer. Soc. 52 (1969) 3. 20. 3.H. Davies et al., "The Mechanism of Defection of Zircaloy-Clad Fuel Rods by Internal Hydriding", Proceedings of Joint Topical Meeting on Commercial Nuclear Fuel Technology Today, Toronto, Ontario, 1975 April. 21. .l.C. Wood, "Interactions Between Stressed Zircalo/ Alloys and Iodine at 30Q°C", 3. Nucl. Mater. 23 (1974) 63. 22. M. Peehs, G. Kaspar and K.H. Neeb, "Cs and I Release Source Terms and Fuel Internal Chemistry from Irradiated LWR Fuel", Presented at OECD- NEA-CSNI Specialists' Meeting on Water Reactor Fuel Safety and Fission Product Release in Off-Normal Conditions, R1SO National Laboratory Denmark, 1983 May 16-20. 23. R.A. Lorenz, .1-R. Collins, A.P. Malinauskas, O.L. Kirkland and R.L. Towns, "Fission Product Release from Highly Irradiated LWR Fuel", NUREG/CR- 0722 ('->RNL/NUREG/TM-2S7R), Oak Ridge National Laboratory, 1980 Februai Ik. D.O. CarnpbJl, A.P. Malinauskas and W.R. Stratton, "The Chemical Behaviour Oi fission Product Iodine in Light Water Reactor Accidents", Nucl. Tech. 53 (1981) 111. 25. D.F. Torgerson, D.J. Wren, .1. Paquette and F. Garisto, "Fission Product Chemistry under Reactor Accident Conditions", AECL-7659, 19S2 September. 26. M. Peehs, R. Manzel, W. .Schweighoter, W. Haas, !:. Haas and R. Watz, .1. Nucl. Mater. 97 (1981) 157. 27. A.H. Booth, "A Method of Calculating Fission Gas Diffusion from UO_ Fuel and its Application to the X-2-f Loop Test", AECL-496, 1957 September. 28. S.D. Beck, Batelle Memorial Institute Report, BMI-1433 (1960). 29. L.D. Nobel, Status Report ANS 5.4 (1977) p. Ill A-l. 30. C.S. Rim and W. Preble, Status Report ANS 5.4 (1977) p. Ill B-l. 31. C.A. Friskney and .VI.V. Speight, .1. Nuci. Mater. 62 (1976) 89. 32. 3.A. Turnbull, C.A. Friskney, 3.R. Findlay, F.A. Johnson and A..7. Walter, 3. Nucl. Mater. 107 (1932) 168.' 33. Background arid Derivation of ANS 5.4 Standard Fission Product Release Model, American Nuclear Society Working Group 5.4, N1JREG/CR-25Q7, (1982). 34. D.R. Olander, "Fundamental Aspects of Nuclear Reactor Fuel Elements", TID-26711-P1 (1976), Chapter 1 5. 35. P. Bourgeois and 3. P. Stora, "Behaviour of Fission Products in PWR Primary Coolant and Defected Fviel Rods Evaluation", presented at the 5th Internationa! Conference on Structural Mechanics in Reactor Technology, Berlin, Germany, 1979 August 13-17. 36. S. Glasstone, "The Elements of Physical Chemistry", D. Van Nostrand Company (1946), pp. 551-556. 37. 3.A. Turnbull and C.A. Friskney, 3. Nucl. Mater. 71 (1978) 238. 3S. 3.A. TurnbuK and M.V. Speight, "The Relation Between Fission Product Release and Fuel Microstructure in High Burnup UO ", Proceedings of the Workshop on Fission Gas Behaviour in Nuclear Fuels, Karlsruhe, EUR 6600 EN, 1978 October 26-27. 39. B. Lustman, Chapter 9, "Irradiation Effects in lJranium Dioxide", Uranium Dioxide: Properties and Nuclear Applications, 3. Belle, Ed., U.S. Government Printing Office, Washington, D.C. (I960, pp. 431-666. 40. A.D. Appelhans and P.E. McDonald, "Fission Gas Release in LWR Fuel Measured During Nuclear Operation", Idaho National Engineering Laboratory (1980). 41. 3. Crank, "The Mathematics of Diffusion", Second Edition, Oxford University Press (1975), pp. 326-351. 42. P.W. Frank and K.H. Vogel, "The Theory of Failed Fuel Element Location and Detection," Bettis Technical Review, WAPD-BT-3, 1957 August, pp. 9S- 109. 43. 3.3. Lipsett and R.D. MacDonald, "Another View of Fission Gas Release from Defected CANDU Fuel Elements", presented at the IAEA Specialists Meeting on Defected Ceramic Fuel, Chalk River, 1WGFPT/6, 1979 September. 44. W. Mickeley and F. Felix, 3. Nucl. Mater. 42 (1972) 297. 45. R. Lindner and H. MaUki:, Z. Naturpondep 14a (1959) 582. 4(>. L:. V.tuist'.-r et. al., "Escape of Fission Products from Defective Fuel Rods of Light Water Reactors", Nuci. Eng. and Design 64 (19S1) 81. 47. li. I'. Lawrence, "A Review of the Diffusion Coefficient of Fission Product Rare Gases in Uranium Dioxide", 3. Nucl. Mater. 71 (1978) 195. '(9. R.U. Bird, W.L. Stewart d\\d E.N. Lightfoot, "Transport Phenomena", Wiley, New York 'I960), Chapter 16. 50. CM. Criss and J.W. Cobble, "The Thermodynamic Properties ol High Tempera tore Aqueous Solutions. IV. Entropies of the Ions up to 200 'C and the Correspondence Principle", 3. Amer. Chem. Soc. 86 (1964) 5385, 51. C.M. Criss and J.W. Cobble, "The Thermodynamic Properties of Hr-;h Temperature Aqueous Solutions. V. The Calculation of Ionic Heat Capacities up to 200 °C. Entropies and Heat Capacities above 200 "C", J. Amer. Chem. Soc. 86 (1964) 3390. ')?.. F. Garisto, " i'iicrmodyn.i:nirs of Iodine, Cesium and Tellerium in the Primary i-U:at-Transport System under Accident Conditions", AECL-77S2, 19S2 November. 53. CRC Handbook of Chemistry and Physics, 63rd Edition (1982-1983), p. D- 64. 54. R. Warlop, R. Chenebault and 3.P. Stora, "Fission Gases and Halogens Release Out of Failed Fuel Rods", Proceedings of the ANS Topical Meeting on Reactor Safety Aspects of Fuel Behaviour, Sun Valley, Idaho, I9S1 August 2-6. 55. 11.3. Lutz and W. Chubb, "iodine Spiking-Cause and Effect", Trans. Am. Nucl. Soc. 28 (1978) 649. 56. K.H. Neeb and E. Schuster, "Iodine Spiking in PWRs: Origin and General Behaviour", Trans. Am. Nucl. Soc. 28 (1978) 650. 57. 3.3. Lipsett, CRNL, private communication. 58. R.M. Carroll and O. Sisinan, Nucl. Sci. Eng. 21 (1965) 147. 59. C. Kittel, "Introduction to Solid State Physics", 5th Edition, Wiley, New York (1976), p. 411. 