ML19227A327

Fission Product Behavior During Severe LWR Accidents: Modeling Recommendations for the Melcor Code System, Volume I: Fission Product Release from Fuel.

ML19227A327
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Issue date:	09/30/1988
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NUREG/CR-448 1 SAND85-2743 R3, R4, R7 FISSION PRODUCT BEHAVIOR DURING SEVERE LWR ACCIDENTS:

MODELING RECOMMENDATIONS FOR THE MELCOR CODE SYSTEM Volume I: Fission Product Release From Fuel D. A. Powers Published: September 1988 Sandia National Laboratories Albuquerque, NM 87185 Operated by Sandia Corporation )- .

for the U.S. Department of Energy U.S. NUCLEAR REGULATORY COMM\SS\ON Technical library ~ :__ ~

Report Collection * :: --,=..:::-~

Prepared for Division of Reactor System Safety Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commissiori Washington, DC 20555 Under Memorandum of Understandin g DOE 40-550-75 NRC FIN No. Al339

ABSTRACT Phenomena that influence fission product behavior during severe accidents at light water reactors are reviewed and recommenda-tions for the modeling of these phenomena in the MELCOR code system are presented. Specifically . modeling recommendati ons are presented:

1. for the grouping of fission products into chemical classes:

2. for release of fission products from degraded fuel in-vessel. during high pressure ejection of melt from the vessel; during steam explosions. and as the result of core-concrete interactions :

3. for the condensation onto and evaporation of fission prod-uct vapors from structural and aerosol surfaces. and of steam onto and from aerosols:

4. for the agglomeratio n and deposition of aerosols: and

5. for the removal of fission product vapors and aerosols by emergency safety features (e.g .. sprays. suppression pools. ice condensers. filters).

iii/iv

TABLE OF CONTENTS Volume I

1. Introduct ion 1-1 Reference s 1-6

2. Isotopes. Elements. and Chemical Classes 2-1 2.l An Introducto ry Descriptio n of Severe Accident source Terms and This Chapter 2-1 2.2 Definition s of Radioactiv e Materials 2-3 A. Fission 2-3 B. Beta Decay 2-4 C. Other Decay Processes 2-5 D. Neutron Capture 2-5 E. Other Capture Reactions 2-12 2.3 Inventorie s 2-14 A. Radioactiv e Materials 2-14 B. Justificat ion of Elemental Phenomeno logical Source Terms 2-21 C. Elemental Inventorie s of Fission Products 2-29 D. Need to Consider Nonradioa ctive Inventorie s 2-31 E. Inventorie s of Nonradioa ctive Materials 2-34 F. Chemical Classifica tion of the Elements for source Terms Models 2-38 2.4 Recommen dations for MELCOR 2-50 Reference s 2-51

3. Release of Fission Products and Generation of Aerosols During the In-vessel Phases of a Severe Reactor Accident 3-1 3.1 An Introducti on to the In-vessel Source Term and the Objective s of this Chapter 3-1 3.2 Nomenclat ure 3-4 V

TABLE OF CONTENTS (cont.)

3. 3 Fundamentals of the Release Process 3-7 A. Thermodynamics of Vaporization 3-9 B. Phase Distribution of Fission Products 3-29 C. Kinetics of Vaporization 3-35 D. condensation and Nucleation 3-42 E. summary of the Fundamentals of Vaporization Processes 3-50 3.4 Extant Models of In-Vessel Release 3-51 A. Gap Release 3-51 B. Diffusion Release 3-53

c. Meltdown Release 3-62 The Reactor Safety Study Model 3-63 The Light Bulb Model 3-64 The IDCOR Model 3-65 3.5 The CORSOR Model 3-68 3.6 Discussion of the First Order Assumption 3-75 3.7 Modifications of the CORSOR Model for Use in the MELCOR Code 3-82 A. Modifications to Account for surface Area Changes and Dilution During Core Degradation 3-86 B. Modifications to Account for Gas Phase Mass Transport 3-95 Flow Around a Sphere 3-102 Natural Convection From Upward and Downward Facing Surfaces 3-107 Flow Perpendicular to the Rod Axes 3-107 Flow Parallel to the Rod Axes 3-108 Effects of Discontinuities 3-111 Flow Through a Debris Bed 3-113 Correlations for Steel Structures 3-115 vi

TABLE OF CONTENTS (cont.)

C. Radionuclide Release From Fragmented Core Debris 3-117 3.7 Recommendations for MELCOR 3-118 References 3-120

4. Fission Product Release and Aerosol Generation Within the Reactor Containment 4-1 4.1 Introduction and Definitions 4-1 4.2 Primary Fissions Product Release 4-4 A. Release Associated with Melt Ejection 4-4 Recommendations for MELCOR Development Concerning the Source Term From Pressurized Melt Ejection 4-14 B. Release Associated with Core Debris Interactions with Coolant 4-15

• c.

Recommendations for MELCOR Development of a Source Term Associated with Steam Explosions Release During Core Debris/Concrete 4-24 4-24 Interactions Recommendations for the MELCOR Model of the Source Term From Core Debris/Concrete Interactions 4-39 D. Fission Product Release by Leaching 4-39 Recommendations to MELCOR Concerning the Treatment of Ex-vessel Leaching 4-'-42 4.3 Secondary Fission Product Release in containment 4-42 A. Resuspension of Deposited Aerosols 4-43 Recommendations to MF;LCOR Concerning Aerosol Particle Re-entrainment 4-49

• vii

• B.

TABLE OF CONTENTS (cont.)

Secondary Release From Water 4-50 Iodine Partitioning 4-50 Recommendation to MELCOR Concerning Iodine Partitioning 4-53

• Mechanical Release From Water 4-54 Recommendation to MELCOR Concerning Re-entrainment from Water 4-56 4.4 Conclusions 4-59 References 4-60 Volume II

5. Fission Product Transport and Deposition Including Vapor Condensation and Aerosol Agglomeration 5-1

6. Engineered Safety Features 6-1

7. Size of the Fission Product Behavior ODE Set 7-1

• viii

LIST OF ILLUSTRATIONS Figure Title 2.1 Some Important Beta Decay Reactions 2-6 2.2 Beta Decay Chains Initiated by Processes Other Than Fissioning 2-7 2.3 The Uranium Decay Series 2-8 2.4 The Thorium Decay Series 2-9 2.5 The Actinium Decay Series 2-10 2.6 The Neptunium Decay Chain 2-11 2.7 Fission Yields for 235u 2-15 2.8 Burnup of TMI Fuel Rods in Megawatt Days per Metric Tonne Uranium 2-18 2.9 Enrichment Pattern of Fuel in the TMI Unit 2 Core 2-20 2.10 Effect of Nonradioactive Aerosols on *the Time Dependence of the Concentration of Radioactive Aerosols 2-33 2.11 Competition Between Reaction of Te with Steel and Reaction of Te with Silver Aerosols 2-35 3.1 Poynting Correction Factors for Several

. Temperatures as a Function of*pressure 3-16 3.2 Vapor Species Produced by Barium oxide Vaporization as a Function of PH 2 /PH 2 o at 2000 Kand a Total Pressure of 10 Atmospheres 3-19 3.3 rand LRSS for Barium Oxide Vaporization as a Function of PH 2 /PH 2 o at 2000 Kand a Total Pressure of 10 Atmospheres. 3-21 3.4 Nucleation Rate of Tin at 2000 Kasa Function of the Super-saturation of the Vapor 3-46

3. 5 Comparison of Observed Releases of Fission Products From uo 2 at Temperatures Between 2273 and 2473 K with Those Calculated with the Light Bulb Model 3-66 ix

• Figure 3.6 LIST OF ILLUSTRATIONS Title Compariso n of Cubicciot ti*s Models of Fission Gas Release in Stearn and Inert Environme nts 3-69 3.7 Compariso n of the Temperatu re Dependenc ies of Release Rate Coefficie nts Calculated with the Original CORSOR Model and with Parameter s for the Model Modified to Have an Arrhenius Temperatu re Dependenc e 3-74 3.8 Compariso n of the Prediction s of Cesium Release by Two Models of the Release Kinetics Assuming the Core Heats at 4K/s to 2500 K 3-83 3.9 Compariso n of the Prediction s of Cesium Release From Two Models of the Release Kinetics Assuming the Core Heats to 2000 Kat 4K/s and to 2800 Kat 0.3 K/s 3-84 3.10 Effects of Heating Rate on the Release of Cesium 3-91 3.11 Effects of Burnup on Release of Cesium From Fuel Heated from 700 Kat lK/s 3-92 3.12 Effects of Initial Grain Size on Release of Cesium From Fuel Heated From 700 Kat lK/s 3-93 3.13 Effects of Melting and Slumping of the Fuel on Release of Cesium 3-94 3.14 -Effects of an Obstacle 1 Hydraulic Diameter Wide on the Relative Sherwood Number 3-114 4.1 Sequence of Photograp hs Taken During Expulsion of 2.5 Kg of Melt From a Vessel Pressurize d to 40. Atmospher es 4-6 4.2 Size Distributi on of Aerosols Produced During Pressurize d Ejection of Melts 4-8 4.3 Size Distributi on of Debris Produced When Melt is Ejected From a Pressurize d Vessel into Scaled Models of a Reactor Cavity (SPIT Test Series) 4-9 4.4 Speciation of Ruthenium Vapors in Air as a Function of Temperatu re 4-19 X

LIST OF ILLUSTRATIONS Figure Title 4.5 The Sum of the Partial Pressure of Ruthenium-Bearing Vapors in Various Atmospheres as a Function of Temperature 4-21 4.6 Size Distribution of Debris Formed by Melts Involved in Steam Explosions 4-22 4.7 Aerosol Production During Interaction of 200 Kg Molten Steel at 1700°C with Concrete 4-27 4.8 Aerosol Production Rates Estimated for Core Debris/Concrete.In teractions at the Surry Plant 4-30 4.9 Estimates of the Amount of Tellurium Remaining in the Core Debris During Interactions with Concrete 4-33 4.10 Estimates of the Release of Ba and Sr During Core Debris/Concrete Interactioris 4-34 4.11 Decontamination of Aerosol-laden Gas by a Saturated Water Pool 7 Meters Deep as a Function of Mean Particle Size 4-37 4.12 Decontamination of Aerosol-laden Gas by a Saturated Water Pool of Various Depths 4-38 4.13 Dependence of Normalized Particle Adherence Force on Relative Humidity 4-47 4.14 Resuspension of Glass Particles From a Stainless Steel Plate as a Function of Gas Velocity and Particle Size 4-48 4.15 Bounding Estimates Obtained with the Brockmann Model of Entrainment of Water During Containment Depressurization as a Function of the Contain-ment Hole Size 4-57 4.16 Mean Particle Size Predicted with the Brockmann Model of Entrained Water During Containment

. Depressurization as a Function of the Size of the Hole in Containment 4-58 xi

LIST OF TABLES Table Title 1.1 Fission Product Processes 1-4 2.1 Thermal Neutron Capture Cross Sections for Elements Found in Reactor Structures 2-13 2.2 Comparison of Fission Yields From 235u 92 and 239pu 2-16 94 2.3 The B-Decay Series Involving Te, I, Xe, and Cs Isotopes 2-28 2.4 Fission Product Inventories in a PWR Core 2-30 2.5 Compositions of Important Structural Alloys 2-39 2.6 Classificatio n of the Elements into Chemically Similar Groups 2-43 2.7 Alphabetical Listing of Elements and Their Classificatio n 2-44 2.8 Importance Ranking of Radionuclide s in Terms of Inventory, Dose, Curies, and Mobility 2-49 3.1 Features of Severe Reactor Accidents That Ought to Affect Release 3-3 3.2 Estimates Made in the Reactor Safety Study of Radioactivit y Release During In-vessel Stages of a Severe Accident 3-5 3.3 Popular Equations of State 3-13 3.4 Popular Models for Activity Coefficients 3-17 3.5 Some Vapor Species That Were Not Considered in the Reactor Safety Study

• 3-23 3.6 Experimental Partition Coefficients for Species Between uo 2 and Iron 3-34 3.7 Parameters for the Gap Release Model Developed at Oak Ridge 3-54 3.8 Parameters for Booth Diffusion Model 3-57 xii I_

LIST OF TABLES Table Title 3.9 Coefficients for the CORSOR Model 3-72 3.10 Some Kinetic Expressions for Solid Decomposition Reactions 3-76 3.il Some Data From Out-of-~ile Tests of Radio-nuclide Release From Irradiated Fuel Rods 3-78 3.12 Kinetic Parameters and the Chi~squared Statistic for the Quality of Fit of Three Models to the Cesium Release Data 3-81 3.13 Mass Transfer Coefficients for Configurations That Develop During Core Degradation 3-103 4.1 Radiological Effects of Refractory Fission Products in Comparison to Cesium and Iodine 4-3 4.2 Solubilities of Steam and Hydrogen in Core Debris* 4-12 4.3 Radionuclide Release Associated with Steam Explosions in the Reactor Safety Study 4-17 4.4 Release During Core Debris Interactions with Concrete as Estimated in the Reactor.

Safety Study 4-25 4.5 Elements and Vapor Species Considered in the VANESA Code 4-29 4.6 Default Compositions for Aerosol From Core Debris Interactions with Concrete 4-40 4.7 Comparison of Air Flow and Acceleration as Mechanisms for Aerosol Removal 4-45 4.8

• Effects of Particle Composition and Surface Characteristics on Particle-Surface Adherence 4-45 4.9 Effect of surface Roughness on Particle Adherence 4-46 4.10 Some Relevant Solution Phase Equilibria 4-51 xiii

CHAPTER 1 INTRODUCTION Probabilistic Risk Assessment. The probabilistic assessment of the risks of severe core damage accidents at a nuclear power plant is called a PRA. A PRA analysis identifies and delineates those combinations of events that can lead to a core melt acci-dent. and estimates the frequency of occurrence of each such combination of events and of the consequences of each event combination.

The first two nuclear . reactor PRAs. those for the Surry and Peach Bottom nuclear power plants. were performed as a part of the Reactor Safety Study [l] using analytical methods that were later implemented in the computer codes. MARCH [2]. CORRAL [3].

and CRAC [4]. During the last decade. user experience and peer reviews have identified serious deficiencies in this series of PRA codes including (1) inadequate or inconsisten~ treatments of important phenomena or plant features. (2) coding that does not easily permit the uncertainties associated with predictions obtained using these codes to be estimated. (3) code structures that do not facilitate incorporation of alternative or improved phenomeno.logical representations. (4) interfaces that are poorly matched. and (5) poor documentation.

To overcome these deficiencies the Nuclear Regulatory Commission (NRC) initiated in 1982 a major multi-year program called MELCOR that has as its objective the development of a new system of risk assessment codes. the MELCOR Code System. which (1) models appropriately all phenomena essential to the descri~-

. tion of severe -Light Water Reactor* (LWR) accidents. (2) provides credible predictions of the consequences of severe accidents.

(3) permits meaningful estimates of the uncertainties associated with those predictions to be made. and (4) has a structure that facilitates the incorporation of new or*a1ternative phenomenolo-gical models.

Architecture of _the MELCOR Code System. The MELCOR code system will be .structured. modular. integrated (matched inter-faces). and portable (coded in ANSI FORTRAN 77). Discrete phenomena

• or groups of closely coupled phenomena will be coded in separate modules. This will facilitate modification or re-placement of phenomenological representations. Modules will be variably dimensioned. which will allow system nodalization (com-partmentalization) and the size of sets of ordinary differential equations . (ODEs) to be easily changed. Because all parameter values will be externally accessible. sensitivity and uncer-tainty studies will be relatively convenient to perform with the MELCOR code system (at least by comparison to other PRA codes).

1-1

The MELCOR code system will have four structural levels:

Level 1. executive control; Level 2. data management; Level 3, phenomenolog ical representatio ns; and Level 4, numerical imple-mentations. Levels 3 and 4 are likely to be closely coupled.

Ex-plant consequences (i.e.. heal th effects and economic consequences ) will be solved wholly separately from in-plant thermal-hydr aulic processes and fission product behavior, which will be closely coupled but solved separately. For each time step. the solution for the thermal-hydr aulic equations wiil be developed simultaneous ly for all control volumes (-15 for the reactor

• coolant system. -10 for the containment building. -1 for the auxiliary building). Then. using the thermal-hydr aulic solution as input. the fission product behavior equations will.

be solved. one control volume at a time. Where necessary. the solution for fission product behavior from the previous time step will be used to support solution of the thermal-hydr aulic equ~tions during the current time step.

• Phenomenolog ical Assessments. In order to identify those phenomena essential to the description of severe LWR accidents (i.e .* the set of phenomena that should be treated by the MELCOR Code System). a series of phenomenolog ical reviews have been performed as part of ( or in support of) the MELCOR Program.

Reviews of thermal-hydr aulic processes [ 5. 6] and ex-plant con-sequence phenomena [ 7-10] are reported elsewhere. This report presents the results of the review of fission product behavior conducted as a part of the MELCOR Program.

Fission Product Behavior. During the analysis of hypothet-ical* severe accidents at Light Water Reactors. fission product behavior is modeled in order to develop realistic source terms as a starting point for the prediction of the ex-plant conse-

• quences of the accident. The essential features of an ex-plant source term are the masses and identities of the radioisotope s released from tlle failed LWR containment. their chemical and physical forms. and the heat and moisture content and release time and duration of the plume that contains them.

Specificatio n of t*he masses. identi ti.es. and forms *of the radioisotope s released to the environment upon containment failure requires (1) calculation of the rates of release

• of radioactive materials from overheated or molten fuel. (2) speci-fication of the chemical and physical forms of the released radioactive materials (e.g .* CsI vapor. aerosol of a given chemical composition) . ( 3) calculation of their rates of trans-port through and deposition and resuspension within the primary system and the containment. and (4) specificatio n of changes in their chemical and physical forms during transport. deposition.

or resuspension . Accordingly. this report will discuss the 1-2

• processes species (release, agglomeration, deposition, (vapors, aerosols), and physical states resuspension),

(gas-borne, deposited or condensed on surfaces, suspended or dissolved in water), that must be treated in order to develop source terms adequate for the calculation of ex-plant consequences. Determi-nation of the heat and moisture content and the release time and duration of the radioactive plume will not be discussed, since these quantities are generally not calculated by the fission product behavior portions of severe accident risk analysis codes.

Processes. Review of pertinent literature including documentation for published fission product behavior codes suggests that the processes listed in Table 1.1 should be treated by the fission product behavior modules of the MELCOR code system. When a process listed in Table 1.1 can take place by different mechanisms, Table 1.1 also 1 ists those mechanisms that make significant contributions to its rate. . This review concluded that adequate mathematical representations are available for each mechanism and process that should be treated by the MELCOR code system.

Species and States. Because the rate of change with time of the mass of a species (vapor or aerosol) in a state (location within a control volume) can be appropriately represented by an ordinary differential equation comprised of terms which give the contribution of individual rate processes to the total rate of change of the species, the MELCOR fission product behavior equa-tions will consist of a set of ordinary differential equations.

Since a separate ODE is required to describe each species in each

• state in which it can exist, detailed descriptions of fission product behavior (descriptions that involve many species and many states) can easily produce fission product behavior ODE sets that are very large (-500 ODEs). Since routine MELCOR calculations probably will be unacceptably slow if the fission product ODE set cannot be held to something like 50 ODEs, this report will also present the technical basis for adequately modeling fission prod-uct behavior using a number of species and states that produces an ODE set of approximately 50 ODEs (as few as 25 for scoping calculations; as*many as 100 for sensitivity calculations).

Report* Organization. Reduction of the size of the MELCOR fission product ODE set to a computationally tractable size, by limiting the number of species and states modeled by the MELCOR code system, is examined in Chapters 2 and 7 of this report.

Chapters 3 through 6 review the rate processes that significantly influence fission product behavior and recommend a representation for each process.

1-3

• Species Table 1.1 Fission Product Processes Process Fission Product Release from Fuel Vapors Chemical Reactions Gas Phase (gas-borne)

Solution Phase (dissolved in water)

Solid Phase (on surfaces)

Condensation on Aerosols and Surfaces Brownian Diffusion Turbulent Diffusion Evaporation from Aerosols and Surfaces Intercompartment Flow Removal by Engineered Safety Features Sprays Ice Condensers Suppressions Pools Filters Fans Decay Heat

• Aerosols Formation Gas-to-Particle Conversion Mechanical Aerosolization Agglomeration Brownian Coagulation Turbulent Coagulation Gravitational Coagulation Deposition on Surfaces (walls. equipment)

Brownian Diffusion Turbulent Diffusion Gravitational Settling Thermophoresis Diffusiophoresis Resuspension from surfaces Intercompartment Flow Removal by Engineered Safety Features Sprays Ice Condensers Suppression Pools Filters Fans Decay Heat Steam Condensation on Aerosols Evaporation from Aerosols 1-4

Chapter 2 begins with an examination of radioactive decay and isotope effects. then develops the case for reducing the number of species modeled by negiecting isotope effects and grouping chemical elements into classes. and finally recommends a set of element classes for use in the modeling of in- and ex-vessel release processes. In-vessel release processes are then discussed in Chapter 3 and ex-vessel processes in Chapter

4. Chemical reactions of vapors and natural vapor deposition processes. and natural deposition processes for aerosols and aerosol agglomeration mechanisms are reviewed in Chapter 5.

Removal of gas-borne species by Engineered Safety Features (ESFs) is discussed in Chapter 6. Chapter 7 examines methods for modeling aerosol agglomeration and recommends a method for use in the MELCOR code system. discusses the number of aerosol species required by the recommended agglomeration method. and then presents the technical basis for reduction of the fission product behavior ODE set to a tractable size by 1 imi ting the number of states modeled and by further reduction of the number of species modeled by combination of the chemical classes developed in Chapter 2 into components.

Lastly. for convenience this report has been divided into two volumes: Volume I. Fission Product Release From Fuel. and Volume II. Vapor and Aerosol Processes. Thus. Chapters 1 through 4 are presented in Volume I and Chapters 5 through 7 in Volume II.

1-5

REFERENCES

1. U.S. Nuclear Regulatory Commission, Reactor Safety Study An Assessment of Accident Risks in U.S. Commercial Nuclear Power Plants, WASH-1400 (NUREG-75/014), October 1975.

2. R. 0. Wooton and H. I. Avci. MARCH (Meltdown Accident Response Characteristics) Code Description and User's Manual, BMI-2064 NUREG/CR-1711 Battelle Columbus Laboratories, Columbus, OH, October 1980.

3. P. C. Owzarski and A. K. Postma, CORRAL Code User's Guide Addendum to Appendix J of Appendix VI I of the Reactor Safety Study - An Assessment of Accident Risks in U. s.

Commercial Nuclear Power Plants, WASH-1400 (NUREG-75/014),

October 1975.

4. L. T. Ritchie, J. D. Johnson, and R. M. Blond, Calculations of Reactor Accident Consequences, Version 2

( CRAC2): Computer Code User's Guide, NUREG/CR-2 3 2 6, SAND81-1994, Sandia National Laboratories, Albuquerque, NM, February 1983.

5. G. G. Weigand, et al., Thermal-Hydraulic Process Modeling in Risk Analysis: An Assessment of the Relevant Systems, Structures, and Phenomena, NUREG/CR-3 98 6, SAND84-1219, Sandia National Laboratories, Albuquerque, NM, August 1984.

6. S. R. Greene, Realistic Simulation of Severe Accidents in BWRs Computer Modeling Requirements, NUREG/CR-2940, ORNL/TM-8 517, Oak Ridge National Laboratories, Oak Ridg*e, TN, April 1984.

7. R. M. Ostmeyer and J. c. Helton, Exposure Pathways Models for Accidental Radiological Releases, Sandia National Laboratories, Albuquerque, NM (in preparation).

8. G. E. Runkle and R. M. Ostmeyer. An Assessment of Dosimetry Data for Accidental Radionuclide Releases, NUREG/CR-4.185, SAND85-0283 Sandia National Laboratories, Albuquerque, NM, August 1985.

9. J. S. Evans et al., Health Effects Model for Nuclear Power Plant Accident Consequence Analysis, NUREG/CR-4214, SAND85-7185, Sandia National Laboratories, Albuquerque, NM, July 1985.

10. R. P. Burke, et al., Economic Risks of Nuclear Power Reactor Accidents, NUREG/CR-3673, SAND84-0178 Sandia National Laboratories, Albuquerque, NM, April 1984.

1-6

CHAPTER 2 ISOTOPE S. ELEMENTS. AND CHEMICAL CLASSES 2.1. An Introduc tory Descrip tion of Severe. Acciden t Source Terms and This Chapter severe acciden ts at commerc ial nuclear power plants would involve damage to the reactor fuel. emission s of radioac tivity.

and general plant conditio ns more drastic than those consider ed in the design and safety analysis of the plants. Great interes t has develope d in severe reactor acciden ts since the publica tion of the Reactor Safety Study [l] and the mild. but still beyond-design-b asis. acciden t at the Three Mile Island Generat ing Station [2]. The interest arises because there is the possibi l-ity the severe reactor acciden ts could lead to the uncontr olled release of radioac tivity from a nuclear power plant which would have life-thr eatenin g conseque nces and produce long-ter m property damage. Because of this possibi lity. severe reactor acciden ts make the largest contribu tion to the risk that must be associat ed with the use of nuclear power [3].

Acciden ts of sufficie nt severity to produce dire conseque nces have never occurred in U.S. commerc ial nuclear power plants.

The progress ion and conseque nces of these acciden ts can only be estimate d in analytic studies.

• Analytic studies of severe reactor acciden ts consist of several key element s:

1. The probabi lity that a severe reactor acciden t might be initiate d is estimate d.

2. The phenome na that arise in a severe acciden t are describe d and calculat ions made to determin e if and when uncontr olled release of radioac tivity will occur.

J

3. The amount of radioac tive materia l that might escape the plant is calculat ed.

4. The consequ ences of exposing people and property to the radioac tivity expelled from the plant is estimate d.

The lack of experien ce with severe reactor acciden ts has made exercise s of this type difficu lt and the results uncerta in.

sirong biases have been built into the analytic studies so that any errors in the analyses will accrue toward overpre dicting the severity of acciden ts that go beyond the design basis of the plants.

2-1

• power Past analyses of severe accident s have come under substan tial criticis m because of feelings that the conserv atism of the anal-yses to err~on the side of overpre dicting acciden t severity has_...---

been carried too far.

plants may be There is a percepti on that modern nuclear better able to cope with even the severes t acciden ts than has been admitted in the past. The relative ly inconse quential events associat ed with the acciden t at Three Mile Island Unit :Jf2 have bolstere d the confiden ce that natural processe s have been neglecte d which will substan tially reduce the amount of radioac tive materia l inflicte d on the environm ent.

even if acciden t phenomen a lead to containm ent failure.

The assessm ents of acciden t phenomen a and the estimate s of radioac tivity release are the elements of severe acciden t analyses that appear to embody the greates t conserva tism that can be removed by further. more careful study. The further studies of these elements may allow enginee ring bounds on the calculat ions to be replaced by realisti c evaluati ons based on mechan istic. physica l processe s. Many research programs are now underway to provide the greater understa nding of severe acciden t phenomen a and the behavior of radioac tivity necessar y to conduct more realisti c analyses .

This documen t addresse s the subject of radioac tivity behavio r during severe acciden ts. Analysis of the behavio r of radioac tive materia ls during severe acciden ts begins by dividing the behavio r into several elements :

1. Release of radioac tive material from the reactor fuel so it can be transpo rted.

2. Transpo rt of the radioact ive materia l to location s where it can escape the confines of a reactor plant.

3. Behavio r of the radioact ive materia l while it awaits developm ent of a pathway out of* the plant or the chance to follow such a pathway.

The first of these elements of severe acciden t analysis .

release of radioac tive materia ls from the reactor fuel. can be further classifi ed in terms of (a) release from fuel within the reactor vessel. and (b) release from fuel that has escaped the reactor vessel. The processe s that lead to II in-vesse l II and 11 ex-vess el II release are discusse d in Chapter s 3 and 4 of this documen t.

Before delving into the release and transpo rt processe s. it is useful to establis h what material s are released and how much of each materia l might be present during a reactor acciden t.

Establis hing the invento ries of materia ls that might be released in a reactor acciden t is the first objectiv e of this chapter.

It is found that there are many radionu clides whose release ought 2-2

to be of interest. Further. nonradioactive species from struc-tural materials. control rods. fuel cladding. and the like may be vaporized and may form aerosols during an accident. Since vapors of these nonradioactive species should affect behavior of the radionuclides. their release. too. is of interest. Quite clearly. the number of releasable materials that could be of interest gets quite large. Tracking the behavior of all these materials could strain the capacity of even the largest computer models. Consequently. definition of a basis for categorizing and simplifying the materials released during a severe accident i~ a second objective of this chapter.

2.2. Definitions of Radioactive Materials

_ Radioactive materials are produced by a variety of processes during normal operations of nuclear power plants:

A. Fission .

Unstable nuclei can spontaneously fragment to produce.

usually. two daughter isotopes that may also have unstable nuclei. Some important isotopes and their half-lives* for spontaneous fissioning are:

• Isotope 236u 92 Half-Life for Spontaneous Fissioning*

73.6 y 23Bu 8 X 1015 y 92 240pu 1.2 X 1011 y 94 244cm 1. 4 X 107 y 96 2s2cf 66 y

• 98 256Fm 2.4 h 100

"'Abbreviations used in this report in connection with half-lives are: year= y: days= d:. hours= h: minutes= m: seconds= s 2-3

Far more important than spontaneous fissioning is the fissioning of unstable nuclei brought on by neutron bombardment. Fissile nuclei in commercial light water reactors are:

235u. 239pu. 24lpu. and 233u 92 94 94 92 Normally. fissioning of a nucleus is thought to be a "binary" process. that produces two daughter nuclei. But. once in about 200-500 normal. binary. fission events a third particle is formed

[4~6]. M6re rarely. four or more nuclei are formed during fissioning. Alpha particles are the most common additional nuclei formed in higher order fission processes. But. other nuclei can be formed. Comparative yields (normalized to the 4He yield set equal to 100) of nuclei for higher order fissioning of 252cf are listed below [6]:

1.1 0.63 6.42 0.008

• 100 1.95 0.06 Li 0.126 Be 0.156 Ternary fissioning is such a rare event it is normally neglected.

But. it.is obvious ternary fissioning can be a source of tritium.

Products of. fissioning are not simply described. These products will be discussed in the section below dealing with inventories.

B. Beta Decay The nuclei produced by fissioning are typically quite unstable and radioactively decay. The most important decay process involves emission of an electron (_~e ~ B-). a neutrino *

• 2-4

and often a gamma ray. This is called beta decay and it results

• in increasing the atomic number of the decaying isotope by one.

with no change in the mass number . . Some of the important decay chains initiated by nuclear fissioning in light water reactor fuels are shown in Figure 2.1. Beta decay chains initiated by processes other than fissioning are shown in Figure 2. 2.

that naturally occurring isotopes can undergo beta decay.

Note Some of these processes are listed in Figure 2.2.

c. Other Decay Processes Other nuclear decay reactions are (a) emission of a gamma ray (y). (b) emission of a positron (B+) and an antineutrino.

and (c) emission of an alpha particle c~ = ~He). Four decay chains of importance to light water reactor safety are shown in Figures 2.3-2.6. These are the (a) uranium decay chain. (b) the thorium decay chain. (c) the actinide decay chain. and (d) the synthetic neptunium decay chain.

~ecay processes of various natures are continually being discovered. For instance. in 1983 a two proton decay reaction was first discovered [7]:

22

_B_+_ 12Mg D. Neutron Capture Absorption of a neutron does not necessarily 1-ad to fission-ing of* a nucleus. The unstable isotope created by absorption of a neutron can instead decay by other processes.

Within *light water reactor fuel. neutron capture is respon-sible for* formation of transuranic elements. Some example reactions and the decay processes set off by these reactions are:

239 240 94Pu + n -+ 94Pu + 'Y 23Bu + n -+ 239u 92 . 92 + 'Y 240 94PU + n -+

241 94PU + 'Y -

B-241 95Am 241 95Am + n -+

242 95Am + 'Y B-242 96cm 2-5

• 93 JS Br -

8-93 36 l.Js 93 Kr - - -

8- 37 Rb S.8s 8-93 38 Sr 7.Sm 8-93 39 10.2h* 93 Y ----

8- 40 9.Sx105y 93 Zr - - - - -

8- 41 Nb (Stable) 72\ 4.1* lJJ* 87\ 52* 2.4\ 20.8h 13311 Xe Te 8-\ ~

I*-,.

52 54

~ -

13] 133 s~ 13\ 52* I 51 SJ

\28\

4.1'11 8-133 52 Te~---~

8-

\

98.6\

20.8h 8-133 54 Xe S.27d 8-13]

ss CH (Stable) 30\ 6.7h 135*

Xe 135 Te-30& 135 l

I 8- 54 11'. ,.

52 8- SJ N

I

°' \

70\

6.7h 8-

~

135 54 Xe 9.2h 8-135 55 Cs 2.6x10 6 y B-135 36 Ba (Stable) 4\ 24.4s 136

~ Xe (Stable)

I 8- 54 137 52 Te 3.Ss 8-137 53 \

I 24.4H I.

. 137 Xe 3. 911 137 Cs I

92\ 30.ld 13-

. 137*

56 Ba 2.57111 96\ B- 54 8- 56

~ll7 Ba (Stable) 8\ 0- 56 Figure 2.1. Some Important Beta Decay Reactions (Half-Lives Indicated Above Arrows to Products)

• A. Neutron Capture Initiation 239 92 u

23m

.a-239 93 Np 2.3d 13-239 94 Pu 241 15y 241 Pu Am 94 a- 95 242 242 Am Cm 95 13- 96 234 24d 234 l.lm 234 Th Pa u 90 13- 91 .s- 92 94 n 95 65d 95 35d 95 Zr -----+- Zr Nb Mo (Stable) 40 40 .s- 41 .s- 42 B. Naturally Occurring Isotopes 14 5770y 14 C N cs.table) 6 .a- 7 40 l.3x109v 40 K (rtat'l. abund. = 0.0118\) Ca (Stable) 19 .a- 20 48 2

Ca (nat' 1. abund. = 0.18\)

2x1ol6y a-48 21 Sc 41h

.a-48 22 Ti (Stable) 87 4.7x1olOy 87 Rb (nat'l. abund. = 27.85'\) Sr (Stable) 37 .a- 38 Figure 2.2 Beta Decay Chains Initiated by Processes Other Than Fissioning 2-7

5 4 2.4Bxl 0 y 5

l.1Bm 24.ld 4.5lxlO y 7.52xl 0 y 234Tb ..,.__ _ _ __

226Ra ..,.__ _ __

a. a. -100,a - a- a.

1622y a.

l. Js 99.96\ 19.7m 214 l.6x10 -4s 0.02\ J.osm .. 21eAt ----- ----- ~ Po

~ I \

N 91.Bh 222Rn _ _ _,..

I a- a- a.

I co a-a.

99.98\

3.05m 214

\ -.~~_ __,... .,

a.

Pb~

26.Bm /

a-

-a-- 1.32a /

5.0ld a-13B.4d 206 Pb (Sta ble) ----- -

a.

Figur e 2.3. The Urani um Decay Serie s

. 10

1. 39xl0 y 6.7y 232Th* 228Ra

a. .a-6.13h .a-54.Ss 3.64d 224 1 - 9Y 220Rn - - - - -

Ra - - - -

a. a. a.

0.1586 a.

66.3\ 60.6m 3xl0 -7 s 212Po 212Pb 10.6h 212Bi I .a- a. ~

208Pb (stable)

,.a-

\ 60.6m

. 208Tt 3.lm

/

33. 7\ a. .a-

. re 2 .4.

F 1gu The Thorium Decay Series 2-9

B 7.llxlO y 235U 231Tb a.

25.6h a-18.17d 22y 98.B'\

r::--

227Tb ~

219 80

11. 7d (I.

223Ra a-

"' 227Ac 3.4Bxlo 4 y (I.

231Pa N

I I-'

\ 22m a-223Fr ~

22y

a. 1. 2\

/

0 3.926 (I.

0.32\ 2.15m 0.528

,-~~~~~~ 211P

/ a- o.~

l.BJxlO -2 s 36.lm

- - - ~ 211Bi (I. a-

"'- 2.15m 4.79m JI

"'-----~-~~ 207Tl _______/

99.68\ <I. a-Figure 2.5. The Actinium Decay Series

27d 237N 233P 93 p 91 a

a. .a-5

1. 62xlO y a.

10d 14.8d 7340y 221F 225A 225R 229Th 87 r 89 C 88 a 90

a. .a- a.

4.8m a.

2% 47m 2.2m 0.018s 8.3h 209 217At - - - - ~ 213B.1 209Pb B.1 BS . 83 82 ----- 83 a.

\ 47m 213 8 4 Po 4.2xl0 s

-6/ 13-98% 13- a.

Figure 2.6 Neptunium Decay Chain 2-11 I

Neutron capture is responsible for making structural materials in a reactor rad:i,.oacti ve. The . abi 1 i ty of s tructura 1 materials to capture a neutron depends on the 11 neutron capture cross section" of isotopes in the material. These cross sections depend on the energy of the neutron. For light water reactors.

so-called thermal neutrons--.energies on the order of kT. where k is the Boltzmann constant and Tis the absolute temperature--are of greatest interest. Thermal neutron capture cross sections for isotopes of structural materials in light water reactors are listed in Table 2.1.

Absorption

• of neutrons by structural elements can produce unstable nuclei. Som*e of the radioactive products of neutron capture by structural materials are also shown in Table 2.1 along with the half-lives and decay processes of these product isotopes.

Generation qf radioact.ive species in structures by neutron capture is probably not important for severe accident analyses.

At shutdown. radioactive species in structures in a PWR core with a fuel burnup of 33,500 MWd/ton will decay at a rate of about 3 x 107 curies. Fission products and actinides in the fuel will decay at a rate of about 2 x 1010 curies.

Most of the radioactivity of structures comes from the isotopes [B]:

Slcr 19% of curies at shutdown 39% of curies at shutdown 4% of curies at shutdown 60mc 0 12% of curies at shutdown 9Szr 9% of* curies at shutdown 8% of curies at shutdown 117msn 5% of curies at shutdown Activation products produced in some types of concrete that could be of interest are 63 . .

• N1(t 112

= lOOy), 54 Mn(t 112 = O.BSy),

152 41 5 39 = 270y). and Eu ( t = 13y). Ca(t 112

= 10 y), Ar(t 112 112 14c(t 1 ; 2 = 5700Y).

E. Other Capture Reactions Besides neutrons. capture of alpha particles and electrons can produce new unstable isotopes. Some example reactions are:

2-12

Table 2.1 Thermal Neutron Capture Cross Sections for Elements Found in Reactor Structures Cross Natural Section* Product Half-Isotope Abundance (%) (Barns) Isotope Life Decay Process 50v 0.24 -200 51V 51V 99.76 4.5 52v 3.77m B-50cr 4.31 17 5lcr 27.8d B-52Cr 83.76 0.8 53Cr 53Cr 9.55 18 54Cr 54Cr 2.38 0.38 55cr 3.5m B-55Mn 100 13.3 56Mn 2.58h B-54Fe 5.82 55 2.7y 2.5 Fe Electron capture 56Fe 57 91.66 2.7 Fe 57Fe 58 2.19 2.5 Fe 58Fe 59 0.33 1.0 Fe 45d B-59co 60 100 18 co 5.27y B-. "Y 58Ni 59 4 67.88 4.4 Ni 8xl0 y Electron capture 60Ni 61 26.23 2.6 Ni 61Ni 62 1.19 2 Ni 62Ni 63 3.66 15 Ni 92y B-64Ni 65 1.08 1.6 Ni 2.56h B-. "Y 107Ag 51.82 40 lOBAg 2. 4m B-. Electron capture 109Ag 48.18 84 llOAg 249d B-llOCd 12.39 0.2 111 mcd 49m "Y lllcd 12.75 12

? cd 112Cd 24.07 o.o3 113 mcd 14y B-. "Y 113Cd 12.26 21,000 114 mcd 114Cd 28.86 115 1.24 cd 43d B- * "Y 116Cd 117 7.58 1.4 cd 3.2h B-113:rn 114 4.28 63 In 5od* "Y 115In 95.72 200 ll 5 min 54m B-112Sn 0.96 113 1.3 sn 113d Electron Capture 116Sn 14.3 0.006 117 msn 14d "Y 118Sn 24.03 0.01 119 msn 250d y 120Sn 32.85 121 0.14 sn 75y B-122Sn 4.92 123 0.2 sn 40m B-124Sn 5.94 0.204 125 msn 9.4m B-90Zr 91 51.46 0.1 zr 91Zr 92 11.23 1 zr 92Zr 17 .11 0.2 93Zr 9.5xl0 5 y B-94Zr 17.40 0.1 95Zr 65d B-. -y 96Zr 2.80 0.1 97Zr 17h B-

• These cross-sections adsorption.

do not take into account resonance such resonances are approximately accounted for by increasing the cross-sections by 45%.

2-13

23su + a. --+ 241P + n 92 94 u 239P + a. --+

242c + n 94 u 96 m 195 195Pt 79Au + oe --+

78 Precisely speaking. the term fission product should be reserved for the daughter isotopes produced during fissioning and possibly the isotopes produced by the beta decay chains initiated by the fissioning. Here. however. the term II fission product 11 will be used to mean any radioactive material. regardless of how or whe~e it was produced.

2. 3. Inventories A. Radioactive Materials The first step in estimating the release of fission products is to determine the inventory of fission products available for release. It will be shown in later sections that inventory does.

in fact. affect the release rate. Fortunately. calculation of the fission product inventory has become a well-develop ed technology.

If fissioning of the 235u isotope were a homolytic process.

the nuclear reaction would be 235u + n--+ 2 11sPd 92 46 Rather than yielding two palladium isotopes. the 235u fission-ing yields a wide variety of isotopes. The probability that fissioning will yield a particular isotope is bimodally distri-buted with respect to the atomic mass number of the isotope.

Peaks in the distribution occur for atomic mass numbers of 137 and 97. The distribution does depend slightly on the energy of the neutrons causing the fissioning. The fissioning yields for 235u subjected to thermal neutrons are plotted against the mass number of the product isotope in Figure 2.7.

Fission yield also depends on the fissile isotope. The fission yields for 235u and 239pu are compared in Table 2. 2.

Entries in the table are the probabilities in percent that fission will yield the indicated material. Since each fission 2-14

1.0 0.1

~

m C

m 0

a:

&l, 0.01 0.001 0.0001.___...._........__.........__.._ __.__ _.____......___..._.....__..____.._ _ _...____.

40 60 80 100 120 140 160 180 ATOMIC MASS NUMBER

• Figure 2.7. Fission Yields for 235u 2-15

Table 2.2 and 239P [9]

• Comparison of Fission Yields From 94 u Fission Product* Yield {%) Yield {%)

Group from 235u from 239P 94 u 92 Zr. Nb 29.8 20.4 Y. La. Ce. Pr. Nd. 53.4" 47.1 Po. Sm. Eu. Ga Ba. Sr 14.9 9.6 Mo 24.0 20.3 Ru

• Te, Rh. Pd 26~3 51. 6 Cs. Rb 22.6 18.9 I

• Te 1.2 7.0

.Xe

• Kr 25.1 24.8

• 2-16

• event yields two daughter products. the columns in Table 2. 2 each sum to 200 percent. Notable features of the compariso n of 23Su and 239pu fissioning are (1) the higher yield of metals (Ru. Te. Rh. Pd) in 23 9pu fissioning and ( 2) lower yields of both the Ba.Sr and the Zr.Nb groups.

in a To determine the absolute amounts of fission products reactor core requires:

1. The extent of fissioning and capture that has taken place.

2. The enrichmen t of the fuel in fissile isotopes.

3. The time and power history over which fissioning took place.

The need to know how much fissioning took place is obvious since the absolute isotope yield is the product of the probabili ty a fission event will prortuca tha iaotopa times the number of fission events. The irradiatio n history of fuel is usually reported in terms of 11 burnup. 11 which includes both fissioning and capture.* Unfortuna tely. the fuel in reactor cores does not burn up uniformly . The burnup history of fuel assemblie s in the Three Mile Island Core just prior to the accident are shown in Figure 2.8 (only one quarter of the core is shown in this figure; the rest of the core and the burnup histories of fuel assemblie s in the rest of the core are symmetric ally related about the centerline s .shown* in figure).

As a rough rule. burnup decreases with distance from the center of the core. This is because neutrons that would have been captured or would have continued the nuclear chain reaction if they were generated deep within the core have more of a chance to escape unproduct ively when they are generated near the peri-meter of the core. Fission product inventorie s would of course vary. approxima tely. as do the burnups throughou t the core.

• There are two conventio nal units of burnup. Percent burnup is the amount of fuel atoms destroyed by both capture and fission.

Thus 1-percent burnup means that 10 kg of uranium have been converted in 1 metric tonne of fuel metal atoms. The other unit is megawatt days thermal per metric tonne of uranium.

Conversio n between the units is difficult because capture creates fissile plutonium that can act as a fuel~ A 1-percent burnup correspon ds to 6760 MWd/t u. if credit for the plutonium is not.taken and 7765 MWd/t U if credit is taken.

2-17

4008 3512 3091 3187 2513 3206 3675 2479 3511 3234 3316 2965 2988 2927 2885 2107 3099 3280 3026 2974 2471 2835 3074 1713 3185 2971 2996 2675 2729 2395 2281 2511 2991 2502 2736 2349 2129 1404 3204 2902 2808 2410 2128 1494 3672 2911 3048 2280 1403 2478 2106 1711

- I Figure 2. 8. Burnup of TMI Fue 1 Rods in Megawatt Days per Metric Tonne Uranium [10) 2-18

The variations in burnup are not smooth functions of distance from the center of the core because the fuel is not uniformly enriched in fissile 235u. The initial enrichment of fuel assemblies in the Three Mile Island Core are shown in Figure 2.9.

(Again. only one quarter of the core is shown.) The fueling pattern consists of an outer ring of highly enriched material

( 2. 96 percent 23 5u). Within this ring there are alternating assemblies of medium enrichment (2.64 percent 235u) and low enrichment (1.98 percent 235u) fuel assemblies. The isotopic distributions of fission products in these fuel elements will be different even if burnup were the same. Powers [ 11] has used these differences in isotopic abundances in both uranium and plutonium to infer from samples of released material the damage pattern to the TMI core.

The time duration over which a level of burnup occurs affects the fission product inventories because the daughter isotopes of fissioning and the products of neutron capture are unstable ~nd radioactively decay. Progress along the decay chains described above is a strong !unction* o! time and so. too. is the isotopic mix of fission products.

Reinspection of the decay chains described above and the complicated nature of. products of the fission process. as well as the complexities described above concerning irradiation history and enrichment. should be enough to persuade even the most dogged that calculations of inventories is a complicated activity. Fortunately. the problem has been avidly pursued and is particularly susceptible to computer solution. Within the United States. the computer code ORIGEN has become an especially popular tool for solving the fission product inventory problem

[12]~ The basic algorithm ~olves systems of coupled. moderately stiff differential equations. A typical version of ORIGEN tracks the evolution of 1064 isotopes with half-lives greater than

• 1 second [8]. It is backed by an extensive library of nuclear data concerning half-lives. branch decay probabilities. and capture cross sections. Output is provided in terms of gram atoms. curies. and thermal power.

