ML20116A514
| ML20116A514 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 06/30/1995 |
| From: | Powers D SANDIA NATIONAL LABORATORIES |
| To: | NRC |
| Shared Package | |
| ML20116A512 | List: |
| References | |
| NUDOCS 9607260129 | |
| Download: ML20116A514 (86) | |
Text
_ _ _ _ _ _ _ _ _ _ _ _ _ _
TECIINICAL EVALUATION REPORT MONTE CARLO UNCERTAINTY ANALYSIS OF AEROSOL BEHAVIOR IN THE AP600 REACTOR CONTAINMENT UNDER CONDITIONS OF A SPECIFIC DESIGN - BASIS ACCIDENT PART1 I
I D. A. POWERS l
Sandia National Laboratories Albuquerque, NM 87185 I
I l
June 1995 I
I I
[
[
D DO O 200003 A
ABSTRACT A Monte Carlo uncertainty analysis of aerosol behavior in the AP600 reactor containment during a hypothetical 3BE accident is described. The analysis used fixed (not uncertain) boundary conditions for pressure, containment atmosphere temperature, mole fraction stream in the atmosphere, rate of steam condensation from the atmosphere, and rate of heat removal from the atmosphere. The NUREG-1465 radionuclide source terms to the containment were also treated as certain inputs to the analysis. Uncertainties considered in the Monte Carlo analysis are nonradioactive aerosol mass, aerosol properties, thermal and momentum accommodation coefficients, primary aeroso! particle size and coefficients in correlations for turbulent natural convection processes.
Uncertainty distributions for decontamination factors and decontamination coefficients were constructed using nonparametric order statistics. Results are compared to " point" values calculated by others for the same problem using the NAUAHYGROS model. It is found that effective decontamination coefficients calculated in the Monte Carlo uncertainty analysis are smaller than average decontamination coefficients calculated with the NAUAHYGROS model.
Results of the NAUAHYGROS calculations exceed the 90 percentile of uncertainty distributions developed in the Monte Carlo uncertainty analysis. The discrepancy may be due to a large nonradioactive aerosol source term used in the NAUAHYGROS calculations.
e l
l i/ii
TABLE OF CONTENTS Eggg ABSTRACT i
I.
STATEM ENT OF TH E ISSU E..............................
1 A. B ACKG ROU ND.....................................
1 B. THE ISSUE 2
II. TH E A PPRO A C H......................................
2 l
A. OVERVI EW.......................................
2 B. CONTAINMENT GEOMETRY AND ACCIDENT BOUNDARY l
CO ND ITI O N S......................................
4 C. SOURCE TERM 12 1.
Radionuclides....................................
12 2.
Nonradioactive Aerosol Mass..........................
13 D. UNCERTAINTIES CONSIDERED IN THE MONTE CARLO ANALYSIS 17 1.
Mass Multiplier to Account for the Chemical Form of Radionuclides..
17 2.
Nonradioactive Aerosol Production.......................
18 i
3.
Thermal Conductivity of Aerosol Particles 19 4.
Particle Material Density.............................
20 5.
S hape Factors....................................
21 l
I 6.
Accommodation Coefficients.
22 7.
Diffusiophoretic Scattering Kernal 26 8.
Natural Convection Length Scale........................
27 9.
Turbulent Energy Dissipation Rate.......................
27 l
- 10. Friction Velocity..................................
28 l
l III. RES ULTS...........................................
28 l
A. EXAM PLE CALCULATION.............................
28 B. MONTE CARLO UNCERTAINTY ANALYSIS 31 C. COMPARISON TO NAUAHYGROS RESULTS.................
36 l
l IV. CONCLUSIONS.......................................
43 V. REFEREN C ES........................................
43 APPENDIX A. TABULATIONS OF BOUNDARY CONDITIONS INPUT TO THE MECHANISTIC MODEL USED FOR THE MONTE CARLO UNCERTAINTY ANALYSIS..................
A-1 APPENDIX B. IABULATED UNCERTAINTY DISTRIBUTIONS.......... B-1 iii
l l
LIST OF FIGURES Figure Face 1
Containment Pressure as a Function of Time 5
2 Containment Atmosphere Temperature as a Function of Time 6
3 Mole Fraction Steam in the Containment Atmosphere as a Function of Time..
7 4
Rate of Steam Condensation From the Containment Atmosphere as a Function of Time...................................
8 5
Rate of Heat Removal From the Containment Atmosphere as a Function of Time..........
9 6
Thermal Accommodation Coefficients for Various Gases Interacting with Glass Surfaces as Functions of Temperature......................
23 7
Overall Decontamination Coefficient (solid line) and Median Aerosol Particle Size (dashed line) as Functions of time for the Example Calculation 29 8
Deposition Velocities Due to Various Mechanisms as Functions of Time for the Example Calculation................................
30 9
Uncertainty Distributions for the Gap Release Decontamination Factor l
at Selected Ti mes......................................
33 10 Uncertainty Distributions for the Effective Decontamination Coefficients l
for Gap Release Material at Selected Times......................
38 11-Instantaneous Values of the Decontamination Coefficient Calculated with l
the NAUAHYGROS Computer Code..........................