60. CRC Handbook of Chemistry and Physics, 56th Edition (1975-1976), p. F-86. 61. 3.F. Palmer, "The Fuel Rod Activity Monitoring Problem in Candu Part IV - A Study of the Activity Released from a Defected Oxide Fuel Element During Powf-r Cycles", RCE-10, Chalk River, 1963 February. 62. A.M. Man/.er, AECL-EC, private communication. 63. F.R. Cambell et. al., "In-Reactor Measurement of Fuel-to-Sheath Heat Transfer Coefficients Between UO, and Stainless Steel", AECL-5400, 1977 May. 64. D.C. Groeneveld and F. Mancini, "Tables of Thermodynamic Properties 65. R. Boiialumi - Course Lectures for CHE-I523S "Nuclear Reactor Engineering", University of Toronto, 1983. 66. L.S. Tong and 3. Weisman, "Thermal Analysis of Pressurised Water Reactors", 2nd Edition, AN.S (1979). 67. O.T. Nishimura, "Summary of Loops in the Chalk River NRX and NRU Reactors", AECL-6980, 1980 December. 68. 1.3. Lipsett, I.L. Fowler, R..1. Dinger and H.L. Malm, "A Wide Range Ge Gamma-Ray Spectrometer for On-Line Measurements of Reactor Cooling Water Activity", IEEE Transactions on Nuclear Science, Vol. NS-2'->, No. 1, 1977 February. APPENDIX A Computer Code Description Computer codes used in the thesis are briefly described in this Appendix and includ?;: A.I The GRAAS Code A.2 The SUMRT Code A.3 The LATREP Code A.* The FISSPROD Code A.5 The MLSQQ Code For each code the following format is adopted: (i) Title: The code identification and a brief description is given, (ii) References: References are given for user instructions. (iii) Sample Input: Input for the sample FFO-102-2 experiment (element A7E) is given. (iv) Sample Output: Output for the sample FFO-102-2 experiment (element A7FI1 is given. The author would like to acknowledge the following code assistance at CRNL. The GRAAS code was prepared and run by the Reactor Loops Branch as part of the experimental data acquisition process. Several LATREP test cases were originally prepared by W. Heeds of the Reactor Physics Branch for particular trefoil geometries (these cases were slightly modified by the author for different fuel enrichments). The author would like to thank M. Milgram and R.L. da Silva of the Reactor Physics and Fuel Engineering Branches respectively for their assistance with the FISSPROD code. Finally, I would like to thank J. Blair of Math and Computations for deriving a generalized function of the independent release equations for use in MLSQQ. '•M. A-' The GRAAS Code (i) Title GRAAS Version 3.0 - GRAAS takes as input the mass storage file of gamma-ray spectra and calculates the energy, area and relative error in the area of photopeaks with a high confidence level. (ii) Reference 1. C.A, Wills, "User's Guide for GRAAS Version 3.0", AECL-7601, I')82 .lanuary. (i i i) Sample Input INPUT DATA = 5 INPS1 =1^5 NUMB = 1 ISTCH = I IFNCH = .} 35 INPUT TATA FOR SUMMATION OF SPECTRA, LIMCOUN = LIMTIME CONF LEVEL = 99.9ii CHAN/INCH = 2JJ.C0 ILIST I AREA ICAL ISG INPF2 1 5 0 1 (iv) Sample Output SUMMARY CF RESULTS PEAK PCJIT I ON COUNT-RATE ERROR (CHAN ft L> KEV) (C/S) 1 3 0.61 .1676E»C3 .66G4E-C 1 2 253,16 150. 74 .336 2E + C2 • 2-13E+C 3 3 277 ,i*2 16 5.31 .1747E+02 . 6 15 2 E+0 0 329.ec 13 6. 77 .7 A.2 The SUMRT Code (i) Title SUMRT - SUMRT takes as input identified peaks for a number of spectra from the GRAAS code and produces a listing of the concentration and/or release rate over a period of time. (ii) References 1. C.A. Wills, "User's Guide for SUMRT", to be published, 1982 July. (iii) Sample Input RECIRCULATING VOLUME = 15C.S RECIRCULATING TIME = lj<«.9 LEAK RATE = .57GG->Ci MAINSTREAM :jPtCT?.OMriTER OPTIONS IPRINT = 3 IPLOT = ? ITAPc = ^ LISTINGS WILL S£ ^Ot OF CONCZNTRAT ION RELEASE: kATE PLOTS WIuL iSz. PRODUCE. 0 FOR CONCENTRATION -.ELEASE KATE NO TAPt! WILL iii PROOUCZQ RELEASE RATES WILL BE CALCULATE RELATIVE t?SOi? TOLERANCE = .iOOOCE + 01 WINOOW FASA-ltTF^! = .2000JI*1?! NUMBER OF CENTIMETRES PER DAY FOR PLOTTING = i.CO CONCENTRATION ^LOTTING LIMITS ARE MAXIMUM = 8 MINIMUM = 1U \ELEASt RATt PLOTTING LIMITS ARE MAXIMUM = a M IMUM = i** X AXIS PLOTTING LIMITS ARE. tfAXIIJH = 81/03/17 ut«GC MINIMUM = *l/CU/wb -jluO NUMBER OF SPECTRA R£AO FROM INPUT TAPE = 16£»«» TRAP \UM3c 11 TRAMSPO'T T I Mr! .•: 1/0*4/ jt : :: ] . ?.u 3 3/17 Jj:jC 7 GA^MA A iNC,: ICN -X 7J-' GA S NUCwIDt c.NE R-,V HALF LI* - : F T KR85M 15b .90 Hi.. <4.) F T 7 : K'<65M , C HU. -* : r T KR9 7 • *• c HI. 2T T F K3 6 3 lib .32 H2. h« (iv) Sample Output FIS5I0N"P^CJJCT C 3'iC. NT N a T I JNS--GFF OA i i. K -1 951 I MA-^CH 19 5 • -• 7 • 1 '-'7 9 v ^_ t 3 -'+ 11 7. 7C*t •_ + MAxCH 19 1 .5 : -47 7 • 1 s2 • c *• i + 11 7. •j 5 7'•• • ^ • + - i. MA~:CH 13 1 ' .-? E 6 .579 » t *4£ + 11 7. 1 b 1r + I -. + 11 M A •< C H 19 3 6 .9 -t ^ 1 1 L c : + 11 A t -tl £ 4> MARCH 19 j ^1 1 •4 _+ 4. X 7. 73S ,_ 4- ,c+ 11 ;1 e..5 u6 -7 MAS.CH 19 I1 i -. o .512 7 C :+ 11 7. J T 6£ 4> . 3 *• 3 + 11 ^_\ - + 11 1 C ?£ • M6-.CH 1^ i 6 5 1 t . i. .'.:+! I M A -v C H 19 2 ^' 5 a 1 fi * ^_ -+ 11 5. ? 17 >• + 2~z > 11 MAFCH 2 J ' 3> 1 ^. r ." + 11 D «a 37 ;_ 4> MARCH 2 J 1 7 • -t ••- 9 H + 11 5. "> -77 4- FFQ-1Q2-2 S:CO'J:)--f,FP OAT£ -H 19 1 3 s • j 9 1.^5? 7. 1.1it^+11 1.:e5^+ii *+.i4 2?-.+ lj t 1.17e£+ll 1. :59b:+ 11 •*. 3437+1J MA=;CH 19 1^:2? 9.3 2^ + - 1.1 e. - +11 1.: 5it +11 H.346E+1J MA^CH 19 I5:J3 q «!+'-"•••"" •4. ^52:+ 1. ? 1 . 1 <4<+£ + ll MA.- (i) Thle CYCLE 5 l.ATREP -LATRF.P is a rode used by Atomic Energy of Canada Limited (AECL) to calculate reactor lattice parameters for various fuel element and/or bundle designs. (ii) References 1. 