Other codes besides ORIGEN exist to solve the same problem.

The CINDER code. has been mentioned in the 1 i tera ture [ 13]. The British codes RICE and FI SPIN are also available. Proprietary codes of reputably outstanding sophistication are apparently held by reactor vendors.

These computer models do not explicitly treat the radial distribution problem described above. Nor do they consider axial variations in fission product inventories that should parallel the axial power distribution in the core.

2-19

2.64% 1. 98% *l.98% 2.64% 1. 98% 2.64% 2.64% 2.96%

1.98% 1. 98% 2.64% 1. 98% 2.64% 1.98% 2.64% 2.96%

1.98% 2.64% 1. 98% 2.64% 1. 98% 2.64% 2.96% 2.96%

2.64% 1. 98% 2.64% 2.96% 2.64% 1.98% 2.96%

1.98% 2.64% 1. 98% 2.64% 1. 98% 2.96% 2.96%

2.64% 1. 98% 2~64% 1.98% 2.96% 2.96%

2.64% 2.64% 2.96% 2.96% 2.96%

2.96% 2.96% 2.96%

Figure 2.9. Enrichment Pattern of Fuel in the TM! Unit 2 Core [10]

2-20

B. Justifica tion of Elemental Phenomen ological Source Terms The same considera tions that demonstra te the complexit ies of calculatin g the fission product inventorie s also demonstra te that there are a lot of fission products. The fission products are isotopes of a much smaller number of elements. It has become tradition al to analyze the severe accident source term in terms of the behavior of the elements rather than the isotopes. When analyses progress to the point radiologi cal concerns need to be addr~ssed . the isotopic abundance s in the elements released from the fuel are assumed to be the same as they would have been in the fuel were there no release. That is. the assumptio n is made that there are no effects on release or behavior. save inventory changes by radioactiv e decay. that arise because of different isotopes.

An alternativ e to this tradition al approach. would be to develop models of release and behavior that are peculiar to each isotope. This alternativ e would increase. of course. the labor involved in the developme nt of severe accident source term models.

Isotopic differenc e could affect the behavior of fission products in three ways:

• 1.

2.

Isotopic difference s could affect the chemical processes in which fission products engage by altering chemical equilibria .

Isotopic difference s could affect the rates of chemical reaction.

3. Transmuta tion of the elements by radioactiv e decay could alter the release rates or behavior of fission products.

A definitive proof that none of th~ eff~cts are important would be difficult to formulate . Below. evidence is presented that the first two effects are, likely to be insignific ant. The third*

effect. transmuta tion. is shown to be considera ble only for* a few particula r cases. Because of these occasiona l transmuta tion effects. the* tr.adit:ion al approach to source term modeling in terms of elements rather than isotopes may not be universal ly acceptabl ~. But. because the transmuta tion effects are rare and because neither the thermodyn amics nor kinetics of different isotopes are significa ntly different. it may not be necessary to adopt the alternativ e of isotopica lly based source term models.

The chemical processes that affect fission product release and behavior can be identified by systemati cally examining chemical equilibri a. Are these chemical equilibria significa ntly different for the isotopes of a given element?

2-21

• Consider two general equilibriu m reactions . one involving the isotope A and the other the isotope A*:

AB+ C-+ E-AC+ B K =

[AC] [B]

[AB] [C]

[A*C] [B]

A*B + C-+ E-A*C + B K* = [A*B] [C]

The isotopic distortion of the equilibriu m is shown by the ratio of the equilibriu m constants :

[AC] [A*B]

K/K* = [AB]

[A*C]

But this ratio is just the equilibriu m constant for the isotopic exchange reaction:

A*C + AB -+

E- A*B + AC This equilibriu m constant is given by FA*B FAC FA*C FAB where Fi= the partition function of the species i. The

~artition function of the ith species is given by [14]:

(i ) (i )

gel gnucl F.

1

= s.1

( i) to the partition where gel = electronic contributi on function

( i) to the. partition function gnucl = contributi on from nuclear spins

• m*1 = mass of the ith species 2-22

• Ii= moment of inertia of the ith species k = Boltzmann 's constant h = Plank's constant

= r exp(-hu./2 kT) J jli - exp(-huj/k T~

Uj = frequency of the jth vibration Si= symmetry number of the ith species.

Isotopic subs ti tut ion of one element in the i th species will leave, of course, the symmetry of the species unaltered .

Similarly , isotopic substituti on does not alter g~!>. Nuclear masses are so much greater than electronic masses for the iso-topes of interest in reactor accident analyses that electronic motions are little altered when the nuclear mass is changed by one or two atomic mass units (amu).

The partition function for nuclear spin in the species AB can be cast in the form AB (A) (B) gnucl = gnucl gnucl Similar expression s can be written for the species A*B, AC, and A*C. Chemical process can almost never affect nuclear spin so the term g~!~l. is the same whether the atom A is in. the species AB or the species AC.

If the species AB is considered a diatomic species composed of atom A and molecular fragment B. then where r(AB) = equilibriu m bond length between A and B. Since eq electroni c motions are unaffected by isotopic substituti on.

. (AB) (A*B) r eq = reg 2-23

Then. the equilibrium constant for the isotopic exchange reaction is given by K.._ v1b )

fA~

K* A*C f V1"b A*B f "b

_.YL fAB vib If the diatomic approximation for the species is again assumed.

then there will be but one vibration for each species. The frequency of that vibration is given by where fi is the force constant. Since the force constant is dictated by the chemical bonding. the force constant is essen-

• tially unaffected by isotopic substitution . Quite clearly a 1 to 2 percent change in mi makes a very modest change in the vibrational frequency if mi is large. At elevated temperatures the exponential terms in the vibrational contribution to the partition function can be linearized. Then.

3 K = (MA*B))/Z(MAC ) /Z K*

MAB MA*C Clearly. for massive isotopes K* /K deviates 1 it t le from unity.

That is. equilibria are little affected by isotopic abundances.

The next question is whether the approach to equilibrium is sensitive to isotope effects. Melander [ 15] has presented an extensive.rev iew of isotope effects on chemical reaction rates.

Nearly all analyses of these effects evolve from H. Eyring's [16]

transition state theory of elementary chemical reaction rates.*

• Elementary chemical reactions are the actual microscopic. mole-cular transformatio ns that take place in a chemical process.

They are nearly never known except for simple systems that have attracted academic interest. Elementary reactions seldom bear much resemblance to the reactions defined from the stoichiome-try of the process.

2-24

In this theory, molecular collisions give rise to an energetic, but metastable. transition complex:

AB+ C ~ [ABC]~ AC+ B After a brief induction period, the reactants AB and C come into dynamic equilibrium with the transition complex:

AB+ C [ABC]

The rate at which products are produced depends on the concentra-tion of the transition complex ABC. Analysis of the change in concentratio n brought on by isotopic substitution is just an equilibrium analysis much like that above. The reaction rate.

given the concentration of ABC or A*BC. is a ,vibrational analysis. As the temperatures increase the ratio of the rates of reaction of A*B and AB approaches:

_l] 1/2

= [¢s +

MA*C

_l_ + _l_

. MAB MAC It is apparent that for atomic masses on the order of 100. the ratio of rate constants will vary little with changes in. mass of one or two units in comparison to the general uncertainty of the elementary reaction rate constant.

Thus, *isotopes should participate i.n similar chemical reac-tions at iimilar rates. The existence of isotopes need not lead to formulation of isotopically based source term models.

There is a subtle feature of the isotope affect on release kinetics that is not addressed by. this analysis. Some elements produced by fission will have both long and short half-life isotopes. . Long-lived . isotopes borne in the fuel lattice will have an opportunity during the course of reactor operation to migrate and accumulate at the grain boundaries. Short-lived isotopes will not have this opportunity. As a result. once an accident begins. there will be a greater fraction of long-lived isotopes at the grain boundary than short-lived isotopes. If transport through the fuel grains poses a major limitation on the rate of release, then long-lived isotopes of the element will escape more rapidly from the fuel than short-lived isotopes, at least until the inventory of long-lived isotopes accumulated at grain boundaries has been depleted. This effect will be greatest for the more volatile isotopes.

2-25

• Transmuta tion by radioactiv e decay does depend on the isotope in question. in* terms both of the rate and the nature of

• the product. It is easy to imagine situations in which an isotope decays to an element with radically different chemical character and consequen tly radically different behavior during a severe accident. For instance. consider these situation s:

1. The isotope of interest is the product of radioactiv e decay of a noble gas. The isotope of interest is released from the fuel at a rate much slower than the rate of release of the noble gas. Neverthel ess. this isotope *will appear in the emissions from the core during an accident to an extent dictated by the radioactiv e decay of released noble gas.

2. The element of interest is quite volatile and is expected to be released quite rapidly from the fuel. But. a fraction of the element is produced by decay of a fairly refractory species that is not released from the fuel.

Then. release of the element of interest may persist long after condition s of the fuel are well beyond those expected to lead to quantitati ve release. The persisten t release is the result of decay of the refractory species and prompt release of the decay products.

Though these situations can be imagined. it is important to ascertain their significan ce before investing in the labor of developin g isotopica lly based source term models.

At first blush. the situations in which radioactiv e decay might affect fission product behavior mostly involve highly

-volatile species-- the noble gases and. perhaps. iodine. The most important decay processes involving the noble gases and iodine are the B-decay chains.

For radioactiv e decay to have a significa nt bearing on. the source term. three conditions must be met:

1. The inventory of the decaying isotope must be high enough to have a perceptib le effect.

2. The decay process must occur to a significa nt extent during the time frame of interest.

3. The decay process must not be so rapid that it is largely complete before any significa nt release can take place.

Let G be the inventory of the. decaying element and H the. inven-tory of the element that is the product of the decay process of interest. Let Co be the inventory of the decaying isotope and t 112 be the half-life of this isotope. Co' is the inventory 2-26

of the product of decay. were decay to go instantaneously to completion. Assume that an error of E in the release fraction of an isotope is barely tolerable. Then. decay processes need to be considered to avoid an excessive error. when Co/G > E and 0.693 t(min) < 0.693 t(max) h EGJ tl/2 ~ I- EGJ

-ln r-co -ln r-co or Co 1 /H > E and 0.693 t(max)

-ln 11- EH l L Co~

where t(max) is the maximum time of interest and t(min) is the time from reactor scram to the onset of significant fission product release.

Isotopes in the portion of the .B-decay cha in invo 1 ving Te.

I. Xe, and Cs are shown in Table 2. 3. The half-lives of the isotopes and typical inventories in fuel irradiated to about 33,000 MWd/t are also shown in the table. The inventories in this table are provided in the form* of decay rates. Any other unit. such as. thermal power. dose. or moles. might be used. To scan these isotopes for instances of transmutation effects that might have a significant impact on source term behavior. it was assumed that E = 0.1 t(min) = 1200 t(max) = 80,000 The isotopes 132Te and 134Te meet the criterion for concern over radioactive decay effects in source term models. Williams

[17] has discussed the effect of 132Te and the ex-vessel source term. If Te is not released in-vessel because it has bound chemically to unoxidized zircaloy clad. it is available 2-27

Table 2.3 The 8-Decay Series Involving Te, I, Xe, and Cs Isotopes Tellurium Iodine xenon Cesium Atomic Atomic Atomic Atomic Mass tl/2 Mass tl/2 Mass tl/2 Mass tl/2 (amu) ( s) (amu) (B) (amu) (S) (amu) (s) 4 127 3.3xl0 72.8 127 Stable

- 127m(a) 6 9Xl0 0.2 129 4038 250 129 2x10- 5 129m(c) 6.9xlo 5 7xlo- 3 129 Stable 131 1500 761 131 131m 6 867 1x10 5.4 131 Stable l3lm(b) 1Xl0 5 65.5 -

N N

I 132 2.8xl0 5 1259 132 8280 1_277 7.5xlo 4 4.6xlo 5 co 133 120 1044 133 1832 133 1833 133 Stable 133m 3780 692 134 2520 1514 134 3180 2011 134 Stable 7 134 6.9xlo 116. 9 4 4 135 18 792 135 2.4xlo 1728 135 3. 3xl0 344 135 6xlo 13 l.9xlo- 4 136 21 445 136 86 810 136 Stable 6 136 lxlxl0 35.6 137 24 837 137 1681 8 234 137 9.5x10 65.3 138 1020 1579 138 1932 1670 139 41 1246 139 570 1645 140 17 866 140 66 1510

a. Only 2 percent of the 127mTe decays by 8- amiss ion. The rest decays by emission of a y ray to yield 127Te.

b. 52 percent of the l3lffiTe decays by 8- emission. The rest decays by emission of a y ray to yield 131Te.

for release ex-vess el. Ex-vess el release of Te is slow because of the low chemica l activity of the element when dissolve d in metals. Iodine release ex-vesse l is expected to be quite rapid. Because of the decay of 132Te. there is the potentia l of prolonge d ex-vesse l iodine release into the containm ent atmosph ere. This release rate is essenti ally the rate of Te decay since iodine is so promptly purged from the fuel ex-vess el.

Similar ly. protract ed release of iodine can occur in-vesse l if 134Te binds to clad or structur es within the reactor vessel.

As the telluriu m isotope decays. iodine is produced and possibly released even *if conditio ns have long been establis hed that should have allowed rapid. quantita tive expulsio n of all iodine.

Several iodine isotopes meet the criterio n for conside ration.

But. there seem to be no radical conseque nces of iodine transmu -

tation to xenon. This transmu tation can probably be adequat ely handled by inventor y adjustme nts with time.

Decay of 133xe and 135xe meet the criterio n for conside ra-tion. The decay of 133xe is to the stable cesium isotope and so can be treated 'simply by inventor y adjustm ent. Decay of 13Sxe does yield a radioac tive cesium isotope. Because of the decay.

there will always be some cesium suspende d in the reactor atmos-phere if there was xenon release from the fuel. But. because the half-lif e of xenon is very long. the amount of cesium will not be large.

Within the decay series examined here only the 132Te and perhaps the 134Te isotopes seem to deserve attentio n that could not be supplied by source term models based on the chemist ry of the element and neglecti ng transmu tation. A few other examples of signific ant transmu tation effects in radioac tive source term behavior are known. Decay of 140Ba to 140La and its effect on ex-vess el release is such an example.

So few instance s of t~ansmu tation effects make it difficu lt to consider going to the difficu lty of develop ing isotopic ally based source term models. It would be better to treat in an ad hoc manner the instance s where transmu tation effects are importan t and do so within the context of source term models based on the element s.

C. Element al Invento ries of Fission Product s Invento ries of fission products ' for a pressuri zed water reactor with end-of- life fuel are shown in Table 2. 4.

Invento ries for 30 minutes. 1 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br />. 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br />. and 1 day after scram of the reactor are listed in the table. These invento ries

• are just example s to provide an indicati on of the order of magnitud e of the invento ries likely to be encounte red in reactor acciden t analyse s. The reactor core for the example was assumed 2-29

Table 2.4 Fission Product Inventories* for a PWR Core

• Element Tritium Ge 30 Min l.123 0.321 Amount (gram moles} After Decaying: *tor l Hour l.123 0.321 4 Hours l.123 0.321 l Day l.122

o. 321 As 0.105 0.105 0.105 0.104 Se 45.13 45.13 45.13 45.14 Br 17.50 17.50 17.49 17.48 Kr 294.l 294.l 294.0 294.0 Rb 272.0 272.0 272.0 272.0 Sr 717.6 717.6 717.4 716.8 y 366.3 366.3 366.2 365.9 Zr 2439 2349 2439 2439 Nq 37.4 37.4 37.4 37.4 Mo 1995 1995 1996 1996 Tc 510.3 510.3 510.4 511.0 Ru 1265 1265 1265 1265 Rh 230.5 230.5 230.6 231.0 Pd 545.4 545.4 545.4 545.7 Ag 27.38 27.39 27.39 27.42 Cd 32.04 32.04 32.04 32.06 In 0.751 0.751 0.752 0.754

. Sn 21. 71 21. 71 21. 70 21. 70 Sb 7.852 7.844, 7.825 7. 778 Te 203.5 203.5 203.3 202.8 I 103.6 103.6 103.3 102.3 Xe 2380 2380 2380 2381 Cs .1237 1237 1237 1238 Ba 629.2 629.l 629.0 628.4 La 548.8 548.8 548.7 548.6 Ce 1276 1276 1276 1276 Pr 477.0 477.0 477.l 477.5 Nd 1532 1532 15.32 1533 Pm 67.59 67.60 67~61 67.68 Sm 179.5 179.5 179.5 179.6 Eu 53.35 53.35 53.36 53.42 Gd 23.67 23.67 23.68 23.73 Tb 0.565 0.565 0.566 0.566 Dy 0.276 0.276 0.276 0.277 Ho 0.021 0.021 0.021 0.021 Er 0.004 0.004 0.004 0.004 Np 126.3 126.l 125.l 118. 7 PU 2333 2334 2335 2341 Am 16.81 16.82 16.82 16.85 Cm 5.277 5.278 5.278 5.278

• Inventories in this table were taken from Reference 8.

2-30

to consist of 89 .1 metric tons of uranium. The burnup of the fuel was 33,500 MWd/ton uranium produced over 3 years on an 80 percent duty cycle. For more details on the calculations see Reference 5.,

D. Need to Consider Nonradioactive Inventories The consideration of inventories would stop after the amounts of radioactive materials were defined if the classic pathways [l]

to defining source term were followed. This is acceptable in bounding estimates. in which mitigation of the phenomenological source term is not mechanistically evaluated. As outlined in the introductory material. this is not now an acceptable procedure.

Source terms developed now and in the future will have to meet the needs of mechanistic calculations of fission product behavior after the fission products have escaped the fuel. The detailed description of the behavior of fission products released from the fuel are to be found in Chapter 5 of this document. Two of the most important features of the behavior are:

1. Fission product vapors can condense to form aerosols which can subsequently grow. sediment. or deposit on primary system structures and not escape either into containment or into the environment .

• 2. Fission product materials and be vapors bound so containment or the environment.

can they react cannot with escape Both of these processes have the potential of substantially structural into the

. reducing the fraction of the radionuclides released from the fuel that_ eventually escape the reactor plant.

_Temperatures and conditions in the reactor core conducive to the vaporization of fission products are* equally conducive to the vaporization of nonradioactive materials from the core. The extent of vaporization o.f nonradioactive materials that occurs while fission products are being vaporized directly affects the post-release behavior of the. fission products. In particular.

vaporization of* nonradioactive materials will have a direct bearing on the efficacy of the two *source term mitigation processes *mentioned above.

Consider a situation in which a well-stirred atmosphere initially contains 10 g/m3 of radioactive particles. These particles will be lost from the atmosphere by a variety of processes--diffU:s ion to the walls. settling. etc. At the relatively high concentrations considered here and the relatively high concentrations of interest for reactor accident analyses *

• gravitational settling of the particles is the dominant mechanism 2-31

• of particle loss from-the atmosphere.

stirred atmosphere the particles settle incre~sing particle size. The rate of Settling is an especially efficient process because the particles agglomerate.

loss of more In a well-rapidly particles on a variety of factors such as the particle shape and density.

A typical example of the variation in the concentratio n of with depends material in the atmosphere with time is shown as a dashed line in Figure 2 .10. After about 2 hours2.314815e-5 days <br />5.555556e-4 hours <br />3.306878e-6 weeks <br />7.61e-7 months <br /> the mass concentratio n in the atmosphere has fallen to 1 g/m3. After about 34 hours3.935185e-4 days <br />0.00944 hours <br />5.621693e-5 weeks <br />1.2937e-5 months <br /> the concentration is only 0.01 g/m3.

Now considei a situation in which the well-stirred atmosphere initially contains 10 g/m3 of nonradioactiv e aerosol in addition to 10 g/m3 of radionuclide s. Though interest focuses on the radionuclide s. the nonradioactiv e particles also agglomerate both with other nonradioactiv e particles and with radionuclide particles. The rate of agglomeration varies with nearly the square of the particle number concentratio n irrespective of the radioactivity of the particles [18]. More rapid loss of radio-nuclides from the atmosphere would be expected. This is. in fact. what occurs. The solid line in Figure 2.10 is the time dependence of radioactive material concentratio n in the atmos-phere when the nonradioactiv e particles are present. In this case the concentration of radioactive species falls to 1 g/m3 after only 1.5 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br />. The concentration is less than 0.01 g m3 after only 25 hours2.893519e-4 days <br />0.00694 hours <br />4.133598e-5 weeks <br />9.5125e-6 months <br />.

In reactor accident situations. the effects of nonradioactiv e particles may be even more severe than depicted in the hypothe-tical example described above. The inventory of nonradioactiv e species available for release during an accident will be shown.

• below. to be very large. Particle concentratio ns in the atmos-phere from these nonradioactiv e sources can be several times the concentration s of particles formed from radionuclide s. The dotted line in Figure 2.10 is for a situation in which the initial mass concentration in the atmosphere is 100 g/m3. of which 10 g/m3 is radionuclide s. In this case. it takes only O. 5 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br /> to reduce the suspended radioactivity by a factor of 10 and only 2.5 hours5.787037e-5 days <br />0.00139 hours <br />8.267196e-6 weeks <br />1.9025e-6 months <br /> to reduce it by a factor of 100.

Clearly. to* take into account mitigation of radionuclide release by aerosol processes. it is necessary to know the release of nonradioactiv e species. Because nonradioactiv e species come from sources other than the fuel. release models distinct from those used for radionuclides may be needed. The generation of aerosols from nonradioactiv e materials can exceed aerosol generation from radionuclides by well over an order of magnitude.

Next. consider an example of fission product vapors reacting with structures. Sallach et al. [19] have found that tellurium vapors react rapidly with structural steel such as type 304 stainless steel. They have also found that Te vapors will 2-32

CT)"'

E l.!J V 10 1

_, *III*

H a:::

w t-

E 10 ° w

t-10- 1 u

0 H

N D

< 10- 2 I a:::

w w D w

D z

w 10- 3 a..

U)

U) 10 100 1000 10000 TIME (SECONDS)

Figure 2.10. Effect of Nonradioactive Aerosols on the Time Dependence of the Concentra-tion of Radioactive Aerosols. Dashed line is for radionuclides only.

sol id line is f o.r rad ionucl ides and an equal amount of nonradioactive material. Dotted line is for a case in which radionuclides make up only 10% of the initial aerosol mass.

react rapidly with silver. which might be present in the primary system atmosphere. because precious metal control rod alloys are vaporizing. Clearly, a competition for Te vapors can exist. The Te vapors can react with structural metals. and consequently. not become part of the radiological source term. Or, the Te vapors can react with silver aerosols and remain part of the source term provided aerosol processes are neglected.

• The fate of Te vapors depends on the avaiiability of surfaces

--either structural or aerosol--for reaction . . In Figure 2 .11.

the fraction of Te that has reacted with silver aerosol rather than structural steel. and consequently.

• remains a part of the source term. is shown as a function of the silver aerosol concen-tration. For this calculation the aerosol was assumed to consist of 1 µm particles and the steel was assumed to be present as the walls of an 18-inch diameter pipe. This figure shows that the mitigative effect of fission product release caused by fission product reactions with structures can be prevented to a signifi-cant extent if reactive

• aerosols are present along with the fission products. Since the aerosols produced by vaporization of nonradioactive materials can be chemically quite reactive toward fission products. the magnitude and timing of the vapori-zation must be known if the fate of the fission products is to be properly described .

• E. Inventories of Nonradioactive Materials The arguments made above demonstrate how important it is to develop source terms for nonradioactive species likely to be

• vaporiz,e.d from the reactor core. There are some essential dif-

. ferenc-es between the fission product source term and the non-radioactive. source term. The most important of these is that the nonradioactive sources are not intimately associated with a heat

~ource. The attentions concerning the nonradioactive sources should then focus on the most volatile *constituents since it is likely that the host matrix for these constituents will be cool.

at least relative to fuel. Some care must be exercised in making this discrimination among nonradioactive materials in the core.

since materials that might appear refractory readily react in.the high-temperature.. high-pressure steam environment of a reactor to yield volatile products.

Because the nonradioactive materials are not typically associated with a heat source. the contribution of these materials to the aerosol emissions from a reactor core during an accident are diffictilt to define. Inventories of volatile materials* that can make these contributions are not defined simply by the masses of nonradioactive host materials in and adjacent. to the core. Some other means. preferably mechanistic calculation. must be found to determine if the host material gets hot enough for its volatile constituents to contribute to the aerosol emissions. Whether and how much of the host materials 2-34

80

.70 o

Cl) eo 0

a:

Ill C

50 z

0 Q

Ill

40 0

a, m

C

~ 30 l/l.

20 10 0 L..*---'-----'-- --L---....J....- --..l.....---..... .1.-----J 0 25 50 75 100 125 150 175 3

GRAMS A; AER0SOL/m GAS

• Figure 2.11. Competition Between Reaction of Te with Steel and Reaction of Te with Silver Aerosols 2-35

• participate in the vaporization process will depend on the heat-up and melting of the reactor fuel. The behavior of the fuel.

in turn. will depend on the nature of the particular accident in question.

Considerations made to date indicate that the nonradioactive ma~erials most likely to be vaporized from th~ core are:

1. Alloying agents in the fuel cladding.

2. Precious metal control rod alloys.

3. Products of steam reaction with boron carbide or borosil-icate glass control rod materials.

4. Volatile alloy constituents or impurities in the struc-tural steels of the reactor.

Fuel cladding in nearly all light water reactors is either Zircaloy 2 or Zircaloy 4 (stainless steel cladding on the fuel in San Onofre* Unit 1* is a well-known exception). The composi-tions of these alloys are:

Weight Percent of Trace Elements in Zircaloy 2 and 4

• Elementa Sn Fe Zircaloy 2 1.5 0.12 Zircaloy 1.5 0.2 4

Cr 0.10 0.10

.Ni 0.05 a Balance of alloy mass is Zr and< 150 ppm Hf.

Tin is the most vo la ti le constituent of the clad. In a typical pressurized water reactor there will be 250 kg of tin.

In a boiling water reactor there might be as much as 905 kg of tin that can participate in ~he vaporization* process. Other constituents of the clad could contribute only about 1/10 as much

. to the aer~sol as tin. Chromium i~ moderately volatile when in the metallic state (boiling point = 2938 K) or in the highly oxidized hexavalent state (boiling point of cro 3 = 600 K).

The volatility of chromium is significantly depressed when the trivalent state of chromium is stable.

Iron is not especially volatile. except at quite high temper-atures.

• In oxygen both

• Fe ( g) and F-eO ( g) are important gas species. In steam FeOH(g) and Fe(OH) 2 (g) can form. The gas species FeO(OH)(g) has been hypothesized.

2-36

Nickel vaporizes primarily as a metal.

Many pressurized water reactors use an alloy of silver, indium, and cadmium as a control rod material. A typical inven-tory of this control rod alloy in a large pressurized water reactor is:

Silver. (Ag) 2365 kg Indium (In) 442 kg Cadmium (Cd) 147 kg All constituents of this alloy are volatile. A rather thorough thermochemical analysis of the vaporization of this alloy has been done recently [20]. As th~ alloy is heated within the con-trol rod sheath, quite high partial pressures of Cd are produced:

Temperature * (K) Cadmium Partial Pressure (atm) 1000 0.015 1200 0.129 1400 0.598 1600 1. 898 1800 4.671 2000 9.634 Pressure from the cadmium as well as pressurization of the helium fill gas in the rod can cause the control rod clad to rupture

[21, 22]. Once evaporation can take place the cadmium is prefer-entially distilled from the alloy. Subsequent evaporation from

.the Ag-In alloy requires higher temperatures and is not congruent. The rate of vaporization may be controlled in a reactor accident by heat input to the alloy.

Both pressurized water reactors and boiling water reactors use B 4 c control rod materials or borosilicate glass burnable poisons. The predominant neutron absorption reaction is 7L.

3 l. + a.

so that after some period of operation. the rods contain lithium.

A typical boiling water reactor would contain 530 kg of boron.

A pressurized water reactor might contain 82 kg boron and 137 kg Si02.

In steam. boron reacts according to the stoichiometry [23]:

-+

2-37

The product Bz03 will also react with steam to produce boric acid vapors (H2BOz and H3B03). Reactions of these boric acids with fission products are of concern. For instance. the reaction HBOz +Cs!~ HI+ CsBOz is suspected as a means of creating vapor phase iodine in the primary system.

Silicates will also vaporize at high temperatures. The vaporization process can be described by the reactions such as:

Si02(c) +Hz~ HzO + SiO(g)

Si02(c) + 2Hz0 ~ Si(OH)4(g)

Silica, too, is reactive toward Cs!, yielding a silicate and free iodine [23).

Compositions of important structural alloys found in nuclear reactors are listed in Table 2. 5. It is not possible a priori to say how much of a contribution constituents of these alloys could make to aerosol emissions during a severe accident. The contribution depends on the heating of the steel, which in turn depends on the nature of the ~ore. meltdown process. The vaporization of Mn .* Mo, Si. s. and P will make the e.arliest contributions. Vaporization of the major alloy constituents has

. been* discussed above. If reactive vaporization is neglected, then the vapor pressure of 304 stainless steel* is given by [24):

log P(atms) = 6.1210 - 18,836/T(K)

• and the,vapor pressure of 316 stainless steel is given by:

log P(atms) = 6.1127 - 18,868/T(K)

The vaporization of neither alloy is congruent.

F. Chemical Classification of the Elements for Source Term Models There are about 1000 isotopes that are of interest for severe accident source term models. From the preceding discussions it is apparent that the sourc.e term models need not be constructed 2-38

to explicitly predict release and behavior of so many isotopes.

Rather. the models can be constructed to predict the behavior of some 100 elements. This factor of 10 reduction in the effort needed to develop source term models is important. The effort needed to describe release and behavior of 100 elements may still be too much for many applications. Even if the list of elements to be explicitly treated were pared of elements with low inven-tories in the reactor core. only about a factor of two reduction in the source term modeling effort would be achieved.

Table 2.5 Compositions Of* Important Structural Alloys (weight percent)

Alloy Fe Cr Ni Mn Mo Other Elements 0.08 c* 0.045 P; 304 Stainless bal 18-20 8-10.5 2 0.03 S; 1 Si

\

308 Stainless* bal 19-21 10-12 2 0.08 C; 0.045 P; 0.03 S; 1 Si 309 Stainless bal 22-24 12-15 2 0.2 c: 0.045 P; 0.03 s: 1 Si 316 Stainless bal .16-18 10-14 2 2-3 0.08 c: 0.045 P; 0.03 .s* 1 Si Inconel 600 8/ 15.5 76 0.5 0.08 C; 0.008 s 0.25 Cu To further reduce the magnitude of the source term model development effort. another approximation must be introduced.

Historically. the additional approximation is to group the elements into chemically similar categories and explicitly treat only one element from each category in the source term model.

This is exactly. the type of approximation used in the Reactor Safety Study [l]. seven chemical categories were defined a*s listed bel-0w:

1. Noble Gases: Xe. Kr

2. Halogens: 1_. Br 3* Alkali metals: Cs

• Rb

• 4. Alkaline earths:

2-39 Sr. Ba

5. Tellurium group: Te. Se, Sb

6. Transitional metal group: Ru. Mo. Pd, Rh, Tc

7. Lanthanides: La. Nd, Eu, Y, Ce, Pr, Pm, Sm, Np. Pu, Zr, Nb,

u. Th The underlined element in each of the above groups was taken to be the representative of that group. It was this representative element that was actually treated in the Reactor Safety Study source term model. The behaviors of other. elements were assumed to be similar to that of the group representative.

All chemical categorizations of the elements require some subjective , discrimination between the similarities and differ-ences in the chemistries of the elements. The chemistries of all elements are indeed different. The differenc~s can be amplified or muted depending on the chemical environment and the process of interest.

Consider. as an example of the difficulties of chemical categorization of the elements. the noble gases. The very, very weak chemical interactions 0£ Xe and Kr leads nearly all analysts to group these elements and treat them as one species. Certainly for the purposes of estimating the behavior of noble gases at very high temperatures this is an acceptable approximation. Were the attentions switched to the consideration of filtered vents with activated charcoal trapping of the noble gases, grouping of the noble gases Xe and Kr would not be acceptable. Xenon will absorb efficiently on activated charcoal even at surprisingly high temperatures. Krypton. on the other hand. absorbs on char-coal only at low temperatures that would be difficult to maintain in an environment expected* to develop during a severe reactor accident . . Most schemes for filtered venting with noble gas trapping are found wanting because of the chemical differences between krypton and xenon which in other contexts are negligible.

It is apparent then that any categorization of the elements will be specifi~ to a given process and will reflect only some subset of the properties of the elements. As a broader base of information and analysis develops, it will not be surprising if

• exceptions are found or paradoxes develop from the categoriza-tions.

The groupings for the noble gases, halogens, and alkali metals developed for the Reactor Safety Study are defensible.*

As noted above. grouping of the noble gases can fail for situa-tions radically different than the high temperature environments usually of interest in source term modeling. Chemical bonding 2-40

of bromine and iodine are somewhat different but these differ-ences are usually manifest at only low temperatures or in an aqueous medium. Grouping of the alkali metals is particularly acceptable. Even in sophisticated chemical studies Cs and Rb are considered to have nearly identical chemistries.

Difficulties with the Reactor Safety Study categorization begin to appear in the alkaline earth group. Barium and stron-tium have qualitatively similar chemistries. But. in quantita-tive features they are somewhat different. Barium is more easily reduced from the oxide to the metal than strontium. Barium typically exhibits higher vapor pressures than does strontium .

.The Reactor Safety Study authors recognized these quantitative differences. apparently. and . in many cases explicitly treated both elements. For most purposes the quantitative differences between the behavior of Sr and the behavior of Ba may not be of sufficient significance to warrant separate treatment of, the elements. For situations involving release of the elements from fuel some conservatism can be introduced by selecting barium rather than strontium as the group representative.

The remaining chemical categories defined in the Reactor Safety Study (the Tellurium. Transition Metal. and Lanthanides Groups) are most difficult to rationalize. These categorizations ignore both quantitative and qualitative differences in chemistry. Tellurium and certainly selenium are essentially nonmetals. Antimony. on the other .hand. is a main group metal.

Te and Se wil 1

• react with metals much

• as does sulfur to form covalent compounds. Antimony will alloy with metals. When antimony does form a compound with a metal compound. it is typically an intermetallic with metal-metal bonding. There seems

. to be little reason to expect release of antimony to parallel the release of tellurium and selenium in all of the wide variety of chemical circumstances created by severe reactor accidents. The differences in chemistry during transport of antimony and tellurium released from the fuel ought to be even more obvious.

Ruthenium. palladium. and rhodium are platinoids. notable for their lack of reactivity and refractory qualities.

Molybdenum and technetium are early transition elements with a rich oxide chemistry that can develop at the oxygen potentials liable to be present around reactor fuel during a severe acci-dent. There seems to be no reason to expect all these elements to behave similarly during release from the fuel or during transport.

Actinides. lanthanides. and early transition metals. Nb and Zr. are lumped into the Reactor Safety Study' s "Lanthanide" Group. Thereby. the release of practically nonvolatile zirconium is presumed similar to uranium despite the fact uranium can form quite voiatile hexavalent species such as uo 3 and UOz(OH) 2 .

2-41

The conservative approach utilized in the Reactor Safety Study focused on release of radionuclides and largely neglected natural processes that might mitigate this release. Consequent-ly. there was little need in the Reactor Safety Study to consider release of nonradioactive species. As noted above, modern source term analyses do not neglect mitigation and consequently cannot neglect release of the nonradioactive species during a severe accident. These nonradioactive species must then be included in any categorization of the elements.

An alternative to the chemical categorization of elements used in the Reactor Safety Study is shown in Tables 2.6 and 2.7.

This 13-category scheme incorporates.the more important nonradio-active species likely to be vaporized during a severe accident.

It repairs some. but by no means all. of the chemistry approxi-mations made in the Reactor Safety Study.

The categorization of the noble gases. alkali metals.

alkaline earths. and halogens done in the Reactor Safety Study is retained in this alternate scheme. The only change has been to declare barium the representative of the alkaline earth group.

Were the categorization to be used for purposes other than release from the fuel. the representative of the alkaline earth group might be selected to be strontium because of the decay of 140Ba.

Explicit addition of sodium and potassium to the alkali metals has been noted. Also. calcium and magnesium have been added to the alkaline earth groups. These additions have been made to accommodate the release from concrete during ex-vessel interactions of core debris.

Tellurium and selenium constitute a single group in the scheme. Antimony has been incorporated into one of the two Main Group categories.

The Main Group categories are added to accommodate releases of control rod alloy species and tin from the Zircaloy clad. The Main Group elements exhibit a wide range of volatilities. For instance. cadmium boils at 1040 K whereas tin boils at 2543 K.

Consequently. th.e Main Group elements have been split into two categories. Cadmium is taken as the representative of the more volatile Main Group category. Tin. rather than silver. is taken as the representative of the less volatile Main Group elements.

The choices for representatives of the two Main Group cate-gories have been made based on expectations concerning accident analyses. It would be expected that during severe accidents in pressurized water reactors that .the control rods would rupture and expel cadmium. There is so much cadmium. and it would be released so suddenly. it will be important to consider explicitly in ace ident analyses. s i 1 ver. too. might be re leased from the 2-42

Table 2.6 Classificatio n of the Elements into Chemically Similar Groups Representativ e Group Name Element Elements in the Group Noble gases Xe He. Ne. Ar. Kr. Xe. Rn. He. Ne Alkali metals Cs Li. Na. K, Rb. Cs. Fr. cu Alkaline earths Ba Be. Mg* *ca. Sr. Ba, Ra Halogens I F. Cl. Br, I

• At Chalcogens Te o. s. Se, Te. Po Platinoids Ru Ru. Rh. Pd. Re. Os. Ir. Pt. Au, Ni Transition Metals I Mo v. er. Fe. Co. Mn, Nb, Mo. Tc.

Ta, w Tetravalents Ce Ti. Zr, Hf. Ce. Th, Pa. u. Np, Pu Trivalents La AL Sc, Y. La. Ac, Pr, Nd, Pm.

Sm, Eu, Gd, Tb, Dy. Ho. Er. Tm.

Yb. Lu. Am, Cm, Bk, Cf Uranium u u Main Group I Cd ca. Hg* Zn. As. Sb. Pb, Tl. Bi Main Group II Sn Ga, Ge, In, Sn. Ag Boron B B. Si. p 2-43

Table 2.7 Alphabetical Listing of the Elements and Their Classification Element Group Representative Actinium Trivalents La Aluminum Trivalents La Americium Trivalents La Antimony Main Group I Cd Argon Noble Gases Xe Arsenic Main Group I Cd Astatine Halogens I Barium Alkaline Earths Ba Berkelum Trivalents La Berylium Alkaline Earths Ba Bismuth Main Group I Cd Boron Boron B Bromine Halogens I Cadmium Main Group I Cd Calcium Alkaline Earths Ba Californium Trivalents La Carbon Tetravalents Ce Cerium Tetravalents Ce Cesium Alkali Metals Cs Chlorine Halogens I Chromium Transition Metals Mo

. Cobalt Transition Metals Mo Copper Alkali Metals Cs Curium Trivalents La Dysprosium Trivalents La

,Einsteinium Alkaline Earths Ba Erbium Trivalents La Europium Trivalents La Fermium Alkaline Earths Ba Fluorine Halogens I Francium Alkali Metals Cs Gadolinium Trivalents La Gall.ium Main Group II Sn Germanium Main Group II Sn Gold Platinoids Ru Hafnium Tetravalents Ce Helium Noble Gases Xe Holmium Trivalents La Hydrogen Noble Gases Xe 2-44

Table 2.7 (continued )

Alphabeti cal Listing of the Elements and Their Classific ation Element Group Represent ative Indium Main Group II Sn Iodine Halogens I Iridium Platinoids Ru Iron Transition Metals Mo Krypton Noble Gases Xe Lanthanum Trivalents La Lithium Alkali Metals Cs Lead Main Group I Cd Lutetium Trivalents La Magnesium Alkaline Earths Ba Manganese Transition Metals Mo Mercury Main Group I Cd Molybdenum Transition Metals Mo

• Neodymium Neon Neptunium Nickel Niobium Trivalents Noble Gases Tetravale nts Platinoids Transition Metals La Xe Ce Ru Mo Xe

.Nitrogen Noble Gases Osmium Platinoid s Ru Oxygen Chalcogen s Te Palladium Platinoid s Ru Phosphoru s Boron B Platinum Platinoid s Ru Plutonium Tetravale nts Ce Polonium Chalcogen s Te Potassium Alkali Metals Cs Prasedymiu m Trivalents La Promethium Trivalent s La Protactini um Tetravale nts Ce Radium Alkaline Earths Ba Radon Noble Gases Xe Rhenium Platinoid s Ru Rhodium Platinoid s Ru Rubidium Alkali Metals Cs Ruthenium Platinoid s Ru 2-45

Table 2.7 (continued)

Alphabetical Listing of the Elements and Their Classification Element Group Representative Samarium Trivalents La Scandlum Trivalents La Selenium Chalcogens Te Silicon Boron B Silver Main Group I I Sn Sodium Alkali Metals Cs Strontium Alkaline Earths Ba Sulfur Chalcogens Te Tantalum Transition Metals Mo Technetium Transition Metals Mo Tellurium Chalcogens Te Terbium Trivalents La Thallium Main Group I Cd Thorium Tetravalents Ce Thulium Trivalents La Tin Main Group I I Sn Titanium Tetravalents Ce Tungsten Transition Metals Mo Uranium Uranium u Vanadium Transition Metals Mo Xenon Noble Gases Xe Ytterbium Trivalents La Yttrium Trivalents La Zinc Main Group I Cd Zirconium Tetravalents Ce 2-46

control rod alloy. But. the alloy will be quite fluid and should promptly drain from the heated core regions so releases will be minimized. Tin from the fuel clad will be present in both pressurized and boiling water reactors. The tin will remain intimately associated with degrading fuel. It will then be necessary to explicitly consider t\n release.

The platinoids are grouped. Ruthenium is taken to be the representative of this group because of its radiological consequences if it appears in the radiological source term.

Some caution is necessary in the use of this representative.

Rhodium can have greater volatility than ruthenium in the steam/

hydrogen environment of the primary system during a severe accident. Nickel is included j n the platinoid group because of this element's low volatility in steam and hydrogen atmospheres.

A new group is formulated of the early transition elements.

These elements are readily oxidized in steam and hydrogen environments. The oxidized forms of these elements tend to be volatile. Molybdenum is chosen to be the representative of the group because of the diversity of its chemistry and the radiolo-gical importance of this element. Structural elements iron and manganese are included in the group, though it would not be difficult to rationalize a separate ~ategory for these elements.

The structural element chromium is included in the group because of the similarity of its chemistry to that o*f the representative of the group, Mo.

Uranium could easily be incorporated in the early transition metal group. Because of the actinide contraction. uranium exhibits chemistry quite similar to that of molybdenum. In

. particular. the hexavalent state of uranium is quite volatile.

But. because of the obvious importance of distinct, explicit, treatment of uranium during severe reactor accidents, a separate category is reserved for this element.

The lanthanides and actinides are split into two categories.

the trivalent elements and the tetravalent elements. The tetra-valents favor. even at high temperatures, the cubic fluorite

?tructure of uo 2 . Consequently. the activity and volatility of these elements dissolved in uo 2 remains low.

The trivalent elements favor the various hexagonal structures and dissolve in uo 2 only at the. expense of some loss of stability. This loss of stability is reflected by somewhat higher than expected volatility. Yttrium is included with the trivalents, though it is assuredly a transition element. Because of the lanthanide contraction, the chemistry of yttrium is amazingly similar to that of lanthanum.

2-47

,-i...z p

• ~ p'- '\ )_,_,_r--"" .'? .. I I

. 1\.- (I.-. \',;';;)

,-c ,. , . \'- 1-*tvJ"l<-,

+*ti ,f V, 0 2, V

. ./ . \_

At first glance.. /

1/t might

~-~-

seem unreasonable to place pluto-nium among t~e tr1vaLents. It is. after all. present as tetrava-lent* Pu02 1n reactor fuel. But at elevated temperatures plutonium exhibits a distinct tendency to reduce to the trivalent state.

Finally. a separate group is set aside for boron. This category is important only if large amounts of boron or borosili-cate glass are present in the core. Silicon and phosphorous are included in the group because these elementsj tooj reactively vaporize in steam.

Because of* its subjective nature and its dependence on chemical circumstances that are poorly known. chemical categori-zation will never be an entirely satisfactory approximation.

Categorizations. and certainly the selection of the representa-tive element from each group. ought to change as more knowledge develops concerning severe accidents.

Alternatives to chemical categorization have been suggested.

Powers [25] has developed a procedure for allocating scarce research resources to the study of fission products that is ~ased on the attributes of the fission products rather than the simi-larities of their chemistries. The elements are rank-ordered in terms of several attributes. Powers chose (1) inventory.

(2) decay rate. (3) thermal power. (4) melting point. and (5) radiological consequences. Ties are allowed in the ranking to account for uncertainty. The ranks within each attribute group are summed for each element. These sums can be multiplied by penalty functions to account for risk adverse or cost adverse tastes. The rank sums are themselves ranked in rank order until

. (1) .resources are exhausted. (2) the marginal rate of return has fallen to a sufficient level that greater utility is obtained by turning to the next lower rank. or (3) attentions have gone to ranks low enough that the elements are known to be unimportant.

An example.of this type of rank ordering*is shown in Table 2.8.

The rank-ordering procedure has not received universal endorsement and has not been adopted here.

Another procedure that has been suggested is to assume various releases of elements. use the CRAC code [26] to determine the consequences of the release. and from these consequences determine which fission products are most important.

Unfortunately. this proced~re is exceptionally laborious. It requires a great deal more knowledge concerning chemical form and nature of the release than is typically available. Finally. the results change with different assumptions concerning the consequence code.

2-48

Table 2.8 Importance Ranking of Radionucl ides in Terms of Inventory. Dose Curies. and Mobil~ty Element at Indicated Time After Scram Rank 1 Hour 1 Day 100 Days l Cs I Zr

7. T 'l'e u 3 Te Cs Pr 4 Rb Xe Nb 5 Ba Ba Cs 6 Mo Pr Ce 7 Pr Mo Rh 8 La Ce y 9 Np Zr Sr 10 Xe Nb Fe ll Sn Np Ru 12 Sr La Te 13 Nb Sn Ba 14 y Rh Ni 15 u 'l'c Cr 16 Tc Sr Xe 17 Ce Nd 3H 18 Zr y \ Kr

.19 Sb u Sn 20 Br Ru Pm 21 Kr Sm Cm 22 Rh Sb Se 23 Nd Pd Rb 24 Ru Cr Cd 25 Mn Ag Zn

• 2-49

2.4 Recommen dations for MELCOR From the preceding discussion s the following recommend ations for the developme nt of MELCOR are formulated :

1. Radionucl ide inventorie s ought not be calculated within MELCOR. Rather. these inventorie s should be calculated with one of the specialize d codes such as ORIGEN. A set of default values should be included in MELCOR.