40 1
l l
l l
u iv
1 l
LIST OF TABLES (Concluded)
Table Eage B-5 Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 86450 Seconds B-6 B-6 Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 6480 Seconds...........................
B-7 B-7 Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 13680 Seconds B-8
~
B-8 Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 49680 Seconds B-9 B-9 Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 86450 Seconds.......................... B-10 B-10 Uncertainty Distribution of Gap Release Effective Decontamination Coefficient, A, Over the Period 0 - 1800 Seconds B-11 e
B-11 Uncertainty Distribution of the Gap Release Effective Decontamination Coefficient, A, Over the Period 1800 - 6480 Seconds B-12 e
B-12 Uncertainty Distribution of the In-Vessel Release Effective Decontamination Coefficient, A, Over the Period 1800 - 6480 Seconds....
B-13 e
B-13 Uncertainty Distribution of the Effective Decontamination Coefficient, A Over the Period 6480 - 13680 Seconds....................e, B-14 B-14 Uncertainty Distribution of the Effective Decontamination Coefficient, A l
Over the Period 13680 - 49680 Seconds...................e, B-15 B-15 Uncertainty Distribution of the Effective Decontamination Coefficient, A,
1 Over the Period 49680 - 86450 Seconds...................e B-16 I
'I I
I l
vi I
l t
[
LIST OF TABLES Table fage l
NUREG-1465 Pressurized Water Reactor Accident Source Term
{
to the Con tain ment...................................
12 2
{
Uncertain Quantities Considered in the Monte Carlo Uncertainty Analysis...
14 3
Uncertainty Distribution 4 the Decontamination Factor
[
for Gap Release Mate.iai at 86450 Seconds......................
32 4
Summary of Uncertainty Distributions of the Decontamination Factors at Selected Times.....................................
35 5
Summary of Uncertainty Distributions of the Effective Decontamination Coefficien ts........................................
37 6
Comparison of Effective Decontamination Coefficients Found for the 3BE Accident to those Found in the Preliminary Analysis........
39 7
Comparison of Effective Decontamination Coefficients to Averaged
[
Values Obtained with the NAUAHYGROS Code..................
42 A-1 Containment Pressure A-2 A-2 Containment Atmosphere Temperature........................
A-5
[
A-3 Mole Fraction Steam in the Containment Atmosphere...............
A-8 A-4 Rate of Steam Condensation from the Containment Atmosphere......... A-12 A-5 Rate of Heat Removal From the Containment Atmosphere............ A-17 B-1 Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 1800 Seconds..
B-2 B-2 Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 64 80 Seconds................................
B-3
(
B-3 Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 13680 Seconds B-4 B-4 Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 49680 Seconds B-5 r
l V
I. STATEMENT OF TIIE ISSUE This document describes a Monte Carlo uncertainty analysis of aerosol behavior in the containment of the AP600 nuclear power plant under the conditions of a particular, hypothetical, design-basis accident. This analysis was done to assess the conservatism of analyses of aerosol behavior for design certification of the AP600 advanced light water reactor.
A. BACKGROUND Modern analyses of radionuclide releases to the atmosphere of containments of nuclear power reactors recognize that much of radioactive material discharged to the containment atmosphere will be in the form of aerosol particles. This recognition has been codified in the Severe Reactor Accident Source Term recently prepared by the U.S. Nuclear Regulatory i
Commission [1]. The radionuclide releases to the containment (the source term) specified in this document is often called the "NUREG-1465 source term." The NUREG-1465 source term specines releases of seven classes of radionuclides in addition to noble gases that pass I
into the containment atmosphere. With the exception of the noble gases and a small fraction of the iodine, the radioactive materials are considered to be aerosol particles. This description of the radionuclide releases to the containment atmosphere can be contrasted with I
an older source term description (the TID-14844 source term) that emphasized releases of the noble gases and iodine in gaseous form [2].
I Radionuclides suspended in the reactor containment atmosphere can leak from the plant.
Leakage of radionuclides is mitigated by natural and engineered processes that remove radionuclides from the atmosphere. Under design basis ccident conditions, existing I
pressurized water reactors have containment sprays that car, rapidly scrub aerosol particles from the containment atmosphere [3]. Such active, engineered systems for decontaminating the containment atmosphere have not been incorporated into the AP600 design. Instead, l
natural aerosol deposition processes are expected to mitigate sufficiently the amount of radioactive material suspended in the AP600 containment atm3 sphere.
l There are, indeed, many natural processes that will cause aerosol particles to grow and to deposit from a containment atmosphere [4]. These natural processes can take longer to decontaminate the containment atmosphere than do engineered safety systems such as I
containment sprays. Preliminary analyses of the decontamination of the AP600 containment by natural aerosol processes were done using models and boundary conditions better suited for the analysis of aerosol behavior during accidents in existing light water reactors [4].
I These preliminary analyses suggested that decontamination of the AP600 containment atmosphere by natural aerosol processes would, indeed, be slow. A safety concern arose that I
there would be prolonged periods in an accident with relatively high concentrations of radionuclides in the containment that could leak from the plant.