1. Griffiths and VI. Milgrain, "Introduction to the Use of the TESHOM/LATREP Codes on CDC Cybernet", AECL-6780, 1980 September. 2. M. Milgram "A Guide to LATREP (1975)", AECL-5036, 1975 March. 3. I.H. Gibson, "The Physics of LATREP", AECL-2548, 1966 March. (iii) Sample Input TIT FlOGOi NEW TREFOIL 5.C2 X U235 IN 1)233 COt: LflTPEP 5 FL& fMRUC WIDTH AN& O.C SC2 •• SCR .6070 .oil1; ,655f; .8^101 SC^ 7 11 10 3 SCO lO.f.0 .00193 fc.f>5 SCW U2T5 .0M<»2P13 U23tt .f 372*87 0 .118 5 VOIC 1 ZR I SCT aac .!:~r 32^ 32? SGS 3 SGR l.n?41 RGR 1 7 SEP. 0,3 .21209 1.69611 2.15729 2.31775 2.<*57*»5 2.5527 2.6162 2.93688 3.(H5f3 frEM 1 101 1 101 1 101 103 1 R^T 2FP 25C 175 100 60 65 65 65 RED fc.5F .CC29 1.3 2.71 PEW Z" 1 VOID 1 H20 1 AL 1 COG 0.MR957 COT 28C COW H20 1 MOD G HOT 6F MOW h?C .002 020 ,99ft PHE 2?.7 PHI 2.5 WTf OUT STA (iv) Sample Output (Only pertinent information is given below - see Reference 1 for a more complete listing). F100 01 (•Ek TPEFOIl 5.02 7. 0235 IN U238 THIS EDIT IS BASED ON ONE NEUTRON SLOWING OOKH AND LEAKAGE CUE TO A 8UCKLING(N-2) OP KITH A NORMALIZING WESCOTT FUEL FLUX OF .250000£»1* FIXED CUT. OFF FUDGE FACTOP .960000 HEXAG. PITCH 25.700000 PIN RADIUS HY?. CELL RAO. 1.038271 MOO. DENSITY 1.W.35 COOL. DENSITY .5D5357 020 «r. FfrAC. .998000 D2O AT. F9AC. .997777 FUEL/CELL .39961)8 MOO./FUEL 2.553 835 COOL./FUEL 1.963113 30UN0./FUEL AYE. FFR .016283 FUEL * .025249 NOOERATCR R .1115 21.9 .011.70 9 ROASH 1516.50781.5 J3KXY 5.375565 FUEL H. TEMP. 201.7C6J62 TUBE TEMP. 160.295916 HOO. TEMP. 68.565289 DELTA TEMP. 136.706762 VF VM .ODfc'.CS IC* .113823 RCR(O) .9l>7 GEOi SUCKLING C. X-INFINITY 1.519689 K-EFFECTIvE 1.519880 IRRADIATION .066000 FOOR FACTOR PAPAMETERS EPSILON .985990 ETA 1.902193 F .857265 LSSQ 121.595521 LSSatMOD. I 11S.191331 LSQ »53. 016 J*O LSCMMCO.J 1161,?.772 ^66 OFC 1.331875 OFH 1.310 2">IS OTC 1.091603 DTM ^.0 69028 FOUR FACTOR VALUES OF K-INFINITT K-EFFECTIVE 1.51.2833 •1AT. BUCKLING .66963E-03 SIS»1 .l?3<.S«-E-«3 SIGR1 .107999E-01 SIGT1 .109533E-01 SIGA2 .21»;!57QE-0Z SIGYS .3795b.:t or SIGT1CMOO) .110e"illE-01 SIGA2(MODI TIME 30.56 FLU» HHO/TE . 17 J3tT S3H 9t-3b»Tfc»Z" ONIM-0 lO*3SSZ/lf* ISOJ TO» -Id3 0D«32Sl>e9E' At/ZSJ 0043*9*£«' A»/15i TT31 110?i53« 3fl 01 S3nivA dJO ina tJ3XId (d»O QIOA 3Hi AITvniDV) HiV3HS 13flJ 3dV M013B SOI 1*0 »n"lj S 3H1 / 33KJN H3V3 ilOJ 031W101V3 SI *i»3 5NIHOTT0J 3»1 *13 tO-3655698' 0SW8 I0.3t9ZT01« NOTISd3 2J0ISDN 1 d/8 9T-369T69Z' 1010 I0<3i235JT* C/B 253IS T0-3£C460f 11SIS TO*3B9ttOT* 20 T0*3/8T£S:T* TO VHQ A.4 The FISSPROD Code (i) Title FfSSPROO-3 - F1SSPROH is a CRNL fission product accumulation rode which uses CNOF/B-V decay data as input. (ii) Reference;; I. ,VL Milgrajn, "FISSPROn-3 An Expanded Fission Product Accumulation Program Using CNHF/li-V Decay Data," AF.CL-6973, 19S2 November. 1. W.H. Walker, "FISSPROD-2: An Iinproved Fission Product Accumulation Program," AF.CL-3037, 1972. (iii) Sample Input INf=Ul UAIA . r4i"W I INPUT DATA F <\ -FFO- lur?-3 ll'lf FIIMIHT — luruT DB1A—. CUM .iny; • 1" I.I «i).n . b «• •'. i«• + j j .i.Jouf'.:: L. ;. . 11 j». J • F i• 'j rLt luCLir.r FA Til" FISGHF FIT Sfrp uucilii n»ri — INPUT D4TA-- SHFTIHL rRirrI0N FACTO- — IN°UT 0«T»-" •liir.LIlCS /ILL ><«SS .iut£(22 .iu<.£»U Til" FLUX HrSTCOT" Tt MP. STF>' IKPf-fNe^T IN STEP ' R TIMF IBSAIHTirN J CLMUL4TIVF TRD1"r5TION AN3 TTTS UN DSYS ) TOTAL ISRAOIATICN OECav NCUTPONS PFP T£MF Tine 'IMF KILOndGNS C? 0. .3?7<.JE-01 THF CONVEoSIOK FACTO', KC. FISSIOtl'C Pr - ' NDOLTPF SUMM4OV - "»SS TIME ATOMS G?AMS ATOMT G'»»" 8TCI3 GRAM- STEP PER FIJStOli Pt 3 MG OF H.E. TL^ FIS9ICII PC1' "& if H.t. PE1? PIS5ICN PE' "1r. OF H. £ . 56-KP- TIME ATOMS GrATi ATO1? I", = AH~ ATO13 G-aM"" STFP PER FISSIUN |'[R pr, OF H.E. fi» FI^fTCK (FP MC OP H.t. PE' FIS3ICK P£" ~IG 0^ H.E. A.5 The MLSQQ Code (i! Title MLSQQ - MLSQQ is a weighted least squares fitting routine for a (unction of one or inore independent variables with or without user supplied partial derivatives. (ii) References I. AECL FTN Library, ".MLSQQ", Number 1—11 -20, 197S September. (Adapted from LSQQ by L. Evans and FL. Long, 1977 April). Original LSQQ written by "J. Schmidt, 197 3 June and revised hy L. Evans, 197* April. P"0r.RAM BLCIT( INPUT, ni) TnjT ,T APF.1 = INPUT) RE&l y|inO,l)frriOO),WflOO)f'^D(100)'F(1 of Al SDYFIIiJi) ,CTNT< 1 :0l ,HS (5 CO f0HM0N/q»NNqNjT/HjBB ) ,tXt(1)HI(B)( P ,1< «>, F?<8> ,F3 («) INTEGER NHC) EXTERNAL AUX P(l) = 2. ?F-5 D(2) =5. 5F-10 P(^l =1.uF-6 p(i> I =«, oe-in NPX= 1 NC( 11=1 NC ' ?) =1 NC(3) =t NCI '.)-1 _ -ppTN' <*, IOP-Ty L " • • <. FO°I-AT( // * I0PT=*, n, 5X, X(NBX,l),F(lltPtl) N/10fNT/H(«t XI(1) -,Fl, CO If J=l,» r:c= t C3txTS ( Ji/itui nP = S0RT (FUI/XT (J)HI( CS= t'C! )/IX( Jtl I + PJ31 I ) cTs F (iv) Sam)3le Output ^ .llOr\ ll)9 .0013600 Y- .00fc6i«5n .0010310 .0053250 VA9Y VSRV V8RV r VARY • 2200000E- o* 5 oaaoO -35 0r S = lf5.2BD3 .na:caa 916170.2 1662 n 0 Pftfi. - E-05 «?.555i.3 I/ISO. 2«6j 0> 1532071T00q <•«.31.^31 MAPI. P»R. = 325331.9 Q* .2867631^-19 • 125H19E •35 .9269473E-19 t2.OiO22 SR PAR. = 196120.2 • 22a3160E 01 .3160n55E-n9 .1252563E •05 ,9?6?6«?E-n9 S = 1.0.97056 HARQ. PAR. = r .2277481F- 0* .3019956F-09 .1251805" -C5 .927i.939 -ri9 YF ,0 05182". 