2. It is~esirab le that provision be made in MELCOR to have radi~~

• and axial variations in the inventorie s of the radionucl ides.

3. Elemental release models rather than isotopic release models can be used in MELCOR. It is possible that one exception to* this general rule is the release of 1321 and 132Te. . .

4. Release of nonradioa ctive species as well as release of radionucl ides will have to be considere d in MELCOR. This may necessita te separate release models for fuel.

cladding, structura l materials , and control rods.

5. The many elements susceptib le to release during a severe

• • - accident may be grouped into 13 categorie s. The release and behavior of. members of a given category is then described by the release and behavior of a single represent ative element in the category.

tion recommend ed here is shown in alphabeti cal cross index is provided in The categoriz a-Table Table 2.6 and an 2.7.

2-50

References

1. USNRC. Reactor Safety Study: An Assessment of Accident Risks in US Commercial Nuclear Power Plants. WASH 1400.

NUREG 75/04. October 1975.

2. J. G. Kemeny. Chairman. Report of the President's Commission on The Accident at Three Mile Island. and L. Jaffe. Head.

Reports of the Technical Assessment Task Force, Vol. 1.

October 1975.

3. R. s. Denning. "Reduction in Reactor Risk by the Mitigation of Accident Consequences." Proc. ANS/ENS Topic Meeting on Thermal Reactor Safety. Knoxville. TN,

• April 1980. CONF-8 00403. Vol. 1. p. 189.

4. N. Feather. "Ternary Fiss ion--a Review." Proc. . 2nd IAEA Symposium on the Physics arid Chemistry of Fission. Vienna.

28 July-1 August 1969. International Atomic Energy Agency.

1969.

5. R. A. Nobles. Phys. Rev. 126 (1962) 1508.

6. s. w. Cooper. et al .* Phys. Rev. 154 (1967) 1193 .

• 7.

8.

M. D. Cable. J. Honkanen. E. c. Schloemer. M. Ahmed; J. W.

Ewidd. z. Y. Chou 1276.

and J. Cerny. Phys. Rev. C 30 (1984)

D. E. Bennett. Sandia-ORIGEN User I s Manual. NUREG/CR-0987 *

. SAND79-0299. Sandia National Laboratories. *Albuquerque. NM.

October 1979.

• 9. D. R. Olander. Fundamental Aspects of Nuclear Reactor Fuel Elements. UC-796, TID 26711. 1975 . .

10. Personal Communication to D. A. Powe.rs f .rom T. P. Suchocki (GPU) dated 6 June 1978.

11. D. A. Powe.rs. "Plausible Conditions of the TMI-2 Core. 11 Transactions ANS 34 (1980) 563.

12. A. G. Croff. ORNL-5621. Oak Ridge National Laboratory. 1980.

13. "Radionuclide Release and Tran*sport." Chapter 8 in PRA Procedures Guide. Volume 1. NUREG/CR-2300. January-1983.

14. T. L. Hill. An Introduction to Statistical Thermodynamics.

Addison Wesley Pub. co .* 1960 .

• 15. L. Melander. Isotope Effects on Reaction Rates. The Ronald Press Co .* NY. 1960.

2-51

• 16.

17.

S. Gladstone, K. J. Lalder, and H. Eyring, Rate Processes, McGraw-Hill Book Co., 1961.

D. Williams, "Effects of Radioactive Decay Chains on Source Terms," Appendix C in R. J. Lipinski, et al., Uncertainty in Radionuclide Release Under Specific The LWR Theory Accident.

of Conditions Volume II: . Analyses, SAND84-0410/2, Sandia National Laboratories, Albuquerque, NM, October 1984.

18. L. D. Reed, J. A. Gieseke, and H. Jordan, Effects of Radiation on Aerosol Behavior, BMI-NUREG-1943, Battelle Columbus Laboratory, Columbus, Ohio, December 1975.

19. R. L. Sallach, c. J. Greenholt, and A .. R. Taig, Chemical Interactions of Tellurium Vapors with Reactor Materials, NUREG/CR-2921, SAND82-1145, Sandia National Laboratories, Albuquerque, NM, March 1984.

20. D . A . Powers , =B""""e"""'h'""a"""'v--"i---o'-'r"--_o__f=--c----"-o=n---t"""r--"o--"lC-.-....R....o__d__s_____D u___r __i__n....g..___c_o_r_e_D_e-g-r ad at ion: Pressurization of Silver-Indium-Cadmium *Con-trol Rods, NUREG/CR-4401, SAND85-0469 Sandia National Laboratory, Albuquerque, NM.

21. s. Hagan. KfK 27_50. pp. 4 300-4 3 62, Kernf orschungs-zentrum Karlsruhe, November 1978.

22. G. w. Parker, G. E. Creek, and A. L. Sutton, Jr.,

"Influence of Variable Physical Process Assumptions on Core Melt Aerosol Release," Proc. Int'l Mtg.* on Thermal Reactor Safety, Chicago, IL, NUREG/CP-0027, Vol. 2, p. 1078, 1983 .

. 23. R. M. Elrick and R. A. Sallach, Quarterly Report for The Advanced Reactor Safety Research Program, NUREG/CR-2679, SAND82-0904, Sandia National Laboratories, Albuquerque, NM.

24. c. s. Kim, Thermophysical Properties of Stainless Steels, ANL-75-55, Argonne National Laboratory, September 1975.

25. D. A. Powers, unpublished results.

26. L. T. Ritchie, J. D. Johnson, and R. M. Blond, Calculation of Reactor Accident Consequences, Version 2, NUREG/CR-2326, SAND81-1994, Sandia National Laboratories, Albuquerque, NM, February 1983.

2-52

• CHAPTER 3 RELEASE OF FISSION PRODUCTS AND GENERATION OF AEROSOLS DURING THE IN-VESSEL PHASES OF A SEVERE REACTOR ACCIDENT 3.1 An Introduction to the In-Vessel Source Term and the Objectives of this Chapter.

Severe reactor accidents. are, by definition, accidents in which the reactor fuel and clad are heated to the point that they suffer significant damage. Typically, this damage ii presumed to progress through complete melting of .the core and extensive reaction of the fuel cladding with steam.

The cladding on the fuel is often considered to be the first, and in some respects, the most important barrier to release of radionuclides from the reactor core. As soon as the cladding is damaged, radionuclide release begins. Volatile cadionuclides such as Xe, Kc, Cs and I can be nearly qtianti ta-tively expelled from the fuel during core degradation within the reactor vessel. Once radionuclides have escaped the fuel there is at least the possibility that they may escape the power plant.

The volatile cadionuclides, so extensively released during core degradation, are also among the most radiologically consequen-tial. A great deal of the attention in severe reactor accident analyses is devoted to determining the release and behavior of these volatile radionuclides. Over 70% of the discussion of severe accident source terms presented in the Reactor Safety Study [1] is devoted to the escape of volatile fission products from degrading reactor fuel. In some very simplified discussions of severe reactor accidents, there has been the implication that ielease of cesium and iodine from degrading reactor fuel is indeed the entire, substantive source term of radioactivity.

Though thi.s simplification is grossly in error, it is true the release of* Cs and I from degrading reactor fuel is an important aspect of severe accidents.

The approach toward the severe accident source teem taken in the Reactor Safety Study was intended to be "conservative."

That is, errors . in the analysis were to accrue on the side of overestimating the extent of fission product celease--especially the releas*e of volatile radionuclide both from the fuel and from the plant. Recently~ and especially since the accident involving fuel degradation at Three Mile Island, the treatment of radionuclide release presented in the Reactor Safety Study has been questioned [2,3]. Most of the criticism has suggested that the models developed foe the Reactor Safety Study may have been too conservative.* These models neglect natural phenomena that would reduce the amount of radioactive material escaping the fuel that could escape the plant. Criticism that the 3-1

• Reactor Safety Study may hav_e been nonconservative has also appeared. Criticisms of the analyses done for the Reactor Safety Study have focused on release of radioactivity from the plant. But. in every case. the alternate considerations have been based on different portrayals of radionuclide release from the reactor fuel.

Criticisms of the Reactor Safety Study have prompted the initiation or continuation of many analytic and experimental research programs. A recent survey [4] identified 15 major programs to characterize release of radionuclides from reactor fuel as well as several programs to define the behavior of these radionuclides after release. Several analytic efforts that utilize results of the research to define new severe accident source terms have appeared [5-8]. A consistent thrust in all of the recent work has been to relate in a more mechanistic manner the release of radioactive species from the fuel to phenomena taking place during core degradation. That is. generic release estimates applicable to a wide variety of accidents at a wide variety of plants are being abandoned. In the place of these generic releases are models that are sensitive to features specific to the plant and the accident in question.

Development of mechanistic models of release is a formidable task. The diversity of radionuclides and nonradioactive species that are of interest has been discussed in the preceding chapter. Release of these species is an inherently chemical process. So, release models ought* to be sensitive to those features of severe reactor accidents that ought to affect chem is try--notably temperature. pressure. and atmosphere composition. Release is also a transport process. so release

. models ought also to be sensitive to those features of severe accidents that affect transport--such as gas flow velocities.

core geometry. fuel microstructure and clad state.

The definition of severe reactor accidents has progressed considerably since the time of the Reactor Safety Study.

Small-break accidents and accidents initiated by power transients have been found to be* much greater contributors to the potential risks of nuclear power plants (see, for example, References 9 and 10) . Further. it has been found desirable to know not just the potential release of radioactivity. but also how the release varies from one type of accident to another. An indication of the range of variation of accident features that ought to affect release during accidents of interest today is provided in Table 3 .1. Flow velocities through t):le core can vary by 2 to 3 orders of magnitude. Pressures can vary by 2 orders of magnitude. Fuel burn-up can vary by an order of magnitude. Local gas compositions can vary by several orders of magnitude. These wide variations in accident features ought then to cause variations in release of some significant nature .

3-2

• Table 3.1 Features of Severe Reactor Accidents that Ought to Affect Release Feature Typical Range System Pressure 2 - 170 atmosphere Maximum Core Temperature 2200 - 3100 K Heatup Rate of Core 50 K/s Flow Velocities Through. the Core 1 - 200 cm/s Extent of Clad Oxidation 20 - 100%

Ratio of Hydrogen to Steam 0 - 1010 in the Atmosphere Fuel Burnup 1000 - 33000 MWd/ton Time fiom Scram to Core Melting 1 - 32 hours3.703704e-4 days <br />0.00889 hours <br />5.291005e-5 weeks <br />1.2176e-5 months <br /> Developments have taken place since the time of the Reactor Safety Study in the analyses of radionuclide behavior after release from the fuel as well as in the description of the release process. Some of these developments are described in Chapters 5 and 6 of this report. A key input to the tools for analysis of radionuclide rbehavior is the timing of radionuclide release. That is. it is no longer adequate to know what is released and how much is released. It is also necessary to know when radioactive and nonradioactive species are released and how fast they are released.

It is clear.* then. that models of radionuclide release must be much more sophisticated than those adequate for the Reactor Safety. E~sential aspects of modern release models are:

1. 'The models must be sensitive to those features of plants and accidents that make various accidents different.

Generic tables of release are inadequate.

2. Release models must be of mechanistic sophistication compatible with descriptions of subsequent phases of severe accident analyses. That is. seldom will it be adequate to simply assert an integral release fraction without defining t-he timing and chemic a 1 farm of the release.

3-3

3. Both radioactive species and nonradioactive species must be considered in the definition of release models.

The objective of this chapter is first to describe the tech-nology available for developing models of release from reactor fuel during core degradation. Meeting this objective will require reviewing some of the fundamental aspects of the release process. The second objective of the chapter is to discuss models that have been developed and used to describe release from the reactor fuel. An attempt is made to critically review these models in light of the discussions of the fundamentals of release. Final*ly, an objective of the chapter is to specify a release model for the MELCOR code that is at once of sufficient sophistication to meet the essential needs for modern reactor accident analyses yet simple enough to fit within the space and execution requirements of a systems code.

3.2 Nomenclature Despite criticisms of the work, the framework created for the Reactor Safety Study is useful for describing release of radio-nuclides and nonradioactive species during in-vessel phases of an accident. As set down in the Reactor Safety Study and subse-quently modified [11] release in-vessel can be divided into four regimes:

1. Gap Release

2. Diffusion Release

3. Meltdown Release

4. Fragmentation and Oxidation Release Some sense of the magnitudes in each of these release stages is provided in Table 3.2.

As fuel heats, gases within the fueY rod pressurize. At the same time the clad itself weakens. If the ambient atmosphere is at low pressure, the clad will balloon and rupture. Even if this does not occur, eventually the clad ruptures. During normal operation and during early phases of the accident, radionuclides escape the fuel and collect between the fuel pellet and the fuel clad. When the clad ruptures this collected material can suddenly escape the fuel rod. This gap release of radioactivity can itself be divided .into two steps--sudden release during depressurization of the rod and slower release as vapors in the fuel/clad gap diffuse to the point of clad rupture. This release was explicitly considered in the Reactor Safety Study.

It is given only limited discussion here. Quite frankly this release is small. It is so rapid that it probably does not require detailed modeling. Uncertainty in gap release pales in comparison to uncertainties in release during subsequent stages of a reactor accident.

3-4

• • Table 3.2 Estimates Made in the Reactor Safety Study [l] of Radioactivity Release During In-Vessel Stages of a Severe Accident Element Fraction of the Core Inventory That Escapes the Fuel DuringCa)

Gap Diffusion Meltdown Fragmentation Release Release Cb) Release Release Cc)

Xe, Kr 0.030 0.870 0.9 I* Br 0.017 0.883 0.9 Cs, Rb 0.050 0.760 Te, Se, Sb 0.0001 0.150 0.6 Sr, Ba 1 X 10-6 0.100

• Ru, Mo, Pd.

Rh, Tc Nd. La, Eu, Y, Ce, Pr, Pm, Sm, Np, 0.030 0.9

-PU, Zr, Nb 0.003 (a) Leach release in-vessel was not considered.

(b) Diffusion release estimates were split between Gap release and Meltdown release.

( c) Indicates fraction of the inventory remaining in f rag-mented fraction of the fuel that is released. Release was presumed in the Reactor Safety Study to be due to

~xidation of dispersed debris .

• 3-5

• The fuel continues to heat following clad rupture.* During this stage radionuclides migrate to .the surfaces of the fuel and can escape into the fuel/clad gap.

clides can escape the fuel rod.

From this gap. the radionu-This phase of release was not explicitly included in the Reactor Safety Study analyses.

defined shortly after the study was published [11].

It was It has been a regime of great interest and is discussed here.

Further heating of the fuel can lead to melting. Formation of a liquid phase can take place in two ways. Clearly. the fuel or the products of fuel interaction with zro 2 produced by steam oxidation of the clad can melt .. Nominal temperatures for melting of fuel and U02/Zr02 mixtures are 3140 Kand 2800 K. respective-ly. Also the clad can melt. But. it has been found that melting clad can interact strongly with the fuel to form materials that start to melt at temperatures as low as 2170 K [12]. Melting of mixtures of zro 2

• Zr. and u*o 2 is often called II liquefaction 11 to distinguish it from melting of the fuel itself. For most pur-poses this distinction is useful only for specifying temperature and timing. An attempt is made here to retain this distinction.

Liquefaction of the zro 2 /Zr/U0 2 mixture has also been called 11 eutectic formation.". Since it manifestly is not the 11 formation of a eutectic.~ this nomenclature is avoided.

It is possible during the course of an accident that high temperature core debris will interact with liquid water. This might occur if molten or fragmented fuel fell from the core region of the reactor into the water-filled lower plenum of the reactor. It might also occur if water were deliberately injected into the vessel in an attempt to terminate an accident.

The interaction of molten fuel with water can lead to a steam explosion. In the Reactor Safety Study steam explosions we're thought to expel finely fragmented debris into oxidant-rich atmospheres. Vigorous oxidation of the.debris was estimated to cause extensive radionuclide release. This oxidation release is discussed extensively in Chapter 4 in connection with ex-vessel release-and is not treated here.

Fuel/coolant. interactions can be benign in the sense that fragmentation of the fuel is not violent and does not involve broad dispersal of the debris. Still this fragmentation can affect fission product release. A very high surface area is created. Rapid flows of steam across the surfaces take place.

These conditions are conducive to rapid radionuclide release especially if the _debris is still quite hot. Some discussion of release from fragmented fuel is presented in this chapter.

If the fuel is fragmented but not completely quenched by interaction with water. continued release of radionuclides can occur. Until the bed of debris begins to melt. release during 3-6

this stage of the accident* is similar to the diffusion release defined above. though the geometry is quite different. This situation of release from a debris bed can be reached by means other than fuel/coolant interactions. The differences in geometry of debris beds and intact fuel rods lead to differences in the methods for predicting release which are discussed here.

Finally. if the fuel is quenched. radionuclide release can occur by,leaching into the surrounding liquid water. This type of release has not been a serious concern in accident analyses in the past and is not discussed here. The interested reader is referred to the discussion of ex-vessel leaching release in Chapter,4 and the relevant literature [13-16].

One other note on nomenclature refers to the use of the terms. "fission product" and 11 radionuclide~ 11 As stated in Chipter 2. these terms are used interchangeably here even though it is known that not all the radioactive material available in a reactor is produced as a result of fissioning of uranium or plutonium nuclei. The terms are also used to refer to the stable isotopes formed in the decay chains of some important isotopes. This nomenclature ought not to cause confusion.

3.3 Fundamentals of the Release Process

• Release during core degradation is just the conversion of a material in the core to an airborne material (leaching is ignored here). This process can occur by either mechanical means or as a result of chemical processes that convert a condensed species into a vapor species.

Mechanical aerosol formation does occur during core degrada-tion. Lorenz et al. [17] have observed that a small amount of 0

dust 11 is .expelled from fuel rods when the clad balloons and ruptures. *Analyses show this material to be fuel with particle sizes between 5 and 50 µm. Brockmann and Stalker [18] have observed that coarse particulate is evolved when zircaloy clad is burned in air. The sizes and shapes of these particles could be rationalized only in terms of mechanical comminution of the condensed products of Zr oxidation. It is not difficult to imagine that rapid oxidation of cladding by steam could also produce co"arse particulate. Parker et al. [ 19] have observed that when pressurized control rods rupture an alloy of silver and indium is sprayed *about. Mitchell et al. [20] have shown these alloy droplets can have aeroso 1 dimensions. Finally. violent fuel/coolant interactions could produce aerosol-sized particles of water and core debris (see Chapter 4).

In general. release by mechanical mechanisms of aerosol

• formation degradation.

is of a sudden. transitory nature The products of the mechanical processes are 3-7 during core

coarse and would remain airborne for only short periods of time. Compositions of the mechanically produced particulate reflect the bulk composition of the parent material.* That is.

they are neither enriched nor depleted of radionuclide s.

Continuing release of material from the core comes from vaporization --that is. from condensed-to -vapor phase transitions.

Vaporization is responsible for most of the radionuclide release during core* degradation and may be responsible for most of the total mass release. Vapors. when they condense. form very fine particles which can remain suspended for long periods of time.

These particles can be quite enriched relative to the parent material in radionuclide s.

Vaporization can be a simple unary process such as:

[ABJuo -+ AB (gas) 2 or

[ABJuo -+ A (gas) + B (gas) 2 where the symbol [ ]uo means the condensed species is in the 2

fuel lattice. Vaporization can also be a complex process involv-ing reactions of the condensed species with ambient gases (predominant ly H2 and H2 o) to form a volatile species. Examples of these more complex vaporization processes are:

Ce(gas) + 2H 2 o Regardless of their natures. all vaporization processes have some features in common. The driving force for vaporization and the maximum extent of vaporization are specified by differences between existing conditions and thermochemic al equilibrium condi-tions. The rate of vaporization or. equivalently . the rate of approach to equilibrium is limited by kinetic or mass transport factors. The thermochemis try and kinetic factors of release are d~scribed in the subsections below.

3-8

A. Thermodynamics of Vaporization Consider the vaporization of a species A from a host lattice.

A particular vaporization process might be where Ai is some vapor form which may be distinct from the chemical form A dissolved in the host lattice. The driving force for this process is proportional to the difference between the equilibrium partial pressure of Ai in the ambient atmosphere and the actual partial pressure:

ith driving force~ [Pi(eq) - Pi(t)]

Pi(eq) = equilibrium partial pressure of Ai Pi(t) = actual partial pressure of Ai at time t Since [AJhost can vaporize by a variety of processes. the total driving force for vaporization of [A]host is given by:

N driving for release of [A]host = j:l [Pj(eq) - Pj(t)] Kj where where the Kjs are proportionality facto.rs and the summation is over all vapor species formed by A.

As a specific example. the vaporization of barium oxide dissolved in a U02 lattice is examined. Some vaporization reactions of barium oxide into an atmosphere of steam and hydrogen are:

[BaOJuo ~ BaO(gas) 2

[BaoJ 00 * + ~ 2 ~ Ba(gas) + H2 o

. 2

[BaOJuo + 1/2 H2 ~ BaOH(gas) 2

[BaO]uo + H2 o ~ Ba(OH) 2 (gas) 2 Then the driving force for barium oxide vaporization is:

3-9

+ KBa(OH) [PBa(OH) (eq) - PBa(OH) (t)]

2 2 2 There are several features of vaporization processes that are revealed by examining the driving force expression. First, the driving force varies with time. As the actual concentration of the vapor forms approaches the equilibrium concentration

( concentrations are related to partial pressures), the driving force, and consequently, the rate of vaporization go to zero.

In a flowing

• system, such as steam/hydrogen mixtures flowing through a reactor core, the driving force for vaporization is spatially dependent. The driving force can be high at the flow entrance where the ambient vapor concentration of species is low. The driving force falls then along the flow path as the ambient concentration of the vapor species builds up toward equilibrium .

• A second obvious feature of vaporization is that the driving force for vaporization1 increases with the number of vapor species that can form. Analyses that omit species with high equilibrium partial pressures can err badly.

Finally, it is essential, obviously, to know the equilibrium partial pressures. The equilibrium partial pressures determine the maximum extent of vaporization as well as figuring in the

~riving force for vaporization.

consider again the vaporization of the hypothetical species

[AJhost* The equilibrium partial pressure of Ai is given by:

b.G. (T) = -RT 2.n [<t\Pi (eq)/yAXA]

1 where b.Gi(T) = standard state free-energy change for the vaporization process T = absolute temperature ct>i = fugacity coefficient of the ith vapor species

• YA = activity coefficient of 3-10 A in the host material

= mole fraction of A in the host material

= gas constant The values of ~Gi(T) are typically available for most species of interest for reactor accident analyses (21]. If A can be present in only one host material, then XA can be determined from inventories. When A can partition among several condensed host materials there is an additional problem of determining XA in ea~h phase. Discussion of this problem is deferred until later in this section-.

The activity and fugacity coefficients that appear in the equilibrium are seldom known. There are limited data available for the activity coefficients of binary systems that show the activity coefficients can be functions of the system temperature, composition and pressure. Similarly, data for well-known gases show the fugacity coefficients are dependent on temperature,

• pressure, and properties of the vapor species.

The dichotomy between the simple elegance of the thermo-dynamic description of vaporization and the difficulty of implementing this description has been known for a long time.

There has been quite a lot of effort expended to model the activity and fugacity coefficients for complicated systems. The experience gleaned from the use of these models provides a data base on their applicable range. These models will be the subject of discussion in the balance of this subsection.

Activity and fugacity coefficients as used above are measures of the deviation from ideali ty of condensed and vapor phases, respectively. These deviations from ideality arise because the molecular interactions, whether repulsive or attractive, are not the same in mixtures as they are in some pure reference state.

It would seem obvious, intuitively, that*since interactions among molecules are weak in the gas phase, that deviations from ideal-ity would also be small in the gas phase. Extensive studies over the last 100 years have allowed descriptions to be formulated of even these small deviati~ns from ideality in gases. It is conventional to_ express the descriptions in the form of an equation of state. Most of the popular models can be expressed in the form:

RT e )

z = PV V RT = RT

{v - !] }

1 (V - b) (V - b) (V2 + 6V + c)}

where e = RT(6 - a.)

T] = (B - c)/(6 - c) 3-11

The value of z. often called the 11 compr:e ssibility factor:. 11 for:

an ideal system would be one for: all pr:essur: es and temper:a tur:es.

When the system deviates from ideality . z becomes a function of both pressure and temper:a tur:e. Values for: the paramet ers in var:ious forms of the equation of state shown above are listed in Table 3. 3. To make the models as useful as possible for: the widest varietie s of fluids. it has been traditio nal to express function al for:ms of the models in terms of the so-calle d 11 r:educed var:iable s 11 :

Tr:= T/Tc and Pr:= P/Pc wher:e Tc= critical temper:at ur:e Pc= critical pr:essur:e This is quite useful for: well-ch aracteri zed gases. Unfortu nate-ly.* most of the gaseous species of interes t for: the purposes of reactor safety .are not well characte rized and the critica l tempera tures and pr:essure s have never been measure d. Even methods to estimate these critical constan ts require data about the gases that are not known. in gener:al . With the cr:i tica 1 constan ts known. the equation of state must be fit to data to determin e quantita tive values for: the paramet ers. Usually adequate data for the species of interest in severe acciden t analyses are not availab le.

Another popular: equation of state is the Vir:ial Expansio n:

Z = 1 + B/V + c1v2 + D/V3 + ***

. In the nomencl ature of Table 3.3. the paramet ric values in this equation of state can be written as:

B = b - 0/RT C = b2 - 0b/RT + 0 (6 + n)/RT D = b3 - Sb2/RT + 8b(6 + n)/RT - 0(62 - c + n6)/RT The Vir:ial Expansio n is of particul ar: interes t since it.

unlike the empiric al equation s of state in Table 3. 3. has some theoreti cal signific ance. The relation ship between the paramete r:

B and* molecul ar interact ions is well known [32]. Wher:eas the detailed molecula r: properti es are seldom known. they can some-times be guessed~ A Vir:ial equation of state truncate d after the B/V term is often quite accurate until:

P > [T/2] [E YiPc(i)/ E YiTc(i)]

3-12

Table 3.3 Popular Equations of State Model Name and Year It Was Parameters First Suggested e Tl 6 Van der Waals (1873) a b 0 0 Berthelot (1900) a/T b 0 0 Clausius (1880) a/T b 2C c2 Redlich-Kwon g (1949) a/Tl/2 b b 0 1 ew(T) b b Wilson 0 Peng-Ro b.1nson 2 (1976) SPR(T) b 2b -b2 3 b Lee-Erbar-Ed minster (1973)

• SL (T) (T) 0 2 2 1) T]

1. P 0 (T)IR Tc = 0.4275[1 + (1.57 + 1.62 w) (T-l- r r cw 2 2 2 12 2

2. Pc0PR(T)/R Tc = 0.4275[1 + (0.480+1.574<a>- 0.776w )(1 - T! )]

2 2 2 112 2

3. P 8L(T)IR T =0.45725[1 + (0.37464+1.54226 6<a>-0.2699w ) (1 - Tr )]

C C 3-13

where Yi = mole fraction of the species i in the gas phase.

Once an equation of state is known. the fugacity coefficients can be calculated from:

4>.l f [::i] T.V.n. 1

]Fl

- RTdV - ln V

Again. what i~ simple in concept is difficult to imple~ent. and the lack of appropriate data can make it impossible. Fortunate-ly. the deviations from ideality do become small at high tempera-tures if the system is far from the critical. point and pressures are low. The assumptions of ideality become questionable for fission product vapors only near the upper limit of pressures encountered in reactor accidents -150 atmospheres.

Theoretically. an equation of state should provide the infor-mation necessary to correct nonidealities in the condensed phase as well as the gas phase. Even in the simplest systems. this is difficult to achieve. Consequently~ an entirely different formalism has developed for dealing with the condensed phase.

Activity coefficients for the condensed phase are not confidently rationalized away as can be fugacity coefficients.

Thermodynamic laws do show that the pressure dependence of the activity coefficients can be separated from the compositional and temperature dependencies. A general expression of the pressure-dependence of condensed phase activity coefficients is:

where p = pressure of interest PREF = reference pressure where the activity coefficient is known V*l = partial molar volume of the species i in the mixture The reference pressure is usually 1 atmosphere. Partial molar volumes .of species in a mixture are seldom known. It has become common to assume partial molar volumes are equal to the molar volumes of the pure species and that the partial molar volumes 3-14

are independent of pressure. This assumption can only be made if conditions are well removed from the critical point.

With these assumptions the pressure dependance of activity coefficients is given by This express ion shows that activity coefficients increase with pressure. The *factor of increase is called the Poynting correc-tion factor. Poynting correction factors for a species with a partial molar volume of 50 cm3 /mole at temperatures of 1000.

2000. and . 3000 K are plotted against pressure in Figure 3 .1.

Most species of interest here would have even smaller partial molar volumes and. consequently. smaller correction factors.

Clearly. for systems of interest for reactor safety analyses.

the pressure correction of activity coefficients is not especially important.

Quite a variety of models have been developed to describe the compositional and temperature dependence of activity coefficient.

The simplest model is. of course. that of the ideal mixture:

for all i and T This model should represent the asymptote that mixtures approach as temperatures increase.

More exotic models to describe activity-coefficie nts at lower temperatures are summarized in Table 3. 4. It is not difficult to reach a point at which these ~~pirical models cannot be used because of the lack of data. Models that are based on binary interactions are attractive because the necessary parametric data can be extracted from binary phase diagrams which are far more abundant than detailed activity data. Powers [22] has used the Wilson equation to describe activities in the Ag-In-Cd mixture. Powers and Brockmann [ 23] have used regular solution models in their model of fission . product release during core debris interactions with concrete.

Return now to the example of barium oxide vaporization.

Some insight into the v_aporization of this species can be obtained by examining the quantity:

3-15

1. 09 ___,,,,,,-

0:::

D

1. 08 _____ ,,,,,

I-u

< 1. 07 ,.,,

I.J.. T

• 1000 K ,,,,'

z 1. 06 ,,,,,'

D ,,

I-u 1. 05 w ,,,,,'

0::

0:: ,, T

• 2000 K w

D u 1. 04 ,,,,

I I-'

a, ~

z

..... 1. 03 ,,,,,, ..

I-z ,,,'

>- 1. 02 , ,,

D Cl. ,,

1. 01 ,,,,' ..

10 30 50 70 90 110 130 PRESSURE CATMS.)

Figure 3.1. Poynting Correction Factors for Several Temperatures as a Function of Pressure~

• Model Table 3.4 Popular Models for Activity Coefficients BT ln lTk (PREF)]

Ideal 0 Regular Binary B (l - Xk)2 Wilson where NRTL C B UNIQUAC

• BT (lD Tk + ln y.k) where 4>k 4ik c-C ln l.k . 1 - ci,k,x.k + I.D [4>k./Xk] - 2 z

Qk (1 - 8

.t

+ PD e.k

))

ln liB

- Qll:. r- ln N

( . I:

)a:l 8 jAjk.) -

N I:

ia:l

(

~

8 -A *. )]

ja:l

\jA:i 4>i -

• 3-17

From the discussions above, il is apparent that when ideality is assumed in both the gas and condensed phases then:

== - RT 2. n [x_P_B_a_P_H-=2'--l Bao PH2~J l.\GBaOH(T) = - R1' 2.n PBaOH'

[ XBaO2 PH 2

J l.\GBa(OH) (T) = RT 2.n [PBa(OH) 2 J 2 XBaO PH 0 2

Thus, E =

where Ki are proportionality factors that are functions of temperature. It is obvious that the vaporization of barium oxide will depend on its concentration in the host material. It also depends on the composition of the ambient gas. The variations in partial preisures of the various barium-bearirig species as a function of the PH /PHzO ratio at 2000 Kand a total pressure of 2

10 atmospheres are shown in Figure 3.2. In preparing this figure the chemistry of water and hydrogen at high temperatures was also recognized:

3-18

90 w

a:

u, u, 80 w

a:

CL

..J 70 Ba(g) a:

CL 60

\: I I

I I I

a:

< 50

.* I m ** I

..J l

...0< 40 I".

I ** ...

u.

• I I ..

0

~ 30 BaOH ***

I I ..

m 0

\!..

• I I

u, . I

-ww 20 0

I

.* *.* BaO CL u,

10 0 *****

..**** I-*

10-4 10-3 10-2 10-1 1 101 102 103 104 P(H2)IP(H20)

Figure 3.2. Vapor Species Produced at 2000 Kand a Total Pres-sure of 10 Atmospheres by Vaporization of Barium oxide as a Function of PH /PH .

0 2 2 3-19

• Oz HzO 2Hz0 i

i i

20 1/2 Hz+ OH HOz + 3/4 Hz The results in Figure 3. 2 make it apparent that tabulated values of vapor pressures as functions of temperature only are of_ little value in the analysis of severe accident source terms.

The vaporizaticin should be a function of the ambient gas composition. I t should also be apparent that within a reactor core the driving force for vaporization may change since the gas composition changes due to reactions such as the steam oxidation of the zircaloy clad on the fuel.

The analyses done for the Reactor Safety Study did consider effects of gas composition on vaporization though the final release fractions were independent of these considerations.

However. the analyses done for the Reactor Safety Study restricted attention to oxidation reduction reactions of the type

• Thus. for the barium oxide example the formalism of the Reactor Safety Study would yield:

A comparison of E and ERsS is presented in Figure 3.3. The comparison*shows that a more complete description of the chemis-try can yield higher driving forces for the vaporization of species than might be anticipated from the analyses done in the Reactor Safety Study. Higher driving forces do not necessarily translate into higher extents of release. But. the potential certainly exists* for releases much higher than those predicted in the Re.actor Safety Study. This possibility. if realized.

would be. of course. quite contrary to the "conventional wisdom" that releases predicted in the Reactor Safety Study conservative-ly bound the actual releases during severe accidents.

The difficulty with the approach used in the Reactor Safety Study is that important vapor phase species were neglected.

Vapor phase hydroxides figured prominently in the discussion above for Bao vaporization. The vaporization of many other

• species can be enhanced by vapor phase hydroxide formation.

general reaction expression for vapor phase hydroxide formation can be:

3-20 A

10-2 , - - - - - - - . - - - - . . - - - - - . - - - - . . . - - - - - - - - - - - - - - . . . ; _ -

MORE COMPLETE 10-3 CHEMISTRY fl) w cc

=>

~ 10-4 w

. cc Q.

..J

...cc<

10-s Q.

fl) w

(..) REACTOR SAFETY ,'

,~,'

w STUDY ,,

Q.

I fl) 10-&

u.

0

E

=>

fl) ------------------------

10-1 10-4 10- 3 10-2 10-1 1 10 1 102 103 104 Figure 3 . 3 . I: and I:Rss for Barium Oxide Vaporization as a Function of PH2/PH20 at 2000 K and a Total Pres-sure of 10 Atmospheres. I: is shown as the solid line. I:Rss is shown as a dashed line.

3-21

MO( y-n )(OH) 2 n (g) and the corresponding equilibrium expression is:

fiG(T) = - RT 2.n Consideration of vapor-phase hydroxides is hampered by lack

• of data. High-temperature chemical studies are usually done in refractory metal furnaces. Because these refractory metals are easily oxidized. the conditions conducive to vapor-phase hydrox-ide formation have been carefully avoided. By far. the greatest amount of work on vapor-phase hydroxides has been done in the geologic field and in the study of nuclear fallout. What studies have been done show that vapor-phase hydroxides will be important for many of the species of interest for source term development.

A list of known vapor-phase hydroxides is presented in Table 3.5.

Attempts have been made to predict the existence of vapor phase hydroxides for elements that have not been studied experimentally

[2li].

Two other classes of vapor species that were not considered extensively in the development of the source terms for the Reactor Safety Study are the vapor-phase hydrides and mixed-vapor species. A general reaction for the formation of vapor-phase hydrides is fiG(T) = -

PMH 2

PH 0 RT ln -p~- p(Y+Z/

[ MOY H y

2 2

2)l

• Hydride formation clearly depends on temperature and the absolute pressures of both steam and hydrogen. The importance of vapor-phase hydrides has not been explored in any significant way to date. Based on inspection of the terms in the free-energy equa-tion above. it would be expected that the contributions to the gas phase made by hydrides would vary markedly over the course of an accident as well as among various accident sequences.

3-22

• Table 3.5 Some Vapor Species That Were Not Considered in the Reactor Saf~ty Study Fission Produce Representative Significant Suspected

_Category Element Vapor-Phase Vapor-Phase Hydroxide Hydride Alkali Metals Cs CsOH, (CsOH)z Alkaline Earths Ba BaOH. Ba(OH)z BaH, SrH Halogens I HI Chalcogens Te TeO(OH) HzTe Platinoids Ru RhO(OH)

Early Transition Mo MoOz(OH)z Elements CrOz(OH)z

• Tetrc1.valents Trivalents Ce La LaO(OH)

La(OH)z Uranium u UOz(OH)z Main Group Metals ca. Sn InOH, In (OH) 2 SnH. SbH3 SnOH. Sn(OH)z Boron B H3B03, HBOz

• 3-23 i

I L__ _ _ _ _

Mixed-vapor species are those made of two or more atoms whose vaporization is of interest. These species have not been exten-sively studied. CsI(g) is the only well-recognized example.

Vapor-phase tellurides such as AgTe. SnTe. and SbTe are known but seldom have been taken into consideration in the formulation of source terms. The efficiency with which mixed-vapor species transport fission products will lead to greater interest in these species as results of integral fission product release tests become available and attempts are made to rationalize these results.

Another class of species that has not been considered in the past is ions. Thermal ionization of vapors seldom is a major consideration in typical thermochemical*analyses at temperatures less than 2800 K. Ionization would not be important in accident analyses. except that chemistry is taking place in the reactor in an intense radiation field. Though ions formed by the intense radiation are unstable. the continuing exposure to radiation assures that ions are reformed. Thus. a meta-stable equilibrium concentration of ions may well exist in the ambient atmosphere.

Insufficient analyses of the effects of ionizing radiation on chemistry have been undertaken to know if it is an effect of importance. What data are available show that it may be important for iodine and CsI chemistry [33].

Several chemical processes important to the analysis of fission product vaporization have been mentioned to this point.

It is useful to examine how well these processes can be analyzed given that the data available are uncertain. The quantitative expression of the equilibria mentioned above can be written *in the general form:

f = exp (-llG/RT) where f is the quantity to be calculated and the partial pressures* of hydrogen and steam are provided. but are uncertain.

as is the temperature. The quantity llG is derived from tabulations and also may be uncertain. The uncertainty in the quantity f derived from these uncertain data. if cross-terms are neglected. is given by:

• a 2

3-24

• It can be assumed that partial pressures calculated for severe accident scenarios might be 100 percent in error and temperatures might be 10 percent in error. Then 2 + b 2 + (ollG) 2 ~

'6G' 2

10- 2 a RT + (RT)

Rather high quality free-energy data from the various tabulations will be uncertain to about RT and a typical value of 6G might be riRT. Then

.[6:J 2 a2 + b 2

+ 1 + 10

-2 TJ 2

where TJ is a small integer as are a and b.

This derivation illustrates several points:

1. Uncertainties in_ even the best thermodynamic data place a constraint on the accuracy of calculated vapor-phase speciation of about 100 percent.

2. Temperatures produced by even crude thermal analyses of the core meltdown process do not have a tremendous influence on the relative uncertainty in calculated speciation of the vapor.

3 .* By far and away the greatest source of uncertainty in the vapor-phase speciation comes from the uncertainties in steam and hydrogen partial pressures.

Because the equilibrium speciation of the gas phase plays such an important role in determining the driving force for vaporiza-tion. the quality of steam and hydrogen partial pressure calcula-tions is of essential concern. The current state of the art in making these caiculations places a very big constraint on the quality of. fission product source term calculations. Even so.

neglect of these vapor phase speciation issues can lead to errors in the vapor pressures on the order of 103 to 105 percent.

as illustrated by the discussion of Ba vaporization.

To this point. the analysis of thermochemistry has been done by explicitly stating the chemical reactions of interest and evaluating each of these reactions. A key. point in the discus-sions has been the importance of including all the major species.

Such a procedure can easily become overwhelming as the number of elements and species grows. A somewhat more formalized procedure is obviously needed.

3-25

A variety of procedures for analyses of multicomponent chemi-cal equilibria have been developed over the past years [24-30].

These procedures often are based on minimizing the total free-energy, G, of a system where G =En.µ.

i i

µ. = Gf(i) + RT ~n X.y. for condensed phases i i 1

µ. = Gf(i) *+ RT ~n P.~. for vapors 1 1 1

. th .

n. = mo 1 es o f t he i species 1

subject to mass balance constraints:

E fore= 1 to E all species

. . th .

where a. = num b er o f atoms of element e 1n the 1 species 1,e B

e

= moles of element e in the system E = number of elements in the system and non-negativity constraints:

n. > o for all i.

1 The problem as stated is an N dimensional constrained optimiza-tion with linear equality and inequality constraints. A little manipulation of *the equations can reduce the d imens iona 1 i ty to E+l. This. nearly always has to be done. Practical methods for solving nonlinear optimization problems rarely are feasible for dimensions greater than 100. Species of importance in calcula-tion of phenomenological source terms can easily exceed 300 in number [ 2 3 J

• Direct sea*rch and sequential linear programming techniques have been used to solve the optimization problem in the past.

Descent techniques are now almost exclusively used. Some of the more popular descent methods are:

3-26

• 1. STEEPEST DESCENT: Approach to a solution is guaranteed by the first order steepest descent method. The method is not widely used in specialized codes because the rate of convergence to a solution becomes infinitely slow as the solution is approached. Conservation of mass to any specified accuracy is possible at the expense. of increasing number of iterations. The method is attractive because it is robust with respect to initial solutions for the iterative procedure and the programming is simple. The method is used in the PUFF code [31]. Muir has used a modification of the steepest descent method* in the CORCON model of core debris interactions with concrete [24]. The method must be programmed with an arbitrary criterion for terminating the iterations and it will yield only approximate a~swers. The answers can be thermodynami-cally incorrect because they do not conform necessarily to the Gibbs Phase Rule.

2. SECOND ORDER STEEPEST DESCENT: Many of the problems of the first order steepest descent method are solved by the second order. or Newtonian. steepest descent method. Convergence to. an exact solution that does obey the Gibbs Phase Rule is theoretically possible.

In practice. however. the second order method has its own set of problems. Some of these have been described in a recent review [25). The most germane is that convergence to a solution is guaranteed only if the initial solution for the iterative procedure is within a prescribed neighborhood of the exact solution. With increasing complexity of the problem. the allowed neighborhood can become quite small. This is a serious problem even for stand-alone implementations of the method and would be catastrophic for systems codes using equilibria calculations. Programming of the method is very complicated.

Second order methods are widely used. Second order steepest descent is the basis of the RAND Code

[26]. The. most up-to-date implementations of the method are the FLUEQU code [27) and the SOLGASMIX Code

[2a.2gJ. The implementation in FLUEQU is of particular interest since this code provides a steepest descent routine to generate an acceptable initial solution for the second order iterations. SOLGASMIX has been used in the release estimates done for the IDCOR program

[8,32)

3. OTHER DESCENT METHODS: Conjugate gradient, variable metric. and projected gradient methods are all being researched as methods to solve equilibrium problems.

3-27

Results to date suggest that only the projected gradient method offers great advantages over the more conventional descent techniques. The advantage of the projected gradient method lies in its ability to handle mixtures that deviate significantly from ideality. This may not be a tremendously important feature for source term calculations since data necessary to describe strongly nonideal mixtures are not available and ideal mixtures are usually assumed.

An alternative to descent methods for solving complex chemical equilibria problems is the so-called "equilibrium constant method" developed by Brinkley

[30]. This method involves converting the optimization problem into a set of coupled nonlinear equations. To reduce the dimensionality of the problem, the nonlinear equations are formulated in terms of a set of "basis" species that are nearly *always the most abundant species in the system. The equations are usually solved by a Newton-Raphson method.

This method has lost popularity because of the complexity of programming necessary to define suitable basis species for arbitrary problems. This may not be a severe *restriction in codes used to repetitively solve a single problem. The equilibrium constant method is used in the VANESA model of aerosol genera-tion during core debris/concrete interactions [23].

For in-vessel phases of an acciden~. the conditions of the system change enough and are different *enough from accident scenario to accident scenario that coding for basis state definition may be needed.

Regardless of the equilibrium calculation method used there are several well-characterized test problems that can be used to assur*e the validity of the modeling [31]. A completely gas phase problem (pyrolysis of propane) and a heterogeneous problem (iron ore reduction) are particularly useful tests.

The thermodynamic nature of vaporization defines the maximum extent of vapor formation that could occur if time were allowed for the system to equilibrate. A simple method of using this thermodynamic formulation of the vaporization problem could be developed. Steam and hydrogen gases flowing past the melting core could be assumed to equilibrate with the core. These gases would then emerge from the core saturated with the vaporizing species. Simply knowing the saturation partial pressures of the vapor species and the flow rate of steam and hydrogen would be enough to determine estimates of release rates of fission products and nonradioactive materials from the core. Integration of the release rate would yield release fractions.

3-28

The saturated gases emerging from the core would produce the maximum amount of aerosol when they cooled sufficiently to initiate condensation of vapor. This in turn would maximize the natural mitigation of the release by aerosol processes of sedi-mentation and deposition. Saturated gases would maximize the rate of vapor reactions with structural materials. Large quantities of nonradioactive materials will. of course. accen-tuate deposition of radionuclide in the reactor coolant system and the reactor containment.

There is no reason to believe that maximizing the estimates of vapor releaie fiom the reactor core by relying on thermody-namic calculations of vaporization will lead to an upper bound on the radiological source *term. There are. in fact. good reasons to believe the assumption of saturation is not conservative.

The approach to equilibrium is. then. an essential aspect of the probl~m of fission-product vaporization. even when only bounding approximations are sought.* Since the approach to equi-librium is always from below. real gases emerging from the core will not be $aturated in vapor. Condensation of this vapor will not lead to maximum aerosol production and natural mitigation of the releases by aerosol processes will not be maximized .

• B. Phase Distribution of Fission Products The composition of condensed phases play important roles in both the thermodynamics and kinetics of vaporization. Were there a single. condensed phase present during reactor accidents. the

-effects of composition would be easily handled. The initial composition would be known from the inventories and the time evolution of the condensed phase would be a direct consequence of the release process. When more than one phase is present.

then volatile materials could exchange between phases as well as vaporize. This. too. would pose no major difficulty if the condensed phases and the gas phase were all in mutual equili-brium. At equilibrium. the equilibrium partial pressures of vaporous species are the same over all condensed phases.

Condensed phase equilibrium is harder to achieve. unfortunately.

than is equilibrium between a condensed and a vapor phase .

. Equilibrium is achieved by movement of species from regions of excessive concentration to regions of deficient concentration (Note that this does not mean movement from regions of high to regions of low concentration. The terms 11 excessive 11 and 11 deficient 11 refer to free-energies of the species. not their concentrations). Quite clearly. this movement is slower when it is from one condensed phase to another than when it is to or from a gas phase over a condensed phase.

3-29

There are situations in a reactor accident when the duration of condensed phase disequilibrium is the item of principle interest. The process of core melting is a prime example.