I I
L 1
The AP600 reactor containment is, however, quite different than containments of existing pressurized water reactors. External cooling of the containment boundary provides continuing driving forces for the removal of aerosol particles by phoretic processes (diffusiophoresis and thermophoresis). Though these aerosol removal processes are expected
{
to contribute to aerosol decontamination during accidents in existing light water reactors, they become less significant as the containments heat. Analyses of aerosol removal prepared for the design certification of the AP600 reactor using the NAUAHYGROS computer code
{
indicate significantly more rapid (~5x) aerosol removal than is predicted with models designed for analysis of accidents in existing light water reactors.
[
There are many uncertainties that may affect predictions of aerosol behavior under reactor accident conditions. There are uncertainties about the boundary conditions (containment atmosphere temperature, pressure, composition, etc.). There are also phenomenological uncertainties about the prop rties and behaviors of aerosols. These phenomenological uncertainties were treated differently in the NAUAHYGROS calculations than in the model used for preliminary analysis of aerosol behavior in the AP600 containment. Discrepancies in the results of the two analyses might, then, be the result of different treatments of boundary
?
conditions or different treatments of uncertain phenomena.
[
B. TIIE ISSUE To identify the causes of discrepancies between predicted rates of containment
[
decontamination by natural aerosol processes obtained with the NAUAHYGROS code and the preliminary calculations based on existing light water reactors, analyses have been done for
[
the same hypothesized reactor accident using the geometry of the AP600 reactor and the boundary conditions for a particular accident. The results reported here are for a Monte Carlo uncertainty analysis of aerosol behavior in which uncertainties in the containment
[
geometry and uncertainties in the boundary conditions have been eliminated.
Phenomenological uncertainties concerning the properties and behavior of aerosol particles released to the containment atmosphere have been considered. Uncertainty distributions for
[
the decontamination factors and the decontamination coefficients derived from results of the Monte Carlo analyses can be compared to point values for these quantities estimated with the NAUAHYGROS code. The comparison provides an indication of the conservatism inherent
{
in the NAUAHYGROS results with respect to phenomenological uncertainties.
H. THE APPROACH
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A. OVERVIEW
(
To resolve the issue described in Section I, a Monte Carlo uncertainty analysis similar in nature to uncertainty analyses of other aerosol issues described elsewhere [3-6] was undertaken for aerosol behavior in the AP600 reactor containment. This uncertainty analysis
[
paralleled closely an uncertainty analysis of containment decontamination by natural aerosol processes in existing light water reactors [4]. The analyses of natural aerosol processes in b
[
existing light water reactor containments explicitly considered uncertainties in predicted
{
aerosol removal caused by uncertainties in accident boundary conditions (such as containment atmosphere temperature, pressure, composition and thermal hydraulics), aerosol properties (such as particle size, shape factors, etc.) and aerosol processes (collision efficiencies,
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accommodation, slip, etc.). Uncertainties in accident boundary conditions for existing light water reactors had been based on results of analyses of a variety of severe (beyond design basis) accidents done with the Source Term Code Package (7-11). These boundary condition
[
uncertainties were eliminated in the Monte Carlo analysis of aerosol behavior in the AP600 reactor containment by using boundary conditions obtained using the MAAP code to predict conditions a specific accident-the 3BE accident involving a break in an 8" direct vessel
.(
injection ' v. Uncertainty distributions found here reflect uncertainties in aerosol processes, aerosol properties and the source nonradioactive aerosol source term to the reactor containment atmosphere.
f Uncertainties considered in the Mo.;te Carlo analysis are discussed further in Sections II-C and II-D of this report and in gruer detail in Reference 4. Three possible sources of uncertainty in the predicted behavior of aerosol in the reactor containment are implicitly omitted along with explicit omission of the boundary condition uncertainties. It is assumed that the containment atmosphere is thoroughly mixed and that stagnant or compositional stratified layers do not develop. This could be a significant omission since, as discussed below, diffusiophoresis is found to be a dominant mechanism for aerosol removal for the accident considered here. Stagnation could, of course, arrest diffusiophoresis. It is also assumed that electrostatic charging effects on both the agglomeration of aerosol particles and the deposition of aerosol particles can be neglected. Though definitive analyses have not been done, it is thought that neglect of the electrostatic charging effects is a conservative
-[
approximation [4]. That is, electrostatic effects are thought to enhance aerosol agglomeration and deposition.
[
Finally, it is assumed that particles do not grow by water absorption into hygroscopic materials, Though some chemical species suggested to be present in aerosols produced by
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reactor accidents are quite hygroscopic (CsOH and Csl, are examples), it is not established that such materials are actually present. Hygroscopic chemical forms are, in general, quite chemically reactive and can be expected to form species of low hygroscopicity given sufficient time. Furthermore, it is not apparent that hygroscopic materials coagglomerated with large amounts of nonhygroscopic materials will cause significant aerosol panicle growth by water adsorption. In any event, neglect of particle growth by water adsorption is a conservative approximation. (Note, however that it is assumed water will condense in concave pores within particles-see section li-D.5)
[
Independent analyses of aerosol behavior in the AP600 containment were done by others [12]
using the NAUAHYGROS computer code [13]. These analyses yielded " point" values of the aerosol decontamination coefficients since the effects of uncertainties on the predictions of
[
aerosol behavior were not explicitly considered. Comparison of these point values with the uncertainty distributions found in the Monte Carlo calculations reported here can be used to 3
estimate the conservatism inherent in the point values with respect to uncertainties in aerosol properties, aerosol processes and the source term to the containment. This comparison is discussed further in Section 111 of this report.