00097nf, .0017779 .0fl26fi76 .OOfcRlCJ .3^20611 .011721? ,0017fiM i.9?5E-15 .i»D73E -13 -,610*E-lf 1256F-H9 -.1010F -17 .1521F-23 .7506E-"! - -06 -.2i.07E-i.20iee 11T6'Jl »U 'J .lBBTr-09lBBTr09" APPENDIX B The X-2 Loop Model The loop model has been derived in Reference 3 and is used in the SUMRT code to evaluate release rates from measured fission product activity concentrations. This model is also derived below for later reference. The rate of change of the total inventory (Q) of a particular species in the coolant is ,<*iven by the mass balance equation: ] = R if^ oU)-SQft)-"Q(t)-K-Qft) (B.I) where K0(t) = the fission product release rate from the defected fuel element(s) (atoms/s) t, - the loss rate constant due to radioactive decay ( \ ) and transmutation by neutron absorption in the loop coolant (s •) a . the loss rate constant due to loop purification circuits (s ) K = the loss rate constant due to coolant leakage (s"1) Defining the total loss rate constant, A* = ••.+« + »- (B.2) the release rate as a function of time is given by, ) K.;(t) = >. *q(t)+^|ii-' - (n.3) The total inventory Q can be related to the measured activity concentration Cm (Bq/m ) at the spectrometer as follows. Assuming a constant loop cross sectional area A, the concentration of a nuclide q (x meters away from the defected element) is Substituting equation (B.<0 into (ft.5) yields (B.6) Further, for a spectrometer located at the inlet of the test section (see Figure 3.1) at a distance X metres away from the core, the measured activity concentration Cin is <:ra = *i(X) (B.7) or using equation (B.4), (: u XX/u = \(0) e-' (B.8) fn the above equation, we have assumed most of the losses take place down- stream of the sampling location. Now defining the transport time ( 11 r) (from the fuel to the spectrometer) as t = - (B.9) t r u and the loop recirculation time ft ,.) as t = - (B.10) r u the total inventory can be related to the measured activity concentration by, u Qft.) = (f)c:mct)t. where we have used equations (B.6), (B.8), (B.9), (B.10) and the relation V = AL. Finally the release rate is given by, \ f- -v*t , dC RjCt) = 1 1 (1- Note that for a rapid recirculation time t r (as for a power reactor - see Table 3.2) the term in the square brackets in equation (B.ll) reduces to unity for most isotopes of interest. APPENDIX C Booth Diffusionai Release Corrected for Precursor Diffusion The set of i coupled partial differential equations for diffusion in the grain sphere of radius a is given as, ----- , . , | . ] ^ -- l... 7 C -i. C. ^ |C|+B:- (A.I) _JzL = n '•••(• -,• . c:. +x. ,(:._, + .'. Ot i -1 i -1 • i -1 i -1 i - - i - - ^'•- = V c\'~ \c\+x i-ic;-i+!'i where t.', = the concentration distribution of the i*'1 member of a radioactive chain at time t. I', j -= the production rate of the i1'1 species from fission per unit volume. "; = the diffusion coefficient of the itn species. '. j - the loss of species i due to radioactive decay ( ^-) and transmutation by neutron absorption. Generally, the earlier chain members have relatively short half-lives and are unable to diffuse an appreciable distance before decay. Therefore, one can neglect the diffusion terms in (A.I) prior to the parent species (itn -1 equation) A ( o+ B and replacing i _2 'i - ^ i - 1 ''>' p (where (3p= ^ S j ) for steady-state yields, n p p p p (At2) •! <.! d d p p where the subscripts p and d refer to the parent and daughter species -_r t —.- r* i- generalized study. *'5' Adopting his formalism, the fractional release of the daughter isotope is given by T 0 j t (A ^ where Cj* is the total number of daughter atoms per unit volume in the ^rain (C(j* is obtained by neglecting diffusion in (A.2)). Imposing the boundary conditions Cp (r=a) = Cd (r=a) = 0 and using (A.3), the fractional release of the daughter isotope as derived from Kidson's general solution is, A U, , d ii - I iv n d P (A.*) .i- -I ... + d ' dp 'd { i ( + Cnth(/l (A. 5] n?| " " '° "' •••Vr- °~l7' and the Riemann zeta function /, ( 2 ). 2J( 1 /n? ) = ;• :'/f» (A.'t) reduces to, ) (A.6) ,1 :l r / where Avipd == up-pd and U(p,in - ' -(p . d 1 ° (p . d 1 Generally for most isotopes of interest JJT > 10 and since the production rate is proportional to the fission yield, equation (A.6) becomes 1 (A.7) where Y is the cumulative fission yield of the parent isotope and Y^ is the direct fission yield of the daughter isotope. APPENDIX D Diffusion in the Fuel-to-Sheath Gap Figure D.I Coordinate System for a Defect in a Cylindrical Fuel Element Consider a defect of length s. and width m (= p<(.') in a long cylindrical fuel element shown in Figure D. f. The concentration in the gap of the element depends on (D.I) 1 JL + J -AN = 0 id tu.e opeii^g of the defect tHe concentration is identically zero. With the 105 origin of the coordinate system located at the centre of the defect, the boundary condition is satisfied by >•' (4' ± k) - " (0.2) provided w, and 9, are much less than the diffusion length L where, (0.3) Far away from the defect, the concentration must be finite and approach the equilibrium value Rfg/A. This is the particular solution of (0.1) i.e., Np = -JJL (D. I,__^+ JL - .1 = „ p- Tf7^ 3?/ Using the method of separation of variables let Mg = Ht)2U) (D.6) Substituting this expression into (0.5) and dividing by >j>z yields, :)? z 1 1 * + i *l I (0-7) >;-'* F^ Z bz7^ " I/"" The first and second terms only depend on $ and z respectively and can be set equal to separation constants i.e., 1 1 d:> ^ dT^ = Y' (0.8) 10= «• (D.9) ? Y 2 + ,S = |, (D.IO) Symmetry guarantees *(})= $(-$) and Z(z)= Z(-2) , and in view of a finite concentration at a large distance from the defect, the homogeneous solution is given by in- Adding the particular solution (D.4) to (D.ll) and imposing the boundary conditions in (D.2), the general solution is K (0 l2) <•• (. -) - /« ; '••"'" ^ ' .