Equilibrium has not been achieved during this melting process.

else progression of the melting would cease.

Because condensed phase composition plays such an important role in vaporization. it is necessary to include analysis of the variations in phase composition even when equilibrium has not been achieved. A generally useful assumption to make in multi-phase. dynamic. vaporization problems is that gas phases will equilibrate with condensed phases even when the condensed phases are not in equilibrium with each other. This assumption was made to good use in the CORCON model of core-debris interactions with concrete [ 24] and the VANESA model of ex-vessel aerosol generation [23].

During severe reactor accidents there are several points at which compositional relationships between several condensed phases. and possibte disequilibrium in these compositions. are of great interest for the vaporization problem:

1. The fuel itself can be composed of several phases

2. The cladding and the fuel are not necessarily in equilibrium

3. The fuel melting stage. by definition. involves liquid and solid phases

4. once melting is complete there are at least two phases present--a metallic liquid and an oxidic liquid.

If the disequilibrium produced by the fission process is negligible. then reactor fuel during normal operation is probably an equilibrium* system. The fuel has been hot for a long time during normal reactor operations so there has been an opportunity for disequilibrium features to anneal. This may not be entirely true for such things as grain growth and fuel sintering. which are slow because of the refractory nature of reactor fuel. But.

for chemical mixture effects that are important to the issues of vaporization. the assumption of equilibration of the fuel is probably ~ccurate.

• Equilibrium fuel here is used in a chemical thermodynamics sense. 11 Equilibrium fuel is a term that also arises in the 11 discussion of the extent of fuel irradiation. This alternate definition ought not be confused with the chemical equilibrium discussed here.

3-30

• Equilibration of the fuel does not make that fuel single phase.

together The possible presence of fission gas bubbles entrapped in the fuel has been mentioned and is discussed further below.

The fission products of a condensed nature may also cluster and not dissolve in the fuel. Postirradia tion examinations of the fuel show that there are at least three distinct phases in the fuel:

1. A METALLIC PHASE: This phase is composed of the more noble metals. Some compositions of the metallic inclusions, which are typically a .tew hundred micro-meters in size. in uo 2 fuel are [50,51]:

(a) 60 a/o Mo: 24 a/o Ru: 16 a/o Tc (b) 55 a/o Mo: 22 a/o Ru: 17 a/o Tc: 6 a/o Rh where a/o means atom percent.

The elemental yields of the above fission products would typically be: so a/o Mo: 30.6 a/o Ru: 12.8 a/o Tc: 6.4 a/o Rh.

2. AN ALKALINE EARTH PHASE: This phase contains Ba, Sr, and Zr and probably is an alkaline earth zirconate. The phase may exist at low operating temperatures because of the low solubility of Ba and Sr ions in U02. At high temperatures of accident transients, this phase may be absorbed into the fuel lattice.

3. THE FLUORITE PHASE: This is the phase with the fuel and most of the fission products.

In addition to these phases. there have been reports of Cs!

crystals and Te on the surf ace of spent fuel [ 3] . A UPd3 phase has been reported [52].

This phase partitioning of the fuel does not affect the thermodynamics of vaporization from the fuel since it is an equilibrium system. Quite obviously, it may affect the kinetics of vaporization if the rate-controlling factor is condensed phase mass transport.

An interesting problem that seems not to have been examined systematically is how the phase partitioning of the fuel varies with temperature. The most obvious species to undergo changes with temperature is molybdenum. If. at elevated temperatures.

it can be stabilized in the fuel matrix as Mo02, the molybdenum-might be extracted from the metallic inclusions.

The .clad on the reactor fuel and the fuel are usually separated by a very narrow physical gap. This can prevent the clad from chemically equilibrating with the fuel which, in fact, 3-31

• is probably desirable.

fission product release.

But this disequilibrium can affect fuel can react and bind with the clad.

Fission products rejected from the The release of Te may be particularly sensitive to this type of reaction with the clad.

The disequilibrium between the fuel and the clad becomes a far more serious problem when temperatures reach the point the cladding can melt. Zirconium can reduce uo 2 and even dissolve it. There is evidence that the process can occur in the sol id state [ 54] but it becomes most dramatic when the clad melts.

The process of fuel attack dramatically lowers the temperature at which fuel

• 11 melts. 11 and dramatically alters the chemical environment of fission products. The essential features of the proce~s have been studied in some depth by workers at the Kernforschungszentrum Karlsruhe. The essential steps of the process are [55):

1. As Zr(l1.) extracts oxygen from the fuel, the wetting of fuel by clad improves and the extraction process accelerates.

2* When the local oxygen concentration in the fuel has reached the lower phase boundary of the U02-x/U system. the formation of liquid uranium causes the fuel matrix to desinter.

3. Fuel particles become entrained in the melt and are rapidly consumed to form a homogeneous (U.Zr)O melt.

This process is discussed in much greater detail elsewhere in this document. Unfortunately. no experimental investigations of

~he process have examined the behavior of fission products during the attack. Though phase diagrams of the U-0-Zr system have been developed [56). they have not been reduced to a thermochemical characterization that would permit analytic examinations of fission product behavior.

• The simple formation of liquid in contact with its solid form may not at first appear to cause phase partitioning of trace impurities such as fission products. In fact. it does.

and is the bas is of II zone refining II of materials. Consider a simple binary system in which both the solid and the liquid are ideal mixtures. Then the partitioning of the impurity between

• the solid and the liquid phases is given by:

~H (1 T/T) + RT ln (y/x) = 0 m m where ~H = heat of fusion of the impurity m

3-32

• T m

T

= melting point (K) of the impurity

= absolute temperature y = mole fraction of the impurity in the liquid phase x = mole fraction of the impurity in the solid phase This simple model allows some conclusions of the effects of species properties on the phase partitioning:

1. partitioning increases with decreasing heat of fusion

• * *

• i

2. part1t1on1ng increases with the temperature and decreases with increasing melting point of the species of interest.

Partitioning between a 1 iquid and a so 1 id phase wi 11 have its greatest effect on the rate rather than the ultimate extent of vaporization if that rate is controlled by condensed phase mass transport. The analysis above suggests that those species most susceptibl~ to phase partitioning are the less refractory and usually more volatile species. Analysis with models that do not require ideal mixture behavior shows that some refractory species such as Ba and Sr are quite sensitive to phase partitioning.

As melting of the core progresses to completion, substantial

• amounts of structural steel are melted. The precise ratio of steel and fuel in the resulting melt depends very much on the nature of the core meltdown process. Some bounding estimates

• have been.made [57]. Since steel and.molten fuel are largely immiscible, there is the poss ibi 1 i ty of fission products partitioning between the two phases.

The partitioning of fission products between molten steel and molten uo 2 has been studied experimentally [SB]. Results of. these studie*s are shown in Table 3. 6. Unfortunately, the partitioning experiments were done in an inert environment. The par ti tionfng would be expected to be a strong function of the oxygen potential of the ambient atmosphere.

The effects of atmosphere composition and pressure of phase partitioning between steel and U02 can be estimated at least qualitatively by considering the exchange reaction between the phases to be

[MO ] .d + xH X OXl e 2 3-33

Table 3.6 Experimental Partition Coefficients For Species Between uo 2 and Iron Species Wt  % in U02 Wt  % in Fe Zr* 93.8 - 95.6 6.2 - 4.4 Zro 93.6 - 97.3 6.4 - 2.7 2

Y203 93.8 - 97.4 6.2 - 2.6 4

La o 100 ii 10-2 3 Ceo 97.1 2.9 2

Pro 92.4 - 96.5 7.6 - 3. 5 2

SrO 99.4 - 99.5 0.6 - 0.5 Bao 97.8 - 98.6 2.2 - 1. 4 Ru 8.7 - 5.9 91. 3 - 94.1 Mo 6.2 - 7.7 93.8 - 92.3 Nb o 98.9 - 76.9 1.1 - 23.1 2 5 Nb 36.4 - 55.7 63.6 - 44~3

• time dependent

• 3-34

where MOx is a fission product in the oxide form dissolved in the fuel melt and Mis the fission product in the metallic state dissolved in the steel melt. Then the partitioning is given by:

where l'.Gf ( i) = free-energy of formation of the ith species P*J = partial pr:essur:e of species j "Ym = Activity coefficient of the metallic fission product in the metal Xm = mole fraction of the metallic fission product in the metal

-y 0 = activity coefficient of the oxidic form of fission product in the fuel melt Y0 = mole fraction of the oxidic fission product in the fuel melt .

C. Kinetics of Vaporization The need to consider: the kinetics of the vaporization process

.introduces substantial complications in the analysis of .radionu-clide release. The data .requirements expand considerably and the sources of data become quite sparse. But, even an approximate treatment of vaporization kinetics is mo.re .realistic than a pr:ior:i assumption of equilibrium.

The .rate limitations to vaporization a.re due to:

1. Transport of vaporizing species in the condensed phase to a free surface.

2. The time .required for: the condensed-to-vapor: phase change of a surface species.

3. The transport of vapors away from the surface.

The potential always exists for: one or: mo.re of these three processes to limit the .rate of vaporization. Two other:

processes can be .rate controlling for: some vaporization processes:

3-35

• 4.

5.

Transport of reactants such as Hz or H 2 o to the free surface where they convert the condensed species into a volatile chemical form.

The rate of heterogeneous reaction at the surface.

The discussions below concentrate on the first three*of the rate controlling processes. (The last two processes are more specialized and all information to date suggests they proceed rapidly during release from reactor fuel.) These rate limitations operate in series. so the slowest will control the overall rate of vaporization. Some simplification of the analysis is possible if one of the above limitations can be selected as rate controlling. Though this is frequently done.

it is not a wise procedure. The range of conditions that develop in a given reactor accident scenario or among different accident scenarios is sufficiently broad that it is very likely the rate-controlling step varies.

The first rate-controlling step cited above alludes to one very important feature of the kinetics of vaporization--it depends on the amount of free surface area that is available.

The amount of free surface area that can participate in the vaporization process depe~ds. of course. on the nature of core degradation processes. These processes are beyond the scope of this chapter. But. it must be emphasized that data on the variation in the available free surface area is essential input to any kinetic analysis.

To further define the information needs that must be met to conduct a kinetic analysis of vaporization. a simple development is carried out below.

Consider a host material. say UOz. containing a vaporizing species at an initial concentration of* Xb mole fraction. For the species to vaporize. it must be at a free surface. In uo 2

• thece are a variety of means for a species to get to a free surface. Obviously. it can diffuse. It might also nucleate as a bubble in the uo 2 grains or be part of a bubbl.e. This bubble can diffuse to a free surface. The deteimination of how species migrate in uo 2 grains has been an area of active research for many years. This topic is discussed at greater length below in connection with the GRASS. FASTGRASS and similar models. For the moment assume that the migration of a species to a free surface can be characterized by a mass-transport coef-ficient. k2.. Then. the rate at which the species migrate to a free-surface is given by:

3-36

where A = free surface area ns = moles of vaporizing species transported to the free surface Xs = the concentration of vaporizing species at the surface ki = mass transport coefficient.

Estimating the mass transport coefficient. ki. is beyond the intent of the simple discussions here. It is determined in reactor accident situations by the behavior of the fuel during the core meltdown process. There. are several useful correlations for estimating ki and others can be derived by analogy with heat transport to the surface.

Quite clearly. the rate of condensed phase mass transport can limit the rate of vaporization. Since the rate is proportional to concentration. at low concentrations this rate can become slow--approaching infinitely slow. Thus. especially for those species released to a significant extent. condensed phase mass transport must be recognized as a limit to the vaporization process.

At the surface. vaporization is driven by a force propor-tional to the difference between the partial pressure in equili-brium with a mixture of the surface composition. Ps ( eq). and the actual partial pressure. Pg. The quantitative expression of the rate of phase change at ~he surface is often given as:

1 dnv

- -- = 44.33 [P (eq) _ p ]

A dt (MT)l/2 s g where nv = moles of species vaporized M = molecular weight of the vapor species This is just the Hertz-Knudsen vaporization rate expression.

Derivation of this expression requires the assumption that a surface species is nearly gas like. This might seem a severe assumption. Certainly. evaporation rates from single crystals are often slower than would be expected from the Langmuir expression by factors of 0.1 to 10-6 [34]. Metals seem to obey the Hertz-Knudsen vaporization expression well [35]. Other surfaces with pores and cracks or crystals with high defect concentrations approach to within a factor of 2 the Hertz-Knudsen 3-37

expression [34]. Even this deviation can be attributed to failure to properly account for back pressure from vaporized species.

A somewhat superior expression for the rate of surface vaporization tha.t takes into account the necessary difference between the surface temperature. Ts. and the gas temperature.

Tg, is [36]:

1 dnv

-A - - = 2a (4 - 1T) 1 p

g (T

s

) 1/2]-

dt 2-a. ( 2,rM)l/2 - (RT )1/2 g

where a. is a correction factor that is often near unity though it can become quite small. For the simple derivation here. the Hertz-Knudsen expression will be used. It has been found adequate for a number of systems analogous to release during core degradation. For instance. Ward [37] found it adequate for analyzing vaporization of Mn. cu. and Cr from iron at 1850 K.

Continued vaporization will occur only if vapor species are swept away from the surface. The rate at which this occurs is given by:

dn

-1 ___g_ =

A dt where ng = moles of vapor species removed kg = gas phase mass transport coefficient Pg = partial pressure of the vapor above the vaporization surface

= partial pressure of the vapor in the bulk gas R. = gas constant.

Again. the estimation of the mass transport coefficient kg is beyond the scope of this work. Providing the information necessary to calculate this mass transport coefficient is an essential product of calculations of the core degradation process. There are many correlations from which approximate mass transport coefficients can be derived. For instance.

natural convection above a flat plate in laminar flow conditions gives a mass transport coefficient of [38]~

3-38

213 7/6 D 0.14 p AB M p where M = molecular weight of the gas p = density of the gas p = total pressure of the gas DAB = diffusion coefficient of the vapor in the gas phase K = thermal conductivity of the gas Cp = heat capacity of the gas g = gravitational force L = length of surface

µ = viscosity of the gas B = 1/T

• Other correlations chapter.

of this type are discussed later When mass transport in the gas phase is through the pore structure of the uo 2 pellets, then an approximate expression in this

.for kg is where DAK = Knudsen diffusion coefficient for the vapor species

=

4 3

[BRTr/ 2

rMA K

0 r = radius of the pellet 3-39

• Two common expressions for K (1) K 0

= c(d/4) 0 are available [39]:

where c = porosity of the pellet d = diameter of the pores 1 128 1. 2 (2) = 9 nd rgr (1 + ,r/8)

K C 0

3 where nd = 3(1-c)/4,rrgr

'T/C = DAB/DAB(eff)

-1 -1 DAB(eff) = DAB + DAK DAB = diffusion coefficient of the vapor in the ambient gas rgr = grain radius

"[ = tortuosity of pathway All correlations of a suitable type involve the diffusion coef-ficient of the vapor in the gas phase. This diffusion coeffi-cient has not been measured for most of the vapors of interest to the discussions here. Fortunately. the diffusion of gases is far better understood than diffusion in condensed phases.

Theories have been developed that relate the diffusion coeff i-cients of gases to the molecular properties of these gases [40].

Unf or tuna tely. these theories require data that are not usually available

• for vapors of interest here. Some useful approximate descriptions of the gas phase diffusion coefficients include the Gilliland equation [41]:

iiJ 1/2 3-40

where v*1 = the molar volume of the ith gas phase species when condensed, Recently, Singh and Singh suggested [42]:

622 l.79xl0- 3 T1

• L + L]l/2

[MA ~

P[v!'3 v!'3] 2

+

At steady state, the rates at which a vaporizing species is transported to

• the surf ace, vaporizes, and is swept away must all be equal:

dn dn s V dt = dt Then, with a little manipulation , the rate of vaporization , N,

• is given by:

where Pb(eq) = the equilibrium partial pressure of vapor over a mixture of composition Xb*

This simple development of the kinetics of vaporization was carried out to illustrate the. features of a system that .affect its vaporization . In summary, these factors are:

1. temperature

2. absolute pressure

3. flow conditions both in the melt and in the gas phase

4. surf ace a.tea

5. condensed phase composition

6. equilibrium behavior of the system.

3-41

Notice that the first four of these essential quantities are not

• in general. determined by the vaporizing system. These factors must be supplied. Condensed-ph ase composition is an essential feature that is. after being initialized. affected by vaporiza-tion .. If there is but one condensed phase. then the composition of that phase is determined by vaporization . If there are several condensed phases then the equilibrium among these phases and the kinetics of approach for this equilibrium also affect the phase compositions . Finally. the equi 1 ibr ium thermodynami cs of the condensed-to -vapor phase transition. which has to appear in the kinetics because it defines the driving force for vaporiza-tion. is an essential part of the vaporization problem.

This simple development of vaporization kinetics also serves to show how rate control of the process can be affected by the conditions of the system. The first term within the brackets of the above rate expression refers to surface vaporization . The form of the term shows that when temperatures are very high and the vaporizing species have large molecular weights. surface vaporization becomes rate controlling. This situation could be expected late in an accident. when meltdown has advanced quite far and temperatures have reached the point where high molecular weight species such as the second row transition metals.

actinides. and lanthanides are volatile.

Finally. the explicit appearance of composition in the third term shows that as vaporization progresses. mass transport in the condensed phase becomes increasingly important as a rate-control -

ling process. Condensed phase mass transport must eventually always become the rate controlling step if the vaporization process continues long enough.

Quite clearly. it is not possible to 11 legislate 11 a single rate-control ling step for vaporization .

The rate-control ling processes discussed above do not exhaust the possible sources of rate control. For instance, vaporization is an endothermic process. The heat required to produce a mole of vapor can vary from about 9 kcal to more than 130 kcal. Due to an inability to supply heat to the structures. structural materials in a reactor core can be subject to vaporization rate control. It has been suggested th~t heat supply may be the rate controlling step in vaporization of silver and indium from control rod materials [22].

D. Condensation and Nucleation The condensation of vapors is an essential part of radionu-clide transport through the reactor coolant system. As such. it is treated in greater detail elsewhere in this document (see Chapter 5). A brief discussion of the condensation of vapors to 3-42

form aerosols is included here because this process can a_ffect the rates of vaporization from a condensed phase. For the purposes of this discussion. the interest is focused on the homogeneous nucleatio'n of particles from the vapor. For these discussions only species that condense congruently will be considered. Where condensation involves decomposition or reaction of the vapor. the problems of analyzing nucleation are much harder. Unfortunately. incongruent nucleation is also important in reactor safety analyses.

As a gas is cooled or chemical conditions are altered. a point is reached where the vapor is saturated with respect to the pure condensed phase. At this point the vapor can begin to heterogeneously condense on other condensed phases--particular ly solid, structural materials. If the gas is cooled at such a fast rate that the condensation rate cannot keep the gas saturated *

. the gas becomes supersaturated. . It is possible then the con-densed species could homogeneously nucleate to form aerosols.

But. since the free-energy of tiny particles produced by nuclea-tion is increased by surface effects. some high level of super-saturation is necessary before spontaneous nucleation can begin.

Even when this level of supersaturation is achieved. there are kinetic barriers that must be crossed to relieve the super-saturated condition. Once nucleation begins. then the vapors in the gas are presented additional surface area for condensation.

A competition for the excess vapor in the gas is set up between condensation on structures and condensation on the nuclei.

It is immediately obvious why the issue of homogeneous nucleation is important for the analysis of severe accident source terms. Condensat.ion of vapors on solid surfaces removes

. these vapors at least temporarily from the inventory of vapors that will contribute to any radiological source term. Vapors that nucleate and vapors that condense on the nuclei remain, at least temporarily. potential contributors to the radiological source term. The questions to be addressed 1n this section concerning homogeneous nucleation are:

1. what level of supersaturation must be achieved before nucleation can begin?

2. wh*at size are the nuclei?

3. how fast do the nuclei grow?

The thermodynamic condition for equilibrium between a vapor and a condensed phase is equality of the respective free-energies. When the condensed phase is present as a perfectly flat. deep pool. this condition defines the equilibrium vapor pressure. When the condensed phase is present as a finite 3-43

body such as a small droplet. the curvature of the surface decreases the free-energy of the condensed phase. Consequently.

a vapor pressure higher than the equilibrium vapor pressure is necessary to establish a metastable equilibrium with the condensed phase. If the effects of pressure-velum~ work can be ignored--they are usually small--the partial pressure of vapor.

P. in equilibrium with a small droplet of radius r is:

2VC1 2.n (P/Peq) = 2.n (S) = rRT where Peq = normal equilibrium vapor pressure V = molar value of the condensed vapor C1 = surface tension of the condensed vapor R = gas constant = 82.06 cm3/mole-K The equilibrium defined here is clearli unstable towatd fluctua-tions in either P or r.

This thermodynamic* criterion is not enough to characterize the nucleation problem. It is necessary to also know the rate at which nuclei of radius r form. The problem is solved by defining conditions for which the rate of nucleation is detectably large.

Two important theories of nucleation exist. The rate of

.nucleation of particles of sizer in both theories is given by dn(r) dt lPNAr [2<1 MWJ

= z RT

,r NA 1,2 V exp [-t]

where MW = molecular weight of condensed species r

~A = Avogadro's number

= ~3 [vmolar] 2[-~

NA kT 1

[2.n(S)J 2

k = Boltzmann's constant z = parametric discussed below 3-44

nucle ating For pract ical purpo ses. it is conve nient to assum e ~he dropl ets are mono dispe: rse with a :radiu s given by 2Vo r = RT 2.n(S) usua lly taken Also. the pract ical. obser vable . nucle ation rate is This defin ition to be 1 nucle i per cubic centi meter per secon d.

The defin ition of a criti cal nucle ation rate close s the probl em.

to the super -

is arbit rary. but nucle ation :rates are so sensi tive is not rate satur ation ratio . s. that selec tion of the criti cal espec ially impo rtant [46].

diffe r The two theor ies for the homog eneou s nucle ation :rate rate expre s-in their treatm ent of the param eter Zin the above eter z sion. In the class ic Becke r-Dor ing theor y [47]. the param ssful in the is taken to be 1. This theor y has prove d quite succe speci es the nucle ation of other analy sis of water nucle ation and that hydro gen bond in the conde nsed phase .

. the A more :recen t devel opme nt of homog eneou s nucle ation n or 1012 [46]. Nucl eatio Lethe -Poun d theor y. takes z = 1017 [48]

the ally fall betwe en of speci es that do not hydro gen bond typic predi ction s of the Becke r-Dor ing and Lethe -Poun d.

ies might A param etric diffe rence of 1017 or 1012 in two theor In fact. the only signi fican t seem of serio us conse quenc e. of the predi ction diffe rence betwe en the two theor ies is the by a diffe rent criti cal super satur ation . which are typic ally ation of This deam plific

_facto r of 3 or 4 in the two theor ies.

the effec t of the value of Z is becau se of the sens itivit y of the nucle ation rate expre ssion . This same diffe rence in the a 20 perce nt predi cted super satur ation would be cause d by about the conde nsed chang e in the value of o. the surfa ce tensi on of mate rial (see Figur e 3.4). Unce rtain ties of 20 perce nt in tensi ons of surfa ce tensi on are quite possi ble since the surfa ce core mate rials have not been defin itely measu red.

Beck er-Wheth er a conde nsing speci es behav es accor ding to the y seems to depen d on the Dorin g theor y or the Lethe -Poun d theor can

. Those speci es that surfa ce struc ture of the conde nsate ti sf ied minim ize the unsa orien t thems elves on the surfa ce to ring to the Beck er-Do bondi ng poten tial behav e in accor dance theor y. Hydro gen bondi ng speci es--s uch as water or alcoh ols--

are espec ially good examp les of Beck er-Do ring conde nsate s.

tatio n on the Cond ensin g speci es that canno t. by optim a 1 orien surfa ce. minim ize unsa tisfie d bondi ng poten tials conde nsate to be an follow the Lethe -Poun d theor y. Intui tivel y. there seems n for these speci es extra erie:rg y drivi ng force for conde nsatio tisfie d utili zing the unsa that is broug ht on by the advan tages of 3-45

• 20 15 SURFACE TENSION* 339 DYNE/CM (T) "

~

u I 10 U)

I 5 w

I-z Ct= 0 - -*- - - - - -- - - - - - - -

0 w

I I- -5

~

a, w

_J u

)

z -10

....0 l.!)

0

-15

_J

-20 1 2 3 4 SUPERSATURATION RATIO CS)

Fig ure 3.4. Nuc leat ion Rat e of Tin at 2000 Ka sa rati on of the Vap or. Fun ctio n of the sup ersa tu-curv es are mar ked by the assu med surf tens ion of liqu id tin. ace

tly, lower bondi ng poten tial of speci es on the surfa ce. Cons equenation of super satur ation s are requi red to initi ate nucle Lothe -Poun d conde nsate .

ce of a Metal vapor s canno t, by orien tatio n on the surfa Conse quent -

conde nsate , reliev e unsa tisfie d bondi ng poten tials.

and Cd would ly, conde nsatio n of meta llic vapor s such as Ag, Te, ly.

be expec ted to follow the Lothe -Poun d theor y quite close Cond ensat ion of compo unds is not as easil y predi cted.

n long- range Stron gly ionic compo unds such as Cs I would retai dless of bondi ng poten tials at the surfa ce of a conde nsate regar the orien tatio n of the surfa ce molec ules. Cond ensat ion of these stron gly ionic compo unds would be expec ted to more close ly follow Becke r-Dor ing theor y. Cova leht the Lothe -Poun d theor y than the ve some by orien tatio n. relie compo unds. such as Ag 2 Te, could . xides larly . vapor -phas e hydro unsa tisfie d bondi ng poten tial. Simi tage of tatio n to take advan could achie ve ~ome stab ility by orien ach the These speci es may appro hydro gen-b ondin g inter actio ns.

Beck er-Do ring model of conde nsatio n.

conde n-It appea rs. then. that for react or safet y analy ses, ng up and melti satio n prop erties of vapor s produ ced durin g heat- by the ed of the core could span the entir e range bound Becke r-Dor ing and Lathe -Poun d theor ies. In the absen ce of speci es defin itive infor matio n on the conde nsatio n of parti cular the two s.

or obvio us behav ior expec ting. such as for metal vapor bound s must be recog nized . The most appar ent diffe rence betwe en that lower the bound s is that the Lathe -Poun d theor y predi cts than does super satur ation s are requi red to initi ate nucle ation the Becke r-Dor ing theor y.

ior of Fortu natel y. the quest ion of the conde nsatio n behav not be too vapor s durin g nucle ar react or accid ents will proba bly the hot The rate at which vapor s are carri ed out of sever e. most onme nts is fast enoug h for core regio n into coole r envir fy ation s high enoug h to satis accid ent scena rios that super satur y are Beck er-Do ring theor the more strin gent requi reme nts of the quick ly achie ved. When this is not the case, the comp etitiv e domin ate and proce ss of conde nsatio n on struc tures will proba bly the homog eneou s nucle ation quest ion becom es mute.

homog e-The descr iptio n of nucle ation prese nted here is for forei gn bodie s.

neous nucle ation and negle cts the prese nce of any ent.

or accid In the envir onme nt creat ed durin g a nucle ar react wi 11 be sses forei gn bodie s that wi 11 affec t nucle ation proce the Notab ly, gaseo us ions creat ed by prese nt in abund ance.

inten se flux of radia tion can be impo rtant nucle ation sites .

ation in the Russe l [53] has discu ssed the theor ies of nucle theor etica l prese nce of gaseo us ions. Again , the effec ts are of impo rtance but these effec ts are not overw helmi ngly large in ce tensi on.

comp arison to the effec ts of unce rtain ties in surfa or unce rtain ties cause d by.co -cond ensat ion of vapor s.

3-47

The treatment of nucleation has also neglected thermal effects associated with condensation. Clement [ 125 J has shown that the heat liberated during condensation can have an important.

effect on the competition between nucleation of vapors and con9ensation of vapors on structures.

Once the nuclei form. if supersaturation has not been relieved. the nuclei grow either by condensation of vapor or by agglomeration. The rate of growth by vapor condensation is given by dm(r) dt where m(r) is the mass of nuclei of radius r. Growth by agglom-eration of nuc.lei is a more complex problem. While small, the nuclei can be treated as a pseudo-gas. When the nuclei become macroscopic in size (r 2 µm). then the growth process is probably more accurately described by models of aerosol agglomeration.

The preceding development of homogeneous nucleation was restricted to pure vapors and condensed phases. The problem of mixed condensation involving two or more vapor species is a good deal more complex. Camp [ 49 J is currently developing descrip-tions of this process.

Even without detailed results for multi-component condensa-tion

• several important points can be seen. First, from the analyses for pure vapors. it is obvious that surface tension of the condensed phase is an important parameter in determining when a species will nucleate. Since surf ace tensions do not correlate in a simple way with vapor cdmposi tions. there is no reason to suspect that the composition of aerosols will reflect the composition of the vapors. This is especially true when speciation of vapors and aerosols are of interest. Some species that are quite stable in the gas phase are quite unstable in the condensed phase.. Gaseous hydroxides such as Ba (OH) 2 and LaOH are good examples of this.

• Second. the onset of condensation is brought about by super-saturation of the vapor. Supersaturation can arise from changes in temperature. It can also arise when there is a sudden change in the chemical conditions. Consider the barium oxide vapor pressures discussed above. Suppose vaporization of barium oxide were taking place in a hydrogen rich gas brought about by steam reacting _with zircaloy. In hydrogen, the barium partial pressure over barium oxide is quite high. As barium-bearing vapors passed across the boundary layer. they would encounter more oxidizing 3-48

conditio ns as steam constitu tes more of the gas phase. The equilibr ium partial pressure over barium oxide is much lower in the steam-hy drogen mixtures than in nearly pure hydrogen .

Consequ ently. the vapors could be supersa turated and could condense in the boundary layer.

This phenome non of vapor condens ation in the boundary layer is commonly encount ered in the ferrous metallur gy [43]. A "fog line" is frequen tly observed a few millime ters above steel melts.

This fog line is created by the condens ation of alloy constitu -

ents vaporize d from the melt. The vaporiz ation of these alloy constitu ents increase s sharply when a fog line appears and exacts a fairly stiff economic penalty. since alloy constitu ents lost by vaporiz ation are usually quite expensiv e relative to iron.

Hills and Szekely [44] have found that if the concent ration of the vapor is low so it is negligib le in the bulk fluid. then the factor of enhancem ent of the vaporiz ation accompa nying fog line formatio n is approxim ately:

where ~Hv = heat of vaporiza tion Ts= tempera ture of the vaporizi ng surface Tb= bulk gas tempera ture.

When these conditio ns are not met a more accurate expressi on.

that compares well with data [45] for the factor of vaporiz ation enhancem ent is [44]:

~Hv [P s ( eq) - Pb (eq >j Cp RT s RTb where Pb(eq) = equilibr ium partial pressure of the vapor (pure) at the bulk tempera ture c

p

= heat capacity 3-49

~s

' =

Ts in[Ps(eq)J + Ts Rv

~s V = entropy of vaporization.

E. Summary of the Fundamentals of Vaporization Processes.

The preceding review of the fundamentals of vaporization ought to convince anyone that there are significant complications in estimating *the release of radioactive and nonradioactive species during core degradation. A. model that pursued each of the topics raised in the review to any depth would be an imposing creation--far too large to be accommodated in a systems code such as MELCOR. No such extensive model has yet been devised. The MELCOR development effort will adopt. in all probability. one of the simplified models of radionuclide release that is now available. The review then provides a framework for ascertaining what features are included and what

• features are omitted from the available models.

Calculations produced by the MELCOR model should be, of course. as accurate as is feasible. But. equally important. the model should be capable of examining the sensitivity of the calculated results to assumptions . concerning the nature of the plant and the accident in question. The review of the fundamen-tals of vaporization processes defines several features of release processes that ought to be ava i labl'e in the model used in MELCOR:

1. Release should be constrained by the limits imposed by the thermochemistry of the volatile element.

2. Release rates ought to be sensitive to pressure. flow velocity. and gas composition as well as time and temperature.

3._ Release rates should be sensitive to the melting and slumping of reactor fuel.

4. Release rates should be dependent on location in the core.

5. The release model should consider various rate limiting processes such as condensed phase mass transport.

surface reactions. and gas phase mass transport rather than just assuming one of these processes is rate limiting.

3-50

3.4 Extant Models of In-Vessel Release In this section the various models of fission product release that have been used in reactor accident analyses are described. Some attempt is made to comment on how well these models fit with the framework of fundamental properties of vaporization processes outline above~

The organization of the section is along the lines of the description of the in-vessel source term developed in the Reactor Safety Study. That is. the discussions are divided into sections dealing with:

A) Gap Release B) Diffusion Release C) Meltdown Release D) Fragmentatio n Release Release of materials from the core is a continuous process.* The categorizatio n is done merely to mark major phenomenolog ical events in the core degradation process.

A. Gap Release The first dramatic event in a reactor core following loss of adequate cooling is the pressurizatio n. expansion (called ballooning). and rupture of the fuel cladding. More detailed accounts of this process are to be found elsewhere [126] .

.Suffice it here to say that cladding on the fuel can be expected to rupture when the cla*d temperature is between 700 and 1100°c.

-The precise temperature of clad rupture depends on the rate the clad is heated. the system pressure. and the gas inventory of the fuel rods.

When the clad ruptures there is a rapid expulsion of fission products as the internals of the fuel rod pressure equilibrate with the primary system atmosphere. Estimation of the release of fission products that occurs during this period might at first appear to be fairly simple annular flow problem with serious wall friction. It must be remembered though that a substantial portion of the void structure in a fuel rod is produced by cracks, gaps, and pores in the fuel itself. Fission products in these crevices can also contribute to the release.

Experimental studies of gap release have been conducted at Oak Ridge National Laboratory [ 59]. Results of these studies have bean used to develop empirical descriptions of the gap release. The entire process is divided into two steps. The first step. called burst release. is due to the pressure 3-51

equilibration with the primary system atmosphere. This step occurs very quickly, so time resolution of release by this process is not necessary for severe reactor accident analyses.

The mass of the i th radionuclide released during the pressure equalization was found to be:

a..

1 where M*1  ::; mass of the ith radionuclide released (g)

V  ::; volume of gas expelled (cm 3) calculated at the system pressure and 273 K*

M0 (i)  ::; mass of 1*th

- radionuclide in the fuel-to-cladding gap A = internal surface area of the cladding T = absolute temperature at the clad rupture location.

Parametric values, a.i, ai, Ci, were obtained by fitting the model to data. These v,alues are listed in Table 3. 7. The second step in the gap release can be treated as part of the diffusion release discussed next.

3-52

• In addition to parametric values. the model also requires that gap inventories of the radionuclides be provided.

inventories are not especially certain.

Gap Some values recommended in various investigations are shown in Table 3.7.

B. Diffusion Release During the time between clad rupture and fuel melting. fis-sion products are slowly released from the fuel. They must be conducted along the cladding fuel gap to a site of clad rupture.

Early in the accident. the only opening in the clad that will allow fission products to enter the primary system atmosphere is that created by clad ballooning and rupture. As the accident progresses. multiple openings in the clad may develop. It, would be expected that release of fission products during this time period would accelerate. not only because of the temperature increases. but also because continued rupture of the cladding would provide some relief to rate-limiting transport of released fission products to a single rupture site.

The early phases of fission product release by diffusion have been described by the empirical model [59]:

• where M( i)

M( i)

=

=

M (i) 0 1 - exp [-R (i)t/M]

mass (g) of the at time t (hrs).

0 1-0

. th fission product released a.

1 R ( i) = O'i[W/P][M (i)/A] exp [- yi/t]

0 0 w = width of the fuel-to-cladding gap (µm) p = system pressure (MPa)

Again. th~ model parameters O'i* Yi* and ai were found by fitting the model to experimental data. Some values of these parameters are shown in Table 3.7.

When this and the gap release model have been used for accident analysis. the results are lower than those estimated in the Reactor Safety Study. For a 10-minute transient to 1200°c.

the predicted releases of cesium. iodine. and the fission gases

• 3-53

Table 3.7 Parameters for the Gap Release Model Developed at Oak Ridge Parameter Cesium Iodine

a. 3.49 0.163 a 0.8 0.8 e 7420 3770 1900 122 19800 14800 Recommended Gap Inventories

% of Total inventory in the Gap*

Element Reference 7 Reference 1 Reference 59

• Xe Kr Cs 3

3 5

8 8

5

1. 27

1. 27 0.025 I 1. 7 3. 3 0.053 Te 0.01 Sb 0.01 Ba 0.0001 Sr 0.0001

• Note: these are the% of the entire rod inventory. not of just the node adjacent to the breach.

3-54

were 0.025 percent. 0.053 percent. and 1.27 percent of the respective inventories. The Reactor Safety Study suggests gap releases of 3. 1. 7. and 3 percent of the cesium. iodine. and fission gas inventories. respectively. It should be remembered.

however. that the Reactor Safety Study definition of gap release continued longer and to higher temperatures than the above diffusion release model and the preceeding gap release model.

It is clear *from the model predictions that diffusion release at temperatures less than 1000°c is small. and this is not the release_ that is the source of greatest concern in severe reactor accidents. Diffusion release at higher temperatures is faster and more important for accident analyses.

Another empirical model. based again largely on correlation of experimental data. is the CORSOR model [60]. This model was first described in conjunction with the U.S. Nuclear Regulatory Commission* s "NUREG-0772 11 effort to assess the technical basis for changing the source term des~riptions in the Reactor Safeiy Study [5]. It has subsequently been used with the MARCH code for accident analyses. The CORSOR model is intended to treat the entire process of fission product release from the time of clad rupture through rapid diffusion release to gross core slumping and release from molten fuel. A more complete discussion of this model is presented in the subsection dealing with Meltdown Release.

Based on the attempts to describe the process empirically.

it might be concluded that the state of knowledge concerning fission product release from hot. but still solid fuel is poor.

Within the fast reactor safety and development fields. there

• has. however. been a considerable effort to develop detailed mechanistic understanding of the process. Models developed in

~he fast reactor field are now being applied to light water reactor severe accident analysis.* For the most part. these models were designed for normal operating conditions and must be extrapolated to severe reactor accident conditions.

The earliest mechanistic models of fission product release were dedicated to determining the release of fission gases Xe and Kr from the fuel and have come to be known as 11 Booth-type 11 diffusion models [61.62]. These models consider the fuel pellets to consist of grains that are trea_ted as spheres. Each sphere is isothermal. though a pattern of spheres across the fuel pellet can be used to mimic a thermal gradient. Self-consistent temperature profiles can be calculated with the models given a description of the thermal conductivity of the fuel/cladding gap. None of the Booth-type diffusion models appear to have considered heat input to the fuel from clad oxidation. since for fast breeder reactors. this is not a serious problem.

3-55

In the simplest models, transport of fission gases to the grain boundaries is assumed to occur by simple diffusion through a homogeneous medium. If fission gas production can be neglected, as would be the case following scram of a light water reactor. then an approximate solution to the diffusion problem for a grain is:

C ( i)

Ji= D (i) exp [-E(i)/RT] 0 {[~L(i)]-1/2 - l}

0 a where Ji = flux of the ith fission gas out of the grain pores D 0 (i). E 0 (i) = parameters characterizin g the diffusion coefficient of the ith fission product gas in the fuel C0 (i) == initial concentration of fission gas in the fuel grain T(i) == D0 (i)[t/a2] exp[- E(i)/RT]

a == the radius of the sphere that has the same surface to volume ratio as the grain.

This solution is usually applicable up to releases of 80-90 percent.

The models can be used by fitting the model to release data to determine the parameters that characterize the diffusion coefficient of the species in question. Some values of the diffusion coefficient parameters are listed in Table 3.8.

Very early in the use of the Booth diffusion models, it was found that diffusion coefficients determined by different methods were not in good agreement. Quite an extensive base of litera-ture exists showing how corrections to the general diffusion model would yie-ld a more correct description of the release process. The possibility that defects introduced by the fission process trap diffusing species is an especially popular explana-tion of this problem with the simple diffusion models. Models have been formulated to account for these defects [62] and typically involve two additional parameters.

3-56

~

Table 3.8 Parameters for Booth Diffusion Model [65]

Fission D0 (i) E ( i) Temp Range Product (crn/s) (Kcal/mole) (°C)

Xe 3xl0- 6 to 8xl0- 3 61 to 92 800-1600

-5 Xe l. lxlO 72 1500-2000

-4 Xe l.6xlO 67 1500-2000 Xe 3xlo- 3 63 600-2400 I 50 110 900-1500

-3 68 900-1500 I l.9xlO

-3 87 1500-2000 I 3.5xl0

-5 1500-2000 I 1. 5xl0 53.5

-3 59 1400-2500 I 1. 5xl0 Te 90 120 1000-1500 Te 0.56 84 1000-1500

-3 78 1500-2000 Te l.5xl0

-5 58 1500-2000 Te 4.2xlO

-3 Te 6.6xl0 70 1400-2500 Cs 0.04 100 1000-1500

-7 1000-1500 Cs 4.5xl0 40

-3 97 1500-2000 Cs 3.8xl0

-5 52 1500-2000 Cs l.9xl0

-9 6.1 1400-2500 Cs 8.5xl0 Sr 1600 160 1300-1500 Sr 86 140 1500-2000 Sr 86 140 1500-2000 3-57

• Fission* D0 (i)

Table 3.8 (Cont.)

Par:ameter:s for: Booth Diffusion Model [65]

E ( i) Temp Range Product (crn/s) (Kcal/mole) (°C)

-7 24.4 1400-2500 Sr: 4.5xlO Ru 4.2 95 800-970 7 175 1200-1500 Ru 5.0xlo-Ru 0.08 110 1500-2000 Ru 0.09 110 1500-2000

-8 19.2 1400-2500 Ru 8.6xlO

1. 2x10-9 45.6 800-950 Zr:

-6 59.2 1120-1410 Zr: l.6xlO Zr:. Nb 0.167 104 1400-2500

-6 37 1400-2500 Ce 7.2xl0 La 2.2x10- 6 35 1400-2500 y -8 46.4 1150-1450 6.8xl0

-6 56.8 1120-1420 Pr: 3.5xl0

-4 1400-2500 Mo 3.9xl0 54 Arn 0.03 92 1200-1500 Np 2.9 109 1200-1500 Pa 2.5 107.6 1200-1500

-6 56.8 1120-1410 Pm 3.5xl0 Pu 0.34 97.3 1200-1500 Tn 0.16 98 1200-1500 3-58

• Booth diffusi on type models probab ly

• reached their zenith with the public ation of the ANS 6. 5 Standa rd Fission Produc t Releas e Model [64] ~ This model took an empiri cal approa ch to diffusi on by using release data to define coeffi cients .

11 effecti ve 11 diffusi on It also took an import ant step of includi ng a correc tion term for the effects of irradia tion on the diffusi on coeffi cients . Diffus ion coeffic ients for Cs. I. and Te were determ ined relativ e to those found for Xe and Kr. The diffusi on coeffi cients specifi ed by the ANS 6.5 Standa rd are:

D DKr = Dxe = a~ exp (-Q/RT) lOO(Bu /B)

DI/Dxe = 0.575 exp (8900/R T)

Dcs/Dx e = 0.078 exp (12100/ RT)

DTe/Dx e = 1100 exp (-12500 /RT) 2 -1 where D /a = 0.61 sec 0

Q = 72300 cal/mo le B = 28000 MWd/t R = gas consta nt= 1.987 ~al/mo le-K Bu = fuel burn up in MWd/t To summar ize. Booth diffusi on type models assume the release rate is iimited by conden sed phase mass transp ort. No rate limita tion arising because vapors must migrat e through the pore structu re of the pellets or along the fuel-to -cladd ing gap is recogn ized. Diffus ion coeffic ients are peculi ar to each elemen t and are functio ns of temper ature and. in the case of the ANS 5.4 model. fuel burnup . The operati ve geomet ry is the fuel grain which is assumed to be fixed in size.

The diffic ulties with simple diffusi on models of fission gas release prompt ed a consid erable amount of experim ental invest i-gation into fission produc t behavio r within the fuel. Improv ed 3-59

data led to the definition of II deep II traps and II sha l low 11 traps for fission gases that affected the diffusion process.

Eventually. the deep traps were identified as gas bubbles about 10-50 A diameter.

The more modern of the mechanistic models of fission gas release take into account the behavior of bubbles as well as atomic diffusion. the behavior of grains. and the behavior of bulk fuel. The best known of the modern fission gas release codes is GRASS-SST [63] developed at Argonne National Laboratories. GRASS-SST has been the basis of two other codes that deserve mention:

1. FASTGRASS: A faster running version of GRASS-SST.

Speed was achieved largely by using a single. average but time varying. fission gas bubble size.

2. PARAGRASS: A correlational model based on an extensive library of computations with either GRASS-SST or FASTGRASS.

Several other models of the same general type as GRASS-SST have been developed [66] .

Much of the modeling in both GRASS-SST and FASTGRASS has been included to describe the dynamic behavior occurring during the fission process. This modeling is. of course. not important for severe light water reactor accidents. In the brief description that follows. the discussions focus on the phenomena germane to accidents in which the reactor has been neutronically shut off.

The grains in the fuel are viewed as polyhedra with faces and edges rather than as spheres. Fission gases can migrate in the qrain both_ as atomic species and as bubbles. The diffusivities of atomic species and gas bubbles are:

Datomic = 2.lxio-4 exp (-91000/kT)

Dbubble = Datomic (ratom/rbubble) 1

• 62 Q where ratom = radius of the atomic species rbubble = radius of the bubble Q = correction factor to account for lattice distortion by the bubble .

• 3-60

• The correction factor Q is a function pressure and uo 2 material properties.

of the bubble Bubbles collect at the faces of the grains. move about. and co~lesce. The surface diffusivity of the bubbles is size.

Di= (2.4xlo~25;rbubble) exp(-10800/RT)

The migration qf bubbles on the surface of the grains can lead the bubbles to the grain edges. which lead to the interconnected network of porosity in the fuel. Bubble density can saturate at the grain surface [N(max) = 6x1012 bubbles/m2], which opens the grain surfaces to the network of porosity. The release can also be accelerated by microcracking of the fuel. All three of these processes are considered in the model.

o'bvious ly. GRASS-SST and FASTGRASS are very sophisticated and very complex codes. When compared to experimental data involving normal operating conditions or relatively mixed transient heating conditions. these codes yield high-quality predictions. Among these predictions is the nature of burnup on release. Burnup is found to increase the rate of release for burnups up to about 10000 MWd/t. At higher burnups the effects are less dramatic. At about 30000 MWd/t. all the effects of burnup on release have been realized.

Accentuation in the release caused by fuel burnup is the result of two proc~sses in the GRASS-type models. As the inventory of fission gases builds with burnup. it becomes easier for bubbles of the fission gases ,to collect and coalesce to form an interconnected network of porosity that provides release pathways from the pellet. Coalescence is enhanced by grain growth. which sweeps bubbles from the interior of g~ains to the grain boundary. But. grain growth is inhibited by impurities such as radionuclides. Thus. with increasing burnup. it becomes harder for grains to grow. At sufficiently high burnups. a complete network of interconnected porosity may exist in the fuel before an excursion in fuel temperature during an accident begins. Further* irradiation will not add to this network of porosity. . But. further irradiation wi 11 inhibit fission

• products reaching the porosity because of inhibition to the grain growth process. Thus. there is a 1 imi t to the accentuation of release brought on by irradiation.