B. CONTAINMENT GEOMETRY AND ACCIDENT BOUNDARY CONDITIONS Containment geometry data were obtained from the Westinghouse Electric Corporation [12].
Geometry data used in the Monte Carlo analyses are:
10 3
Containment Volume:
4.7927 x 10 cm I
Upward-facing Area:
1.848 x 107 2
cm 7
2 Vertical Area:
7.04 x 10 cm Containment cylinder equivalent height:
4311cm.
These geometry data for the AP600 containment were used in place of the correlations of containment geometry with reactor power used in the analyses of natural aerosol processes in I
the containments of existing light water reactor [4]. Uncertainties ascribed to the geometry correlations, then, do not arise in the analyses reported here.
l Predictions of the containment boundary conditions by the MAAP code for the hypothetical 3BE accident were obtained from the Westinghouse Electric Corporation [12]. Boundary conditions used in the Monte Carlo analyses are:
l contamment pressure, containment atmospheric temperature, e
mole fraction steam in the containment atmosphere, steam condensation rate, and e
rate of heat removal from the containment atmosphere.
e I
These boundary conditions are shown as functions of time in Figure 1 to 5. Note that the origins in these figures correspond to a time 1.6 hours6.944444e-5 days <br />0.00167 hours <br />9.920635e-6 weeks <br />2.283e-6 months <br /> after initiation of the accident when I
the water level has fallen to the top of the active fuel in the reactor vessel [12]. It has been assumed here that no significant release of radioactivity in aerosol to the containment I
atmosphere would occur until the coolant level fell below the top of the active fuel. That is, radioactivity in the coolant that might be dispersed as aerosols in the containment prior to the coolant level falling to the top of the active fuel has been neglected.
The boundary condition data were provided as tabulations. These tabular inputs to the Monte Carlo analyses are reproduced in Appendix A. Linear interpolation among the tabulated values was used in the Monte Carlo analyses. Test calculations indicated no great differences in the calculated behavior of the aerosol were obtained when the boundary conditions were used as piece-wise constants.
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Boundary conditions vary smoothly with time throughout the duration of gap release (0 to 1800 seconds) and during the early portion of the in-vessel release (1800 to 6480 seconds).
After about 3500 seconds, boundary conditions are marked by a series of sharp spikes in temperature, pressure and steam mole fraction. These spikes must reflect fairly dramatic events taking place during core degradation such as melt relocation from the core region into the lower plenum of the reactor vessel. Spikes also occur in the rates of steam condensation and heat removal from the containment atmosphere. Abrupt increases in the calculated rates
[
of aerosol removal can be expected at the times of these spikes in the containment boundary conditions. No consideration of the uncertainties in the existence, magnitude or timing of these spikes was undertaken here. Calculations were done for the Monte Carlo uncertainty
[
analysis in such a way that the effects of these transient excursions on natural aerosol processes were reflected in the results. In the preliminary analyses of aerosol behavior in the AP600 containment, no transient excursions in boundary conditions had been considered.
A broad minimum in the rate of steam condensation occurs over the interval of about 19000 to 27000 seconds. After 28000 seconds, the steam condensation rate rises to a plateau.
Corresponding changes in the other boundary conditions occur at these times. These changes can also be expected to affect the rates of aerosol removal from the containment atmosphere by phoretic processes (diffusiophoresis and thermophoresis). The causes of these changes in
[
the boundary conditions were not investigated as part of this work despite the effects tney could be expected to have on aerosol behavior.
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The computer code used for the Monte Carlo uncertainty analysis internally calculates the difference between the bulk atmosphere temperature and the mean structural surface temperature [4]. This temperature difference, AT, is calculated from the following equations
[
[4,14].
= h
- AT + AHfg th(H O) 2 where
(
Q = rate of heat removal from the containment atmosphere
[
A = surface area
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AHfg = latent heat of steam condensation th(H O) = mass rate of steam condensation, and 2
h* = heat transfer coefficient.
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(
10
The heat transfer coefficient was calculated iteratively from the equations:
k* =
mR(2T - AT) m x(H O)P - Psat(T - AT) 2 k
= k *n / C m
o Co = In(1 + R_) / R Psat (T - AT) / P - x(H O) 2 l-Psat (T - AT)/ P
~
c(Sh) k
=
Sc /3 Re /4 I
2 Re = P [6/ p E
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6=
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8 2
b Gr /2 l
1.185
< g',
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(1 + 0.494 Pr /3)l/2 2
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T 2
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(
Pr = Prandtl number
(
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k (th)c(Nu)Gr g
h=
[
L(1 + 0.494 Pr /3)M 2
and c(Sh) and c(Nu) are uncertain dimensionless coefficients uniformly distributed over the ranges 0.0094 to 0.0376 and 0.0148 to 0.059, respectively.