^"' '"_[! - i Using FickV diffusion law .1 = -JTV\ (D.I 3) the flux into each of the four sides of the defect (see Figure D.I) is := ' " /J •• o"''1' /2 ' (D.l^a) Only these four sides contribute to the total flux since the concentration is assumed to be identically /.cro at t'ie defe<:t face and nearly /.c>ro everywhere in the space beneath the defect. The total release rate R is obtained by integrating the tlux over the four sides (total surface S) such that, -^ (D.I 5) Here dA = ndS where n is the unit normal into the defect from the surface element dS (see Figure D. t). Therefore for each side (D.l6b) and the total release rate is The gap thickness Jpin (D.16) has been replaced by h. Since the dimensions of the defect are much less than the diffusion length L, exponential terms can be approximated by <••'' 'V ""' 1 + -r - .'« " il o '''' •"• 7 - • 1 + ^-- (D. 13) Further, choosing - = u (which is a reasonable physical choice i.e., as f. * • , •' • i> and the concentration becomes independent of z,whereas, for an equal length and width 6 - Y) equations (D.10), (0.17) and (D.18) yield k 2U ll K ,, = ' o fw (0.19) In the above expression the effective defect diameter dc --*Jv/ + M- and R[,, is the constant source into the gap per unit volume of the gap (the gap volume -- J 7T p I h where Ls is the fuel stack length). Hence the fractional release into the coo)ant is given by, < APPENDIX E Rare Gas Diffusion Coefficient from Kinetic Theory The binary diffusion coefficient for a trace noble gas species diffusing in a continuum steam medium can be estimated from Chapman-Enskog kinetic theory. For a gaseous state at low density, the diffusion coefficient "> [2 ('n tne fi approximation) is, V1 • fJNr-l I. OOI.SS.S.s' - ---lrj_ in which M. , M , - molecular weights p = pressure (atin) T - temperature (K) Tj* = kT/El, Oj.,, i ]2/ k - molecular potential energy parameters in (A, K) o'l.])* •- collision integral (function of ^) For inter-diffusion of a non-polar gas (n) and polar gas (p), the molecular potential energy parameters o,-,p and rnp can be estimated from empirical combining laws using the individual Lennard-."Jones (non-polar) and Stockmayer (polar) potential parameters fl Ijfa +(I 1f 1/l nP = n p -" - (E-2) (;np " /cnli:p r-' (E.3) + 2a t u =rt a a s the where >, - ^ '^ t* ^^J^, n n/ n ^ n ' electronic polarizability of the non-polar gas (cm ')) and t* = u2/f/s > o~\) ( \< is the dipole moment of the polar molecule (debyes)). Using the reference values in Table E.I A and assuming a nominal gap temperature of ^700 K (see Appendix F), the low pressure quantity p.!'' is calculated from (E.I) in Table E.I B for a non-polar (Kr and Xe) and polar (H.O) gas pair. The high pressure diffusion coefficient is evaluated in Table E.I C using the expression^ ' Table E.I Calculation of Rare Gas Diffusion Coefficients from Kinetic Theory A. Reference Values Parameter Kr Xe Reference H2° 3.61 4.06 2.65 48 (Tables I-A and 3.10-1) 190 229 380 tS (Tables I-A and 3.10-1) 2.45 x 10-24 3.99 x 10-24 .. 59 (Table 1 -p. 411) — — 1.2 M\amu) 48 (Table 3.10-1) 83.8 131.3 18.015 49 (Table B-l) TC(K) — — 647.2 60 (Table II p. F-86) pc(atm) — 213.3 60 (Table II p. F-S6) B. Calculated Values Coupled Parametric Values Parameter Kr - H?O Xe - H2O Reference 3.10 3.32 Equation (E.2) 304 335 Equation (E.3) 2.31 2.09 Definition for Equation (E.I) 2 1.03 1.06 if8 (Table I-M) cm ' sec" ) .908 .744 Equation (E.I) Experiment Diffusion Coefficient Calculation Parameter FDO-681 FFO-102-2 Reference (Sample 2) atm) 75.5 101 Table 3.2 0.83 0.77 Figure E.i 9.08 x 10-3 6.26 x 10-3 Equations (E.I) and (E.4) 11. (I ' ..,. 1! lip where the correction factor p^]l/(p^l[) ] is derived from Enskog self- diffusion theory and from limited experimental data. Equation (E.I) agrees with experimental data at atmospheric pressure within 12 per cent ; however, the error associated with equation (EA) is difficult to determine as there are practically no data on the pressure dependence of p«&"i2> although unexpectedly good agreement within 12 per cenr was obtained between theory and experiment for the binary mixture of methane and ethane at 136 atm and 313 K. Correction factors for experiments FDO-681 and FFO-102-2 are evaluated using a reduced temperature ( - ) and pressure ( £ ), where Tc and pc is the critical temperature and pressure for H-,O respectively, and Figure E.I. Coolant pressures in Table 3.2 were assumed equal to the equilibrium gap pressures. Average noble gas diffusion coefficients (d&N ) are listed in Table E.I for each experiment. i 1 1 1 ! • I 1 Reduced Temperature 1.0 — -ZZ ~ 0.8 ^^ 0.6 0.4 FDO-681 (LFZ) 4 FFO -102-2 (A7E) —. •—• 0.2 I rt 1 i i i i i i i 0-1 0-15 0.2 O3 0>» CL5 0* 0.8 10 1^ 2JD 3.0 4£ Reduced Pressure (|) Figure E.I Generalized Chart for Seif-Diffusivities of Dense Gases (taken from Reference APPENDIX F Fuel Element Temperature Calculations The gap temperature for element A71: (operating at full power 67 k-.V/rn) is evaluated from methods proposed by Palmer for defected fuel (Reference M - (62) •\ppendix C) and typical AECL - Engineering Company calculations. For each temperature expression reference must be made to Table F.I for appropriate symbol descriptions, values and reference numbers. In summary, the bulk coolant temperature Tj,» sheath