The severe failing of FASTGRASS. that it only treats fission gases. is being corrected at least to the extent that Cs and I a.re being included. The way these species are being incorporated is fairly elegant. Both Cs and I are allowed to migrate in the

• fuel as atomic species:

3-61

• Dr = 2.1x10-4 exp (-91000/RT)

Des= B.53x10-9 exp (-61000/RT)

It is also recognized that these speqies will *tend to vaporize into gas bubbles at the fuel temperatures during accident transients [68]. The partial pressures of these species present in. the vapor state as Cs(g). I(g). and CsI(g) are calculated.

The condensed form of Cs is taken to be cs 2 uo 4 or cs 2Moo 4

• as dictated by the oxygen-partial pressure of UOz+x calculated with ~he Blackburn model [67]. The gaseous forms of cs and I are assumed to saturate the fission gas bubbles and to migrate with these bubbles. It should be noted that there are some questions about the vapor equilibration with gases in bubbles.

The chemistry being added to the GRASS-type models is assumed to be dictated by the fuel. Thus. oxygen potential is created by hyperstoichiometric urania. Condensed forms of cesium are uranates and molybdates. Vapor forms of* iodine are I (gas) and CsI(gas). In this regard. two experimental observations are noteworthy. Kleykamp (69] has found cesium in the fuel-to-clad-ding gap to be in an oxide mixture which contains Zr and Sn but neither u nor Mo. Also. a variety of evidence from studies of Zircaloy stress corrosion cracking suggests that iodine reacts with zirconium. probably to form ZrI 2 [70]. The iodides of zirconium appear stable in radiation fields--unlike Cs! [71].

Thus. to complete the chemistry in these models may require that clad chemistry as well as fuel chemistry be included.

The GRASS and similar type models assume rate control lies.

within the condensed phase mass transport to a free surface. The barrier to release caused by transport through the pore structure

• or along the fuel-to-cladding gap is ~ssumed negligible. The operative *geometry for release is. as in the Booth diffusion models. the fuel grain. Unlike the Booth diffusion models grains are allowed to grow. Also. not all grains are equal.

Surfaces of the grain must be adjacent to the network of inter-connected porosity of the fuel pellet for release to occur. Some chemistry is being incorporated into the models. But. this is chemistry dictated by the fuel and is unrelated to the chemical environmeit created by the steam and hydrogen atmosphere surrounding the core.

c. Meltdown Release Meltdown release presumably begins with liquefication of the fuel. Distinguishing this stage of release from release while the fuel is solid makes good physical sense. Mass transport in 3-62

• the condensed phase should greatly accelerate with the formation of liquid. The nonideality of liquid mixtures is typically much less than in solid mixtures. so significant changes in the thermodynamic driving force for release would be expected.

Finally. the cladding should have lost its integrity by the time of fuel melting so any rate limitation posed by transport of vapor species to a rupture in the clad has disappeared.

As noted in the discussion of phases present during an acci-dent. there is some ambiguity about when meltdown release should start because of liquified clad attack on the fuel pellets.

There is presumably some transient period in which there is the potential of rate limitation by both diffusion from an eroding solid to the liquid phase. and through the liquid phase to a free surface.

Clad attack on the fuel could result in chemical transforma-tions of the radionuclides that could effect release. For instance. noble metals such as Ru. Rh and.Pd present in the fuel as isolated nodules might dissolve in the molten clad. Dissolu-tion. as noted in section III-A. ought to reduce the driving force for vaporization of these species. Refractory oxides such as Bao might be reduced to the metallic state by clad attack.

Since the meta 1 is more vo la ti le than oxide. re lease of barium might be accentuated by liquefication.

Experimental evidence on the effect of liquefication is mixed. Apparently, out-of-pile tests with highly irradiated fuel rods reveal no dramatic change in release when liquification occurs [86]. In-pile tests with low irradiation fuel rods show a dramatic effect [87].

Modeling of the meltdown release. has been attempted many times. Only a few of these attempts ire described here.

The Reactor Safety Study Model. To assess the magnitude of fission product release during the melting phase of a severe reactor accident. a series of thermochemical calculations were done in the Reactor Safety Study to determine the equilibrium partial pressure of fission-product-bearing vapors. The vapor-phase chemistry of the fission products was restricted to simple-oxidation-reduction:

Activity coefficients were taken to be unity and pressure invariant ( idea 1 mixture assumption). Temperatures were fixed at 3100 K. An unlimited supply of 1000 psia steam was assumed.

3-63

• Rate control was assumed surface vaporization. so:

to be due to the l imitations of where Mi= molecular weight of the dominant vapor species of element i Ri = release rate 6f element i Pi= equilibrium partial pressure of the vaporizing species.

The results of these analyses. tempered with some laboratory data. were used in an undetermined way to define release fractions for elements during the meltdown process. Time resolution of the release was obtained by determining. with the antecedent of the MARCH code. when a node within the core melted. Upon melting. this node was assumed to release the entire proportion of the meltdown release fraction that could be ascribed to the node.

The Reactor Safety Study model of release was intended to yield an upper bound. Since behavior of the released material as it passed through the primary system into containment w~s not carefully treated. release rates were not of great concern. The restrictions on the vapor phase chemistry imposed on this model raise questions as to whether an upper bound release was really determined by this model. Neglect of nonradioactive materials

~l~o makes the model useless for modern source term analyses.

The Light Bulb Model. The "Light Bulb" Model of fission product release is mechanistic in the sense that it assumes gas phase mass transport is the rate-controlling process in release

[72]. The model could be called semiempirical. in that it.does require one experimentally determined release parameter. The rate of* release is given by the expression for gas -phase mass transport rate control into a bulk gas with negligible fission product content:*

K. P. ( eq)

1. dn(i) 11 1

=

A dt RT 3-64

• where n(i) = moles of the ith species released A= surface area Pi(eq) = equilibrium partial pressure of the ith species.

The rate parameter is specified to be 312 112 0.001858 T (1/M. + 1/M )

1 D. =

1g 2 P[(o. + o )/2]

1 g p = total pressure M*1 = molecular weight of the vapor phase fission product Mg = molecular weight of the ambient gas

• and Og = collision parameters for the gaseous C1.

1 molecules b = parameter determined from experimental release data.

The empirical parameter is theoretically dependent on the temperature. gas composition and pressure. and the nature of the released species. In practice. o is determined from one data point in a data set of interest. When this parameter is determined. the model does quite a* good job correlating experimental data (see Figure 3.5).

The "light bulb model" presents an alternative to all the previously discussed models. Rate control .lies in the gas phase mass transport away from the free-surface rather than condensed phase mass transport to *the free-surface.

The IDCOR Model. IDCOR [ 32] has developed a release model based on a suggestion by Cubicciotti [73] that fission product release is controlled by sintering of uo 2 . Sintering of U02 3-65

• 0.100 0.80 6 TELLURIUM 0 CESIUM 0.60 STRONTIUM

c 0 t-3: ~

C w,... ~

0.40 0

BARIUM CERIUM RUTHENIUM t-~ X U0 2

< ..J 0.20

..J w

, C uo

..J :I um ..J 0

C ::,

wm 0.10 0 u, t-

< ::c 0.08 0

• ~ CJ 0 w-cc ..J 0.06 z~

0_w cc t- ..J 0.04 X u::

<cc LL

I

• X 0.02 0.01 0.02 0.03 0.05 0.1 0.2 0.3 0.5 0.7 1.0 MEASURED FRACTION RELEASED (23)

Figure 3.5. Comparison of Observed Releases of Fission Products From uo 2 at Temperatures Between 2273 and 2473 K with Those calculated with the Light Bulb Model.

3-66

is accelerated in steam [74, 75]. Cubicciotti argues that the rate of sintering in st.earn is correlated with the rate of uo 2 oxidation by steam. He then used oxidation rate data by Bittel et al. [76] and Jain's short-cylind er diffusion model [77] to derive a release expression for fuel pellets in steam:

2 F. (t) = 1 - [l - 4 (TH/Tr) l/ ] [ 1 - 4(-r p /,r)l/2 + -rp]

l

.th where Fi(t) = released fraction of the 1- species 2

'tH = Dt/H 2

"(

p = Dt/r 2

D = 0.0099 exp(-28000/T ) m /s T = absolute temperature (K)

H = length of a fuel pellet - 13xlO -3 m

-3 m r = radius of a fuel pellet - 6.4xlO t = time (s)

When the ambient atmosphere is inert* or reducing, Cubiciotti favored use of Malen' s uo 2 grain growth model [78] to predict release:

312 F. (t) = 1 - [l + 2kt/d J-1 0

-8 where k = 1.46 x 10 exp (-32100/T) 5 m d = initial grain size - lxl0-0 Cubiciotti does not provide an indication of how he would alter the grain growth rates with fuel burnup .

• 3-67

A comparison of releases obtained wu:.n Cubiciotti is inert and steam atmosphere models is provided in Figure 3.6. The presence of steam accelerates release by about a factor of 100 at temperatures of 1300-1700K. Steam has a decreasing effect on release as temperatures rise.

As written. the models by Cubiciotti really apply only to fission gases. For more refractory species. the release fractions are reduced by a factor of where PT= total pressure Pi= equilibrium partial pressure of the pure species at temperature T.

For the IDCOR implementation of Cubicciotti I s model. SOLGASMIX

[28.29] was used to calculate the equilibrium partial pressures of the refractory species.

The IDCOR model presents yet another approach to kinetics of.

vaporization. Here rate control is limited by the diffusion of a reactant into the host material. Release is then independent

• of the radionuclide in question except for the dependence of the equilibrium partial pressure. The analysis of the equilibrium partial pressure is completely different than that used in con-nection with the GRASS code. The partial pressure is independent of the fuel and very dependent.on the ambient atmosphere composi-

. tion. The IDCOR model does not provide an explanation of how cladding affects the release.

The IDCOR model ought to be considered a mere hypothesis.

When compared to data. the model at best provides an upper bound on these data. Examination of data in detail shows release has not proceeded as has been hypothesized in the model.

3.5 The CORSOR Model The CORSOR model [5.7] is part of the U.S. NRC 1 s current Accident Source Term Reassessment effort. CORSOR is used in conjunction with the MARCH model of core degradation [78] and an ad hoc model of gap release to predict both radionuclide and nonradioactive species release within the reactor vessel during a severe accident. As currently used. release predictions with CORSOR are made only when the core is intact. though it may be melting or liquefying. Once core material slumps~ release calculations are usually terminated. However. in some cases.

the release calculations have been continued up to the point of melt penetration of the reactor vessel.

3-68

-3 u:.-

0 C,

.2 -4 w

I O'I IC

-5

-6 0 1 2 3 4 5 6 7 8 9 10910 [t(s)]

Figure 3.6. Comparison of Cubicciotti's Models of Fission Gas Release in Steam and Inert Environments.

• The CORSOR model is an empirical correlation of a variety of experiment.ally determined release fractions. Most of the data that are the basis for the CORSOR model come from the SASCHA tests at the Kernforschungszentrum in Karlsruhe. West Germany

[79-85) and the hot cell tests {HI and HT Series) done at Oak Ridge National Laboratory [86-89.91.92). The SASCHA tests used simulated fuel doped with fission products to a level expected for fuel with a burnup of 44000 MWd/t. The samples were heated under a variety of atmospheres at pressures up to 2 bars. The Oak Ridge tests used irradiated fuel rods heated in atmospheres initially composed of steam and an inert carrier at a pressure of about 1 atmosphere.

To derive the model it was assumed that release could be described by the first-order rate expression where K. {T) = temperature-dependent release rate coefficient 1

for the ith element Fi{T) = fraction of the ith element remaining in the fuel at time t.

-The temperature dependence of the release rate coefficient was assumed to be:

K*1 {T)* -- A*1). exp{B*1)*T).

where T = temperature in Celsius

. th*

A.. and B .. = release rate parameters for the 1 ~

1) 1) species in the jth temperature regime.

Temperature regimes used in CORSOR are:

{1) 900 - 1400°c

{2) 1400 - 2200°c

{3} > 2200°c 3-70

Tne paramet ers in the release expressi on were evaluate d by comparis on to experim ental data. These data are. in all cases.

the integral release achieved after a protract ed exposure of a sample to elevated tempera tures. Consequ ently. it is necessar y to integrat e the release rate to make the comparis on to the data. Where tempera ture changes are involved in the sample's history. these changes were assumed to proceed at a linear rate:

T :::: a. + flt Then the release rate expressi on is easily integrat ed to:

F.(O) - F.(t) 1 1 .. t])}

1 - exp {(H 1).. /G .. )(1 - exp[G 1) 1)

where Hij :::: Aij exp (a.Bij)

• The unusual form of the tempera ture depende nce of the release rate coeffici ent in the CORSOR model was chosen obvious ly to facilita te the integrat ion during changes in tempera ture.

A set of paramet er values for the CORSOR model is shown in Table 3. 9. CORSOR is being *maintai ned. As new experim ental data are obtained . improved paramet ric values are derived .

Consequ ently. the values listed in Table 3. 9 may not be the latest version of the paramete r set for CORSOR. One recent modific ation of the CORSOR model has been made to accommo date the possibi lity that Te released from the fuel may bind to unbxidiz ed Zr metal and not escape the core. To accommo date this possibi lity, the release rate coeffic ient of Te is reduced by a factor of 40 wheneve r 5 percent or more of the Zircaloy clad has not been oxidized [94].

CORSOR is the only release model that treats all the diverse elements of interest for reactor acciden t analyses ~ It is also the only model other than the Reactor Safety Study model that treats release over the entire tempera ture range of interes t.

The close relation ship between the model and experim ental data also provides an attract ion. By empiric ally cor re la ting data.

the need to identify and to describ~ a host of detailed mechanis ms is avoided. At the .same time the coupling to experim ental data limits .the applica bility of CORSOR without extrapo lation. For 'instanc e. all data that are the basis for 3-71

Tai.Jiu J.9 Coefflclente for the COR60R Hodel 117J-167J K 117J-167J K 1673-2473 K 1671-2473 K 2473 K 2473 K Single Arrhenlue CURSOR Acchenius CORSOR Arr hen I ue COR60R Arrhenlua Coefficient E K_ 0 (111n- 1

_ u_i__ _e_1_ __e_l_ _e_l__ __I_ -=.l _ __>

c. 7.SJ1IO-l 2 U.Ul42 J. 9156110 4 55573 2.02110- 1 0.00607 2.5248110 4 55091 1.74110- 5 0.0046 4.608110 5 68640 ),504110 4 55591 U.00886 45.042 34674 2.02.10- 1 0.00667 2.52481!0 4 55091 1.74110- 5 0.0046 4, 608110 5 68640 1.108110 4 50l7l Xe 7.02110- 9 0.00886 45.042 14674 2.02Xl0- 7 o,00667 2.5248110 4 55091 1.74110- 5 o.0046 4 .60Hxl0 5 68640 1.1oex10 4 5037 l Kr 1.02110- 9 0.00886 45.042 34674 2.02110- 7 0.00667 2.5248110 4 55091 1.74110- 5 o.0046 4, 608110 5 68640 1.108xl0 4 5037.1 3

• re l.H81IO-l 2 0.01150 3405.7 52B33 9.39xlO-B 0.00630 2844.2 52035 1.10110- 5 0.00411 2.424110 4 61328 6. 085xl0 545911 Sr 2.74110-e 0.0036 2.6464xlo- 4 14089 2.78110- 11 0.00851 4319.1 70453 9Xl0- 7 0.0037 217. 7l 55210 2),786 w

I Ua 7.50110- 14 0.0144 652.626 56356 8.26110- 9 0.00631 259.966 52117 1.38110- 5 0.0029 51. 387 43273 524,4 554 7(;

-.J N Sb 1.~ xlo- 12 0.0120 280.085 50094 5.88xl0- 9 0.00108 3534.B 58477 2.56110- 6 0.00426 1,1502110 4 63566 2602,2 5651 ;:

Ay 3.88110-lO 0.0135 3405.7 52813 9.39110- 0 0.00630 2844.2 52035 1.18110- 5 0.00411 2,424110 4 61328 ,.085110 1 5459(1 HU 5.01110- 12 0.0115 26.877 45006 5.93110- 0 0.00523 29.80 41197 3.7110- 5 0.0020 1,2587 2984] 24.381 44051 HU l.J61lu-ll 0.00768 0.004312 30056 1.36110- 11 0.00760 81.422 6l43J 1.,110- 6 0.0024a 0.5827 )7006 3. 776 49402 6.64110- 12 o.00631 6.409110- 5 24695 6.64110- 12 0.00631 0.209 52117 l.48xlo- 7 0.00111 1,5164110- 1 26411 o,ollH 39977 s11u 13 o.OU768 1.585110- 4 30056 5110- 13 0.00768 2,9935 6l4JJ 5xlo-ll 0.00768 1,261110+ 5 114599 1,090 55811 6.64110- 12 0.00631 6.409xlo- 5 24695 6.641io- 12 0.00631 0.209 52117 1.,0110- 1 0.00177 1.s1,4110- 3 26411 0,01374 39977 Cid~ Sn 1.9110- 12 0.0128 280.085 50094 5.88xl0- 9 0.00708 3534.8 58477 2.56110- 6 0.00426 1,1502110_, 6356, 2602.2 56512 litruct 6.64110- 12 0.00631 6. 409Xlu- 7 24695 6.646110- 12 0.00631 0.00209 52117 1.,0110- 11 0.00117 1,51,110- 5 2,411 0.0001374 39977 Fu.

101 CORSOR 100* -----

_ARRHENIUS (WITH REGIMES)

ARRHENIUS (WITHOUT REGIMES)

-....I C

10-1

-zE t- 10-2 w

0 LL 10-3 LL w w I

-..J 0

,i::,. 0 w 10-4 t-c(

a:

10-s 1o-6 L-...IIC.....!:....ll-~-L.---1'---'-....:....L_._L-.......--1--L.....1&1.-.i....--'-----"-..____.__.._......._

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 TEMPERATURE (K)

Figure 3.7. Comparison of the Temparature Dependencies of Release Rate Coefficients Calculated with the Original CORSOR Model and with.

Parameters For the Mod~f Modified to Have an Arrhenius Temperature Dependence.

• the reactor core is treated as indepenn"'nr of releases from adjacent nodes.

equilibrium and This violates the vapor concentrations thermodynamic principle described in Subsection III that release rates ought to be proportional to the difference between vapor concentrations at in the ambient Releases from a given node ought not to be independent of gas.

releases from adjacent nodes.

CORSOR contains no explicit representation of surface area.

Minimal changes in the surface areas for release--such as those caused by grain growth. microcracking of the fuel. etc.--may be hidden within the empirical coefficients of the model. More substantive changes in surface area. such as those that accompany fuel melting or liquefaction. cannot be treated easily by altering the release coefficients. No formalism is included in the model to describe dilution of the condensed phase as clad and fuel mix and melt. In mariy applications to date [7]. CORSOR predictions of release have been stopped when core slumping is assumed to begin. Continued application of CORSOR as molten core material begins to slump and the surface-to-volume ratio of the material changes dramatically is clearly in error.

The CORSOR model relies on a lot of physical and chemical processes being adequately represented by the assumed rate expression and empirical parameters~ Unfortunately. the

• f irst~order rate expression assumed in the model is not a very flexible t"ormat for the representation of these processes.

all the empirical descriptions of heterogeneous processes. some of which are listed in Table 3.10. the hardest to rationalize is the first-order rate description [96].

Of Data available to date for evaluating the CORSOR model have been integral releases

• measrired. typically. posttest. These data do not test the validity of the first order assumption. Some examination of the

~irst order assumption is made below.

3.6 Discussion of the First Order Assumption The assumption that the kinetics of radionuclide release from the fuel is dependent to first order on the radionuclide concen-tration in the fuel is widely accepted. This acceptance arrives despite the fact first order dependence has not been demonstrated experimentally. Sophisticated fuel behavior models do not predict a first order dependence. The assumption of first order behavior is apparently an approximation made to simplify the modeling. Models involving first order composition dependence and Arrhenius-type temperature dependence.are notorious for being sufficiently flexible to fit" data involving radically different mechanisms. It is of interest then to ascertain if the assump-tion of first order kinetics is likely to have any appreciable

• effect on predictions of radionuclide release.

3-75

CORSOR were acquired at pressures of less than 2 atmospheres whereas reactor accidents can involve pressures in excess of 100 atmospheres. Unappreciable errors may arise then when CORSOR is applied to pressurized accident sequences.

Because CORSOR is the state-of-the-art model for analysis of release during core degradation including melting. it has been examined closely in the past. A variety of criticisms have been formulated.

One of the -most frequently raised criticisms is the unusual temperature dependence of the CORSOR release rate coefficients.

Most would prefer to see an Arrhenius temperature dependence:

where. K0 (i) and Ei are release rate parameters for the ith species and T is the absolute temperature rather than the temperature in Celsius used in CORSOR. First. it must be noted that the Arrhenius form of the temperature dependence is no more 11 fundamental 11 nor theoretically sound that the temperature depen-dence used now in CORSOR. Especially when applied to reactions involving solids or liquids. the Arrhenius temperature dependence is just an empirical correlation of experimental observations.

To be sure. this base of ~xperimental observations is quite large.

Second, it should be noted that the CORSOR temperature-depen-dence can be readily converted to have the Arrhenius form. This can be done retaining the temperature regimes defined by the model (which may indeed have some physical significance) or by fitting to a single Arrhenius expression for the entire tempera-ture range of interest. Results of such a conversion are shown in Figure 3.7. Parametric values derived by the conversion are shown in Table 3.9. Others (127. 128) have made this conversion to the Arrhenius form and have obtained different parametric values.

The activation energies. Ei, available from the Arrhenius*

expression- are sometimes interpreted as physically significant.

For instance. Andriess~ and Tanke [95] have noted the similarity of the activation energies for cs. I, Xe. and Kr release to the activation energy for oxygen diffusion in the U02+x lattice.

Such interpretations may be useful for some insights about further experiments. They ought not be the basis for extrapola-tion of the CORSOR model. The parameters [K 0 ( i) and Ei] are simply too highly correlated and the data base too sparse to attach much credence to the interpretation of the Ei values .

I *

• In application. CORSOR, is used on a node-by-node basis in accident analyses. However. the release from a given node in 3-73

Ta .10 some Kinetic Expressions for Solid Decomposition Reactions Mechanism F(f)*. G Cf)**

1. Prout Tompkins f(l-f) ln(f/(1..:.f))

2. Topotactic f2/3(1-f)2/3 3* lD Diffusion l/2f

4. 2D Diffusion -1/ln(l-f) (1-f)ln(l-f) + f 113 -1) 213

5. 3D Diffusion 3/2((1-f)- (l-2f/3} - (l-f) 112 2

6. D3 l.S/((l-(l-f)l/ 3 )/(l-f)S/J) ({l+f)f -1) 113 2

. 7. DS (l/(l-f) -1) 314 114 w 8. P4 4(1-f)(-ln(l-f.)) (-ln(l-f))

I

...J 112 112 a, 9. P2 2(1-f){-ln(l-f)) {-ln(l-f))

213 113

10. P3 3(1-f)(-ln(l-f)) (-ln(l-f))

114 314

11. P4/3 * (4/3) (1-f) (-ln(l-f) ) (-ln(l-f))

113 213 12~ P2/3 l.S(l-f}(-ln(l-f)) {-ln{l-f))

13. First Order 1-f -ln(l-f)

' 2

14. Second Order (1-f) f/(1-f) 112 112

15. 2D Phase Bound 2(1-f) l-(l-f) 213 113

16. 3D Phase Bound 3{1-f) l-(l-f)

17. Jander Approx. 3(1-f)2/3/2{1-(1-f )l/3 ( 1- ( 1-f) 1/ 3) 2

• for df/dt = fractional rate= F(f)k(T)

• • for.integrated rate expression G(f) = K{T,t)

Dat~ fo~ the release of cesium from itLadiated fuei ob~ained in tests at Oak Ridge National Laboratory are shown in Table 3.11. These data were obtained by heating fuel in flowing steam to an arrest temperature. The sample was held at the arrest temperature for a prescribed length of time and then cooled. At least early in the cooling. temperatures fell at a near constant rate. Heating rates. arrest temperatures . and hold times for the ORNL experiments are shown in Table 3.11.

The heating and cooling ramps of the tests pose an added complexity to analysis of the release data. For some of the tests. the durations of the heating and cooling stages constitute a major portion of the time the irradiated fuel specimen was at elevated temperatures . To properly analyze these test results the release that must have occurred during heating and cooling should be recognized.

Assume the rate of radionuclide release is described by the e.xpress ion:

df dt where f = fraction of the radionuclide that has escaped the fuel F(f) = function that describes the compositiona l dependence of the release rate R = gas constant t = time Ta= arrest temperature (K)

K0 and E = parameters to be determined from release data.

If the temperature is fixed. the release rate is easily integrated_ to yield

_g1__

F(f) =

where F1 = release that occurred before the arrest tempera-ture. Ta* was reached 3-77

u Table 3.11 Some Data From Out-of-Pile Tests of Radionuclide Release From Irradiated Fuel Rods [97]

T Fraction of Test a flt .B 13' (K) (min) (K/s) (K/s) Cs Released HI-1 1673 30 0.97 0.6 0.0204 HI-3 2273 20 2.78 1.67 0.577 HI-4 2123 20 1. 93 1.58 0.319 HT-1 1598 10 9. 9 12.2 0.00224 HT-2 1718 7 11.1 11.1 0.0964 HT-4 1673 0.33 18.5 11. 0 0.06108 Ta= Arrest temperature.

flt= Time the fuel was held at the arrest temperature .

.B = Rate of temperature rise during heatup of the fuel to the arrest temperature .

.B' =. Rate of temperature fall during cooling at the fuel from the arrest temperature.

3-78

..._,, F 2 = release that occurred by the end of the time sample was held at the arrest temperatures t 1 = time the arrest temperature. Ta, was reached the t 2 = time when cooling the sample from the arrest temperature began.

• To treat the case when the sample is being heated. it is convenient to transform the release kinetics expression. Assume temperature increases a.t the constant rate. .8. to the arrest temperature Ta. Then.

df Ko dT = .8 F(f) exp (-E/RTa)

Integration of this expression yields K

df __Q exp(-E/RT)dT F(f) = .8 where Fo = release that had occurred prior to the start of the experiment which is typically assumed to be zero T 0 = temperature of the fuel at the start of the experiment.

The integral on the right-hand side of the above equation cannot be reduced to elementary functions. A variety of approximations for this integral have. been f6und. Coats and Redfern [98]

described the most popular approximation:

T 2 RT I exp(-E/RT)dT = E (1 - 2RT/E) exp(-E/RT) 0 Gorbaschev [99] has suggested a somewhat more accurate approximation:

3-79

• J 0

T  ?

RT-exp(-E/RT )dT = (E + 2 RT) exp(-E/RT )

Van Tets [100] has derived an expansion that allows the integral to be evaluated to any desired level of accuracy.

With expressio ns for the integral of the ,temperatu re dependence during isotherma l periods and during periods of heating at a co~stant rate. it is possible to fit a model to the Oak Ridge data. Here three models of the compositio n data are considered :

1. First order dependenc e:

F(f) = 1 - f

2. Three-dim ensional phase boundary model:

213 F{f) = 3(1 - f)

3. Three-dim ensional diffusion model:

3 F(f) = 1.5[(1 - f)-l/ - l]-l The first of these models is. of course. the conventio nal assump-

• tion. The motivatio n for the second model. three-dim ensional phase boundary motion. is the suggestion by Cubicciot ti that

~elease is controlled by sintering . It must be emphasize d.

though. that this second model is not either identical to or a reformula tion of Cubiccio tti' s model. The motivatio n for the third model. three-dim ensional diffusion . is the formulatio n of release processes in the GRASS-SST code where diffusion of radionucli des is heavily emphasize d. Again. this third model is not intended to be an approxima tion or a simplific ation of the GRASS-SST code.

The parameter s K0 and E were adjusted for each of the three models to get a best fit in the least squares sense to the cesium release data in Table 3.11. The quality of the fit was judged from the chi-square d statistic 3-80

• where:

x2 =

N N

I:

i=l (f

obs -

f calc )

= number of data points 2

fobs= observed release fraction f ~ calculated release fraction.

ca 1 c Parametric values derived in this way and the values of the chi-squared statistic are shown in Table 3.12.

Table 3.12 Kinetic Parameters and the Chi-Squared Statistic for the Quality of Fit of Three Models to the Cesium Release Data K (S-l) x2 Model 0 E(cal/mole)

First order 0.855 34.617 0.073

.3d phase boundary 1. 732 41.513 0.0527 3d diffusion 7869 86.280 0.04297 The first thing to note about results in Table 3.12 is that both the three-dimensional phase boundary model and the three-dimensional diffusion model actually fit the data better than does the first order model. If linear statistics are actually applicable to this least-squares fitting problem. then the quality of the fits are not significantly different. To a relatively high level of confidence it can be said all three models fit the data equally well.

The next feature of the results to note is the value of the parameter E. Values of E. the activation energy. differ by only about 15 percent for the .first order and the three-dimensional 3-81

phase boundary models- But. the three-dimensional diffusion model yields an activation energy nearly twice that obtained with the -first order model. This illustrates a very important point.

The activation energy for the release of radionuclides cannot be derived from integral release data if the compositional depen-dence of the release rate is not known. Physical interpretation of activation energies derived from data. assuming a particular compositional dependence of the release rate. is an idle exercise. Activation energies derived in this way are simply empirical parameters and ought not to be used as a basis for extrapolating away from the underlying data base.

So far. it has been shown that alternative models will describe the release data as well as does the assumed first order model. What remains to be done is to show whether the precise form of the model will make any significant difference to release predictions. To do this. a single node of fuel in a degrading core is considered. Release from this node is treated as it is in the CORSOR model. That is. release is strictly a function of time and temperature. It is independent of flow.

gas composition. pressure. or release from adjacent nodes. Two situations are considered then:

1. The node heats so that the temperature rises at a constant rate of 4 K/s to 2500 K. The temperature is then fixed at 2500 K.

2. The node temperature rises at 4 K/s to 2000 K and thereafter rises at 0.3 K/s until it reaches 2800 K.

The first of these scenarios is reminiscent of the core heatup predicted with the MARCH code [78]. The alternative scenario reflects somewhat the effects that nat1Jral circulation and the like are thought to have on core heatup [101]. Cesium releases predicted with the first order and the three-dimensional diffusion models for the two heating scenarios are shown in Figures 3. 8 and 3. 9. In general. the diffusion model yields higher release rates early in time and lower releases late in time than does the first order model. The maximum release rate during th~ MARCH-like heating scenario is nearly 10 times the maximum release rate in the heating scenario based on calcula-tions that include natural circulation. In the natural circulation case. cesium release continues for nearly twice as long by first order kinetics than by diffusion_kinetics.

3.7 Modifications of the CORSOR Model for use in the MELCOR Code None of the models described in the preceding section are entirely satisfactory. Clearly. the GRASS-SST and FASTGRASS 3-82

0 z

0 u

w (fJ 40

'z 0

....u t-4

< 30 DIFFUSION 0: 30 lJ..

w 0:

w w 20 I U) a, w

w

..J w

0:

X 10 0

0 0

0 FIRST ORDER 1000 2000 3000 4000 TIME (SECONDS)

Figure J.B. Comparison of the Predictions of Cesium Release by Two Models of the Release Kinetics Assuming the Core Heats at 4 K/s to 2500 K.

CJ z

0 9

u w

(/)

8 z

D I-u 7 30 DIFFUSION

~ 6 LL w 5 I-w

~

I CD

~

w

(/)

4

., ., /

w

_J .3 ., .,

w / FIRST ORDER

~ / '*

0 X 2 / '

0 0

D 1 1000 2000 3000 4000 TIME <SECONDS)

Figure 3. 9. Compariso n of the Predictio ns of Cesium Release From Two Models of the Release Kinetics Assuming the Core Heats to 2000 K at 4 K/s and to 2800 Kat 0.3 K/s.

• models are the most sophisticated .

model has many attractive features.

in reactor analyses [7]. The deficiencies CORSOR model all stem from its close But, and it tl1ey do not t.reat all the radionuclide s of interest and their complexity precludes them from inclusion in a systems code such as MELCOR.

has and association already the The CORSOR been used virtues with of the experimen-tal data. The CORSOR model is. essentially. a correlation of experimental data. As such, the effects of many phenomena and processes have been encompassed by the empirical parameters of the model. But, the data base from which these empirical param-eters are derived is quite limited. Use of the model for circumstance s well removed from those that arise in the experi-mental data base is a concern~ Unfortunatel y, reactor accident analyses frequently require release estimates for situations in which the CORSOR model extrapolates the data base. For instance, many of the most important reactor accidents involve core degra-dation within a reactor vessel pressurized to over 150 atmos-pheres. The CORSOR data base involves tests at pressures no greater than about 2 atmospheres. Gas flows through the core of a reactor can be quite slow--sometim es velocities as low as 1-2 cm/s are estimated. Yet. the CORSOR data base involves tests with gas flows on the order of 30 cm/s. Core degradation eventually leads to melting and slumping of the core materials.

In many analyses to date, the CORSOR model has been used only up to the time the core slumps. There has been. recently. a tendency to continue to apply the CORSOR model throughout slumping and collapse of the core.

The CORSOR model can be modified to broaden its range of applicability . In the sections belo*w this is done to take into

_account the effects:

1. Changes in the surface area and geometry of the core materials.

2* Dilution of the fuel by interaction with the fuel cladding, and

3. The effects of ambient pressure and flow velocities through the core.

In making *these modification s, some of the conceptual difficul-ties with the .model are corrected:

4. Release does not exceed the limit prescribed by the thermochemis try of the volatile material,

5. Release becomes reversible,

6. Release at a given location becomes dependent on releases from preceding locations along the flow pathway, and

7. The effects of fuel burn up and initial grain size are explicitly depicted in the model.

3-85

The modifications made to the CO~SOR model do not include ~11 the phenomena known or suspected to affect radionuclide release. A barrier to broader modification of the model is the limitations 0 on size posed by the systems code. Another b arrier is that it is not always clear if processes and phenomena were operative in release experiments and consequently are reflected by the CORSOR release rate expressions.

A. Modifications to Account For surface Area Changes and Dilution During Core Degradation The CORSOR release rate expression for the volatile element

i. altered to have an Arrhenius temperature dependence but retaining the assumption of first order kinetics. is:

dF.

dti = K0 (i) (1 - Fi) exp [-E(i)/RT]

where Fi is the fraction of the element i that has been released by time t. Suppose attention is focused on a single node of the core which contains a volume V 0 of fuel. Let the initial amount of element i present in this fuel be .Ni(O) moles .

Then. the release rate expression can be rewritten as:

dNi(t) N. (t}

1 l 1

= K'(i) exp [-E(i)/RT]

dt o . Ni(O) V where K' (i) = V K (i). N. (t) is the number of moles of the ele-

. 0 0 0 1 .

ment i still present in the fuel. and V is the volume of core material containing element i.

Suppose now that the free surface through which release takes place has an aiea BA where A is the geometric surface area of the fuel and B is a* coefficient that relates the geometric surface area to the actual surface area. Then. the rate expression can be further.modified to be:

• dNi(t) N. ( t)

= K~(i) exp [-E(i)/RT] BA iv dt V K (i) 0 0 where K"(i) = and is the geometric surface area to 0

3-86

• volume ratio cf release rate coefficients .

1n the tests to The term Ni(t)/V is the concentration of element i in the condensed phase at time t.

def ir1e the Initially. element i is dissolved in just a volume V0 of fuel. But, as core degradation progresses, CORSOR oxidized cladding can be incorporated into the fuel and this will reduce the concentratio n of the element i and consequently its rate of release. For typical pressurized water reactor fuel.

there are o. 56 moles of zirconium clad for each mole of urania fuel. Were al 1 of this clad to be oxidized and incorporated into the fuel, the concentration s of the volatile elements would be reduced by about 30 percent.

Incorporation of clad into the fuel will assuredly occur when the clad and fuel melt. If clad incorporation is complete then the release rate expression would have to be modified to ~e:

dNi(t) Ni(t) dt

= K" (i) exp [-E(i)/RT] BA 1.44 V o 0 ignoring thermal expansion. the volume change of melting, and any excess volume of mixing fuel and clad.

Dilution of the fuel can also occur prior to melting. In pressurized accident sequences clad collapses onto .the fuel and can chemically attack the fuel. This attack has been extensively studied recently [102]. If it is assumed that the volatile

• element instantaneou sly redistribute into the zone of fuel/clad interactioni then the release rate expression becomes:

dN. ( t) l dt = K;(i) exp [-E(i)/RT] BA [Vo+ v(t)]

dv(t) 3 o where dt = 0.814 exp [-20,785/T] cm/sand v(O) =

The coefficient B also presents some difficulties . Once melting has occurred, the geometric surface area and the actual surface area are the same. so B = 1.

Prior to melting. Bi~ more complex because the fuel is not fully dense.

In the Booth-type diffusion models, the solid fuel was hypothesized to consist of spherical grains of diameter "a.

11 3-87

• Then B - ! [::]

where V0 /A 0 is* the fuel volume divided by the geometrical surface area. The hypothesis in the Booth models is that all surfaces of the_grains contribute to the release process and that the grains are fixed in size. It is now recognized that neither of these. hypotheses are correct. Only the surfaces of grains adjacent to interconnecte d porosity of the fuel can contribute to the release. The nature of the pore network is affected both by the past irradiation history of the fuel and the behavior of volatile species in the fuel. The FASTGRASS model involves elaborate descriptions of how porosity is affected during normal fuel operation and during the core degradation process. Here. a simpler description is developed.

Assume only a fraction E of the grain surface contributes to the release process. Assume Eis a function only of fuel burnup.

In examining the effects of fuel burnup on release. authors of the ANS 5.4 model concluded the release rate increased with burnup as E(Bu) = E 0 exp [1.6 Bu/10.000]

where Bu is the burnup in units of megawatt days per metric ton

• of uranium.

It is also understood now that the fuel grains will grow in an accident transient. A model by Mal~n used in Cubicciotti I s model is 4

a(t.T) = a [1 + (2.92xl0 t/a~) exp (-32100/T)]

0 where a 0 is in units of micrometers.

Time scales for core degradation in a severe reactor accident are estimated typically to* be on the order of 1-2 hours [7]. The Malen growth model indicates that temperatures must exceed about 2200 K for grain growth to be significant for such short times.

Experiments with solid. irradiated fuel such as those listed in Table 3 .11 probably did not involve significant grain growth with the possible exception of test HI-3 [86]. The rate coefficients derived from these tests for the CORSOR model do not reflect. then. any significant grain growth.

3-88

for Grain growt h is treat ed here simpl y as a mecha nismGrain for relea se.

reduc ing the actua l surfa ce area avail able rate of growt h can have anoth er effec t which enhan ces theimpu rities relea se. As grain boun darie s migra te they can sweep to the void struc ture betwe en the grain s. In the case of react or nucli des.

fuel the impu rities can be. of coui:s e. vola tile radio can escap e When these radio nucli des reach to void netwo rk they No modi ficati ons of the CORSOR model is made hei:e to the fuel.

refle ct this effec t.

for The Malen mo<;lel of grain growt h is stric tly appli cable in As noted urani a in inert or sligh tly reduc ing circu mstan ces. oxidi zing in the descr iptio n of Cubi cciot ti*s model grain growt h can be very rapid . Follo wing the sugge s-and espe ciall y in steam s model foi:

tion made by CUbi cciot ti. an alter nativ e to* Malen

• growt h is grain growt h in steam might be const ructe d assum ing urani a.

propo rtion al to the rate of steam oxida tion of n in stron gly oxidi zing envir on-Circu mstan ces of fuel degra datio so-ca lled ments are rare. Cons equen tly. no such model of the "steam iinte ring" of U02 is devel oped here.

effec ts into the Incoi :pora ting grain growt h and burnu p CORSOR model yield s the rate expre ssion :

dNi(t )

dt grain size of the fuel in µm and !Ct) wher e. d 0 = initi al is defin ed by:

4 dE<tl =

2.92X l0 exp (-32.1 00/T]

dt d2 0

the absol ute with the initi al. cond ition that ((0) = 1 and T is the rate For this incor porat ion it was assum ed that temp eratu re. with a fuel coeff icien ts foi: the CORSOR model were. deriv ed from In of 10 µm.

• burnu p of 28,00 0 MWd/ t and initi al grain sizes ng ps varyi fact, fuel used in tests at lower temp eratu res had burnu of the fuel betwe en 15.00 0 and 39,00 0 MWd/ t. Initi al grain sizes are seldo m repor ted.

simp ler:

When the fuel is lique fied the modi fied model becom es dN. (t) ANi( t) 1 = Ko Ci) exp I_ ERT{ i)]

dt 4.225 l V 3-89

Note that the modified CORSOR model developed here has retained the original assumption of first order kinetics. This was not necessary. In fact, an entirely similar development could have been conducted for any one of the other kinetic models mentioned above such as the three-dimens ional diffusion or the three-dimens ional phase boundary models.

The modified model that has been derived here is still quite crude. In some cases processes and phenomena have been omitted simply because it is unclear whether these processes or phenomena are already reflected in the rate coefficients of the original CORSOR model. There are ?lso cases where significant phenomena known not to be reflected in the coefficients have been omitted.

Sweeping of radionuclides by grain boundary migration and the effects of fuel/clad interactions are areas where the model could be refined further.

Though the modified CORSOR model derived here is still crude.

it can be used to demonstrate the effects on radionuclide release of fuel and accident features other than just time and tempera-ture. The modification s to CORSOR are arrested here to demonstrate some of these effects.

In Figure 3.10 the extents of cesium release from fuel heated from 700 Kat rates of 0.1. l, and 10 K/s are shown as functions of temperature. Liquefaction and fuel/clad interactions were neglected in preparing this figure. The burnup and initial grain size were assumed to be 28. 000 MWd/t and 10 µm. respectively .

The effect of heating rate on release is as would be expected.

As the heating rate decreases there is an opportunity for more

.extensive release at any given temperature.

The sensitivity of the extent of release to heating rate shown in Figure 3.10 can be used to evaluate the sensitivity of cesium release to burnup and initial grain size shown in Figures 3. 11 and 3. 12. respectively . For these plots heating rates were taken to be 1 K/s. From these figures. it is apparent that burnup and initial fuel grain size can have effects on release comparable to the effects of heating rate.

In Figure 3. 13 cesium release from fuel during a stylized me.l tdown sequence is shown. Again. it is assumed the fuel is heated at 1 K/s from 700 K. However. it was assumed that once a temperature of 2200 K was reached clad began to be incorporated into the fuel. After 100 seconds at 2200 to 2300 Kall the clad was assumed to have been incorporated in the fuel. Then. it was assumed that the fuel began to slump into a spherical mass.

After 400 s i t was assumed the fuel was part of an 80 ton spheri-cal mass. of fuel and clad. The releases predicted neglecting the fuel/clad interactions . melting. and slumping are shown in the figure for comparison. The comparison shows that fuel/clad interaction of the type hypothesized here has a small but detect-able effect. Slumping of the molten fuel has a more dramatic 3-90

- - ,...,. ....._,.._,,. - ~

1.0 BURNUP = 28000 MWd/1 INITIAL GRAIN SIZE = 10 µm 0.8 w

(/J

,ct; w_, 0.6 w

_,a:

,ct; z

w 0 0.1 K/s I .... 0.4

'°I-' 0

~

a:

u.

0.2

\

0.0 1200 1500 1800 2100 2400 2700 3000 3300 TEMPERATURE (K)

Figure 3.10. Effects of Heating Rate on the Release of Cesium.

419 1.0 ,--..,.---r-r-..,.---r--ir--,----r--i~-r----r-- ,--r------.-....------.-..-----

0.8 HEATING RATE= 1 K/s INITIAL GRAIN SIZE= 10 µm w

U)

Ill(

w

..J w 0.6 a:

..J Ill(

z w 0 BURNUP = 28000 MWd/t BURNUP = 8000 MWd/t I I- 0.4

'°N 0 Ill(

a:

I.&.

0.2

\ \

0.0 1200 1500 1800 2100 2400 2700 3000 3300 TEMPERATURE (K)

Figure 3 .11. Effects of Burnup on Release of Cesium From Fuel Heated From 700 Kat 1 K/s.

1.0 HEATING RATE= 1 K/s BURNUP = 28000 MWd/t 0.8 w

u,

~

w

..J 0.6 w

a:

..J

~

z 0

w I

ID 0

• o.4 w ~

a:

u..

0.2 0.0 l......J.--..L......L..ll!!::!:;..lllllllllll..:ii:iC::::C.......1-....J......J-.....J........J~'---.l.-....L..~....J.........L~L-......l 1200 1500 1800 2100 2400 2700

• 3000 3300 TEMPERATUR E (K)

Figure 3 .12. Effects of Initial Grain Size on Release of Cesium From Fuel Heated From 700 Kat 1 K/s ..

1.0 HEATING RATE= 1 K/s INITIAL GRAIN SIZE = 10 µm 0.8 BURNUP = 28000 MWd/t w

~

(/J c(

w NEGLECTING INCLUDING

...I w 0.6 MEL TING & SLUMPING MEL TING & SLUMPING a:

...I c(

z w 0 I

IC

~

.::0 0.4 c(

a:

LL 0.2 0.0 L.......L..-...L----"~.L-.. .-'--.-C:;;.......L.....-........-..L...---"~.L-.....J.---'- ...........1~........-..L...--"'~"---'--... ...---Ji

- 1200 1500 1800 2100 2400 2700 3000 3300 TEMPERATUR E (K)

Figure 3.13. Effects of Melting and Slumping of the Fuel on Release of Cesium.

• effect. The very small surface to volume ratio that develops as the molten sphere grows leads to very much reduced release rates.

B. Modifications to Account for Gas Phase Mass Transport The description of radionuclide release from fuel has focused in the past nearly exclusively on the limitations in the condensed phase. Assuredly, this rate limitation is quite important at low temperatures and for the more volatile species such as Cs, I, and the noble gases. The exception to this concentrated attention on condensed phase mass transport is Miller I s so-called 11 light-bulb 11 model in which condensed phase mass transport is assumed a negligible resistance to release and gas phase mass transport *is considered a dominant resistance.

The many diverse circumstances that can be hypothesized for severe reactor accidents make it apparent that neither gas phase nor condensed phase mass transport can be exclusively the source of release rate limitations. In this section, the CORSOR model is modified to account for the possibility of gas phase mass transport resistance to release.

Before delving into the modifications of the model, it is important to understand qualitatively* how radionuclides will behave once they escape the fuel. Early in an accident radionu~

elides that emerge from the urania lattice will enter a network of interconnected porosity that provides a pathway to any gap between the fuel and the clad. The radionuclide vapor will have to traverse this pathway in order to reach a breach in the clad from which it can escape into the bulk flow of gas through the reactor core. If the clad has 11 ballooned 11 due to internal

• pressurization during an accident, a substantive gap will exist between the fuel and the clad. In this case, the primary resistances to release of the radionuclide once it has escaped the urania lattice are:

1. Transport through the pore network to the fuel/clad gap, and

2. Possible* chromatographic resistance brought on by reaction with the clad and revaporization within the fuel/clad gap.