C. SOURCE TEIG1
- 1. Radionuclides The radionuclide source term to the reactor containment atmosphere for the Monte Carlo uncertainty analysis was taken to be certain and to be that specified in NUREG-1465 for the
[
gap release and the in-vessel release phases of a pressurized water reactor accident. This source term is shown in Table 1. Releases specified in NUREG-1465 for the ex-vessel and r
the late in-vessel phases of a severe reactor accident were not considered for this work with a l
design-basis accident.
Table 1. NUREG-1465 Pressurized Water Reactor Accident Source Term to the Containment Fraction of Initial Core Inventory Released to the Containment During the Gap Release In-Vessel Release Element (0-1800 s)
(1800-6480 s)
I 0.05 0.35 Cs 0.05 0.25
{
Te 0
0.15 Sr 0
0.03 Ba 0
0.04
[
Ru 0
0.008 Ce 0
0.01 La 0
0.002 The NUREG-1465 source term is specified in terms of the fractions of initial core inventories
[
of radionuclides released at constant rates over various phases of an accident. To convert these release specifications to radioactive aerosol mass, it is necessary to know the core inventories of radionuclides. For this comparison work, however, the elemental releases used
[
in the Monte Carlo analyses were chosen to match the elemental releases specified by the L
12
1 1
source term adopted for calculations of the hypothesized AP600 accident with the NAUAHYGROS model. The source terms of radionuclides for the uncertainty analyses, then are:
l Release Rate (grams element /s)
Gap Release In-Vessel Release Element (0-1800 s)
(1000-6480 s) f Cs 6.I1065 10.3415 I
0.49998 1.3461 f
Te 0
0.405983 Ba 0
0.51284 Sr 0
0.30341 l
Ce 0
0.022435 12 0
0.00414526 Ru 0
0.101496 The chemical forms that will be adopted by radionuclides released to a reactor containment atmosphere are quite uncertain. For the Monte Carlo uncertainty analyses, the elemental release masses were multiplied by a factor to account for possible oxidation and hydration of the elements. These multiplicative factors were treated as uncertainties in the Monte Carlo analysis as described in section II-D. Specific chemical forms of the radioactive elements were adopted for the analyses done with NAUAHYGROS [12]. The implied mass factors for the NAUAHYGROS source term are shown in Table 2.
l
- 2. Nonradioactive Aerosol Mass j
Radioactive materials are not the only aerosol released into the containment atmosphere i
during an accident. Nonradioactive materials that form aerosols are also generated in an accident. These nonradioactive aerosols will agglomerate with radioactive aerosols and j
enhance the removal of both classes of aerosol. Unfortunately, there is a poor understanding of the releases of nonradioactive aerosol materials during reactor accidents. The i
NAUAHYGROS point estimates were obtained assuming that the ratio of nonradioactive
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aerosol mass to radioactive aerosol mass was 0 throughout the gap release phase and about 3.6245 during the in-vessel release phase of the 3BE accident. The releases of nonradioactive aerosol mass were taken to be uncertain in the Monte Carlo uncertainty analyses.
j Furthermore, the ratios of nonradioactive aerosol mass to radioactive aerosol mass were taken to be different during the gap release and the in-vessel release phases of the accident. The treatment of these uncertainties is described in Section II-D. In general, the ratios of the nonradioactive mass to radionuclide mass used in the Monte Carlo analyses are smaller than the value of 3.6245 used for the NAUAHYGROS calculations. Some compensation for this discrepancy is provided by the treatment of radionuclide chemical form in the Monte Carlo analyses.