outside temperature Tso, sheath inside temperature Tsi, and fuel surface temperature Tfs are calculated using an iterative procedure from the general expression: I 1 r . r . h (F.I) SH -. C K s ;; Ii SsIi V,v. T5 = bulk coolant temp. Tso = sheath outside temp. Tsj = sheath inside temp. Further, the gap temperature T« is defined as g - With reference to Table F.I and equations (F.I) and (F.2), the following results are obtained for experiment FFO-102-2: Tb 255 °C Tso = 301 °c Tsi = 357 "c Tfs = 561 "c } T 459 C (732 K) S = °c Palmer obtained a gap temperature of ^670 K for an element (of typical CANDU design) operating at <*6 kW/m (at nominal CANDU PHT temperature and pressure conditions). This intermediate linear power was similar to that experienced by LFZ CfS kW/rn). Therefore, a nominal gap temperature of '>p700 K is appropriate for gap diffusivity calculations (in light of temperature uncer fainties in the above calculation). The diffusion coefficient increases roughly as the 1.65 power of T (at high temperatures) and hence the diffusivity is not strongly influenced by the temperature differences [or each experiment from the chosen nominal vaJue. Table F.I Symbols Used in Temperature Calculations Symbol Definition Value Used Reference or Calculated Number Empirical constant (nv2) .05 A Free flow area (m2) 3.626 x 10 — b Fuel burnup (MWh/kgU) 52 Table 3.3 c Empirical constant ^ 2.0 61,63 C Specific heat capacity (evaluated a' T^ and p) v.jvj^"^ rrc": f.Sffl 64 Equivalent hydraulic diameter r= -„—&£& 1 ,_•, (t.978 x 10"3 — m ^ ' X. nl'tted perimeter; l J 21 8.01 x 10" 65 Reference number (MWh/fission) 1026 65 Reference number (fissions/m^) 8 6] Sum of temperature jump distances for both surfaces ( LITI) Coolant mass velocity ( = 1*1/A) ',,,"^7) 3061 — Heat transfer coefficient for gap \ Heat transfer coefficient for gap =h, + h ) ( h^' ) 61,63 Symbol Definition Value Used Reference or Calculated Number k n . r _ m' 1 ) i Heat transfer coefficient for gap for solid component anR^r 1.75 61,63 1 Heat transfer coefficient for sheath to coolant f = k .\ti/D ) {-••,. -1 35.4 61 s c c c' *• m • • ' c. Meyer hardness of softer solid (Zircaloy) (kg/crn^) 8x 193 61 k Coolant thermal conductivity (evaluated at T^ and p) '—<-r) 0.6197 64 Thermal conductivity of the gas (steam) present in the surface roughess "valleys" (evaluated at Tg and p) ,'_!;_] 0.07399 64 Harmonic mean thermal conductivity of the 2 surface materials 6.185 61 =2k k /(k k 1 s u s u m' C Sheath thermal conductivity (evaluated at TS[) f—rp) 13.00 66 (p. 78) Average sheath thermal conductivity (evaluated at (T..+T, 1/2) (— 12.87 66 (p. 78) Thermal conductivity of UO2 surface (evaluated at Tfs) 65,66(p- 7*) Reference number f—A-r] 65 Mil ' {.' Coolant mass flow (kg/s) 1.11 Table 3.2 Symbol Definition Value Used Reference or Calculated Number Nu Nusselt Number (= o . 02 3 Re ' I'r '') 2S4.4 61 -\- 10.5 Table 3.2 P Coolant pressure (MPa) Interfacial pressure forcing surfaces together (-=Y , t ./ r . j (MPa) 9.6 61 Pi Pr Prandtl Number (= y C / k 1 .S321 61 q' Element linear heat rating (kW/m) 66.6 Table 3.3 Q Total loop power for trefoil carriage (kW) 89.3 Sheath inside radius (m) 6.125 x 10~3 Table 3.1 rsi Sheath outside radius (m) ____^_ 6.555 x 10"3 Table 3.1 rso /R '. + R , R Root mean square of surface projections {-! L_ ^1 f. n) "... .7 5 61 V'R; Arithmetic mean roughness heights of the fuel and cladding surfaces Rl -,.7 61 in contact (ym) R2 .\,.S Re Reynolds Number ( = GD /p) [A3 x 105 61 t Real separation of sheath and fuel surfaces (urn) 0 61 Sheath wall thickness (m) 0.^3 x 10"3 Table 3.1 Symbol Definition Valued Used Reference or Calculated Number Bulk coolant temperature Cc) 255 Equation F.I Fuel-to-sheath gap temperature CC) 459 Equation F.2 T Inlet coolant temperature CO 247 in Table 3.2 Fuel surface temperature ( C) 561 Equation F.I Sheath inside temperature Cc) s i 357 Equation F.I Sheath outside temperature Cc) 301 Equation F.I Yield strength of sheath (MPa) 137 61 Empirical constant 0.5 65 Void fraction of UO (%) 2.4 Table 3.1 Reduced UO temperature ( = __ T K_ .561 — 2 " 1000K-' 64 Dynamic viscosity (Evaluated at Tb and p) 1.066 x 10"* 3 3 UO2 density (kg/m ) 10.71 x 10' Table 3.1 Based on iterative procedure 117 APPENDIX G Thermodynamic Calculations Consider the equilibrium reaction CsKs) t Cs (aq) + r~(.-iq) k..i where the equilibrium constant Keq for the reaction is This constant is related to the Gibbs energy of reaction .'GR by the relation The Gibbs energy of reaction is obtained from the expression products roactdnts (G.4) where AGf is the standard Gibbs free energy of formation for a given species. The free energy for each species in equation (G.I) is evaluated at a nominal sheath inside temperature of 623 K (350 °C) below. i) Ionic Species (Cs and I) Gibbs energy values at higher temperatures can be calculated from 298 K values if the entropy at 298 K S°(298) and heat capacity Cp (as a function of temperature) are known, by the exact thermodynamic relation: AG°(T) = AG^(298) - S°(298)[T-298] - T / ^ dT + / C° dT (G.5) 2 98 ?98 Equation (G.5) may be approximated using a Criss-Cobble treatment ' if experimental heat capacity data is limited i.e., iGj(T) = AGJC98) - S°(J9S)[T-:981 - T-Cgl^ln^ + co^^r (G.6) where F°IT? = S"°(T?) ~ ^"(T]) LP'TJ In Tp/T] (G.7) For equation (G.7) a linear entropy correspondence between 298 K and T is assumed, S'(T) = n(T) + b(T)[SlJ(298)-5.OZ] (G.S) In the above equation Z is the ionic charge and a(T) and b(T) are parameters previously evaluated from experimental data up to 473 K (200 °C) (the validity of extrapolation above this temperature is uncertain). Using reference values in Table G.I A, extrapolated free energy values are calculated (by an appropriate integration using average heat capacities for the particular temperature ranges) and are listed in Table G.I B. Table G.I Calculation of Free Energies at 623 K (350 °C) for the Ionic A. Reference Values Cs+ (aq) I (aq) Parameter A Gf (298) (kc:al/mole)(?3) -69.79 -12.33 So(29a)(cal-deg-l-inol.