The low temperature experiments with clad, irradiated fuel that provided the CORSOR release rate coefficients examined this circumstance. That is, there were relative large gaps between the fuel and the clad in these tests. Thus, the CORSOR release fully reflect iesistances to radionuclide rate coefficients release in these circumstances.

3-95

• In a ~1.~bbuL i£~d r:eac1:.or: accident: sequence. the clad need not "balloon. 11 Rather. as high temperatu res are reached the high. external. pressures could cause the clad to collapse onto the fuel. A very narrow fuel/clad gap would then exist. The gap would be further complicate d as chemical interactio ns between the clad and fuel progress. The nature of resistance s to radio-nuclide release in this circumstan ce would be qualitativ ely similar to those arising when the clad balloons. However. the distance a vapor must travel through narrow pore structure s to reach a breach in the cladding might be longer. On the other hand. because the clad and the fuel are in intimate contact. and the clad and fuel chemically interact. there may be more frequent breaches in the clad through which radionucl ides can escape.

As temperatu res rise further. the interactio n of the fuel and the clad lead to liquid formation . At this point the clad no longer constitute s a major barrier to release. Experimen tal studies of fuel rod melting have been conducted extensive ly by Hagan et al. [105]. If oxidation of the clad by steam has been extensive . there is a tendency for liquid to flow downward in the annular space between the solid fuel and a zro 2 shell.

Even so. there are frequent breaks in the shell through which radionucl ides could escape. If clad oxidation is not extensive .

then what little zro 2 has been formed dissolves in the liquefied fuel/clad mixture and the melting clad provides little resistance to release.

Once a radionucli de migrates to a free surface adjacent to bulk flow through the core. there is still a resistance to escape that must be negotiated . The radionucl ide vapor must traverse a

.boundary layer between the free surface and the bulk flow.

The gas phase mass transport resistance posed to vaporized radionucl ides while the clad is present is complex. Some sort of a model of this process could be formulated assuming. say.

that transport through the flow passages was by Knudsen diffusion . Mean pore diameters and transport distances could be hypothesiz ed and an additiona l release resistance incorpora ted into the model. These effects will be most important only for the more volatile radionucl ides. Vaporizat ion of species such as Sr. La. and the like will not be extensive until liquefacti on begins and* the resistance to release posed by the clad and the clad/fuel gap has disappear ed.

The resistance to release posed by the boundary layer between the condensed phase and the bulk flow *through the reactor core is pandemic. It is operative throughou t the accident and affects the release of all radionucl ides.

Here the complex resistance to release that arises because of the clad is neglected . It is assumed that limitation s on the release that arise from suc.h resistance s are adequatel y reflected 3-96

• by the CORSOR release ~ate coefficients. Tnis assumption is open to doubt simply because the data base used to develop the release rate coefficients does not include the diversity of circumstances that can be hypothesized to arise in reactor accidents.

from this assumption is yet another area where the model developed here could be refined further.

Relief The modification of CORSOR to account for gas phase mass transport will be confined here to the examination of the effects of the boundary layer between bulk flow and the condensed phase.

The rate expression for release from the condensed phase derived in the previous section can be written in the form, dNi(t) ,dC. ( t) l.

= AK(i) exp [-E(i)/RT]

dt dx where K ( i) is a complex function of burnup. grain size. and physical stat~ of the condensed phase and dCi(t)/dx is the gradient in volatile element concentration in the condensed phase. This gradient can be expressed as:

• _where dCi(t) dx c.l. (t) - c.l. (surface)

E, Ci(t) = bulk concentration of the volatile element Ci(surface) = concentration of the volatile element at the condensed phase surface E, = length scale.

When resistances. other than condensed phase mass transport are neglected. Ci(surface) is asstimed to be zero. When these other resistances are to be considered. allowance for a finite surface concentration must be made and the release rate expression becomes:

dN. ( t) l.

= AK'(i) exp [-E(i)/RT] [C.(t) - C.(surface)]

dt . l. l.

Examination of the other resistances to release must provide an estimate of the unknown surface concentration.

3-97

• to Suppose now that a surface of area A 1 in a node is exposed the bulk flow of gases through the core.

expression for the rate at which a volatile element passes through the exposed surface* into the bulk flow is given by:

A general dN. ( t) A1 k

~ [P 1(surface) - Pi(bulk)]

l

=

dt where Pi(surface) = vapor pressure at the surface

= partial pressure in the bulk gas phase

= gas phase mass transport coefficient.

If a quasi-steady state has been reached then the rate at which element i is released from the condensed phase must equal the rate

• at which it passes through the area exposed to the flow.

Thus.

dNi(t) dt

= AK' (i) exp [-E(i)/RT] [C.l (t) - c.l (surface)]

_To progress in the analysis it is necessary to relate the surface concentration of element i to the* partial pressure Pi(surface).

It was unnecessary in the development of the condensed phase mass transport equation to specify the chemical form of the migrating species. Specification of the chemical form of the vapor species can be deferred. but not avoided entirely. by recognizing that regardless of the complexity of the chemistry the surface partial pressure can be specified as:

c.1 (surface)

Pi(surface) = P~(eq)

Pmolar where Pmolar = moles of condensed species per cubic centimeter of condensed phase 0

P (eq) = equilibrium partial pressure that would

• i develop uver the pure migrating species i under the ambient conditions.

3-98

• Simil arly. an equili brium partia l pressu re can be assoc with the conce ntrati on of eleme nt i in the conde Ci(t) nsed phase:

iated

- - - P~(eq )

Pmola r Then.

dNi(t) [P.(t) - P.(su rface) ]

= AK(i) exp [-E(i) /RT] P 1 dt P~(eq ) mo ar 1 1 Elimi naiing the unknow n partia l pressu re P.(sur face) yields :

1

+ RT ]

A'k g P~(eq )

1 or.

dN. ( t) 1 =K [Ni(t ) -

dt Total

• Vpmol ar l 1 RT

.where KTota l = AK' (i) exp [-E(i) /RT] pmola r +

or.

dFi(t) =KTo tal.[ Pi(bu lk)]

1 - Fi(t) - P. (o) dt Vpmol ar 1 3-99

where Pi ( o) 1s the partial pressure 1...11d 1... would develop over the condense d phase had no release occurred .

Inspecti on of this revised release model shows that several importan t effects not availabl e in the origina l CORSOR model have been introduc ed. First, the release of volatile s. is now reversib le. That -is, if the vapor concent ration in the bulk gas phase is sufficie ntly high, the flux of element i is back into the condense d phase. The release of element i from a. particu lar node in the core is depende nt now on the extent of release from nodes that precede it along the flow path. Chemist ry of the element i has been introduc ed albeit formally at this point.

This chemist ry will have to be made explici t before the rate expressi on can be applied. Once the chemist ry is explici t, it will be possible to recogniz e changes that occur in the chemica l conditio ns along the flow pathway. Because the chemist ry is included , the revised release model assures that vapor phase concent rations do not exceed the thermoch emical limit appropr iate for the ambient tempera ture and chemica l conditio ns.

To apply the model for release develope d here, it is necessar y to have values of the mass transpo rt coeffic ient, kg.

It is possible , in principl e, to determin e kg in a totally theo-retical manner. But, the exercise can be enormou sly complex .

Solution of the equation s can be done usually in only a very approxim ate manner. Consequ ently, cor relation s of experim enta 1 data are an attracti ve source of informa tion on the mass transpo rt coeffic ient. Such correlat ions are not univers al in nature. Separate correlat ions have been ,develop ed for various flow and geometry configu rations.

The patterns of gas flow through a degradin g reactor core are poorly known. It is likely that the geometry of the core as it

• degrade s evolves in a very complic ated fashion. Details of this evolutio n .may not be, however, exceptio nally importa nt for the*

analysis of radionu clide *release . Here a stylized descrip tion of the degrada tion process is outlined . This descrip tion emphasi zes 11 limiting 11 core geometr ies that_ have at least a transien t existenc e during the degrada tion process. Though these 11 limiting geometr ies and gas 11 flows may be complic ated in detail, they can be idealize d to be simple-f orms for which correlat ions of experim ental data are availab le.

When the core degrada tion process begins, the fuel consists of vertica l arrays of rods. These rods may be distorte d somewha t as a result of clad ballooni ng and rupture. The simples t descrip tion of gas flow through the core during this early stage of an acciden t is flow parallel to the rod axes. This type of flow has been enforced in out-of-p ile release experim ents with irradiat ed fuel rods [86,88-9 3]. This is also the flow pattern sought in recent in-pile. core degrada tion experim ents [87]. It 3-100

• is the flow pattern allowed by the MARCH model [7] of core degradatio n. It is probably a particula rly accurate descriptio n of flow during boil-off of coolant from the core.

Once most of the coolant has bofled fiom the core. the flux of steam into the core drops sharply [103]. Heatup of the fuel means that a significa nt temperatu re differenc e exists between the core and structure s above the core. This temperatu re differenc e will induce natural circulatio n of gases through the core [104]. In pressurize d water reactors. the open lattice of fuel will be exposed in some regions to a flow perpendic ular to the rod axes. Fuel in boiling water reactors is unlikely to. be exposed to such perpendic ular flows since fuel bundles are shielded in channel boxes.

As the degradatio n process proceeds. cladding will interact chemically with the fuel and liquid will be formed. Here. it is supposed that liquefied clad and fuel drains down the rod. This draining has been observed in out-of-pi le experimen ts [105] and is described in greater detail elsewhere [103,106] . The flow is not necessari ly continuou s. Rather. liquid forms first in an especially warm region.. flows downward until it freezes temporari ly. It then remelts. as does some of the underlyin g material of the rod.

• This combined mass then flows down along the rod until it is again frozen.

Not all the fuel in a particular location need be liquefied as a result of interactio n with the clad. That which is not may remain in place until much higher temperatu res are reached. It is more likely though that once the cladding is lost. the fuel

. that - is not liquefied will collapse into a debris bed composed of coarse particles . Temperatu res in this debris bed may become high enough that the bed material melts and flows down through the core.

As more liquefied material forms. the individua l streams of melt flowing down the rods coalesce into a single mass of liquid.

This mass is character ized here as a sphere though it is undoubt-edly a far more complex shape. Initially . the flow pattern around a sphere. can be used to determine the mass transport coefficie nt. As the mass becomes a significa nt fraction of the core mass* the geometry might better be character ized as one consisting of a downward facing surf ace and an upward facing surface. At low flows. the mass transport in the gas phase from these surfaces is determine d by natural convectio n.

In summary. the stylized descriptio n of core degradatio n presented above requires that mass transport coefficie nts be known for the following geometrie s and flow patterns:

3-101

Longitudi nal flow parallel to the axes of the rods with and without di scont inui ties created by clad ballooning or fue 1 liquefacti on.

1. Transvers e flow perpendic ular to the axes of the rods.

2. Flow around a spherical mass.

3. Flow through a debris bed.

4. Natural convection flow from a downward facing surface and from an upward facing surface.

Experimen tal data are available in greater abundance for convectiv e heat transport than for convective mass transport . A conventio nal approach is to draw an analogy between heat and*

mass transport . Then correlatio ns of data for heat transfer can be used to estimate the mass transfer coefficie nts.

The mass transfer coefficie nts for the geometrie s and flows that arise in the simplified descriptio n of core degradatio n presented above are summarized in Table 3 .13. The bases for these values are discussed below .

• Flow Around a Sphere.

sphere has been much studied.

Heat and mass transport around a The correlatio ns shown in Table 3 .13 provide values averaged over the surface of a sphere.

such. the correlatio ns are most useful when the sphere As the sphere diameter increases . local variation s in the mass transport become important .

is As small.

Schutz [ 109] has studied the local mass transport under natural convection condition s. He finds the minimum mass transport occurs at an angle of about 135° to the direction of the flow. Mass transport at angles less than 90° and larger than 140° is relatively insensitiv e to the angle.

Mass transport coefficien ts from surfaces bounded by angles greater than 140° can be as much as two times the mass transport from surfaces bounded by an angle of 90°.

The natural convection regime of flow can be character ized in greater detail than shown in the table:

Nsh(natur al convection ) = 2 + K(NGrNsc )l/4 K = 0.3 for 0 < NGrNSc < 50 K = 0.4 for 50 < NGrNSc < 200 6

K = 0.5 for 200 < NGrNSc < 10

• K = 0.6 for 3-102 6

10 < NGrNSc < 10 8

• .13 Mass Transfer Coefficients for Configurations That Develop During Core Degradation Geometry, Flow, and References Sherwood Number Limitations Flow around a sphere [107,108]

8 244 Sh NGrNsc>l0 , K=0.0254 N°*

3c b=0.5 d = diameter of sphere w

I I-'

0 µ=gas viscosity w

p = gas density NRe = dvp/µ v = gas velocity 114 5 10 Natural convection Sh = 0.27(N N ) 3xl0 <NGr<3Xl0 Gr Sc from a downward facing surface L = characteristic length of surface

Table 3.13 (Continued)

Geometry. Flow.

.and References Sherwood Number Limitations 114 5 7 Natural convection Sh= 0.54(N Sc NGr ) 10 <NGr<7Xl0 from an upward.

facing surface Sh= 0.12(N N )l/J Sc Gr L = characteristic length 6f surface Flow parallel to rod Sh= Nu(laminar) + A N0~ 8 Nl/J Re Sc w axis [114.115.118.119]

I t-'

0

~

20 Nu(laminar) = [7.SSx - 6.3x-b] [l - 3.6x/(3.2+x )]

b = 17x(x - 0.81)

X = S/D 2

A= [0.042x - 0.024)[1.103x triangular arrays 2 0 2 A= [0.026x - 0.006][1.273x

• square arrays The length dimension in Sh and NRe is the rod diameter

Geometry, Flow, and References Sherwood Number Table 3.13 (Continued)

Limitations Sh N defined in text Effects of a discon- Sh(*}= min max tinuity in flow [121]

NRe<3000 K = 0.426 + 0.113 log 10 (N~e> - 2.25c K > 0.895 - 2.25t NRe>3000 and 253 2 m = - 30.34 N;~* c smooth tubes 2

m > - 4c

- 0.344 + 0.35 log 10 (NRe) - 2.25t and NRe>3000 and K = min rough tubes

- 1.8478 + 1.2466 loglO(NRe>

2

- o.1298 [log (NReO)] - 2.25c 10 K ~ 0.885 - 2.25£ 4 N-1.2) 2 m = - (l + 4.9xlo Re t 2

m ~ - 4£

Table 3.13 (Concluded )

Geometry, Flow, and Reference s Sherwood Number Limitation s where sh(*) = Sherwood number for undisturbe d flow C = blockage factor which is the fraction of the flow occluded by rods and the obstacle y = distance from the front edge of the flow discontin uity along the rod 1qow through a Sh = ~ = 2 2

+ 3c NnRe Nl/3 Sc NRe > 80 and debris bed [122] DAB 1 - (l-c)l/3 isotherma l w debris beds I

0 d

p = particle diameter O'I C = porosity of the bed 2-n 28 4.65*N;~*

3n-l =

Nl/2 + 0.2 N2/3) Nl/3 Flow perpendic ular to Sh = a + (0.5 Re Re Sc the axes of the rods 114 a = 2/[2.n{l + 2/[0.468(N GrNSc) J}]

3 9t?D LlT NGr = µ2T D = diameter of a rod Dvp NRe = µ

• with Natural Convection From __ Upward and Downward Faci nrr ~11rr;:icec::.

The correlations shown in Table 3 .13 are actually for natural convection from upward and downward facing squares. The correla-tions were developed from correlations of natural convection heat transfer by replacing the dimensionles s Prandtl number (Cpµ/k) the dimensionless Schmidt number (µ/pDAB). Density differences that drive natural convection are assumed the result of temperature differences between the bulk gas and the condensed phase surface temperature with no contribution from the vaporizing material.

Based on Schutz*s data for natural convection from a sphere the length scales in the correlations can be taken to* be:

L(upward) = 0.7 D(equivalent )

L(downward) = 1.6 D(equivalent )

where D(equivalent ) is the dia*meter of the sphere containing an equivalent amount of mass as the body in question.

Flow Perpendicula r to the Rod Axes. The correlation in Table 13 for mass transfer during flow perpendicula r to the axes of the rods was developed from a correlation proposed by Whitaker for heat transfer from staggered tube arrays [110]. The transforma-tion to mass transfer was accomplished by replacing the Prandtl number and Nusselt numbers in Whitaker I s correlation with the Schmidt and Sherwood numbers. respectively . A natural convection correlation appropriate for a single cylinder was then added to

• the expression. Again. density differences that drive natural convection were assumed to be the result of temperature differ-ences between the bulk gas phase and the condensed phase surface

~ith no contribution from the changing c~mposition of the gas.

Whitaker*s correlation was developed to comply with the theoretical condition that in the absence of natural convection the convective heat transfer from a single cylinder should go to zero as velocity goes to zero. Correlations of experimental data at low flow rates such as that obtained by Collis and Williams [_1.11]:

45 Nu= 0~24 + 0.56 N~~

for air and 0.02 < NRe < 44 support this condition.

An alter.11ate correlation found from actual mass transport

• studies of flow perpendicula r to the axes of tubes is [112]:

3-107

68 No. 33 Sh = 0.169 [1-0.5 exp(-0.69 N)] N0° Re Sc where N is the number of rows of tubes.

Whitaker I s correlation does not describe data for in-line tube arrays as well as data for staggered tube arrays.

Flow Parallel to the Rod Axes. Investigations of flow parallel to the axes of the rods have concentrated on situations in which ~he Reynolds number is high. Weisman [113] derived the following correlations for water flow through bundles:

Nu= C NO.B Pr 113 Re where C = 0.042 S/D ~ 0.024 for square arrays with 1.1 < S/D <1.3 c = 0.026 S/D - 0.006 for triangular arrays with 1.1 < S/D < 1.5 s = center-to-center rod separation D = rod diameter.

Dingee and Chastain [114] found adequate correlation of data for water flow through various types of arrays with a Dittus-Boelter type equation:

0.8 Nl/3 Nu = O

• 023 NRe Pr in which the dimension for the Nusselt and Reynolds numbers is the equivalent hydraulic diameter.

Sparrow et al. [115] have analyzed the problem for triangular arrays and laminar flows. They present a nomograph for the average Nusselt number which can be approximated by the expressions:

3-108

~

I r

I t

~

Nu= 3.6 + 16.25(SiD ) for l < S/D < 1.4 Nu= 10 + 9.23(S/D) for S/D > 1.4 The dimension for the Nusselt number is the rod diameter in this r case.

Gimble et al. [120] ha~e examined parallel flow in a

~ configura tion proposed for early nuclear power plant fuel .

Their experimen tal data were obtained with air and for Reynolds

• numbers between 8000 and 30,000. Heat transfer data were

~ correlated by the expression 0.00104 + 0.347/X where B = 0.00434 + X X = S/D The length scale for the dimension less parameter s is the rod diameter.

There have been several studies of parallel flow for liquid metals. Dwyer [116,117] presents the correlatio ns:

2 0 86 Nu= 6.66 + 3.126X + l.184x + 0,0155 (~RePr)

• 4 for 100 < RePr < 10 1 52 0 8 0

• 27 Nu= 7 + 3.Bx * + 0.027 (~RePr)

• x 5

for o < RePr < 10 and where X = S/D

~ =

3-109

and (LM/V)max values are pLesented in a graph. Dwyer recommends for the low turbulence regime the correlation for molecular conduction:

Nu= - 2.79 + 3.97x + l.025x2 + 3.12 log 10NRe - 0.265 (log10NRe)2 Ushakov et al. [118] cite the following correlations:

3 67 Nu = Nu(laminar) +

• 2 90x where a= 0.56 + 0.19X

-b Nu(laminar) = 7.55x - 6.3x b = 17X (X - 0.81)

X > 1. 3 and 87 Nm Nu = Nu o + B N°*Re Pr where m = 0.4 + (2 + 4N )-l Pr B = 0.0083{1-exp[-10.4 (x-l)-O.l a]} + 0.008(X - 1) a= 1 + 4/(1 + lONpr) for O <Pr< 10 and 10 4 < NRe < 10 5 . Values of Nu 0 are reported to be tabulated, but this author could not retrieve the document.

Some values Nu 0 from Reference 118 are:

~

Nu X 0

1. 5 14 I

• 1. 4 13

1. 32 12 3-110

-- 1.15 1.113

1. 01 0

u.

8

1. 7 The recommended correlation for the Sherwood number is derived from the correlation by Ushakov et al. (118] of Nu(laminar) and Weisman*s (113] description of turbulent flow.

Values of the Nussel t number for laminar conditions match well tabulated values in Reference 119.

Effects of Discontinuities. In the stylized description of core degradation outlined above, melt flowing down a rod would freeze temporarily on the rod. This introduces a discontinuity in an otherwise smooth rod. Discontinuities could also be created by clad ballooning and rupture. The mass transport and t heat transport consequences of melt formation and freezing have apparently not been investigated. It is readily apparent that the efficiency of mass and heat transport should go up when flow encounters a discontinuity such as melt frozen on a rod.

Hassan and Rehme (121] have investigated the effects on heat transfer caused by a grid spacer. They found that the increase in the local Nusselt number could be correlated in terms of the Reynolds number and some geometric factors. The 11 blockage factor 11 created by an obstacle is an important geometrical quantity in the correlation. This blockage factor is just the fraction of the flow area occluded by the rods and the obstacle.

The Hassan and Rehme model asserts that about one hydraulic diameter ahead of a blockage the local Nusselt number begins to rise to a maximum. The rise rate is given by Nu(y) = l +

Nu(undisturbed) t where Dh =*hydraulic diameter y = distance from the leading edge of the obstacle A = LA/2Dh for NRe < 3000 or for rough surfaces A = LA/Dh for smooth surfaces and NRe > 3000 LA = obstacle length 3-111

After passin g the obstac le the distur bance caused by the obstac le begins to decay. The relati ve Nuss el t numbe r is then given by Nu(y) 1

= min Nu(ma x). K[~ N N ]ml Nu(un distur bed) h Re Pr x) is where values of K and m are given in Table 3 .13 and Nu(ma given by 2Nl/2 1 + 0.174 E Re for rough Nu(ma x) = min and surfac es 1 + [3. 3 + 72. 700 N;!* ] c 2 2 2 112 l + 0.174 E NRe for smoot h Nu(ma x) = min and surfac es 2.4 1 + 6.38 + 4550 NRe-O .B E Nu(y) /Nu(u ndistu rbed) is never allowe d to be less Of course .

than one.

r The corre lation for the increa se in the Sherwo od numbe create d from the Hassa n and caused by a flow disco ntinui ty was mass Rehme corre lation by assum ing the relati ve effec ts on same. Based on the transp ort and heat transp ort were the ed above. slump ing simpl ified descr iption of core meltdo wn outlin se in the rod melt or local clad balloo ning create s a local increa diame ter. Block age fac~o rs are ~hen~ for triang ular arrays :

2 0.907 Dmax E =

S2 and for square arrays 2

0.785 Dmax E =

3-112

wher:e Dmax 1.s r.ne maximum rod diameter at the discontinuit y.

The correlations also account for surface roughness of the rods. Surface roughness has an effect only at Reynolds numbers greater than 3000. For the purposes here. it is recommended that the correlation for rough surfaces be used when the flow discontinuity is created by melting. Otherwise. the smooth rod correlation should be adequate.

Plots of the effects of discontinuit ies on local Sherwood numbers as functions of distance and Reynolds numbers are shown in Figure 3 .14.

• A somewhat simpler expression for the effects of discontinu-ities can be derived from correlations of heat transfer data by Gimble et al. [ 120 J. These investigator s examined the effects of a transverse grid spacer and* correlated their data in the turbulent regime (8000 ~ NRe < 30,000) with the expression:

Nu 112

= (0.0850 + 0.612/x )N;~

0.00780 + 0.350/x

a. = 0.00257 + X Then. in the turbulent regime Sh = A NRe 1-a.

N!~ 3sc 1/3 112 )

where A = (0.0850 + 0.612x-0.00780 + 0.350/x

a. = 0.00257 + X This correlation yields an overall effect rather than a local effect. Because of the way data were obtained by Gimble et al.

the correlation applies only to regions beyond the location of the obstacle in the flow path.

Flow Through a Debris Bed. The recommended correlation in Table 3.13 is one provided by Rowe and Claxton [122]. It is for fixed. isothermal beds with NRe > 80. For low Reynolds numbers. correlations appropriate for flow over single sphere should be used.

3-113

m C

UJ 1.8 NRe = 6000 a:

...,.,, r----,/

-z C

1.6 I

\

\\

I'

.r::.

I

\\

\

w I

0 UJ IQ 1.4

, NRe = 600 I-'

a:

I-'

~  ::, 1.2 ****1* '*, ... ... ... . ' '

'.'Ii, ' /

1- .... ... ...' ' ' __________j C

.r::. 1.0 N Re = 60000

• • • • • • --:, :a,

~--~u~--------

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

0.8

-5 0 5 10 15 20 25 30 35 DIMENSIONLESS DISTANCE - Y/Dh Figure 3.14. Effects of an Obstacle 1 Hydraulic Diameter Wide on the Relative Sherwood Number. Flow blockage was taken to be 0.35 and formulae for rough tubes were used to prepare this figure.

Whitaker [llOj has offered an alternate correlatio n of heat transfer data that appears adequate to Reynolds numbers of up to 10:

Nu = (O

• 5 Nl/Z O 2 N213 ) Nl/ 3 Re +

• Re Pr Should gas velocitie s become high enough to fluidize the debris bed, then the following correlatio n [123] may be used to obtain gas phase mass transport coefficie nts:

Sh = 0.374 Nl.2 Nl/3 Sc for 0.1 < NRe < 15 Re Sh = 2.01 Nl. 5 Nl/3 for 15 < NRe < 250 Re Sc where NRe = d p vp/µ.

Correlatio ns for Steel Structure s. Vaporizat ion of constit-uents of steel can be important for some accidents . A major fraction of the steel in a reactor core is configured as long vertical surfaces. The Sherwood number and consequen tly the gas phase mass transport coefficien t for this type of surface subjected to forced conve_ction can be found from correlatio ns for flow along a flat plate:

1. Laminar flow: Sh = 0.646 Nl/Z N 113 Re Sc

2. Turbulent flow: Sh = 0.0365 NOB Re The length dimension used for both the Sherwood and Reynolds numbers is the length of the structure .

To evaluate the gas phase mass transport coefficie nt, it is necessary to have the diffusion coefficie nt of the volatile species in the ambient gas. The ambient gas is. to a first approxima tion, a mixture of steam* and hydrogen. Especiall y at

• higher temperatu res. the ambient gas becomes more complex since species such prevalent .

as H(gas). OH(gas), and O(gas)

If this comple*xity is neglected , then the diffusion coefficie nt of a volatile species in the ambient gas mixture, DAm* is given by 3-115 become more

where D A,H = diffusion coefficient of A in hydrogen 2

D diffusion coefficient of A in steam A,H 0 =

2 p . = + PH 0 T PH 2 2 The binary diffusion coefficients and D .

A,H 0 2

can be found from:

• 3. 2xlo-4 Tl. 622 PT where Pis in atmospheres.

The viscosity of the ambient gas, which is assumed to be predominantly steam and hydrogen, can be found from the Herning-Zipperer equation [124]:

µmix= 4.24 PHO+ 1.41 PH 2 2 0 674 where = l.9xl0- 6 T *

• 3-116

• C. Ra dio nu cli de Re lea se Fro Th e pre de gra de s fro the mo lte n ce m

din po in ol rt g

tac dis ha th t

s at cu fu ssi el be the en on s

ro ds for po m Fra gm en ted Co re De bri hav me e ad dre sse d :re lea se as to a slu mp ed mo lte n po

d. som e hy po the siz ed ol ca sca de s fro m the s

co re the co re ol.

ac cid

re on ce en t gio l.

n sc en ari os as se :re ac tor ve sse the low er ple nu m of the to fra gm en t int o int o a wa ter po ol in co re de br is ca us es it Su dd en qu en ch ing of the a pa rti cle bed co uld als o rin g the oc cu r if Fo rm ati on of pa rti cle s. ter ial s du to ov erh ea ted co re ma wa ter we re spr ay ed on co: re de gra da tio n *pr oc ess

. Th e rti cle bed is for me d. it ma y no t be co ola ble is On ce a pa de b:r ola nt mi gh t be in su ffi cie nt to kee p the be su pp ly of co ma y and the bed s t:ru ctu :re qu en ch ed . O:r. the pa rti cle siz e and kee p the co re de b:r is can no t flo od the bed su ch tha t co ola nt . it wi ll he at to ch ed . If the bed is no t co ola ble pa rti cle s qu en dio nu cli de s and cie nt tem pe: rat u:r es th at the rel ea se of :ra be mo dif ied to su ffi Th e CORSOR mo del can e.

oth er vo lat ile s can :re sum de br is be d.

m a p:r ed ict th is :re lea se f:ro rti cle s wh ich sum e the de br is has be en f :ra gm ent ed int o pa As sum e the As o sp he res wo uld hav e dia me ter s dp .

if def orm ed int de br is bed s a:r e pac ked so th at the po ro sit y of the i f:ro m the pa rti cle the vo lat ile ele me nt

• is E. Th e :ra te of :re lea se of bed is giv en the n by :

dF_

dt

.l.

=

GKbed dpp mo la:r

[l -F i( t)

Pi (bu lk)

Pi (o )

J RT

_l _ 1 + 0 Kb (i) ex p[- E( i)/ RT ] Pm ola :r wh ere =

kg Pi( eq )

Kb ed Kb (i) = 2.7 5x l0

-3 K (i) exp [1 .6 Bu /10 00 )

0

[!:]~

f:ro m the fu el or hav e no t bee n an ne ale d if bu rnu p and po ro sit y qu en ch ing .

if fu el me lte d p:r io: r to

• 3-1 17

gas flow throu gh If the bed is assum ed isoth erma l and that the icles . then the the bed is not suff icien t to levit ate the part [122 ):

gas phase mass trans port coef ficie nt is given by K _ DAB g - dp I 2 l _ {l-E )l/3

+ l__ [d pu oPg 3c µ Jn[pgDABµ Jl/3 J wher e Uo = supe rfici al velo city of gas throu gh the bed Pg = gas dens ity in g/cm3

µ = gas visc osity and n is defin ed by the equa tion ci U p ]-0.2 8 2-n 3n-l

= 4.65 [ µ g po s that for any Insp ectio n of the rele ase* rate expr essio n show if vola tile conc entra tions seve re comm inutio n of the debr is and excl usiv ely by d almo st are not too smal l. relea se is cont rolle case . grea ter is the mass trans port in the gas phas e. When this be need ed. In atten tion to the mass trans port coef ficie nt may is isoth erma l may be part icula r. the assum ption that the bed are then coup led remo ved. .Hea t and mass trans port in the bed expr essio n is se

.and a subs tanti ally more comp licate d relea deriv ed (123 ).

3.7 Reco mme ndati ons for MELCOR relea se.

1. The MELCOR mode l shou ld inclu de mode ls of gap of the relea se durin g heat ing. melt ing. and slum ping core . and relea se from fragm ented debr is.

gap relea se is _ recom mend ed . to MF;_LCOR.

2. The - ORNL in the Inve ntori es of the fuel/ clad gap that. part icip ate The inve ntor ies used in gap relea se are not certa in. care in Refe rence 7 are recom mend ed to MELC OR. Some may be meri ted since sele cting the gap inve ntori es conc lusio ns draw n in seve re accid ent analy ses have a tende ncy to 11 creep 11 into desig n basi s cons idera tions wher e they may not be appl icab le.

ter is The modi fied CORSOR mode l deriv ed in this chap

3. form of recom mend ed to MELCOR. Unlik e the orig inal can be appl ied durin g CORSOR. this modi fied vers ion 3-118

• mej.ting and slumping.

composition to be The modified model also allows the effects of fuel burnup. initial grain size of the fuel. ambient pressure. gas flow velocities. and gas recognized in the analyses.

Recommended default values for burnup and initial grain size are 28.000 MWd/t and 10 µm. respectively .

4. If MELCOR will permit core debris to quench and fragment then a model of release from the fragmented debris is needed. The model outlined here is recommended. If release* from the debris in this state is significant. an improved model may be needed .

• 3-119

1. USNRC, Reactor Safety Study: An Assessment of Accident Risks in US Commercial Nuclear Power Plants. WASH-1400.

October 1975 and especially R. L. Ritzman et al. "Release of Radioactivity in Reactor Accidents. 11 Appendix VII to the report.

2* Report of the President's Commission on the Accident at Three Mile Island, J. G. Kemeny, Chairman. August 1979 and also the Reports of the Te. Library of Congress Card Number 79-25694 ISBN 0-935758-00-3

3. D. o. Campbell. A. P. Malinauskus. and W. R. Stratton.

Nucl. Tech. 2.1, p. 111 (1981).

4. USNRC. Fission Product Release and Transport Research:

Existing Experimental and Analytical Program Needs, NUREG-1053, to be published.

5. USNRC, Technical Bases for Estimating Fission Product Behavior During LWR Accidents. NUREG-0772, June 1981 .

6. s. J. Niemczyk and L. M. McDowell-Boyer. Interim Source Term Assumptions for Emergency Planning and Equipment Qualification, NUREG/CR-2629. ORNL/TM-8274. and Technical Considerations Related to Interim Source Term Assumptions for Emergency Planning and Equipment Qualification, ORNL/TM-8275. September 1982 Oak Ridge National Laboratory, Oak.Ridge. TN.

7. J. A. Gieske. et al. Radionuclide Release Under Specific LWR Accident Conditions-Volumes 1-6, BMI-2104, Batelle Columbus Laboratory, Columbus. OH.

B. IDCOR. Industry Degraded Core Rule Making Program.

Subtasks 11.1, 11.3, 11.4, and 11.5.

9. G. J. Kolb. et al .* Reactor Safety Study Methodology Appli-cations Program: Oconee #3 PWR Power Plant, NUREG/CR-1659, SANDB0-1897, Rev; Sandia National Laboratory, Albuquerque.

NM. May 1981.

10. Commonwealth Edison. Inc .* Zion Probabilistic Safety Study, 1981.

11. P. Baybutt, "Radionuclide Release and Transport. 11 Chapter B. PRA Procedures Guide, Volume l, NUREG/CR-2300, January 1983 .

12. C. Politus, KfK-2167,. 1975.

3-120

13. D. A. Powe.rs. Transac tions American Nuclear Society . l!_.

p. 563 (1980).

14. Y. B. Katayam a. "Leachin g of Irradiat ed LWR Fuel Pellets in Deionize d and Typical Ground Water." BNWL-2057. Pacific Northwe st Laborato ry. July 1976.

15. T. T. Vanderg raaf. L. H. Johnson. and D. W. P. Lau.

Leaching of Irradiat ed CANDU uo 2 Fuel. 11 Scienti fic Basis for Nuclear Waste Managem ent. p. 335.

16. u. B. Ekland and R. Forsyth. Leaching of Irradiat ed uo 2

.Fuel. KBS Report 70. February 1978.

,

'._~~ ~*-)

17. 'R. A. Lorenz. J. L. Collins. and A. P. Malinau ~kus.

Nuclear Technolo gy * .!§.. p. 404 (1979).

18. J. Brockma nn and T. Stalker. Sandia Nationa l Laborat ories.

Albuque rque. NM. unpublis hed results.

19. G. Parker. G. E. Creek. and A. L. SUtton. Jr .* "Influen ce of Variabl e Physica l Process Assumpt ions on Core Melt Aerosol Release ." Proc. Int'l Mtg. on Thermal Reactor Safety. Chicago . IL. NUREG/C P-0027. Volume 2. p. 1078.

1983.

20. J. P. Mitchel l. A. L. Nichols. and J. A. H. Simpson. "The Charact erizatio n of Ag-In-Cd Control Rod Aerosols Generate d at Tempera tures Below 1900 K. 11 CSNI Special ists Meeting on Nuclear Aerosols in Reactor Safety. Karlsruh e.

West Germany . Septemb er 1984.

21. Major sources of data necessar y to calculat e ~Gi(T) a.re:

a. D. R. Stull and H. Prophet. JANAF Thermoc hemical Tables~ .2nd edition. NSRDS-NBS37. June 1971.

b. M. W. Chase et al. 11 JANAF Thermoc hemical Tables 1974 Supplem ent." J. Phys. Chem. Ref. Data 3. pp. 311-480 (1974).

b. M. W. Chase et al. 11 JANAF Thermoc hemical Tables 1975 Supplem ent." J. Phys. Chem. Ref. Data 4. pp. 1-175 (1975).

c. M. W. Chase. Jr. et al. 11 JANAF Thermoc hemical Tables 1978 Supplem ent." J. Phys. Chem. Ref. Data 7. pp.

793-940 (1978).

3-121

• d. M.

1982 W.

REFERE?'lCES Chase. Jr.. et al. 11 JANAF Thermoc hemical Tables Supplem ent. 11 pp. 695-940 (1982).

J. Phys. Chem. Ref. Data 11.

e. I. Bar in. and o. Knacke. Thermoc hemical Propert ies of Inorgan ic Substanc es. Springe r-Verlag . 1973.

f. I. Barin. o. Knacke. and o. Kubache wski.

Thermoc hemical Properti es of Inorgan ic Substan ces, Supplem ent. Springer -Verlag. 1977.

. g. K. c. Mills. Thermod vnamic Data for Inorgan ic Sulphid es, Selenide s and Tel lurides. Butterw orths.

London. 1974.

h. R. A. Robie et al. Thermod ynamic Propert ies of Mineral s and Related Substanc es at 298 .15 K and 1 Bar 5

(10 Pascals) Pressure and at Higher Tempera tures.

Geologi cal Survey Bulletin Q452.

i. D. D. Jackson . Thermod ynamics of Gases Hydroxi des.

UCRL-51 137. 1971.

j. P. E. Blackbu rn and c. E. Johnson . ANL 42. Argonne Nationa l Labs. 1982.

k. F. Garisto . Thermod ynamics of Iodine, Cesium, and Telluriu m in the Primary Heat Transpo rt System Under Acciden t Conditio ns. Atomic Energy of Canada. Ltd .*

AECL-77 82.

1. D. D. Wagman. et al. "The NBS Tables of Thermod ynamic Propert ies. 11 J. Phys. Chem. Ref. Data 11 ( 19 82)

Supplem ent 2.

m. R. Hultgren . R. L. Orr. P. D. Anderson . and K. K.

Kelley~ Selected Values of Thermod ynamic Propert ies of Metals and Alloys. J. Wiley and Sons.

22. D. A. Powers. Control Rod Behavio r During Core Degrada tion I: Pressur ization of Ag-In-Cd Control Rods. NUREG/C R-4401.

SAND85- 0469. Sandia Nationa l Laborat ories. Albuque rque. NM.

Septemb er. 1985.

23. D. A. Powers and J. E. Brockma nn. VANESA: A Mechan istic Model of Radionu clide Release *and Aerosol Generat ion During Core Debris/C oncrete Interact ions. NUREG/C R-4308.

SAND85- 1370. Sandia Nationa l Laborat ories. Albuque rque. NM.

July 1986.

3-122

1:l'Cl'Cl'Cln't:11'1', .,'t:'lr"' , .,... - - .... ! --- - -=-'

L\.uL" u.l\.ul"'-C.;;) \ \...VU I, l. UUt:U J

24. J. F. *Muir. et al.. CORCON-MODl: An Improved Model for Molten- Core/Co ncrete Interact ions. NUREG/C R-2142.

SAND80- 2415. Sandia Nationa l Laborat ories. Albuque rque. NM.

1981. .

25. W. R. Smith. Industr ial and Enginee ring Chemist ry, Fundame ntals 19. p. 1 (1980).

26. W. B. White. s. M. Johnson. and G. B. Dantzig . J. Chem.

Phys. ll, p. 751 (1958).

27. T. Gerlach . FLUEQU. unpublis hed code used in the calculat ions for Referenc e 5.

28. G. Eriksson and E. Rosen. Chem. Scripta ~. p. 193 (1973).

29. G. Eriksson . Acta Chem. Scana. ~. p. 2651 (1971).

30. S. R. Brinkley . Jr .* J. Chem. Phys. 15. p. 107 (1947).

31. D. A. Powers in Advanced Reactor Safety Research Quarter ly Report April-Ju ne, 1979. NUREG/CR-0984 SAND79- 1597. Sandia Nationa l Laborat ories. Albuque rque. NM. Novembe r 1979.

32. Electric Power Research Institut e. Technic al Reports 11.1, 11.4 and 11.5 Estimati on of Fission Product and Core Materia l Charact eristics . Atomic Industr ial Forum. October

• 1983.

33. K. Konashi . T. Yato. and H. Kaneko. J. Nucl. Mat'ls 116,

p. 86 {1983).

34. G. A. Somorja i. "High Tempera ture Vaporiz ation Mechani sms." p. 73 in High Tempera ture Technolo gy Proceed ings of the 3rd Internat ional Symposiu m. Asiloma r.

CA. 1967.

35. J. P. Hirth and G. M. Pound. Condens ation and Evapora tion.

(Pergamo n Press. New York. 1963).

36. s. E. Ziemniak . "A Study of Interfac ial Resistan ce to Mass Transfe r at High Evapora tion Rates." Thesis. Renssel aer Polytech nic Institut e. August 1968.

37. R. G. Ward. J. Iron and Steel Institut e. 201. p. 11 (1963).

R. A. Lorenz. "The Vaporiz ation of Structu ral Materia ls in 38.

Severe Acciden ts." Proc. Int'l Mtg. on Thermal Nuclear Reactor Safety. Chic~go. IL. NUREG/C P-0027. 1983.

3-123

• 39.

K~~~K~NC~S (Continued )

E. A. Mason. A. P. Malinausk us. and R. B. Evans. J. Chem.

Phys.!§.. p. 3199 (1967).

40. S. Chapman and T. G. Cowling. Mathemat ical Theory of Non-unifor m Gases. 2nd edition. Cambridge Press. 1961.

41. E. R. Gilliland . Ind. Eng. Chem.~. p. 681 (1934).

42. P. c. Singh ands. Singh. Int. Comm. Heat Mass Transfer

10. p. 123 (1983).

43. E. T. Turkdogan . P. Grieveson . and L. s. Darken J. Metals

.§.. p. 21 (1962).

44. A. W. D. Hills and J. Szekeley. Int* 1 J. Heat and Mass Transport 12. p. 111 (1969).

45. E. T. Turkdogan and K. c. Mills. Trans. AIME 230. p. 750 (1964).

46. F. F. Abraham. Homogeneo us Nucleatio n Theory. Academic Press. 1974.

47. R. Becker and W. Doring. Ann. Phys. (Leipzig) 24. p. 719 (1935).

48. J. Lethe and G. M. Pound. J. Chem. Phys. 1.§.. p. 208c (1962).

49. w. Camp. Sandia National Laborator ies. unpubli~h ed results.

so. B. M. Jeffery. J. Nucl. Mat 1 l. 22.*p. 33 (1967).

51. J. I. Bramman. et al .* J. Nucl. Mat 1 l ~. p. 201 (1968).

52. F. Schmitz. et al. Int 1 l Mtg. on Fast Reactor Fuel and Fuel Elements. p. 336 (1970).

53. K. c*. Russel. J. Chem. Phys. so. p. 1809 (1969).

54. M. W. Mallett.* A. F. Gerds. A. W. Lemmon. Jr .* and D. L.

Chase. BMI-1028 (1956).

55. P. Hofmann. D. Kerwin-Pe ck. and P. Nikolopou los. Physical and Chemical Phenomena Associated with the Dissolutio n of Solid uo 2 by Molten Zircaloy-4 . PNS-Nr 675812.

Kernforsch ungszentru m Karlsruhe . 1982.

3-124

REFERENCES (Contin ued)

56. C. Politu s. KfK 2167 (1975).

57. D. A. Powers . 11 Chemic al and Physic al Proces ses of Reacto r Core Meltdow n. Chapte r 4 in Core Meltdow n Experi mental Review . SAND74 -0382 (Revisi on) NUREG -0205. Sandia Nation al Labora tories. Albuqu erque. NM. March 1979.

58. J. Fische- r. J. D. Schilb . and M. G. Chasan ov. J. Nucl.

Mat . .!!!_. p. 233 (1973).

59. R. A. Lorenz . J. L. Collin s. and A. P. Malina uskus.

Nuclea r Techno logy * .1.§.. p. 404 (1979) .

60. R. A. Lorenz . 11 Status of Valida tion of the CORSOR Comput er Code Used for the Accide nt Source Term Reasse ssment Study. 11 in Review of the Status of Valida tion o*f the Comput er Codes Used in the NRC Accide nt Source Term Reasse ssment Study (BMI-2 104). ORNL/T M-8842. Oak Ridge Nation al Labora tory.

61. A.H. Booth. AECL CRDC-7 21. Atomic Energy of Canada . Ltd .

1954.

62. D.R. Olande r. Fundam ental Aspect s of Nuclea r Reacto r Fuel Elemen ts. UC 736 TID 26711. 1975.

63. J. Rest. GRASS- SST: A Compre hensive , Mecha nistic Model for the Predic tion of Fission -gas Releas e in U02-Ba se Fuels During Steady -State and Transi ent Condit ions.

NUREG /CR-020 2. ANL78- 53. Argonn e Nation al Labora tory. June 1978.

64. s. E. Tu.rner . et al.

• Backgro und and Deriva tion of ANS5. 4 Standa rd Fission Produc t Releas e Model. NUREG /CR-250 7.

Januar y 1982.

D. M. Haalan d. 11 Releas e of Radioa ctivity from the Core.

11 65.

Chapte r 7 in Core Meltdow n Experi mental Review .

SAND74 -0382 (Revis ion). NUREG -0205. Sandia Nation al Labora tories. Albuqu erque. NM. 1977.

66a. W. Hernin g. J. Nucl. Mat'ls . 114. p. 41 (1983) .

66b. I. R. Brearly and D. A. Maclne s. SINGAR-A Model to Examin e Fissio n Produc t Releas e in Accide nt Studie s. SRD R-258.

Safety and Reliab ility Direct orate. UK Atomic Energy Author ity. June 1983.

3-125

REFER~N~~~ (Continued )

66c. K. Malen, AFISS-A Computer Code for Calculatio n of Accident Fission Product Release from Fuel Rods.

Studsvik/N F(p)-81/62 , 1981.

67. P. E. Blackburn . J. Nucl. Mat'ls . .i§_. p. 244 (1973).

68. S. W. Tam. P. E. Blackburn . and C. E. Johnson. "Effect of Core Chemistry on Fission Product Release. 11 Proc. Int' 1 Mtg. on Thermal Nuclear Reactor Safety. Chicago, IL, NUREG/CP -0027. Vol. 1. pp. 101-110. February 1983.

69. H. Kleykamp. J. Nucl. Mat'ls. §...1.. p. 109 (1979).

70. 0. Gotzmann. J. Nucl. Mat'ls. 107, p. 185 (1982).

71. D. Cubicciot ti and J. H. Davies. Nucl. Sci and Eng. 60,

p. 314 (1976).