f L
13
1 l
l Table 2. Uncertain Quantities Considered in the Monte Carlo Uncertainty Analysis Values used in the Plausible Range of Distribution of NAUAHYGROS Quantity Values Values Calculations Mass multiplier to account for the chemical forms of radionuclides released to the containment I
1.0 to 1.38 uniform 1.0 Cs 1.05 to 1.22 uniform 1.12 I
Te 1.0 to 1.25 uniform 1.0 Sr,Ba 1.18 to 1.67 uniform 1.18 I
Ru 1.0 to 1.47 uniform 1.0 Ce 1.17 to 1.22 uniform 1.22 I
La 1.11 to 1.17 uniform 1.17 Nonradioactive aerosol I
mass to radioactive aerosol mass during:
gap release 0.01 to 1.0 log-uniform 0
in-vessel release 0.5 to 2.0 uniform 3.6245 ae,rosol material density 2.8 to 4.5 uniform 3
I during) gap release (g/cm Aerosol material density 3.25 to 10.96 log-uniform l
during)in-vessel release (g/cm I
Material thermal conductivity of aerosol released during:
- the gap release 0.023 to 0.0022 log-uniform Value for water (cal /cm-s-K)
I 4
- the in-vessel release 0.1 to 3x10 log-uniform Value for water (cal /cm-s-K)
I L
14
[
Table 2. Uncertain Quantities Considered in the Monte Carlo Uncertainty Analysis f
(Continued)
{
Values used in the Plausible Range of Distribution of NAUAHYGROS Quantity Values Values Calculations Coefficient to describe 10~3 to 0.5 log-uniform NA contact resistance Coefficient in the 0.0148 to 0.059 uniform NA correlation of the heat transfer coefficient f
Coefficient in the 0.0084 to 0.0376 uniform NA correlation of the mass transport coefficient Parameter relating the 0.1 to 1.0 log-uniform NA natural convection mass
[
transport length scale to containment height Fractal dimension of 1.5 to 2.24 uniform NA particle agglomerates Diameter of primary 0.02 to 0.2 log-uniform NA f
aerosol particles ( m)
Coefficient in the 0.1 to 1.0 log-uniform 1/3
[
expression for collision efficiency Coefficient m the 0.0 to 0.6 uniform implicitly fired
[
expression for momentum accommodation coefficient
{
Coefficient in the 0.0 to 0.6 uniform implicitly fixed expression for the thermal accommodation coefficient f
((s), term to account for 0.35 to 0.383 uniform NA the gas / surface potential
[
in the Cs parameter L
for the model of the thermophoretic deposition f~
l r
15 i
l 1
[
Table ' Uncertain Quantities Considered in the Monte Carlo Uncertainty Analysis
{
(Concluded)
Values used in the
(
Plausible Range of Distribution of NAUAHYGROS Quantity Values Values Calculations
((t), term to account for 1.263 to 1.296 uniform NA the gas / surface potential in the temperature jump parameter for the model of thermophoretic deposition
((m), term to account for 0.996 to 1.020 uniform NA the gas / surface potential
{
in the momentum jump parameter for the model of thermophoretic
{
deposition (012). Parameter to select 0 to 1.0 uniform 0
among models for the
[
diffusiophoretic scattering kernal
[
((u ), parameter in the 0.1464 to 0.5370 uniform NA definition of friction velocity
[
[
[
[
[
[
r L
16
1 D. UNCERTAINTIES CONSIDERED IN TIIE MONTE CARLO ANALYSIS Uncertainties considered in the hionte Carlo uncertainty analysis of aerosol behavior in the AP600 reactor containment are listed in Table 2. Each of the uncertainties is characterized by a parameter with a plausible range of values and a distribution of values within this range.
In general, uniform and log-uniform distributions have been used for the uncertainty analyses reported here. In the hionte Carlo uncertainty analyses, values of the uncertain parameters are randomly selected in accordance with their respective subjective probability distributions.
Calculations of aerosol behavior are carried out, the results accumulated, and a new set of parametric values is selected. The process is repeated and results are accumulated until there is a 99 percent confidence that 95 percent of the range of values of the results has been sampled. The accumulated set of results is analyzed using nonparametric, order statistics to
{
define uncertainty distributions for the calculated quantities. Additional information on the construction of uncertainty distributions from the accumulated results of hionte Carlo analyses can be found in Appendix A of Reference 5.
Each of the phenomenological uncertainties considered in the hionte Carlo uncertainty analysis of aerosol behavior in the AP600 reactor containment is briefly discussed in the subsections that follow. Synoptic justifications for the plausible ranges of parametric values are presented. Additional, more detailed information including a description of the rationale for selecting the high entropy distributicas for values within the respective ranges can be found in Reference 4.
- 1. Afass Multiplier to Account for the Chemical Form of Radionuclides The NUREG-1465 source term specifies elemental releases. In general, radionuclides will not all be in elemental form when they reach the containment. The exact chemical form adopted by the radionuclides is, however, not well known. It is often suggested for instance that cesium is released into the reactor containment as CsOH. But, CsOH is quite a reactive species and may be easily converted to Cs2CO by reaction with carbon dioxide in the 3
containment atmosphere, or it might be converted to CsBO by reaction with boric acid 2
vaporized from the reactor coNant. Similarly, iodine is often thought to be present as CsI.
It can, however, be further oxidized to CsIO or it can react with ozone produced by 3
radiolysis of the atmosphere to form IO +x where x may be between 0 and 1. On the other j
2 hand iodine may be present in the containment atmosphere as AgI which exhibits none of the i
hygroscopic properties of Csl.
The additional aerosol mass created by radionuclide reactions with species such as carbon dioxide, oxygen or steam that would otherwise be gaseous in the containment will affect the removal of earosols from the atmosphere. This additional mass must, then, be considered.
The additional mass is accounted here by multiplying the aerosol mass of each radionuclide by a factor. The factor is uncertain because the chemical forms of the radionuclides under conditions that prevail in the reactor containment are not known. Plausible ranges for the multiplicative factors were selected by considering limiting chemical forms of the radionuclides:
17
[
l l
[
Plausible Chemical Plausible Range of Multiplicative
(.
Element Forms Mass Factors 1
I~;103 1.0 to 1.38 Cs CsO1/2; Cs(CO )l/2 1.05 to 1.22
{
3 Te Te ; TeO2 1.0 to 1.25 Sr SrO; SrCO3 1.18 to 1.67 Ru Ru ; RuO3 1.0 to 1.47
{
Ce CeO.5; CeO2 1.17 to 1.22 I
La 120; lao.5 1.11 to 1.17 I
[
The NAUAHYGROS calculations considered specific chemical forms for the radionuclides.