-1)(53) 31.80 26.6 Cp[!;^ (cal-deg-'-mole-1/51* 34 -64 Extrapolated Entropy Parameters^!/ T(,<) a(T) b(T) a(T) b(T) 47 3 23.3 0.711 -30.2 0.981 523 29.9 0.630 -38.7 0.978 573 36.6 0.548 -49.2 0.972 623 43.3 0.465 -58.0 0.96S Average Heat Capacities Above 200"C (cal-deg-^mole"') 44 -85 (-0 I ",73 C 49 P =5?3 -117 54 -107 0 Gibbs Free Energies AGf (623) kcal/mole M/mole Cs (aq) -84.97 -355.5 I" (aq) -11.64 -48.7 11«.' ii) Csl The free energy for a temperature above 298 K can be calculated from the expression fiC^(T) = AC:',!(298) - [T where the energy function function i(T) = 220.810 + 41.8119 lnX + 1-267?10- + Li223. X' X + I32.292X (G.10) and where X = T x 10" . Hence using equations (G.9) and (G.10), and AG{ (298) = -340.6 kJ/rnole , the free energy of formation at 623 K is AGf (623) = -387.5 kJ/rnole. Finally using equation (GA) and the above results, the Gibbs energy of reaction A G^ - -16.7 k3/mole and therefore equation (G.3) yields an equilibrium constant Keq = 25. APPENDIX H Selected ENDF/B-V Decay Data Isotopic Decay Mode» Branching U-235 Yield (atoms/fission) Decay Constant Chain Fraction Direct Cumulative Half-Life X (s-1) (AMZ) 85 Ga 31 ( S-G) 1.000 2.939(-08) 2.939(-08) 86.97 ms 85 Ge 32 ( B-G, D.N.-G) (.800, .200) 4.410(-05) 4.413(-05) 249.96 ms 85 As 33 ( 8-G, D.N.-G) (.780, .220) 1.521 (-03) 1.5581-03) 2.03 s 85 Se 3* (B -G) 1.00 9.219(-03) 1.053(-02) 31.00 s 85 Br 35 (8 ->• M.S.) 1.00 2.520(-03) t.3O5(-02) 2.87 m 4.025(-03) 85m Kr 36 ( B-G, I.TVG) (.789, .211) 1.325(-05) 1.306(-02) 4.48 h 4.298(-05) 87 Ge 32 88 Ge 32 ( B-C) 1.00 2.410(-07) 2.410(-07) 129.00 ms 88 As 33 ( B-G) 1.00 3.239(-04) 3.241 (-04) 134.83 ms 88 Se 34 (6-G, D.N.-G) (.995, .005) 3.337(-03) 3.661 (-03) 1.50 s 88 Br 35 (B-G, D.N.-G) (.932, .068) 1.672(-02) 2.042(-02) 16.00 s 4.332(-02) 88 Kr 36 ( B-G) 1.00 1.475(-02) 3.550(-02) 2.84 h 6.780(-05) 131 Cd 48 (B-G) 1.00 6.998(-07) 6.998(-07) 106.17 ms 131 In 49 (B-G, 6-M.S., D.N.-G) (.8834, .1000, .0166) 2.906(-04) 2.913(-04) 280.00 ms 131m Sn 50 (B-G) 1.00 39.00 s 131 Sn 50 (B-G) 1.00 8.539(-03) 8.828(-03) 50.00 s 131 Sb51 (S-G, 6+ M.S.) (.932, .068) 1.698(-02) 2.581 (-02) 23.00 m 131m Te52 (8-G, l.T.-G) (.80, .20) 2.055(-03) 3.810(-03) 1.25 d 6.418(-06) 131 Te52 (B-G) 1.00 9.368(-04) 2.575(-02) 25.00 m 4.62K-04) 131 I 53 ( P- G, B-> M.S.) (.9891, .0109) 4.1541-05) 2.884(-02) 8.04 d 9.978(-07) 132 Cd 48 (B-G) 1.00 5.669(-08) 5.669(-08) 135.72 ms 132 In 49 (B-G, D.N.-G) (.959, .041) 6.742(-05) 6.748(-05) 120.00 ms 132 Sn 50 ( B- M.S.) 1.00 5.709(-03) 5.774(-03) 40.00 s 132m 5b 51 (8-G) 1.00 8.758(-03) 1.453(-02) 2.80 m 132 Sb 51 (8-G) 1.00 1.338(-02) 1.338(-02) 4.20 m 132 Te 52 (B-G) 1.00 1.492(-02) 4.283(-02) 3.26 d 2.46 K-06) 132 I 53 (S-G) 1.00 1.674(-04) 4.3001-02) 2.30 h 8.37 K-05) Isotopic Decay Mode * Branching U-235 Yield (atoms/'fission) Decay Constant Chain Fraction Direct Cumulative Half-Life X (S-I) (AMZ) 133 In 49 (B-G) 1.00 3.987(-07) 3.987(-07) 111.63 ms 133 Sn50 (B-G, D.N.-G) (.9998, .0002) 1.459(-O3) 1.459(-O3) 1.47 s 133 Sb 51 ( B-G, 6-M.S.) (.58, .42) 2.225(-02) 2.373(-02) 2.48 m 133m Te 52 (S- G, l.T.-G) (.87, .13) 2.847(-02) 3.844(-02) 55.40 m 2.085(-04) 133 Te 52 (6-G) 1.00 1.297(-02) 3.174(-02) 12.45 m 9.279(-04) 133m I 53 (I.T.- G) 1.00 6.873(-04) 6.873(-04) 9.00 s 7.702(-02) 133 I 53 (B-G, B- M.S.) (.9712, .0288) 1.126(-03) 6.699(-02) 20.80 h 9.257(-06) 133m Xe 54 U.T.- G) 1.00 2.079(-05) 1.950(-03) 2.19 d 3.663(-%) 133 Xe54 (S-G) 1.00 7.06S(-06) 6.702(-02) 5.25 d l.528(-06) 134 In 49 (8 -G) 1.00 4.069(-08) 4.069(-08) 80.56 ms 134 Sn 50 (S-G, D.N.-G) (.83, .17) 1.124(-04) 1.124(-O4) 1.04 s 134m Sb 51 (B-G) 1.00 2.638(-03) 2.638(-03) 850.00 ms 134 Sb 51 (B-G, D.N.-G) (.999i, .0009) 4.36M-03) 4.458(-03) 10.70 s 134 Te52 (B-G) 1.00 6.172(-02) 6.902(-02) 41.80 m 2.764(-04) 134m 1 53 ( B- M.S., l.T.-> G) (.02, .98) 3.496(-03) 3.496(-03) 3.70 m 3.122(-03) 134 I 53 (6-G) 1.00 4.826(-03) 7.727(-02) 52.60 m 2.196(-04) 135 Sn 50 (8-G, D.N.-G) (.914, .086) 6.339(-06) 6.339(-06) 417.77 ms 135 Sb 51 (B-G, D.N.-G) (.86, .14) 1.457(-O3) 1.463(-03) 1.82 s 135 Te 52 (8-G) 1.00 3.l24(-02) 3.254(-02) 19.20 s 3.610(-02) 135 I 53 (B-G.B- M.S.) (.835, .165) 3.O3O(-O2) 6.297(-02) 6.61 h 2.913(-05) 135m Xe 54 (I.T.- G) 1.00 I.713(-O3) !.210(-02) 15.29 m 7.556(-04) 135 Xe54 (fi-G) 1.00 7.059(-04) 6.539(-02) 9.09 h 2.118(-05) 137 Sb 51 (8-G, D.N.-G) (.8, .2) 5.236(-04) 5.236(-04) 477.85 ms 137 Te 52 (B-G, D.N.*G) (.978, .022) 3.837(-03) 4.256(-03) 3.50 s 1.980(-0I) 137 I 53 (B-G, D.N.-v G) (.928, .072) 2.804(-02) 3.224(-02) 24.50 s 2.829(-02) 138Sb51 (B-G) 1.00 6.589<-07) 6.589(-07) 173.36 ms 138 Te 52 (B-G, D.N.-G) (.944, .056) 6.740(-04) 6.747(-04) 1.60 s 4.3321-01) 138 1 53 (8-G, D.N.-G) (.974, .026) 1.530(-02) 1.594(-02) 6.50 s 1.066(-01) 138 Xe 54 (8- G) 1.00 4.77K-02) 6.424(-02) 14.13 m 8.176(-04) * B-» (M.S., G): Beta minus transition to a (meta-stable, ground) state D.N. -*G: Delayed neutron transition to a ground state l.T.