72. C. E. Miller. Jr .* Nuclear Applicati ons~. p. 1 (1968).

73. D. Cubiccio tti. Nuclear Technolog y 2.1, p. 5 (1981).

74. W. I. Stuart and R. B. Adams. J. Nucl. Mat'ls. 21!, p. 201 (1975).

75. M. J. Bannister and W. J. Buykx. J. Nucl. Mat'ls . .§.1..

p. 57 (1977).

76. J. T. Bittel. L. H. Sjodakl. and J. F. White. J. Am.

Ceram. Soc.~. p. 446 (1969).

77. S. C. Jain. Proc. Roy. Soc. (London) A 243, p. 359 (1957).

78. R. o. Wooton and H. I. Avci. MARCH 1.1 (Meltdown Accident Response Character istics) Code Descriptio n and User's Manual. NUREG/CR -1711, October 1980.

79. H. Albrecht. V. Matschoss . and H. Wild, "Experime ntal Investiga tion of Fission and Activatio n Product Release from LWR Fuel Rods at Temperatu res Ranging from 1500-2800 °C. 11 Proc. Specialis ts Mtg. on the Behavior of Defected Zr Alloy Clad Ceramic Fuel in Water Cooled Reactors. CONF-7909 35-3 (1979).

3-126

REFERENCES (Continued)

80. H. Albrecht and H. Wild. 11 Investigation of Fission Product Release by Annealing and Melting LWR Fuel Pins in Air and Steam." Proc. Topical Mtg. on Reactor Safetv Aspects of Fuel Behavior. Sun Valley. ID. August 1981.

81. H. Albrecht. 11 0ut-of-Pile Release Tests Under Core Mel ting Conditions. 11 OECD-NEA-CSNI I IAEA Specialists Mtg. on Water Reactor Safety and Fission Product Release in Off-Normal and Accident Conditions. 1983.

82. H. Albrecht and H. Wild. 11 Behavior of I. cs. Te. Ba. Ag, In. and Cd During Release from Overheated PWR Cores. 11 Proc. Int 1 l Mtg. on LWR Severe Accident Evaluation. August 1983 Cambridge. MA. paper TS4.2.

83. H. Albrecht. K. Nolte. and H. Wild. Project Nukleare Sicherheit. KfK 2950. Kernforschun gszentrum Karlsruhe.

West Germany. 1980.

84. H. Albrecht. K. Nolte. V. Prech. K. H. Simon. and H. Wild.

Project Nukleare Sicherheit. KfK-3250. Kernforschun gszen-trum Karlsruhe. West Germany. 1981.

85. H. Albrecht. V. Matschoss. K. Nolte. and H. Wild. Project Nukleare Sicherhei t. KfK-27 50. Kernforschun gszentrum Karlsruhe. West Germany. 1978.

86. M. F. Osborne. R. A. Lorenz. K. S. Norwood. J. R. Travis.

and C. S. Webster. Data Summary Report for the Fission Product Release Test HI-3, NUREG/CR-333 5 ORNL/TM-8783 , Oak Ridge National Laboratory. Oak Ridge. TN.

87. D. J. osetek. K. Vinjamuri. D. E. Kuders. and R. R.

Hobbins. 11 Iodine and Cesium Behavior During the First PBF Severe Fuel Damage Test. 11 Proc. Int 1 1 Mtg. on LWR Severe Accident Evaluation paper TS 4.3. Cambridge. MA. 1983.

88. R. A. Lorenz. et al .* Fission Product Release from Highly Irradiated Fuel Heated to 1300-1600°C in Steam.

NUREG/CR-138 6, ORNL/NUREG/T M-346. Oak Ridge National Laboratories . Oak Ridge. TN. December 1980.

89. R. A. Lorenz; et al .* Fission Product Release from BWR Fuel Under LOCA Conditions. ORNL/NUREG/T M-388, Oak Ridge National Laboratories . Oak Ridge. TN. July 1981.

90. R. A. Lorenz. J. L. Collins. and A. P. Malinauskus .

Fission Product Source Terms for the LWR Loss-of-Cool ant Accident. NUREG/CR-12.8 8, ORNL/NUREG/T M-321. July 1980.

3-127

REFERENCES (Continued)

91. M. F. Osborne. R. A. Lorenz. J. R. Travis. and c. s.

Webster. Data Summary Report for the Fission Product Release Test HI-1. NUREG/CR-292 8. ORNL/TM-8500 . Oak Ridge National Laboratories . Oak Ridge. TN. December 1982.

92. M. F. Osborne. R. A. Lorenz. J. R. Travis. c. s. Webster and K. s. Norwood. Data Summary Report for the Fission Product Release Test HI-2. NUREG/CR-317 1. ORNL/TM-8667 .

Oak Ridge National Laboratory. Oak Ridge. TN.

93. M. F. Osborne. R. A. Lorenz. K. s. Norwood. and R. P.

Wichner. "Fission Product Release Under LWR Accident

__t;a.. .g"'-"-._....;:;o...;;.n:;.._"""L=WR=-....;:;s.....e;._v;.. ;e:;.;r:;;..e.;;._--=-=A::.;:c.....c;;..:i;;..d:;;..e=n=t conditions

• 11 ""'"P___r __o__c......'---I___n____t_*___l'--__M Evaluation paper TS 4.1. Cambridge. MA. 1983.

94. R. A. Lorenz. E. C. Beahm. and R. P. Wichner. "Review of Tellurium Release Rates from LWR Fuel Elements Under Accident Conditions." Proc. Int'l Mtg. on LWR severe Accident Evaluation. paper TS 4.4. Cambridge. MA. 1983.

95. C. D. Andriesse and R. H.J. Tanke. Nuclear Technology.§_§ _.

p. 415 (1984).

96. D. A. Young. Decompositio n of Solids. Pergamon Press. 1966.

97. R. A. Lorenz. "Status of Validation of the CORSOR Computer Code Used for the Accident Source Term Reassessment Study." in Review of the Status of Validation of the Computer Codes Used in the NRC Accident Source Term Reassessment Study (BMI-2104). T. s. Kress. editor.

ORNL/TM-8842 . Oak Ridge National Laboratory. Oak Ridge. TN.

98. A. W. Coats and J. P. Redfern. Nature 201. p. 68 (1964).

99. V. M. Gorbaschev. J. Thermal Analysis~. p. 349 (1975).

100. A. Van Tet~. Thermochemic al Acta 17. p. 372 (1976).

101. V. Denny and B. Raj Sehgal. "Analytical Predictions of Core Heatup/Lique faction/Slump ing" paper TS-5.4 in Proc.

Int'l Mtg. LWR Severe Accident Evaluation Vol. 1.

August 28-September 1. 1983. Cambridge. MA.

102. B. D. Johnston. The Zircaloy-Uran ium Dioxide Reaction. SRD*

R294. Safety and Reliability Directorate. United Kingdom Atomic Energy Authority. Culcheth Warrington. Great Brltian. September 1984.

3-128

REFERENCES (Concluded) 103. J. Rivard. Review of In-vessel

=-.;a...;._;;::..=.;;.;;...__""'-"'_--'=-=---- -=-=.=..::;c=.._~=-=='-="=-=-==---=-= Models.

Meltdown =-=-==-=-==-=

NUREG/CR-1493. SAND80-0455. Sandia National Laboratories.

Albuquerque. NM. July 1980.

104. D. Wi 11 iams and J. B. Rivard. "Range of Possible Net Release from the RCS. 11 Appendix B in R. J. Lipinski. et al. Uncertainty in Radionuclide Release Under Specific LWR Accident . Conditions. Volume 2. SAND84-0410/2. Sandia National Laboratories. Albuquerque. NM. February 1985.

105. s. Hagan. et al. Projekt Nuklease Sicherheit. KfK-2750 4300-62. Kernforschungszentr um Karlsruhe. West Germany.

November 1978.

106. J. Rivard. "RCS Assessment for MELCOR. 11 Chapter 2 in Thermal-Hydraulic Process Modeling in Risk Analysis: An Assessment of The Relevant Sys terns, Structures. and Phenomena. NUREG/CR-3986. SAND84-1219. Sandia National Laboratories. Albuquerque. NM. August 1984.

107. R. L. Steinberger and R. E. Treyba 1. AI CHE J. ~. p. 227 (1960).

108. D. c. T. Pei. C. Narasimham. and W. H. Gauvin. Proc. Symp.

on Interactions between Fluids and Particles-. Institute of Chemical Engineering. London. June 1962.

109. G. Schiltz. Intern J. Heat and Mass Transfer ~. p. 873 (1963).

110. S. Whitaker AIChE J. 18. p. 361 (1972).

111. D. C. Collins and M. J. Williams. J. Fluid Mechanics ~.

p. 357 (1959}.

112. H . s myc z e k and J . zab 1 o ck i. _P_r_._..c..N.....a_u__k_____I__n=s=---t . . ._ .....I __n_z__.___c__h__e__m_.

Urzadzen Cielplnych Politech. Wroslaw ~. pp. 261-266 (1974); CA:82:142094a.

113. J. Weisman. Nucl. Sci. and Eng.~. p. 78 (1959).

114. D. A. Dingee and J. W. Chas ta in. 11 Hea t Transfer f ram Parallel Rods in Axial Flow,"" Reactor Heat Transfer Conference of 1956. J.E. Viscardi. editor. TID-7529 pt. 1.

p. 462, 1957.

115 . E.

• M. Sparrow, A. L. Loeffler. Jr.. and H. A. Hubbard, Trans. ASME J. of Heat Transfer, pp. 415-422, November 1961.

3-129

• 116.

117.

n~~~tt~NC~~

0. E. Dwyer. AIChE J. ~.

(Continued)

O. E. Dwyer. Nucl. Eng. Design 10. p. 3 (1969).

p. 261 (1963).

118. P. A. Ushakov. A. V. Zhukov and N. M. Matyukhin.

Teplofizika Vysokikh Temperatur 1:.2, p. 1027 (1977).

119. R. K. Shah and A. L. London. "Laminar Flow Forced Convection in Ducts."

Supplement 1. Academic Press. 1978.

Advances - -in

---

- - - - - - -Transfer Heat =---

120. R. E. Gimble. W. H. Bell. and S. L. Fawcett, Heat Transfer and Friction-Flow Characteristics of Cylindrical Parallel Rods with Transverse Cylindrical Spacers, AECD-3975.

Batelle Memorial Institute, Columbus. OH. 1954.

121. M. A. Hassan and K. Rehme, Nucl. Technology g, p. 401 (1981).

122. P. N. Rowe and K. T. Claxton. Trans. Inst. Chem. Eng . .1}_,

p 10 T321 (1965) .

• 123.

124.

.125.

0. Mathews. Trans. Can.

F. Berning (1936) .

C. F.

and L.

Inst. Min. Met. g. p. 97 (1939).

Zipperer. Gas Wasserfach.

Clement. Aerosol Growth in Vapour-Gas Mixtures 1]_, p. 49 Cooled Through Surfaces. TP. 897, AERE Harwell. May. 1982.

126. A. D. Emery. D. B. Scott. and J. R. *Stewart. Nucl.

Technology 11 (1971) 474.

127. M. R. Kuhlman. D. J. Lehmicke and R. o. Meyer. CORSOR User*s Manual. NRC Report NUREG/CR-4173, BMI-2122, Battelle Columbus Laboratory. Columbus. OH. March. 1985.

128. J. L. Kelly. A. B. Reynolds, and M. E. McGown, Nuclear Science and Engineering~ (1984)184 .

• 3-130

• 4.1 FISSION PRODUCT RELEASE AND AEROSOL GENERATION WITHIN THE REACTOR CONTAINMENT Introduction and Definitions An acciden*t severe enough to melt the reactor fuel in a light water reactor will lead to release of radioactive material from the fuel. This released material. primarily in the form of aerosols. may escape into the reactor conta1nment and. perhaps.

from there into the environment. The nature of radioactive material released from the fuel~-its composition. form. release rate. and integral release fraction--is called the "source term."

Radioactive material released from fuel that has penetrated the reactor pressure vessel is the "ex-~essel source term".

Ex-vessel release of radioactive material is one of the four release processes considered in the Reactor Safety Study [l].

At the time of the Reactor Safety Study. little was known about any of the release processes. Approximate calculations . possible then. placed the greatest emphasis on release from fuel within the reactor primary system. The relatively volatile species emitted from the fuel during the early stages of a severe reactor accident were assumed to pose the greatest radiological threat.

In an effort to provide bounding estimates of released radio-activity that would be applicable to the severest accident at a wide variety of nuclear plants. the analyses in the Reactor Safety Study [2] neglected many processes that mitigate the source term. One consequence of the conservative approach was

. to make the ex-vessel source term appear less significant than the source terms from in-vessel processes.

The more sophisticated understanding of severe accident source terms that has developed since the Reactor Safety Study has kindled a greater interest in ex-vessel release processes.

Modern treatments of source terms distinguish between radioactive material released from the fuel--the "phenomenolo gical source term 11 --and the radioactive material that escapes from a reactor plant--the "radiologica l source term 11

• Much of the new interest in the ex-vessel source term arises because of the mechanistic relationsh-ip between the phenomenolog ical and the radiological source

• terms. as well as the inherent nature of ex-vessel release of radioactive material. Some specific reasons for this interest are:

1. Ongoing studies of fission product behavior under reactor-accid ent conditions have shown that much of the

.radioactive material released in-vessel may not escape 4-1

• the reactor pr1mary inventor y of material the radiolog ical contribu tion of system in the source term.

material and containm released contribu te ent availab Proport ionately .

ex-vess inventor y may be greater than heretofo re supposed because ex-vess el releases are less sus~ept ible to mitigati on el

~u to le the for the this during transpo rt from the point of release to the reactor containm ent.

2. Radioac tive materia l released ex-vess el includes more refracto ry isotopes than does the in-vesse l release. The qualita tive nature of the radiolog ical source term may be changed if the ex-vesse l release contribu tions are greater than expected .

3. Aerosol processe s naturall y mitigate the phenome nologica l source term. Signific ant delays between in-vesse l emission s of radioac tivity from the fuel and gross containm ent failure are possible and provide an opportu -

nity for great redtictio n in the amount of materia l released in-vesse l that will escape into the environm ent.

The ex-vess el sources are likely to be operativ e even after gross containm ent failure has occurred . Then the ex-vess el sources are less suscept ible to mitigati on by aerosol processe s.

4. The aerosol processe s that can cati&e such mitigati on of the in-vesse l source proceed among particle s whether they are radioac tive or not. The copious emission of non-radioac tive materia ls typicall y associat ed with the ex-vess el sources provides a means to greatly enhance mitigati on of the phenome nologica l source term. particu -

lar*ly. that portion of the source term created of the ex-vess el source term could lead to both quanti ta ti ve an~ qualitat ive changes in the perceive d radiolog ical conseque nces of severe reactor acciden ts.

The second of the above points deserves some elabora tion.

Fission product releases during the ex-vess el debris interact ions do involve the more refracto ry elements since volatile species would escape the fuel before the . onset of ex-vess el phenome na.

The radiolog ical .effects of refracto ry fission products have not received a great deal of attentio n in the past: first. because the releases of these elements were deemed small. and second.

because the effects would be swamped by the releases of large amounts of cesium and iodine from fuel in the vessel. If the volatile species such as iodine do not escape the reactor coolant system, then the radiolog ical conseque nces of releasin g refracto ry fission product species need further examina tion.

Results *of a first attempt to do so are assemble d in Table 4.1.

To prepare this table. the radiolog ical conseque nces of the 4-2

'!'able 4.1 RadiologicaL-EfEec~ s of Refractory Fission Products in Comparison to Cesium a~d Iodine [6]

Relative Early Element Bone-Marrow Dose I 1. 0 Cs 0.1 Te 0.6 La 0.8 Ce 0.2 Pr 0.0001 Nd 0.3 Np 1. 2 Pu 1 X 10-6 Mo 0.1 Relative Element Long Term Dose Cs 1. 0 Ce 0.21 Nb 0.7 Zr 1. 4 Ru 0.7 4-3

release of 10 percent of the cesium inventory and 10 percent of the iodine inventory were normalized to unity. The consequences of the release of 10 percent of the inventory of other.

selected. isotopes were then determined on this relative scale.

It is apparent from these results that the refractory isotopes can be every bit as consequential as the volatile isotopes that have received so much attention in the past.

In the sections that follow. the current state-of-the-art in predicting the ex-vessel -phenomenological source term is described. To present this discussion. it is convenient to divide the topic into two categories--primar y ex-vessel source processes and secondary source process. The primary source processes give rise to release as a direct consequence of the -

ex-vessel behavior of the fuel. Release of radioactivity during (1) ejection of fuel from the primary system into the reactor containment. (2) interaction of fuel and core debris with concrete. and (3) ex-vessel interaction of molten material with water are all primary source processes. Leaching of radioactive materials from core debris by groundwater should the reactor basemat be penetrated is considered also to be.a primary process.

Secondary source processes are those that arise because of the behavior of materials previously released from the fuel whether this release occurred during the in-vessel or ex-vessel stages of an accident. Resuspension of deposited aerosols and radiolytic release of iodine in sump waters are exampl*es of secondary processes.

The focus of the discussions below is on the release of radioactivity from the fuel ex-vessel. Mitigation of this

.phenomenological source term by the presence of nonradioactive aerosols and enhancement of the source by secondary processes have become quite important aspects of severe reactor accident analyses [ 3]. To meet the needs of these analyses. release of nonradioactive materials from concrete and structural materials in a reactor containment are also - discussed. The processes by which the phenomenologica 1 ex-vessel source term is converted into a radiological source term are reserved for treatment elsewhere [4].

4.2 Primary Fissions Product Release A. Release Associated with Melt Ejection The ex-vessel phase of a severe reactor accident begins with the expulsion of core debris from the reactor coolant system.

Most previous analyses of severe reactor accidents have devoted little attention to the details of the expulsion process.

Reactor accident phenomena have been described in these previous studies as though the coolant system were depressurized--a 4-4

situation appropriate for accidents initiated by large breaks in thG coolant sysLem. Consequently , expulsion of the molten core material from the primary system was considered to be driven by gravity. Some small amount of fission product and aerosol release could come from the core debris as it fell from the primary system into the reactor cavity. But, any error caused by neglecting this release has been judged small in comparison to uncertainties concerning aerosol generation and fission product release associated with the behavior of the core debris once it has been expelled. This judgement is supported by the results of recent tests with large-scale uo 2 melts expelled under the force*of gravity from a furnace [4].

The past systematic analyses of severe reactor accidents have concluded unanimously that accidents initiated by large breaks in the primary coolant system do not dominate the risk

,associated with the commercial use of nuclear power (for examples. see References 1 and 7). Accidents initiated by small breaks in the coolant system or transient events are more frequent. Descriptions of the phenomena during accidents initiated by small breaks or transients assuming a depressured primary system have been criticized [5]. It is expected that prior to melt expulsion in these more frequent accidents. the primary system would be at or near operating pressure. Even in boiling water reactors where operation procedures dictate primary system depressuriza tion during off-normal events. the system would be at an elevated pressure (> 200 psig) throughout the process of core melt formation and up to the time of melt expulsion.

Henry has attempted to determine how the process of melt expulsion might be affected if the reactor coolant system were pressurized [7]. His analysis concluded that hydrodynamic phenomena exist which could disperse the core debris broadly if it were expelled from a pressurized system. The fraction of the core so broadly distributed (nominally 50 percent) could easily be quenched and kept cool so it would not further interact with materials outside the coolant system. Consequently . this debris would not be a continuing source of fission product release or aerosol generation.

These first attempts to ascertain how expulsion of the core debris from a pressurized primary system might affect the course

• of ex-vessel phases of a severe reactor accidents have not con-sidered fission product release and aerosol production during melt expulsion. Early attempts to study melt ejection from pressurized systems have demonstrated that the ejection process can be a formidable source of aerosols [BJ. Figure 4.1 is a series of photographs taken of an experiment in which a thermitically generated melt weighing 2.5 kg was ejected from a vessel pressurized to 40 atmospheres. Aerosol production begins 4-5

t=1.15S MAXIMUM AEROSOL et. oud%

Figure 4.1. Sequence of Photographs Taken During Expulsion of

2. 5 Kg of Melt From a Vessel Pressurized to 4 O Atmospheres.

4-6

in this experiment with the initial emergence of melt and con-tinues throughout the expulsion process. The aerosol production becomes so intense. the experimental apparatus is completely obscured about one second after the*start of the test.

Samples taken during this and similar tests show a size dis-tribution that may be trimodal (see Figure 4.2). Modes appear at 0.5 µm. 5 µm and at a larger size--nominally 65 µm [8]. Th.e finest particles seem to be composed of compact agglomerates of 0.1 µm particles. The material of size near 5 µmis composed of nearly spherical particles that have the appearance of frozen liquid. The coarse mode material consists of both spherical and granular shapes. These particles. too. may have been liquid droplets once. The irregular shapes of some of the particles may have been caused by shrinkage during solidification or because the particles were broken during sampling. These coarse parti-cles may not represent a mode in the aerosol size distribution.

They may. in fact. be the "tail" of the distribution of very coarse particulate debris produced by the pressurized melt ejec-tion. The aerosol sampling equipment was used in tests to date does not provide a very accurate characterication of the coarser material.

Pressurized melts have also been expelled into scaled models of reactor cavities. Aerosols collected during these tests have size distributions with only two modes. The fine mater ia 1 ( <l

µm) is similar to that described above. There is no indica-tion of aerosol material concentrations in the 3-8 µm size range. There is a significant amount of coarse material. Again.

this coarse material collected with the aerosol sampling equip-ment is probably the "tail" of the size distributed debris particulate produced during expulsion from the reactor cavity model. This debris has been characterized by fiash x-rays as it emerged from the cavity and by post-test sieve analyses. The material has been found to be log-normally distributed in size with mean particle sizes of 0.4 to 0.8 mm and a geometric standard deviation of about 3. 4 (see Figure 4. 3). This size distribution implies that less. than 4 percent o~ the mass expelled from the cavity would have particle sizes of less than 50 µm.

Few measurements of the mass of expelled melt converted into aerosols have been reported. In tests involving melt expulsion

• into a reactor cavity. O. 5-1 percent of the melt mass aerosolized. About half of this material was smaller than 10 µrn and about 35 percent was smaller than 1 µm. In tests involving melt expulsion into a gravel bed. 0.3 to 6 percent of the melt mass was estimated to be in the form of aerosols.

several mechanisms of aerosol generation may be operative in the pressurized melt ejection tests:

4-7

Dp = 0.5 MICRON Dp=5 MICRON Dp = 65 MICRON 100 90 I

80 I I

l~TEST 11

?f.

70 I I

Q. 60 C

C) TEST 8 50 0

~

~ 40

?f.

<]

30 20

~----...

r-.J 10 _ __. r--'

---

, - - - --J o._________~.....---"'

0.1 1 .0 10 100 D (µm)

Pae

• Figure 4. 2. Size Distribution of Aerosols Produced During Pressurized ~jection of Melts. Test 11 was done with CO 2 as the pressurizing gas, and test 8 was done with N2 as the pressurizing gas.

4-8

w 99

~

C/J 98 C

....c(w 95 90

....C/J 80 zc(

70

c 60

.... 50 C/J

. rn 40 w

...J 30 rn 20

~

I rn c(

.c

~

10

....z 5 w 2 0

a: 1 w 0.5 D.

0.2 0.1 0.05 0.01 '----.J---L--1--1-L.L.L..U.--....L.--'-....L.-L ...L.LJ...&..L----L.-J--'--'-J.-.1-'-'~---'--'"-.. ._..._.........~ ....

10µm 100µm 1000µm 10mm *1oomm SIEVE OPENING SIZE Figure 4.3. size Distribution of Debris Produced When Melt is Ejected From a Pressurized Vessel into Scaled Models of a Reactor cavity (SPIT Test series).

• 1.

2.

3.

simple vaporization of volatile species from the melt.

disruption of the jet of melt by hydrodynamic processes or by effervescence of gases dissolved in the melt, pneumatic atomization of the melt at the point of discharge from the pressure vessel. and

4. chemical reaction of coarse debris lofted into the atmosphere by the expulsion process.

Vaporization of melt constituents followed by condensation of these vapors is the most obvious means of aerosol production.

Photographic records of pressurized melt ejection suggest this mechanism is operative in the tests (see Figure 4.1). The finest particles observed in the pressurized melt ejection tests have been attributed to this vaporization process. Microscopic examination of the O. 5 µm particles shows that these particles are pro.bably agglomerates of yet finer particles. The sizes of these finer particles. 0.05-0.1 µm, are consistent with a nucleate condensation mechanism of formation.

The vaporization process should yield particles whose compo-sitions reflect the relative volatility of melt constituents rather than the bulk melt composition. In reactor accident

• situations. this aerosol could be enriched in fission products relative to the* bulk melt.

enriched The vaporization aerosol could be in steel constituents because of the high vapor pressures of these constituents relative to reactor fuel oxides.

The rate of aerosol formation by vaporization depends on the melt surface area. If the melt stream is compact as depicted in the analyses to date. the fractional aerosolization of the melt will vary with the reciprocal of the diameter of the melt stream.

If. on the other hand. the melt stream disintegrates because of aerodynamic forces or other processes *to create more surface area. the aerosolization by vapor formation will become invariant with respect to scale. X-ray photographs of melt jets emerging from pressurized vessels show the melt to be very disrupted and not compact [BJ.

Disintegration of the melt jet can lead to aerosol formation

_because melt droplets streaming at high velocities through the nearly stagnant atmosphere are unstable. These

• droplets wi 11 disintegrate until surface tension forces can balance the inertial forces on the droplets. Pilch [9] has investigated this process and has found that the criterion for droplet stability is:

We 4-10

~

where V

p_

D y =

=

=

droplet velocity density of the atmosphere (T.rl--!::

diameter of the melt droplet, and CJ = surface tension Pilch 1 s analysis suggests that disintegration of melt drop-lets will yield an

• aerosol with a mass mean diameter of 60-70

µm~ This aerosol is consistent ~ith the coarsest aerosol observed in th~ pressurized melt ejection tests. Unfortunately, sampling such coarse aerosols is difficult, so it has not been possible to verify all of Pilch 1 s predictions with the test data.

Aerosols produced by the aerodynamic mechanism will have compositions similar to those of the bulk melt. The fraction of melt aerosoiized by this process depends on how disrupted is the melt jet. If melt jets are as disrupted as observed in tests of pressurized melt ejection. then.the fraction of melt aerosolized will be scale independent. If the jet remains compact. then droplets of melt that .disintegrate to form the aerosol are produced by Helmholtz instabilities at the melt stream surface.

In this case. the fraction of the melt converted to aerosols will vary with the reciprocal of the stream diameter .

• The stability of the melt jet is obviously a critical feature of pressurized melt ejection.

of gas effervescence.

Powers [10] has suggested that melt jets under accident conditions will not be stable because Gases in the primary system of a nuclear reactor during a severe accident are predominantly steam and

.hydrogen. Steam and hydrogen will dissolve in molten core debris. Some estimates of the solubilities of these *gases in the oxidic and metallic phases of core debris under severe accident conditions are listed in Table 4. 2. The solubility of the Hz in iron was obtained from the correlation [11]:

. 4 log (!10) = -1637/T + 2.1326 + 0.5 log 10 PH.

10 2 where t = atomic fraction hydrogen in solution T = absolute melt temperature (K)

PH = partial pressure of hydrogen (atms) 2 Solubilities for hydrogen and steam in uo 2 were obtained with Blander*s correlation for gas solubility in molten salts [12]:

4-11

ln (R'T'C/P) Q _ 1 ()Llvl 01 6 where cr = surface tension of the melt (dyne/cm) 3 C = concentration of the gas in solution (moles/cm) 3 R = gas constant (cm -atmospheres/K) r = radius of the dissolved gas molecule (cm)

P = partial pressure of the dissolving gas in the atmosphere surrounding the melt prior to ejection (atms)

Blander's correlation probably produces a lower bound on the true solubility of steam in UOz since it ignores chemical effects known to greatly increase the solubility of steam in high temperature melts [13].

Table 4.2 Solubilities of Steam and Hydrogen in Core Debris Temperature Partial Pressure Solubility

( OK) (atm) (liter gas-STP/liter melt)

Oxide Metal

, H2 HzO Hz HzO H2 HzO 2800 75 75 0.43 0.62 39.55 15 135 0.086 1.10 17.71

1. 5 0.009 5.6 1800 75 75 0.132 0.24 18.97 15 135 0.026 0.42 8.47

1. 5 0.003 2.66

• 4-12

Inspection of the variation in gas solubility with ambient pressure shows that there will be a tremendous driving force to desorb gas when molten material emerges from a pressurized vessel into an environment of near normal atmospheric pressure. This is especially true for the metallic phase in which the volume of gas that must desorb is many times the volume of melt. The desorption process should radically disrupt the melt stream.

Tarbell [14] has verified the disruptive effect of effervescing gases in tests that compare melt ejection from

. vessels pressurized with nitrogen or with carbon dioxide. In tests with nitrogen, which is quite soluble in high temperature melts, the emerging jets disintegrated into fine droplets. In tests with the vessel pressurized with co 2 , which is much less soluble than nitrogen, the melt stream remained compact as it emerged though some surface disruption due to Helmholtz instability was evident.

Effervescence of gas can also be a source of aerosols.

Bursting gas bubbles will throw off aerosol particles 1 to 10 l!m in diameter [15]. These aerosols will have the bulk melt composition. The fraction of melt aerosolized in this way should be approximately scale-independent.

Another mechanism of aerosol formation during melt ejection arises if both gas and melt can emerge from the breach in the vessel simultaneously. This pneumatic atomization is likely to develop during later stages of melt ejection of a reactor acci-dent but may not have been operative in tists to date. Analysis of this process by Pilch [ 16] showed that it can yield UOz aerosols 1-10 lilil in size and steel aerosols 2-60 l!m in size .

.The fraction of melt aerosolized by this process will depend critically on the details of the breach in the vessel and the melt ejection process. Simple, scoping calculations indicate up to 10 percent of a core melt could be converted into aerosols this way.

Most of the aerosols produced by melt ejection processes are quite unlike aerosols produced by other severe reactor accident phenomena. With the exception of those aerosols generated as a result of vaporization, the aerosols produced during melt ejec-tion have the bulk melt composition.

Both the oxide and the metallic phases of a core melt are quite reactive in the steam and air atmospheres likely to be present in reactor containments. If aerosol emissions are as intense under accident conditions as in the tests, cloud effects will prevent the aerosols from cooling rapidly. The hot, perhaps molten, aerosols produced by melt ejection would be expected. to react rapidly once they emerge from the reactor cavity into the reactor containment .

4-13

The air oxidation of U02 has been studied extensively (see for example References 17 and 18). Bittel [19] has examined steam oxidation of solid uo 2 . Oxidation of uo 2 appears to be a two step process in which first U40~ or u o 3 7 is formed which sub-sequently reacts to form u 3 oa. Both reaction steps are mildly exothermic. Substantial structural change brought on by the oxidation causes the condensed material to fragment.

Cubaciotti [20] has argued that sintering and oxidation of U02 will allow fission products to escape the uo 2 matrix and, presumably, form new aerosols. Cubaciotti has formulated a rate expression* for this type of release based on Bittel's rate of steam oxidation of U02.

The high potential reactivity of metallic melt ejection aerosols is worrisome not only from concerns over the release of radioactivity but also concerns of containment integrity. Recent reactor accident analyses have indicated that much of the zirco-nium clad from the reactor* core will not have been oxidized at the time melt penetrates the primary vessel [7]. The rapid, exothermic, oxidation of fine particles of metal containing zirconium could be a dramatic event in the containment. It could influence hydrogen generation and def lagra tion. The abi 1 i ty of equipment to survive the rapid oxidation reaction is an interesting question.

Nelson [21] has studied the nature of metal particle oxida-tion in air. Particles of zirconium 250 µmin diameter ignite spontaneously when dropped into an air column. After these particles have burned for about 0.23 s, they disintegrate in a brilliant flash to yield finer rapidly burning particles. Such

.behavior is also observed in pure nitrogen, except the reaction is nitriding instead of oxidation.

Nelson's experiments did not address the behavior of zirco-nium diluted in either steel or uo 2 . Nelson does suggest iron, chromium and manganese will combust in air and emit finer aerosol particles.

Experimental studies of other metals burning in oxygen suggest that the- deflagration process may also generate aerosols and release fission products [22].

Recommendations For MELCOR Development Concerning the Source Term From Pressurized Melt Eje*ction. The information available concerning aerosol formation during pressurized melt ejection is not adequate for defining a highly mechanistic model of the process. - The duration of the process is quite short, amounting to only a few seconds. Consequently, a detailed model of the process may not be important for a comprehensive code such as 4-14

• MELCOR. Until further evidence from experimental studies becomes available, the following approximate_ description of the high pressure melt ejection source term developed for a study of source term uncertainties [23] may be adequate:

1. 1 percent of the mass expelled from the reactor coolant system is assumed to be instantly converted into aerosol.

2. The size distribution of the aerosol is described by two log-normal distributions. Mean sizes are o. 7 and 30 µm. The geometric standard deviations are 1. 6 and 2, respectively. Half the mass of aerosol is apportioned to each of the distributions.

3. The composition of the coarser mode material is taken to be the bulk melt composition.

4. The composition of the finer mode in the size distribution is taken to be:

(a) alkali metals as Cs 0.8 w/o (b) alkaline earths as Bao 3. 6 w/o (C) halogens as I 0.2 W/0 (d) chalcogens as Te 0.3 w/o (e) platinoids as Ru 3x10-5 W/0

( f) early transition as FeO 17 W/0 (g) tetravalents as ceo 2 4 w/o (h) trivalents as La 2 o 3 2.7 w/o Ci) uranium as UOz balance Cj) volatile main group as Cd 20 W/0 (k) main group as Sn 18 w/o A check must be made in the code to assure that the emissions of an element do not exceed the inventory. If the inventory is exceeded, the composition numbers above would have to be re-normalized.

The energetic effects on the containment atmosphere produced by high pressure melt ejection constitute a serious threat to the containment integrity. Though not considered in detail in this chapter, these effects should be considered in the MELCOR code. Approximate models for these effects have been formulated by Pilch [°24].

B. Release Associated with Core Debris Interactions with Coolant.

For many types of accidents. in most reactors. the cavity below the reactor pressure vessel may contain water at the time melt penetrates the vessel. Even if water is not present in the cavity initially, it could possibly be poured onto the melt later. either as a natural consequence of the accident 4-15

• progression or as result of some accident mitigation strategy.

In any case. it is very likely that ex-vessel core debris interactions with water will occur.

The subject of core debris interactions with water has occupied a great deal of attention in the past. The concerns over these interactions have focused on the possibility of steam explosions that rupture the primary vessel or the reactor con-tainment building. To a lesser extent. there has been concern that the quasi-static pressurization of containment brought on by* steam generation during the interactions might exceed the capabilities of *reactor containments.

The structural consequences of violent core debris interac-tions with water are not at issue here. The question addressed in this section is the fission product release that should accompany core debris interactions with water. particularly when those interactions take the form of a steam explosion. The Reactor Safety Study did associate a release with steam explo-sions and this release is listed in Table 4. 3. Rather large release fractions are associated with the volatile halogens and noble gases in this release estimate. The estimate is. however.

based on the inventory of the element present in the melt parti-cipating in the explosion. Whether the explosion took place in-vessel or ex-vessel. most of the noble gases and the halogens would have already escaped the fuel. The steam explosion release fractions for these elements estimated in the Reactor Safety Study are not especially significant.

A high release fraction is associated also with tellurium.

Again. this release estimate is not especially significant.

Were

• the steam explosion not to occur. tellurium. release from the melt would still be nearly complete because of releases associated with other in-vessel and ex-vessel processes.

Omissions in the Reactor Safety Study estimate of steam explosion release might be significant. No releases of the alkali metal group elements (Cs. Rb). alkaline earth group elements (Sr. Ba). and the lanthanide group elements (La. Ce. u.

Zr. Nb. Pm) are considered.

The Reactor Safety Study estimate of nearly complete ruthe-nfum relea~e. and by implication nearly complete release of the analogous metals Mo. Pd. Tc. and Rh. is significant. The combi-nation of all other events in a severe reactor accident would release 8 percent of the ruthenium inventory according to the Reactor Safety Study. Participation of only 10 percent of the

.reactor core in a steam explosion would yield an equivalent release of ruthenium.

The Reactor Safety Study estimate of steam explosion release was prepared under the handicap of a total lack of pertinent.

4-16

• Table 4.3 Radionuclide Release Associated with Steam Explosions in the Reactor Safety Study [l]

Element Release*

(%)

Xe, Kr 80-100 I, Br 80-100 Te, Se, Sb 40-80 Ru** 80-100

• Percent released of the inventory of the indicated element remaining in the melt involved in the explosion.

• • Also stands for Mo, Tc, Pd and Rh

• 4-17

• nuclear-reactor-related data.

steam explosion process.

The rather dire structural conse-quences of steam explosions predicted in the Reactor Safety Study have prompted considerable research into the fundamentals of the Unfortunately, none of these research efforts directed their attentions to the fission product release caused by steam explosions. The research has provided a good physical portrait of steam explosions and enough information to permit a limited re-evaluation of the Reactor Safety Study release estimate.

There appear to be two steps essential to the steam explosion process:

1. When molten core debris enters water.

• the melt coarsely fragments into droplets i about 1 cm in diameter, intermixed and surrounded by coolant in film boiling.

2. The steam film surrounding the coarse fragments collapses permitting efficient. transfer of heat from the melt into the coolant and consequently, rapid steam formation.

Thermal shock, quench fragmentation, or mechanical shock by the rapid steam generation reduces the debris to fine particulate material which is* ejected into the atmosphere. Within the primary system, this atmosphere is a mixture of steam and hydrogen. Within the containment, air may also be present.

The considerations that led to the Reactor Safety Study estimate of steam explosion release were directed toward the behavior of the fine particulate debris thrown into the

. atmosphere. Experiments by Parker [ 25] have shown remarkable ruthenium release when irradiated fuel pellets are heated in air. The speciation of ruthenium vapors in air as a function of temperature shown in Figure 4.4 suggests the high release rates are probably due to

• formation of Ru.04 (g) or Ru03 (g). The rate of ruthenium release observed in Parker's experiments followed different kinetic paths above and below B00°C which parallels the kinetics of uo 2 oxidation in air [13,14]. In this, Parker's results are consistent with Cubaciotti*s argument that oxidation of the uo 2 is a key first step in the release of fission products [20].

In the current position of superior, but still far from adequate, information, it is possible to er i tique the Reactor Safety Study analysis of the steam explosion release on several grounds:

1. Whereas in irradiated fuel rods ruthenium may be present as isolated alloy nodules containing 20-25 percent Ru

[26], by the time a steam explosion can occur, the 4-18

• SPECIATION OF RUTHENIUM-BEARING GAS IN AIR 0 Ru04

~ Ru03 90 e Ru02

.t. RuO 80 en

,c CJ CJ 70

-za:

,c w 60 m

I 2

-wz 50

c a:

I&.

0 40 30 20 10 1000 1500 2000 2500 TEMPERATURE (K)

Figure 4.4. Speciation of Ruthenium Vapors in Air as a Function of Temperature.

4-19

• ruthenium will probably have been incorporated as a very dilute constituent of the metallic phase of the core melt.

form to the a

In this dilute alloy, reaction of ruthenium to volatile rates oxide should be greatly slowed relative observed in Parker*s experiments since the mechanism hypothesized by Cubaciotti is unavailable.

2. Even if the ruthenium is isolated in a urania matrix as in Parker I s experiments, the time the urania particles remain suspended in the containment atmosphere may be too short to achieve the very high release rates implied by the

• release estimated in the Reactor Safety Study.

Chemical conditions to which fragmented debris is exposed may not be conducive to high releases.

3. If release of ruthenium does occur as expected in the Reactor Safety Study, the other fission products notably the alkali metals, alkaline earths and the lanthanides should also be relea~ed.

The second of these points is most critical to the re-assessmen t of the steam explosion source term.

In the first step of the steam explosion process, the coarse, very hot, fragments are immersed in a strong oxidant, water. As shown by Corradini [27] this strong oxidant also attacks the bulk debris to form significant amounts of hydrogen. The vapor film surrounding the coarse fragments at this state is not steam, but rather a mixture of steam and hydrogen.

The sum of the partial pressures of ruthenium-be aring gases in equilibrium with pure ruthenium or ruthenium dioxide is shown in Figure 4.5 as a function of temperature for several values of the ratio of hydrogen partial pressure to steam partial pres-sure. Also shown is the partial pressure of ruthenium-be aring gases when the atmosphere is air. Clearly, when even small hydrogen partial pressures exist, the partial pressure of ruthenium-be aring gases is significantly depressed relative to the partial pressure in the air. Because hydrogen is formed, the volatility of ruthenium must be quite low during the first stage of the steam explosion process. Total release of ruthenium during this stage must also be low since the volatility is low and the a-uration of the coarse fragmentation and intermixing process is short (-0.2 s).

The steam explosion comminutes the debris into fine parti-cles. These particles have been characterized in some of the steam explosion research programs. In general, the characteriza -

tion has been by sieve analysis over the size range of 104 to 45 µm. Some typical size distribution data are shown in Figure 4. 6. No characteriza tions of the debris in the size 4-20

RUTHENIUM PARTIAL PRESSURE AT VARIOUS OXYGEN

• -3 POTENTIALS

-4

-5

-.0

II

-6*

a:

Q.

+ ., -7 0

II a:

Q.

+ -8 N

i Q.

+ -9 0 PH 2

II -- = 10-e a:

Q. PH20

+ -10

II a:

Q.

en

~ -11

.S2

-12

-13

-14 1000 1500 2000 2500 TEMPERATURE (K)

Figure 4.5. The Sum of the Partial Pressures of Ruthenium-Be aring Vapors -in Various Atmospheres as a Function of Temperature.

4-21

• 0.01 0.1 0.2 AEROSOLS~ 1 .. DEBRIS 99.99 99.9 99.8 OPEN CIRCLES= DAT A 1 FROM WINFRITH MFTF SERIES 99 2 98 SINGLE DROP 5

w EXPERIMENTS WITH FeO ** 95 w

N ci5 a:

w I-10 20

\ ** 0 90 80

~

en a:

w

..J

<: 0 ..J w 0 <:

a: 30 70 ~

. C, u..

0 rn 40 50 0

0

• ** 60 50 en u..

0

£ Cl) rn

~

60 70 0. 8 o*

• 40 30 en

~

w w

> 80

• 488 20 >

~

..J

=>

~

=>

u 90 95

...****,;l

• -3e 10 5

~

..J

=>

~

=>

u

't*..**,.

98 99 *** fl 2 1

99.8 0.2 99.9 "-DARKENEq DIAMONDS=DATA 0.1 FROM SANDIA'S FITS B TEST SERIES 99.99 0.01 1 10 100 1000 10,000 PARTICLE DIAMETER (µm)

Figure 4.6. Size Distribution of Debris Formed by Melts Involved in Steam Explosions.

4-22

-~~-------\-

interval typical of aerosols that will remain suspended for long periods of time have been reported. If the characterization of the debris size distribution as log-normal is accepted. then it is possible to estimate the amount of material in the aerosol size range (taken here. arbitrarily. to be < 38 µm). It is apparent from such estimates that aerosol formation by steam explosions is an insignificant contributor to fission product release.

The route to significant ruthenium release from debris formed by steam explosions lies through chemical reaction of the debris to form volatile ruthenium oxides. If the steam explosion takes place within the reactor pressure vessel and the vessel does not rupture. the atmosphere encountered by the ejected debris is a mixture of steam and hydrogen. The suppression of release described above for the first stage of. the steam explosion process will also be operative for debris in the vessel atmos-phere. The suppressive effect of the atmosphere is likely to be stronger since the debris will. of necessity. be cooler than the coarse fragments formed in the first stage of a steam explosion.

When the steam explosion takes place ex-vessel. the chemical constraint on ruthenium release is not present. To estimate the release possible when debris is injected into an.air atmosphere.

it is necessary to consider the kinetics of release. The kinetics will depend on the temperature of the debris and the surface area of the debris. Total release will depend on these factors and the time the particles are suspended in the containment atmosphere.

Recent analyses of the steam explosion process show that the

_time particles are suspended in the containment atmosphere is a critical factor that controls the release of ruthenium (28).

The* mass weighted mean residence time of the particles of fuel is only a _few seconds. Unless a strongly exothermic reaction can be triggered when these particles* are injected into the containment atmosphere. there is insufficient time to achieve releases exceeding a few percent.

The likelihood of causing the particulate material ejected during a steam explosion to burn is much less than the likelihood of igniting aerosol particles produced by pressurized ejection.

The steam *explosion particles are much coarser than the pres-

. surized ejection particles; they have been cooled to lower temperatures because of their interaction with water; and they have already been extensively oxidized during early stages of the steam explosion process (27).

____________ _'.J.'h_Qµ_gh __ t_he_s_e __ ar_guments-- ..cannot- be- -c-on-si-dered-- -def-in-it-ive- i-n -- -- --

the absence of supporting experimental data. they are cause for questioning the rather high ruthenium release fractions cited in the Reactor Safety Study.

4-23

• Recommendations for MELCOR Development of a Source Term Associated with Steam Explosions. The following recommendations are made concerning the treatment of the steam explosion source term in the MELCOR code:

1. The generation of aerosols during a steam explosion takes place over such a small period of time that the MELCOR model need not include a highly mechanistic description of the process.

2. Aerosols produced by the steam explosion can be assumed to amount to a constant fraction of the melt mass participating in the explosion. This fraction should be user adjustable. A default value of o. 2 percent would be appropriate.

3. The size of the aerosol

• should be user selected with a default value of 10 µm. The composition of the aerosol may be assumed to be the bulk melt composition.

4. There is no need to consider the aerosol produced by steam explosions to be enriched in volatiles. In latter versions of MELCOR. a more* sophisticated . treatment of aerosol composition may be adopted if ongoing research indicates a need .

• c. Release During Core Debris/Concrete Interactions The most frequently mentioned source of aerosols and fission products outside the reactor coolant system is that associated with* core debris/concrete interactions. This source was recognized in the Reactor Safe*ty Study. Experimental studies have verified the existence of the core debris/concrete interactions sour~e term and established some important features of the source.

The Reactor Safety Study analysis of the core debris/

concrete interaction source term considered only the release of radioactive constituents that were present in the debris when it penetrated the

• reactor vessel. Qualitative thermochemical arguments were used to define ultimate release fractions for various ca~egories of fission products. These release fractions are listed in Table 4.4. The time-dependencies of fission product release were assumed t6 be the same for all fission products and to be of the form

• 4-24

Table 4.4 Release During Core Debris Interactions with Concrete as Estimated in the Reactor Safety Study Fission Product Release*

Xe, Kr 100 I ' Br 100 cs. Rb 100 Te. Se. Sb 100 Ru. Rh. Pd, Mo. Te 5 Ba. Sr 5 La. Nb. Eu. Y. Ce, Pr 1 Pm. Sm, Np, Pu. Zr. Nb

• %of the amount remaining in the core debris at the start of interactions with concrete 4-25

.th where VRF. (t) = release fraction of the 1 element at time 1

t(min.).