The multiplicative mass factors implied by these assumed forms are compared in Table 2 to
{
the uncertainty ranges for these factors used in the Monte Carlo uncertainty analysis. In general, the implied multiplicative factors used in the NAUAHYGROS calculations fall within the uncertainty ranges used for the Monte Carlo analyses.
- 2. Nonradioactive Aerosol Production Reactor accident source terms focus on the release of radionuclides to the reactor of radionuclides to the reactor containment. From the perspective of containment decontamination by natural aerosol processes, the nonradioactive aerosol mass in the
[
containment atmosphere is just as important as the radioactive aerosol mass. Accurate assessments of aerosol behavior in the containment atmosphere must take into account the nonradioactive aerosol mass. Unfortunately, much less is known about the releases of
[
nonradioactive aerosols to the containment atmosphere than is known about releases of radionuclides to the containment.
It is certainly recognized that there are sources of nonradioactive aerosol that are potentially large. In the case of pressurized water reactors, boric acid vaporized from the coolant or cadmium from the reactor control rods could be massive sources of aerosol. Tin from the fuel cladding, uranium oxides from the fuel, or constituents of steel from the reactor intervals are other potential sources of nonradioactive aerosol mass. At the elevated temperatures of reactor core degradation these materials could vaporize. As the vapors emerge from the core region into cooler portions of the reactor coolant system and, eventually, into the containment, the vapors can condense to contribute to the aerosol in containment.
Nonradioactive aerosols will coagulate with radioactive particles to create indistinguishable airborne particles. The effect of the nonradioactive aerosol is to increase the airborne mass and thereby increase the driving forces for aerosol particle growth. It is generally true that
[
large aerosol particles are more rapidly removed from the containment atmosphere than are smaller (but not very small <0.1 m) particles. Thus, increasing the nonradioactive contribution to the aerosol mass suspended in the reactor containment is expected to increase the rate of decontamination by natural processes.
There is not now a highly reliable basis for estimating how much nonradioactive aerosol mass will be released to the containment atmosphere. The final version of NUREG-1465 does not provide quantitative guidance though an earlier draft suggested about three hundred kilograms 18
[
[
of nonradioactive mass might be released to containment during the in-vessel release phase of
{
an accident. It is usually thought that temperatures are so low in the core region during the gap release phase of an accident, especially in a depressurized accident such as that considered here for the AP600, that not much nonradioactive material is vaporized from the reactor core. The nonradioactive source term becomes more important during the in-vessel release phase of an accident.
Because both the vaporization of radionuclides from fuel and the vaporization of nonradioactive materials are strongly influenced by temperature, it appears reasonable to assume as a first approximation that the nonradioactive aerosol mass will be proportional to the mass of radionuclides. The proportionality constant is, of course, quite uncertain.
Here, for the Monte Carlo uncertainty assessment, the proportionality constant between nonradioactive and radioactive aerosol mass during the gap release phase (0 to 1800 seconds) was taken to be log-uniformly distributed between 0.01 and 1.0. These relatively low values of the proportionality constant were selected to reflect the fact that temperatures in the core are low during the gap release phase of the accident so that vaporization of materials not intimately associated with reactor fuel ought to be low.
[
The proportionality constant between nonradioactive and radionuclide-bearing aerosol masses during in-vessel release is taken to be uniformly distributed between 0.5 and 2.0. The midpoint of this range approximates results obtained in accident analyses for NUREG-1150
(
[15] and the QUEST study (16]. The upper limit was chosen to acknowledge that past studies of aerosol production omitted some possible sources of nonradioactive aerosol mass. The lower bound on this range was chosen to reflect the fact that releases of nonradioactive
[
aerosol are likely to be most extensive during the later stages of core degradation when it is more likely that aerosol formed in the reactor coolant system will not successfully negotiate a pathway to the reactor containment.
Analyses of aerosol behavior done with the NAUAHYGROS code assumed that the ratio of
[
nonradioactive aerosol mass to radioactive aerosol mass was zero during the gap release phase of the accident and about 3.642 during the in-vessel release phase.
- 3. Thermal Conductivity of Aerosol Particles The thermal conductivity of aerosol particles enters into the expression for the deposition velocity of aerosol particles by thermophoresis. This deposition velocity decreases with increasing thermal conductivity of the aerosol particle.
A general aerosol particle will be a porous conglomerate of primary particles which themselves may be composed of several chemical species. The thermal conductivities of such complicated materials have, of course, not been measured. Estimating the thermal
[
conductivity of aerosol particles is complicated by the contact resistance between primary particles and the fact that liquid water fills the pore structure of the conglomerate.
c 19
l For the Monte Carlo analysis an effective particle thermal conductivity, k(effective), is
(
defined by:
bc k(effective) =
. p( (3 _,)
2k d(pr) + -
3 kp where c = packing fraction (see subsection 5).