-G: Isomeric transition to a ground state APPENDIX 1 Loop Design and Measurement I.I Description of the Loop In 1977 the X-2 Loop was completely rebuilt as an extended fuel defect loop. The pertinent design parameters for the loop are summarized in Table l.l(67)(see Figure 3.1 b). Table I.I The X-2 Loop Design Parameters (Courtesy of Atomic Energy of Canada Limited) Loop Typ« Extended defect and LOCA, pressurized water Reactor NRX Reactor Lattice Site(s) H24 downflo* Nominal Thermal Flux HI 8 x 1013 n.cm" . s~L Cosine Flux Length 303 cm ( 119. 3 in. ) Desiqn: Pressure 13.9 MPa ( 2,000 lb/m Flow- 1.1 kq/s ( 8,700 lb/h) Temperature 336 oc ( 637 °F) Heater (loop) ^) 112 kw Boiler N/A kw Heat Removal 200 kW Surge Tank Volume 0.057 m3 1 2.01 ft3) Pump Head!3' 170.7 m ( 560 ft 1 Construction Material stainless and carbon steel Coolant 3 3 Operating Volume 0.173 m ( 6.11 ft ) 3 3 Circulating Volume 0.146m ( 5.16 ft ) 3 3 Total Volujne 0.203m I 7.17 ft ) Chemistry (normal) pH 10(LiOH), 5-25 cmVkg H2 Purification: Flow 0.063 kg/s ( 500 lb/h) Ion-Exchange I.D. 7.8cm I 3.07 in.) Resin Volume 4200 cm3 ( 0.148 ft3) Monitors: Gamma Main pipe before the test section inlet Delayed Neutron After full-Elow filters Y - Spectrometer See text Test Section: Pressure Tube cold-worked Zr-2is wt.% Nb, other zr alloys Material 9.44 m ( 31 ft.) Length 38 mm ( 1.5 in.) Internal Diameter can be installed to decrease internal Flow Tube diameter Out-Reactor Test Section (1) Axial peak flux at the cell boundary. (2) Heaters for heating the coolant in the pressurized water mode - excludes heaters in the surge tank, boilers> etc. (3) Head in metre [feet) of flowing fluid. i.! i For the newly designed loop extensive on-line gamma-ray spectro'netry was installed at several locations (see Figure 3.1 a). One spectrometer, fixed at the inlet of the test section, is ijsed to measure the gaseous and dissolved fission £roducts (GFP). A second movable spectrometer is capable of scanning three separate zones of the loop piping; each zone consists of six different piping s irfaces, typical of the construction materials found in a power reactor. This particular spectrometer is dedicated to the study of the depositing jjssion groducts (DFP). The third spectrometer is located in the sidestream circuit, where the background activity is lower, and therefore more sensitive measurements can be made. Experiment FDO-681 was irradiated prior to 1977 when the loop only had a single monitoring zone. The spectrometer was located at the outlet of the test section because of generally low activity release. For experiments FFO-102-2 and FFO-103, only data measured by the GFP spectrometer were processed. 1.2 Spectrometer Design Both the new and old monitoring systems for the loop employed an intrinsic germanium spectrometer - model 1129-P2 (before 1977) and model GE4112-PGA (after 1977). The spectrometers have a resolution of generally better than 2 keV (FWHM) at 122 keV. The count rate for the spectrometers is kept within specified limits by using various levels of attenuation with collimators of different sizes (in addition, for the redesigned system, two rectangular detectors are also used in combination with a collimator). Dimensional data for the detectors as well as the detector/collimator combination used in each experiment are given below: Table 1.2 Detector/Collimator Combination for Experiments FDO-681, FFO-102-2 and FFO-103 Detector No.* Collimator Width Experiment I1 25 rnin (largest) FDO-631 1 25 mm (largest) FFO-102-2 2 25 mm (largest) FFO-103 * Detector No.: 1' = diode .\, 1 - diode R, 2 = diode B + diode C Diode Sue: A (diam. of IS.5 mm), B (25 mm x 6 mm), C (25 mm x 23 mm) (each diode has a thickness of 5 mm) The detector efficiency and geometry factor for the GFP spectrometer have been reported in Reference 1 of Appendix A.2 (for specified detector and collimator arrangements). Reference 68 discusses the general principles in the design of the spectrometry system, including a description of the cryostat- detector configuration, internal shielding effectiveness, switching arrangement and detector characteristics. 1.3 Discussion of Error Errors reported in Table k.\ for the isotopic fractional releases are generally within 20 per cent for most isotopes although a large error of 71 per cent is reported for Kr-87 in experiment FFO-103. This latter error follows directly from a large variance in the area of the full energy photopeak at 403 keV (the relative error calculated by the GRAAS code - see Appendix A.I - is approximately 3-'+ times larger than that for the other krypton isotopes). Since a greater level of attenuation was used for experiment FFO-103, because of the higher activity levels in the coolant (see Section 1.2), a prominent Compton background and relatively low count rate for Kr-87 are probably responsible for this large variance. In particular, the prominent Compton continuum completely obscurs the lower intensity peak for the shorter-lived isotope Xe-138. A systematic error is also introduced in the calculation of the fractional release as a consequence of an 8 per cent uncertainty in the loop calorinetry data (see Section 3.2.3). This error has the effect of shifting both the noble gas and iodines lines in the fractional release plots of Figure <*.l for each particular experiment, but does not alter the slope of these lines.