VRF. .th (oo) = release fraction of the 1 element listed 1

in Table 4. 4.

Authors of the Reactor Safety Study were aware that materials other than fission products would vaporize to form aerosols during core debris interactions with concrete. Experimental investigations of these interactions have yielded some informa-tion both on fission product release and the formation of aerosols by constituents of concrete. steel and U02 [29]. The total aerosol production rate has been found to vary from about 5-10 g/m3 of gas (STP) evolved from the interaction of concrete with melts at 1500-1700°C (see Figure 4.7) to over 150 g;m3 when melts in contact with concrete are at about 2400°C.

Aerosol generation has been found to correlate with the superficial velocity of gas sparging through the melt. The contribution of non-fuel species to the aerosol has been observed to be 60-90 percent of the total aerosol in experiments with compositionally prototypic melts.

Murfin. and Powers [30] developed an empirical correlation of the* experimental data for total aerosol production during melt/concrete interactions:

[A] = 104 (24Vs + 3.3) exp [-19000/T(K)]

where [A] = mass concentration {g/m3 STP) of aerosol in gas evolved during core debris/concrete interactions T = absolute temperature (K)

Vs= superficial velocity of gas sparging through the melt {m/s)

When this correlation and an experimentally determined aerosol composition are applied to a reactor accident. 1-10 tons of aerosol are predicted to form. Release fractions for some fission product isotopes (La. Ce. Ba. Sr. and Mo) are predicted to be much higher than estimated in Reactor Safety Study.

4-26

Figure 4.7. Aerosol Production During Interaction of 200 Kg Molten Steel at 1700°C With Concrete.

4-27

• • Study Application of the empirical correlation to accident situa-tions involves such strenuous extrapolation that it is difficult to attach much confidence to the resulting predictions. The predictions do form a basis for questioning the. Reactor Safety estimates debris/concrete interactions.

of the release to associate with core Powers and Brockmann [31] have attempted to formulate a mechanistic model of aerosol formation during core debris interactions with concrete. The operative physics embodied in their model includes:

1. release is assumed to occur both by vapor formation processes and by the mechanics of bubbles breaking at the su~face of a melt.

2. the rate of vapor formation depends on the amount of free surface available. mass transfer in the liquid phase. surface vaporization. an~ gas phase mass transport.

3. the amount of surface available for vaporization is dominated by that created by gases sparging through the melt .

4. vapor formation processes are considered for species in ternary M-0-H systems where Mis the fission product of interest.

5. gases and liquid mix.tures are assumed to be ideal.

6. the model recognizes 250 chemical species made from 27 elements. The elements recognized in the. model are shown in Table 4.5.

Examples of the* predictions from* the mechanistic model called 11 VANESA 11 are shown in Figure 4.8. which is a plot of the estimated rate of aerosol production against the time from the start of core debris interactions with concrete. The calcula-tions were done for the Surry Nuclear Power Plant. The reactor cavity concrete was assumed to be siliceous in nature. The molten core debris was assumed to have spread over an area of 55. 7 m2 at the start of the core debris/concrete interactions. The nature of the core debris interactions in the cavity were estimated with the CORCON code [32]. For the aerosol production rate designated 11 ANS:._Surry-N0Zr 11

• it was assumed that all the Zircaloy clad in the reactor core had been oxidized to Zr02 prior to the onset of core debris interactions with concrete. For the estimate

______ d_e_s i.gna_te_d~ ".ANS.=.Sur r-Y---1-.l2Z-r_._,_ .-- -it --was- -a-ss-umed- th-at-- only- *ha*lf *-th*e*-- -

Zircaloy. was oxidized. Also shown in the figure are aeroso 1 generation rates predicted for the Surry plant with the 4-28

• Table 4.5 Elements and Vapor Species Considered in the VANESA Code Element Vapor Species Hydrogen H. H

• OH. H o 2 2 Oxygen o. o . OH. H o. CO. CO 2 2 2 Carbon CO. CO 2

Iron Fe. FeO. FeOH. Fe(OH) 2 Chromium er. cro. cro

• cro

• H cro 2 3 2 4 Nickel Ni. NiO. NiOH. Ni(OH) 2 Molybdenum Mo. Moo. Moo . Moo . H Moo * (Moo ) .

2 3 2 4 3 2

• (Mo0 )

3 3 Ruthenium Ru. Ruo. Ruo

• Ruo

• Ruo 2 3 4 Tin Sn. sno. SnOH. Sn(OH)2. SnTe Antimony Sb. SbOH. Sb(OH) . Sb . Sb . SbTe 2 2 4 Tellurium Te. Teo. Teo . Te o . H Teo . Te . H Te.

2 2 2 2 4 2 2 SnTe. SbTe. AgTe Silver Ag. AgOH. Ag(OH) . AgTe 2

Manganese Mn. MnOH. Mn(OH)2 Calcium ca. cao. *caoH. ca(OH) 2 Aluminum Al. AlO. AlOH. Al 0. Alo

• Al o

• Al(OH)

• 2 2 2 2 2 AlO(OH)

Sodium Na. Na2. NaOH. (NaOH)2. Nao. NaH Potassium K. K

• KOH. (KOH)

• KO. KH 2 2 Silicon Si. sio. Si02. SiOH. Si(OH)2. Si(OH)4 Uranium u. uo. uo

• uo

• H uo 2 3 2 4 Zirconium Zr. zro. zro

• zroH. Zr(OH) 2 2 Barium Ba. Bao. BaOH. Ba(OH)2 Strontium sr. sro. sroH. Sr(OH) 2 Cesium cs. Cs2. CsOH. Cs2(0H)2. Cs2o. cso. Csl Lanthanum La. Lao. LaOH. La(OH)2 Cerium Ce. Ceo. CeOH. Ce(OH)2 Niobium Nb. NbO. Nb0 . NbOH. Nb(OH) 2 2 Iodine Csl~ HI. 1

• I 2

4-29

/

- - - ANS SURRY 1/2 Zr

.. . .. - ANS SURRY NO Zr I .. * * * * ** *

• MURFIN AND POWERS CORRELATION

• -*- RSS INCLUDING U)

U) 10 2

1:

r:

STRUCTURAL ZR

IE ..

a: ..

-C, U) z 2

U)

~

E w

..J 0

U) 0 a: ...

w

< 10 .**.

0 _ _ _ _ _ _ _....._.._ _ _.......__ _ _-.1..._ _ _-L.._ _ _ ....L..,__ __ _ J 4 8 12 16 20 24 TIME (kiJ~econds)

Figure 4.8. Aerosol Production Rates Estimated for Core Debris/

Concrete Interactions at the Surry Plant .

4-30

• empirical correlation mentioned above and with the release model used in the Reactot Safety Study. Zirconium from the fuel clad-ding. as well as fission product zirconium, were considered in making the release rate estimate with the Reactor Safety Study model.

neglected Otherwise, in estimates structural with this or model.

concrete materials were The mechanistic model predicts that initially high aerosol*

generation rates arise. These rates fall because the melt is quenched somewhat after entering the reactor cavity. Fission product decay heating and, especially in the 11 ANS-Surry-l/2Zr 11 case, heat generated as the metallic phases of the melt are oxidized by* gases from the decomposing concrete, cause the melt temperature to rise. Aerosol generation increases with melt temperature. Eventually, a maximum melt temperature and maximum aerosol generation rate are reached. Following this maximum, the temperature of the melt slowly decreases. Aerosol generation also decreases but much more dramatically because of the inherently exponential dependence of vaporization on temperature.

The mechanistic model predicts that core debris containing metallic zirconium will produce aerosols at greater rates than does core debris in which all zirconium has been oxidized. The effect arises both because the oxidation of zirconium keeps the melt hotter and because *metallic zirconium chemically reduces

• some melt species to more volatile oxidation states.

of residual zirconium by steam from the concrete is complete at about the time of maximum aerosol generation rate.

zirconium has been completely oxidized, predictions for the 11 Oxidation Once the ANS-Surry-N0Zr 11 and 11 ANS-Surry-l/2Zr 11 cases are quite similar.

The mechanistic model of aerosol generation and fission product release during core debris/concrete interactions is of too recent a vintage to have been subjected to extensive valida-tion by comparison with experimental results. It is encouraging that there* is generally good agreement between the estimates of aerosol generation for the Surry case obtained with the Murfin and Powers correlation and the mechanistic model predictions.

Nowhere do estimates obtained with this correlation differ by more than about a factor of two from the model predictions. At early times. estimates obta*ined with the empirical correlation are bracketed by the two mechanistic predictions. At late*iimes, when aerosol generation rates are low, the empirical correlation yields higher estimates than does the mechanistic model.

Estimates of aerosol generation obtained with the mechanistic model or the empirical correlation are unlike predictions obtained with the Reactor Safety Study model. The most important difference is -that -these more recent descriptions of the process L 4-31

show aerosol generation to continue far longer than is predicted by the Reactor Safety Study model. In fact, aerosol generation predicted by the Reactor Safety Study model has stopped when mechanistic predictions indicate the aerosol generation rate has reached a maximum. Predictions of the amount of aerosol suspended in the reactor containment atmosphere and the amount of aerosol that escapes should the containment rupture will differ dramatically depending on which of these models is used to estimate the aerosol source term from core debris interactions with concrete.

Other differences arise between the mechanistic model and the Reactor Safety Study model with regard to the releases of indivi-dual elements. The fraction of tellurium remaining in the core debris as predicted by the two models is shown as a function of time in Figure 4.9. The Reactor Safety Study model predicts the release of this relatively volatile element to be more extensive and more rapid than does the mechanistic model. The extents of Sr and Ba release predicted by the mechanistic and Reactor Safety Study models are shown as functions of time in Figure 4 .10. For these elements, assumed to be present in the core debris as relatively non-volatile oxides, the mechanistic model predicts more rapid and more extensive release than does the Reactor Safety Study model.

Experimental studies necessary to validate and to improve these and other predictions of the mechanistic model are underway.

The mechanistic model includes a description of the effect an overlying pool of water would have on the source term of aerosols to the containment caused by core debris interactions.

Such an effect was neglected in the Reactor Safety Study. The model, essentially a modification of the description of aerosol entrapment from bubbles passing through water formulated by Fuchs [33], is based on the following assumptions:

1. The overlying water pool is in film boiling over the core debris/concrete mixture. The water affects in no way the generation of aerosols from the melt. The aerosols .evolve from the melt into the gas film between the melt and the water pool.

2. Aerosol- laden gas thermally equi 1 ibra tes with the water pool in vapor film between the pool and the melt. The gases are assumed to be non-condensible.

3. The bubbles enter the pool at an initial size of 1 cm.

There are no bubble-bubble interactions.

4* Entrapment of aerosols is by inertial deposit ion from internally circulating. flows, diffusion of aeroso 1 s to the bubble walls and by sedimentation.

4-32

5.0 /ANS-SURRY

-- c,,

=-::

4.0

~

.J w 3.0

E

-z

~

CD RSS-PREDICTION 2.0 3 6 9 12 15 18 TIME (kiloseconds)

Figu.re- 4.-9. -Estimates of the Amount of- Tellu.rium Remaining in the Co.re Deb.ris Du.ring Inte.ractions with Conc.rete .

• 4-33

• VANS-SURRY Sr RELEASE %

20 15 C

w Cl)

..,<w w Ba RELEASE%

a:

'iP-10 RSS MODEL PREDICTION OF Ba AND Sr RELEASE %

5 5000 10000 15000 TIME (s)

Figure 4.10. Estimates of the Release of Ba and Sr During Core Debris/Concrete Interactions .

• 4-34

The expansion of the bubble caused by the loss of hydrostatic head as the bubble rises is taken into account:

YLlLl_ = p + X V atms 1033.6 0

where V

0 R

0

= 0.5 cm p = absolute pressure of the containment atmosphere (atms) atms x = distance from the top of the water pool (cm)

V(x) = volume of the bubble at x = 4 ,r R(x)3 3

Then. if n is the number of aerosol particles within the bubble.

where t = time a.. = impaction coefficient=

1

a. = sedimentation coefficient = lfil s 4RV 3

= diffusion coefficient = 1.8 (D/VR )

V = bubble rise velocity

• 4-35

• g = gravitational constant T = relaxation time pp= particle material density D = kTB k = Boltzmann's constant T = absolute temperature B = C(D )/31rµ D p g p D = particle diameter p

µg = gas viscosity 2r..

C(Dp) = 1 + D [1.257 + 0.4 exp (-0.55 Dp/r..)]

p r.. = molecular mean free path in gas Examples of the decontamination of 4 he aerosol-laden gas by an overlying pool as a function of particle size and as a function of pool depth are shown in Figures 4.11 and 4.12.

Log-normally distributed particle sizes were assumed to make the decontamination calculations shown in these figures. Decontami-nation factors used in these figures are defined as the ratio of mass input to mass that passes through the pool. Note that a minimum occurs in the decontamination factor when plotted

. against pa.rt ic le size. Diffusion is predominantly responsible for the removal of particles of sizes less than this minimum.

Particles larger than the minimum decontamination efficiency size are removed predominantly by impaction and sedimentation.

The particle size range where little decontamination occurs broadens as the geometric standard deviation of the log-normal size distribution increases .

• 4-36

• 1000--~ -.-...;... ,..-,...-. e-r-T"" Mr-,--- -,---~r- r-r-1-rr -r-----r ---r-r-r rrTTI-- ---r--r- i-T"1-r rTI *

= 1.6 *.* I' 0

• I I

I

• I

• .. I

. I I

a:

• I 0 *..

t-0 100 ... .*.* .,, I I

c(

u. /

z ~

0 t-c(

.* ,.,. -,,-' ~

~

~

z

-:E c(

t-w I z

-..J 0

0 10 w

C INPUT AEROS OL MEAN PARTIC LE SIZE (µm)

Figure 4 .11. Decont aminat ion of Aeroso l-laden Gas by a Satura ted Water Pool Seven Meters Deep as a Functio n of Mean Partic le Size.

=*

I I

DEPTH (cm)

I I

I I

a:

700

I

I I

• I 0

t;

• I II ti(

100 500. .* ** I

." I I u..

• z .* *

.: II I I

2 t-

-c 300\

I I I

I

-c

\ * ."

... I/ I

/

1

,r:,.

w I

1-z 0

\\ *. .*

I

/ I

/

CD 0

w 10 ',, **..... ..* ,,' I C

,, ~

0 100 \. ', . ~/

........ .... __ ,,. ~' /'

---

_,,,,,~

/'

INPUT_ AEROSOL MEAN PARTICLE SIZE (µm)

Figure 4.12. Decontamination of Aerosol-laden Gas by a Saturated Water Pool of Various Depths.

• Recommendation for the MELCOR Model of the Source Term From Core Debris/Concrete Interactions. At this stage in development.

the MELCOR code can use a relatively crude model of the source term associated with core debris interactions with concrete.

this end. the following recommendations are mide:

To

1. The rate of aerosol mass generation should be obtained from the Powers-Murfin correlation.

2. The aerosol size distribution can be taken a log-normal with a geometric standard deviation of 2. 3 and a mean size given by the Brockmann equation:

Dp = 0.266 (A/p)l/3 where Dp is the particle diameter in micrometers. A is the aerosol concentration is g/m3-STP. and p is the material density of the aerosol in g/cm3.

3. Aerosol compositions can be provided by the user. Default compositions are shown in Table 4-6. These compositions change with melt temperature and the time after the start of core debris interactions with concrete. A check will have to be made in the code to assure inventories are not exceeded. Eventually these default compositions will have to be replaced with more smoothly varying functions of the melt properties.

4. The effect of an overlying water pool can be satisfac-torily described by the modified Fuchs model.

D. Fission Product Release by Leaching The duration of vigorous core debris interactions with concrete is uncertain. Eventually. these interactions must stop and further erosion or thermal decomposition of the concrete cease. If the core debris has eroded through the basemat. then the core debris is susceptible to leaching by groundwater.

Fission product release by this leaching process* is a long-term.* low-level source of radioactivity that is probably much less a threat to the public than the intense, airborne sources discussed above [34).

• Basemat penetration may allow coolant waters containing radioactive material to drain from the plant into the groundwater system. This source of radioactivity is not considered here. It may. however, far exceed in importance to risk the in-plant radioactivity release by leaching.

4-39

Table 4.6 Default Compositions for Aerosol From Core Debris Interactions with Concrete Early in Time Late in Time after start of core debris after start of core debris interactions with concrete interactions with concrete High Melt Temperature (T > 2200K) alkali metals 0.8 w/o as Cs 0 alkaline earths 3.6 w/o as Bao 3.3 w/o as Bao halogens 0.2 w/o as I 0 chalcogens 0.3 w/o as Te 1.0 w/o as Te Platinoids 3xl0- 5 w/o as Ru lxl0- 5 w/o as Ru early transition 17 w/o as FeO 12.6 w/o as FeO tetra val en ts 4 w/o as Ceo 1.6 w/o as Ce0 2 2 trivalents 2.7 w/o as La o 1 w/o as La o 2 3 2 3 uranium 1. 6 w/o as uo 0.8 w/o as uo 2 2 volatile main-group 20 w/o as Cd 0 main group 18 w/o as Sn 16 w/o as Sn concrete balance balance Low Melt Temperature (T < 2250K) alkali metals 9 w/o as Cs 0 alkaline earths 3.3 w/o as Bao 0.2 w/o as Bao halogens 8.5 w/o as I 0 chalcogens 0.3 w/o as Te 0.5 w/o as Te platinoids 0 0 early transition 8.1 w/o as FeO 24 w/o as FeO tetravalents 0.01 w/o as Ceo 0.001 w/o as Ceo 2 2 trivalents 4xlo- 6 w/o as La o 2xl0- 6 w/o as La o 2 3 2 3 uranium 0.06 w/o as uo 0.04 w/o as uo 2 2 volatile main group 10 w/o as Cd 0 main group 4 w/o as Sn 9.2 w/o as Sn concrete balance balance 4-40

• There have been few systematic studies of leaching of core debris/concrete mixtures expected at this final stage in a severe reactor accident. The .core debris is usually considered a single phase solid in analyses of leaching.

[35] suggests that this would n*ot be the case.

that when mixtures of U02, Recent work by Westrich Westrich found zro 2 and siliceous materials analogous to concrete were slowly cooled (<2 K/s), phase separation took place. The crystal line precipitates from the melt consisted of U02, MgU205, and Zr02, but not ZrSi04. The silica-rich liquid phase would eventually soiidify as a glass. Plagioclase solid solutions (NaA1Si 3 o 8

- CaAl2Si208)

• were observed

• in high silica content systems.

Westrich examined the partitioning of fission products among the solid phases. He finds the fission products whose oxides favor the cubic fluorite structure, such as cerium and zirconium, preferentially partition into the cubic Mgu 2 o 5 phase. Alkaline earths remain in the glass phase. Fission products that as oxides form hexagonal structures enter both phases though concentrations are usually higher in the glass.

Braithwaite and Johnson [36] have examined the leaching of cesium and strontium from mixtures of 11 corium 11 and basaltic concrete. Leaching was done with distilled water and a saline

• solution to simulate sea water.

at 25 and 90°C.

Samples were leached for 3 days over the leaching period O.l-0.85 percent of the cesium was removed from the cerium-concrete mixture and 0.68-2.55 percent of the strontium was removed. The temperature dependence of leaching was small, diffusion was the rate controlling process.

suggesting liquid phase Powers* [37] conducted scoping studies of Mo, U, Zr, Th, Nb, La, Ce, Sr, and Cs leaching from mixtures composed of 34 percent U02, 5. l percent Fe304, 5 .1 percent Cr203 and 48 percent dehydrated basal tic concrete. Samples were leached in bombs for 1. 5-200 hours at temperatures of 80-200°C. Leaching solutions of various compositions were used to simulate different groundwater chemistries. Conclusions from this scoping work included:

1. cs, La, Ce and U were the most easily leached elements.

Only upper bounds on Sr and Th leaching based on the 1

detectability limits could be determined.

2. Solutions containing NaCl and saturated with caco 3 were not more effective leachants than distilled water.

3. Solutions containing sodium phosphate were very effective leachants especially for zirconium.

4. Ferric ion appeared to accentuate leaching. This could be because of the oxidation reaction:

4-41

• uo 2 + 2Fe 3 + a uo 2 2 + + 2Fe 2 +

or the low pH created by the hydrolysis reaction:

Fe 3 + + a FeO(OH) + 3H+

s. Chromate-containin g solutions were not especially effective leachants. which suggests that oxidation of the UOz to soluble uranyl ions is not the primary leaching mechanism.

6. Colloidal suspensions were formed during many of the leaching experiments;

7. The surface area of the solid mixture increased during leaching due to the Zwiebelschale effect [38).

It is apparent. then. that slow leaching of a core debris-concrete mixture that has penetrated the reactor basemat is possible. The leaching may involve subtleties not considered in past analyses. It remains to be demonstrated. however. that leached fission products pose a sufficient threat to merit a more thorough study of the leaching process.

Recommendations to MELCOR Concerning the Treatment of Ex-vesse 1 Leaching. At this juncture. there appears to be no generally satisfactory model for leaching core debris by groundwater. Nor does there appear to be a critical need to consider this process in MELCOR.

4.3 Secondary Fission Product Release in Containment The term "secondary fission product release" is used here to signify the generation of airborne fission product vapors or aerosols by processes not directly connected to the behavior of the core debris.* One such process. the combustion of debris to form aerosols in the reactor containment atmosphere. has been discussed above in connection with release associated with pressurized melt ejection. Three other. secondary. fission product release processes discussed here are:

1. resuspension of deposited or sedimented aerosols.

2* vapor partitioning of dissolved fission products. and

3. mechanical resuspension of fission products trapped in water .

4-42

• There may be other important secondary mechanisms product release to the containment atmosphere.

of Grouping resuspension of aerosols and vapor partitioning of dissolved fission products under the heading secondary processes is not an assessment of the relative importance of these fission processes. Resuspension reverses the natural mitigation of the severe reactor accident source term brought on by the agglomeration, deposition and sedimentation of aerosols. Vapor partitioning reverses the natural or engineered mitigation of the source term brought on by water scrubbing of the containment aerosols. The* secondary release processes, then, may play a critical role in determining the severe reactor accident source term. These processes may well undo much of the mitigation expected by many to substantially reduce the severe accident source term to levels well-below those estimated in the Reactor Safety Study.

A. Resuspension of Deposited Arosols Detailed, mechanistic treatments of the processes leading to the deposition and sedimentation of aerosols have pro 1 if er a ted in recent years. Treatments of the reverse process, aerosol resuspension, have not been attempted to a similar level of detail. This may be because resuspension involves analysis of both the aerosol particles and the surfaces to which they adhere whereas attention concentrates on only the aerosol particle in the analysis of aerosol deposition. It is likely that in any real situation, a dynamic equilibrium between aerosol deposition and resuspension develops. Throughout most phases of a reactor accident, the rate of resuspension is sufficiently small that it can be neglected or accounted for in an approximate manner as an inefficiency in the deposition process.

There are a few instances in hypothesized nuclear reactor accidents in which wholesale aerosol resuspension must be considered:

1. blowdown of the reactor coolant system

2. in-vessel fuel/coolant interactions that lead to high steam generation rates

3. catastrophic depressurization of the containment building.

In these instances, high gas _velocities arise near aerosol-coated surfaces. The surfaces may experience sudden accelerations. High gas velocities and sudden surface acceleration are conducive to efficient particle re-entrainment. Such re-entrainment could reverse temporarily the natural mitigation of the source term produced by aerosol agglomeration, settling and deposition processes.

4-43

• of Aerosol particles are held to surfaces by Van der Walls forces. electrostatic forces. and the surface tension forces of liquid films.

bound to the force dry radical between a It is useful to distinguish between aerosols surfaces and aerosols bound to wet surfaces because differences particle and in adherence forces.

a surface can be defined The adhesive as:

where H is a constant and Dp is the particle diameter. For dry aerosols. H is on the order of 1-60 dyne/cm (see Table 4.7). The adherence force does vary over at least 2 orders of magnitude. depending on the peculiar nature of the particle and the surf ace ( see Table 4. 8) . The irregularity of the surface may contribute to some of this variability (see Table 4.9).

When the particle is bound to a surface by a liquid film.His on the order of 400 dyne/cm.

There is a gradation between the extremes posed by the classificatio n of systems as either 11 dry 11 or "wet". As shown in Figure 4.13. the adherence of a particie to a surface increases

. with relative humidity once a critical humidity (65 percent relative) is exceeded .

• Some data for the resuspension of glass spheres on stainless steel exposed to flowing gas are shown in Figure 4.14.

gas velocities ( < 5 m/s) some small resuspension occurs.

extent until of a

resuspension does not _increase critical velocity is achieved.

much with gas At low Then entrainment The velocity

-increases sharply with flow velocity to 40-70 percent. Once this plateau in the entrainment efficiency is reached. entrain-ment is again relatively insensitive to gas velocity. It appears then that sudden increases in flow velocity will produce some entra-inment. but complete entrainment of all deposited aerosols will be difficult to achieve.

The -force on deposited aerosols produced by flowing gas is given by:

F = 1/2 p g u22. CA p

where Pg = gas density U2, = local gas velocity Ap = ,rDp2/4

• C = [2.87 + 1. 58_ log 10 (x/Dp)]-

4-44 2 for 10 2

< x/Dp < 10 6

Table 4.7 Comparison of Air Flow and Acceleration as Mechanisms for *Aerosol Removal [40]

Particle Force (dynes) Required to Achieve Size (µm) 75% Removal by Air Flow Centrifugation 10.6 - 21.2 0.0195 0.016 21.2 - 31.8 0.056 0.060' 31.8 - 42.4 0.11 0.21 42.4 - 53 0.11 0.26 Table 4.8 Effects of Particle Composition and Surface Characteristics on Particle-Surface Adherence [41]

50µ Force (dynes) Required t;o Remove 98%

Particles of of the Particles from-a surface of Aluminum Brass Glass Enamel glass 0.5 2.85 1. 83 3.63 sand 6.60 0.45 0.06 6.34 charcoal* 0.57 0.32 0.94 2.30

• 4-45

Table 4.9 Effect of Surface Roughness on Particle Adherence (39, 42]

Mean Height of Relative Particle Surface Irregularities Adhesion 0

(A) 150 100 (a) 1000 79 (a) 4000 51 (a) 100000 0 (a) 2160 100 (b) 2920 67 (b) 3430 59 (b) 4826 45 (b)

• (a)

(b)

Adhesion of glass particles to a glass surface at 100%

relative humidity.

Adhesion of quartz particles to Pyrex glass .

• 4-46

w 0

a:

~ 100 w

0 z

/

w a:

w

c Q

_,w

-a:

0

~

50 C

Q.

C w ~----------------------,,,_.

N

E a:

0 0 z

0 20 40 60 80 100 RELATIVE HUMIDITY (%)

Figure 4 .13. Depend ence of Normal ized Partic le Adhere nce Force on Relativ e Humidi ty.

4-47

_ 100

'iP-0 z

w 80 0

LL LL w 60

..I 0

E 40 w

a:

• ..I 0

Cl) 0 a:

w C

20 0

0 20 40 60 80 100 120 140 GAS FLOW VELOCITY (m/a)

Figure 4 .14. Resuspension of Glass Particles From a Stainless Steel Plate as a Function of Gas Velocity and Particle Size ( * = 3 µm. ~ = 4 µm. D = 1.2 µm. o =

20 - 40 µm) .

4-48

x = distance along a surface where re-entrainment begins.

Notice that the local gas velocity. as opposed to the free-stream or bulk velocity is used in this description of the forces.

Because this local velocity will depend on both the surface geometry and the aerosol deposit geometry. it is most difficult to estimate for reactor accident situations.

Brockmann [23 J has advocated using an equation derived by equating binding forces between the surface and aerosol and the flow forces on the aerosol as a criterion for re-entrainment:

4fp gD p p 3Cp g

where f = friction factor = 0.2; Chas a typical value of 0.01 and U is the free stream velocity. This criterion indicates re-entrainment of dry. 1 µm particles occurs at flow velocities of about 2 m/ s. Brockmann asserts that once the er i ter ion is met. re-entrainment will be 90 percent complete. The criterion also indicates that. wet aerosols are unlikely to be entrained by gas flows arising in nuclear reactor accidents.

Particle removal by acceleration of surface has received some study in nonnuclear contexts. This.mechanism of particle resus-pension is often overlooked in the analysis of severe reactor accidents. In view of the many dynamic events postulated to occur during severe reactor accidents. this is likely to be an important process. Where comparisons have been made. the forces to remove particles by gas flow entrainment or by acceleration agree to within about a factor of two (see Table 4.7)

Recommendations to MELCOR Concerning Aerosol Particle Re-entrainment

1. MELCOR .should allow for re-entrainment of aerosol particles during blowdown of the reactor coolant system.

2. since particle deposits in the reactor containment are wet it is probably unnecessary to treat particle re-entrainment during pressurization of the containment.

3* The criterion for re-entrainment during vessel depressurization is:

• 4-49

26p gD p p Pg where His a user supplied force constant with a default value of 1 dyne/cm.

4. The extent of re-entrainment is also a user supplied constant with a default value of 90 percent.

5. No recommendation is made concerning particle resuspen-sion caused by surface acceleration save that it should be noted as a possibility.

B. Secondary Release From Water One of the most important causes of source term mitigation is the entrapment of radioactive species in water. Mitigation of this sort can arise at many points in a severe reactor acci-dent. Effluent from the core may have to pass over or through water as it is carried through the primary system; thus, an opportunity to partition between the liquid and the vapor is presented. For boiling water reactors, radioactive species may have *to pass through the steam suppression pool before they can enter containment. Once in containment, there will very likely be large bodies of water to absorb radioactive species.

Operation of containment sprays can sweep the containment atmosphere of suspended vapors or particles.

The mitigation of the source term that can be provided by water depends not only on the efficiency with which water can entrap radioactive species, but also the permanence of the entrapment. In this section, some of the mechanisms available to reverse water entrapment of radioactive materials are described.

Iodine Partitioning. Modern perceptions concerning the severe reactor accident source term hold that fission product iodine is libe~ated from the core and carried through the reactor primary system as iodide--probably cesium iodide--rather than as i-od ine gas. With few except ions, iodides are quite soluble in water.* Dissolution of any iodides in water would mitigate possible airborne release of the iodine from containment.

Iodide o-) in aqueous *solution can be oxidized to volatile iod \ne (12 ) or to another soluble anion, iodate cro 3 -). Some of the relevant chemical reactions and their associated equilibrium constants at 298K are shown in Table 4.10 .

4-50

Table 4.10 Some Relevant Solution Phase Equilibria React.ion Eguilbriurn Constant 2 [I-J 2 P 112 23 2 l*I° 1

+ 2I (aq ) + 1/ 2 0 2 : I ( a q ) + H 20 [I J/[H+J = 2.6xlo 2 2 02

--+ 4 [H+] 4 /[I ] 2 P 5 = 9.4xlo 16 2I (aq) + 2H 0 + 502 2 410; (aq) + 4H+ [I0-]

02 2 E-- 3 2 I (aq) + H2 o

--+ H+ + I - (aq) + HOI (aq) [H+] [I-] [HOI]/[1 ] = 4.04xlo- 13 2 (- 2

--+ 13 HOI(aq) H+ + 01 [OI ] [H+]/[HOI] = 5xlo-E--

10

= 6.4xlo-

,i,,.

I lJ1 I-'

P /[1 ] = 0.303 1 2 2

--+ 6 3 33 5Agl(s) + 10; + 6H+ [Io;] [H+J /[Ag+] [12] = l.6Bx10

--+

(-

- -17 Agl(s)

--+

Ag+ + I [Ag + ] [I ] = 8.32Xl0 E--

Ca(OH)

--+

Ca 2 + + 20H 2 (-

-4 CaOI-I+ + OH -

--+

Ca(OH) = l.7783xlO 2 E--

• Because there is the potential for iodide in solution to form volatile species. there is the potential for iodide to escape the solution. The tendency for iodine to escape the solution is measured by a partition coefficient which is defined as:

Partition Coefficient -

moles of iodine in solution moles of iodine in vapor Estimates of this partition coefficient have appeared in the literature [43].

Quantitative analysis of the hydrolysis and vaporization equilibria listed above leads to the conclusions:

1. with increasing acidity of the water, the partition coefficient decreases,

2. the partition coefficient increases with dilution of the iodine solution, and

3. the variation of the partition coefficient with temperature depends on the acidity and iodine concentration of the aqueous phase.

Equilibrium analysis of the behavior of iodine species and the partitioning of iodine between the aqueous and vapor phases is not likely to be entirely satisfactory because:

1. radiolysis will affect the partitioning, 2* the gas phase in reactor containment is not at equilibrium especially whenever both o 2 and Hz are present, and

3. other species dissolved in the wa ter--such as cd2+ or Ag+--can alter the partitioning by reacting with iodide to form insoluble precipitates.

The vapor-liquid partitioning of iodine can be responsible*

for long-term, low-level release of iodine. This, of course, is quite different than the prompt, intense release of iodine envisaged

• by the Reactor Safety Study. The radiological consequences of slow iodine release from aqueous solutions are very much mitigated by the rapid radioactive decay of iodine.

Other fission product species. nominally quite soluble in water, will partition between the aqueous and the gas phases.

For instance, ruthenium tetroxide engages in such a process:

• 4-52 Ru0 4 (aq)

Quantitative evaluations of the partitioning of these other radionuclides between the aqueous and vapor phases under reactor accident conditions have not been reported.

Recommendati on to MELCOR Concerning Iodine Partitioning . It is recommended that MELCOR allow for iodine partitioning between water and the containment atmosphere. The equilibrium partial pressure of Iz in the atmosphere can be defined as where equilibrium I 2 partial pressure

= total.iodine concentratio n in water pools (moles/liter)

K = user-supplied partition coefficient with a default value of 1 x 104

• The approach to equilibrium can be calculated knowing the surface area of water pools in the containment~ A. and a mass transport coefficient. Km* appropriate for the flow conditions over the water pools:

PI (t)]

2*

where NI = moles of I in the containment atmosphere 2

2 R = gas constant PI (t) = I partial pressure in containment at time t 2

2 There appears at this time to be no need to recognize partitioning of other fission products between water and the containment atmosphere.

4-53

• Mechanica l Release From Water. Water pools within the con-tainment will contain, for the .reasons outlined above, fission products. These fission products will be dissolved o.r present as particula te. The decay heat f .rom the fission products wi 11 tend to keep the water pools at or near the boiling point as the

.reactor containme nt pressuriz es. Should the containme nt suddenly depressu.r ize, the superheate d water pools will boil spontaneo us-ly. If the dep.ressur iza tion is rapid, vigorous boi 1 ing wi 11

• entrain water droplet laden with dissolved and particula te fission products. That is, sudden depressu.r iza tion can .reverse the mitigation of the severe accident source term provided by water entrapmen t of fission products. The extent. of water entrainme nt by flash boiling depends on (1) the .rate at which the containme nt dep.ressur izes and (2) the geometry of the water pool.

Brockmann [23] has formulated a model of liquid entrainme nt caused by the boiling of water pool during depressu.r ization of containme nt. The pressure within the containme nt during dep.ressur ization is given by:

dP

=

dt where P = pressure t = time V = containme nt volume Q = volumetri c flow .rate The volumetric flow rate depends on the size of the hole in the containme nt. When the flow is choked:

I where Ao = hole area R = universal gas constant T.

= absolute tempera tu.re of the containme nt atmospher e MW = mean molecular weight of the containme nt atmospher e CD = orifice drag coefficie nt = 0.61 When the flow out of the containme nt is subc.ritic al:

4-54

• where Pa is containment.

the pressure of the atmosphere surrounding the The temperature of the water is assumed to adjust to the saturation temperature of water throughout the depressurization 3576 T(K) = + 57.8 11.342 - in P(atms)

The rate at which mass evaporates from the water pools is given by:

= mass evapor~tion rate where

= specific heat of water enthalpy of vaporization of water mf = mass of water in the pool The evaporating water entrains liquid:

m e

E = =

mV where m = mass rate of entrainment e

pf = density of water Pg = density of water vapor K = D jc C

jc = uV (pg)*1/2 /[ga(pf pg)]l/4 4-55

De= 4Uv [ngPglg(pf - Pg)Jl/3 [o/g(pf - Pg)J-1/2 Uv = superficial velocity of water vapor off the pool surface g = gravitational acceleration ng = viscosity of water vapor O' = surface tension of water The size distribution of water droplets entrained by evaporating water is assumed by Brockmann to be lognormal with a geometric standard deviation of 2. 3 and a geometric mass mean diameter, DGM, of DGM = l° /2 D:/2.3 if if D

D C

s >

D D

s C

2 where D 120'/pfUv s

2 D = 4Uvngog/(pfg)

C Some results for a specific accident at the Surry reactor obtained with Brockmann' s model are shown in Figures 4. 15 and 4 .16. The mass geometric mean particle size increases with the area of the hole in containment to a plateau of 50-3000 µm for a hole area of about 100 m2. The entrained mass increases sharply with hole area. Significant entrainment is obtained

• only when holes sizes are large (10-100 ~2).

Recommendation to MELCOR concerning Re-entrainment from Water. Re-entrainment during containment depressurization should be recognized by MELCOR. The model developed by Brockmann is sufficiently simple. -It can be implemented in MELCOR. The containment hole size may have to be a user-supplied value. A default value of 1 m2 would allow a rather modest amount of release by re-entrainment from water pools.

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(I)

(I)

<C

~

C 102 w

z

-a:

<C t-z w 10 1

10- 2 ....__ _ _..___ _ _....___ _ _...__ _ _-'-_ _ __.___ __.

0 1 10 *100 1000 10000 HOLE SIZE (m2)

Figure 4.15. Bounding Estimates Obtained with the Brockmann Model of Entrainment of Water During Containment Depressurization as a Function of the Containment Hole Size [23].

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4 10 LOG-NORMA L DISTRIBUTION Dg = 2.3 ::t .3

- SUSPENSION LIMITED FRAGMENTATION LIMITED 10 1

0.1 ..________ __..........._ _ ___.._ _ _ _.....__ _ __..__ __,

0.1 1 10 100 1000 .10000 HOLE SIZE (m2)

Figure 4 .16. Mean Particle Size Predicted With the Brockmann Model of Entrained Water During Containment Depressuriza tion as a Function of the Size of the Hole in Containment [23).

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4.4 Conclusions The ex-vessel sources of fission produGt release may be categorized as "primary processes" involving the core debris and "secondary processes" that involve resuspension of material that had previously escaped the core debris. Releases of aerosols and fission products associated with- melt ejection from the primary system. core debris-coolant interactions. core debris-concrete interactions and groundwater leaching are the most important primary mechanisms .. Resuspension of aerosols. vapor partitioning of* fission products dissolved in water. and mechanical release of dissolved or su~pended material from water are the most important secondary release processes.

Aerosol and fission product release that occurs when a melt is ejected from pressurized primary system was not recognized in the Reactor Safety Study. Recent analyses of the fission product source term associated with steam explosions suggest* the Reactor Safety Study estimate of this source may have been too high.*

Significant improvements have been made in the capabilities to model fission product and aerosol releases during core debris concrete interactions. The effects of coolant waters on this source term can be estimated. Scoping studies support the con-tention tha~ fission product release by groundwater leaching is not as significant an effect as intense. airborne release of fission products except when very specialized circumstances are present.

Secondary release process can reverse or certainly limit the effectiveness of natural* or engineered source term mitigation features of a nuclear power plant. Of the secondary processes.

only* vapor phase partitioning of dissolved iodide has received great attention. Qualitative indications from a nonnuclear data base suggest there are many instances in a severe reactor acci-dent in which resuspension of deposited or sedimented aerosols would be a serious concern. Data are available to qualitatively assess the likelihood of aerosol resuspension to occur in severe accidents. Similarly. resuspension of dissolved or entrapped material in pools of water by the mechanical action of sparging bubbles or boiling can be quantified. It is apparent that this effect poses a limit to the decontamination that can be achieved with water during a severe accident.

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References

1. U. s. Nuclear Regulatory Commission, Reactor Safety Study:

An Assessment of Accident Risks in u. s. Commercial Nuclear Power Plants, NUBEG-75/014 , WASH-1400, Washington, DC, October 1975.

2. R. L. Ritzman. et al .* "Release of Radioactivit y in Reactor Accidents." Appendix VI I to Reactor Safety Study Reference 1.

3. J. Gieseke, et al.. Radionuclide Release Under Specific Accident Conditions, Volume I: A PWR Analysis, BMI-2104 (Draft). Battelle Columbus Laboratory. Columbus. OH, January 1983.

4. T. Y. Chu. J. H. Bentz. F. E. Arellano. J. E. Brockmann.

M. E. Field, and J. D. Fish, Report on-Large-Sca le Molten Core/Magnesi a Interaction Test, NUREG/CR-343 8, SAND83-1692, Sandia National Laboratories . Albuquerque, NM.

5. J.B. Rivard, "Review of In-Vessel Meltdown Models." Sandia National Laboratories . Albuquerque. NM, July 1980.

6. D. Alpert, unpublished results. 1983.

7. R. Henry. Section 3 in Zion Probabilisti c Safety Study, Commonwealth Edison co .* 1982.

8. W. W. Tarbel 1. J. E. Brockmann. M. Pilch. High Pressure Melt Streaming (HIPS) Program Plan, NUREG/CR-302 5, SAND82-2477. Sandia National Laboratories . Albuquerque. NM, June 1983.

• 9. M. Pilch~ Advanced Reactor Safety Research Quarterly Report, January-Marc h 1982, NUREG/CR-267 9 (1 of 4). SAND.82-0904 (1 of 4). Sandia National Laboratories , ALbuquerque, NM.

10. D. A. Powers. "Gas Solubility in SPIT Melts." Memorandum.

Sandia National Laboratories .

11. M. Weinstein and J. F. Elliott, Trans. Met. Soc. AIME 227 (1963) 382.

12. M. Blander. W. R. Grimes. N. V. Smith and G. M. Watson. J.

Phys. Chem. 63 (1959) 1164.

13. J. Nichols. Contrib. Mineral. Petrol. 74 (1980) 211.

14. W. W. Tar be 11, Technica 1 Highlights /Administrat ive Report for the Nuclear Regulatory Commission Advanced Reactor Safety Reseach Program, March, 1983, Sandia National Laboratories , Albuquerque, NM, May 1983.

4-60

15. M. Toma ides and K .. T. Whitby. "Generatio n of Aerosols by Bursting of Single Bubbles. 11 in Fine Particles : Aerosol Generatio n, Measureme nts, Sampling. and Analysis. B. Y. u.

Liu. Ed .* Academic Press. Inc .* New York. New York.

16. M. Pilch. unpublishe d results.

17. K. A. Peakall and J. E. Antill. J. Nucl. Materials 2.

{1960) 194.

18. M. Iwasaki. T. Sakukrai. N. Ishikawa. and Y. Kobayashi . J.

Nucl. Sci.* Tech 5. {1968) 652.

19. J. Bittel. L. H. Sjodahl and J. F. White. J. Am. ceramic soc i et y 5. 2 * { 1 9 6 9 ) 4 4 6 .

20. D. Cubicciot ti. Nuclear Technolog y 53. {1981) 5.

21. L. s. Nelson. Pyrodynam ics 3. {1965) 121.

22. D.G.C. Robertson and A. E. Jenkens. in Heterogen ous Kinetics at Elevated Temperatu res. G. R. Belton and W. L.

Worrell. eds .* Plenum Press. 1970.

23. R. J. Lipinski. et al.. Uncertain ty in Radionucl ide Release Under Specific LWR Condition s Volume II:

Analyses. SAND84-04 10/2. Sandia National Laborator ies.

Albuquerq ue. NM.

24. M. Pilch. "Direct Heating of Containme nt Atmospher e by Airborne Core Debris~" contributi on to the Containme nt Loads Work1ng Group final report. dated May 3. 1984.

25. G. W. Parker. et al .* ORNL-3319 . Oak Ridge National Laborator y. Oak Ridge. TN. August 1962.

26. B. M. Jeffrey. J. Nucl. Materials 22. {1967) 33.

27. M. Corradini . "Hydrogen Generatio n During Molten-Fu el-Coo lant Interactio ns. 11 Second Workshop on the Impact of Hydrogen on Water Reactor Safety.

28. D. A. Powers. "A Re-Examin ation of the Steam Explosion Source Term During Severe Accidents ." paper IAEA-SM-2 81/34.

Intl. Symp. on Source Term Evaluatio n for Accident Condi-tions. 28 Oct. to 1 Nov .. Columbus. OH. IAEA. 1986.

29. D. A. Powers. "Aerosol Generatio n During Core Debris Interactio ns with Concrete. " 7th Internatio nal Light Water Reactor Safety Informatio n Exchange. Gaithersb urg. MD.

30. W. B. Murfin and D. A. Powers. Report of the Zion Indian Point Study: Volume I. NUREG/CR -1410. SAND80-0 617/l.

Sandia National Laborator ies. Albuquerq ue. NM. August 1980.

4-61

31. D. A. Powers and J. E. Brockmann. "Release of Fission Products and Generation of Aerosols Ou ts ide the Primary System. 11 Appendix c in J. Gieseke et al.. Radionuclide Release Under Specific LWR Accident Conditions, Volume 1:

PWR Analyses. BMI-2104. Battelle Columbus Laboratory, Columbus. OH, January 1983.

32. J. F. Muir. et al.. CORCON-MOD1: An Improved Model for Molten/Core Concrete Interactions. SAND80-2415. NUREG/CR-2142. Sandia National Laboratories. Albuquerque, NM. July 1981.

33. N. A. Fuchs. The Mechanics of Aerosols. Pergamon Press.

1964.

34. Off ice of Nuclear Reactor Regulation. U. s. Nuclear Regulatory Commission. Liquid Pathways Generic Study, NUREG-0440. February 1978.

35. H. Westrich. J. Nucl. Materials 110. (1982) 324.

36. J. w. Braithwaite and J. K. Johnson. Light Water Reactor Safety Research Quarterly Report, October-December 1977.

NUREG/CR-0307. SAND78-0600, Sandia National Laboratories.

Albuquerque, NM. June 1978.

37. D. A. Powers. Advanced Reactor Safety Research Quarterly Report, January-March 1980. NUREG/CR-1594 (1 of 4). SAND80-1646 (1. of 4). Sandia National Laboratories. Albuquerque.

NM.

38. - H. J. Matzke. 11 Actinide Diffusion in Waste Glasses."

Thermodvnamics of Nuclear Materials. Vol. 1.. IAEA. Vienna.

Austria. 1980, p. 311.

39. M. Corn. J. Air Poll. control Assoc. 11, (1961), 566.

40. M. Corn and F. Stein. Amer. Ind. Hyg. Assoc. J. 26, (1965) 26.

41. M. c. Kordeki and c. Orr. Arch. Env. Health 1. (1960) 1.

42. F. P. Bowden and D. Tabor. The Friction and Lubrication of Solids. Clarendon Press. Oxford (1954).

43. J. T. Bell. et al.. 11 Chemistry of Cesium and Iodine."

Chapter 5 in Technical Bases for Estimating Fission Product Behavior During LWR Accidents, NUREG-0772. U.S.

Nuclear Regulatory Commission. June 1981.

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