[
k = thermal conductivity of the primary particles p
k3 = c(k)k = Contact zone thermal conductivity p
0, = 0.1 d(pr) d(pr) = diameter of the primary particles k = thermal conductivity of water g
Both the thermal conductivity of the primary particles and the thermal resistance of the contact zone between primary particles were taken to be uncertain.
The thermal conductivity of primary particles released during the gap release phase was assumed to fall within a range defined by the thermal conductivity of Csl (0.023 cal /cm-s-K)
[
and the thermal conductivity of molten NaOH (0.0022 cal /cm s-K). During the in-vessel release phase metallic materials (Ag, Cd, In, Te and Fe) as well as oxidic materials (UO '
2 U O, Fe2 3, etc.) may be released to the containment as aerosols. Consequently, the 3g O
{
plausible ranje of values for the thermal conductivity of primary particles was expanded to 0.1 to 3x10 cal /cm-s-K.
{
The thermal conductivity of the contact region between particles is quite uncertain. It was assumed for the Monte Carlo calculations that this thermal conductivity would be proportional to the thermal conductivity of the primary particles. The proportionality constant is
[
uncertain. A range of possible values was taken to be 0.5 (essentially no contact resistance) to'10-3 (only point contact between particles).
[
- 4. Particle Material Density The material density of aerosol released to the containment is difficult to predict since the
(
chemical forms of the radionuclides are not known and the nonradioactive aerosol mass is not identified. The material density during the gap release was taken to be uniformly distributed 3
over the range 2.8 to 4.51 g/cm. This range spans measured densities of saturated CsOH
(
solutions and solid Csl. The aerosol material density during the in-vessel release phase was 3
taken to be log-uniformly distributed over the range 3.25 to 10.96 g/cm. This range allows for the possibility that uranium oxides may be major contributors to the aerosol. Note that the
(
actual aerosol particle density is calculated recognizing the particles are porous (see subsection 5).
[
~
- 5. Shape Factors Sh;ae factors partially correct the aerosol physics equations for effects that arise because real aerosol particles are not perfectly dense spheres. Two shape factors arise in the analysis of aerosol behavior in reactor containments, the dynamic shape factor, %, and the collision shape factor, y. Because of the high humidity of the containment atmosphere, water in the pore structure of an aerosol particle composed of coagulated primary particles draws the agglomerate into a nearly spherical envelop so that the two shape factors are equal. Still, these shape factors do not have unit values. The shape factors are taken here to be:
x = y = 1/ a /3 l
where a is related to the packing density by:
cp + (1 - c)pf p
PP where c = packing efficiency of primary particles, p
= primary particle material density, and p
pf = density of material that fills voids in the agglomeration of primary particles.
Here, it is assumed that because of curvature effects the voids within a particle are filled with liquid water. The packing efficiency of primary particles is estimated from a fractal model:
'd ' 3 -df e=
_Pl d
Ps where df = fractal dimension, d
= diameter of primary aerosol particles, and pr d = diameter of the primary particle agglomerate.
p Thus, shape factors differ in general from unity and are dependuit on particle size. The primary aerosol particles that agglomerate to make aerosol particles are not well understood.
For the Monte Carlo uncertainty analysis, the primary particles were taken to have diameters log-uniformly distributed over the interval 0.02 to 0.2
- m. The fractal dimension of aerosol particles was taken to be uncertain over the range 1.5 to 2.2.
21
l In the NAUAHYGROS point estimates of aerosol behavior shape factors were taken to be independent of particle size and equal to one.
l
- 6. Accommodation Coefficients l
Because aerosol removal from the atmosphere of the AP600 containment involves phoretic j
processes (diffusiophoresis and thermophoresis) in such important ways, the momentum and the thermal accommodation coefficients associated with gas-surface interactions could be of some importance. These coefficients have not been measured for the particular combinations I
of gases and aerosol surfaces that can be expected to exist in the AP600 containment atmosphere under accident conditions.
Momentum accommodation coefficients have been measured at temperatures near 300K using
' Milliken oil-drop experimental techniques. These measurements for spherical, liquid (oil) l droplets yield valves near 0.92. Measurements with solid particles have been reported as low
. as 0.7 at room temperature [4].
More data are available for thermal accommodation coefficients which can be measured in low-pressure heat transfer experiments. Some data for the thermal accommodation coefficients of various gasses on glass surfaces are shown in Figure 6 [4].
Theoretical analyses suggest that accommodation coefficients should be:
temperature-dependent, lower for polyatomic gases such as steam than for monatomic gases such as helium,
+
hicrease with the molecular weight of the gas, and momentum accommodation is more complete than thermal accommodation.
The accommodation coefficients are bounded by the values of 0 to 1 and momentum accommodation may be bounded by 0.5 and 1.0.
Useful, simple models for the accommodation coefficients that do not require assumptions or unavailable data about the nature of the particle surface seem not to exist. Consequently, for the Monte Carlo uncertainty analysis ad hoc expressions for the momentum and thermal accommodation coefficients that satisfy the suggestions obtained from theoretical analyses are used:
L m = 1.0 - A exp(-300 /T(K))
l a
exp (-300 / T(K))
4(MW / 44)
I ag=
1-A (1 + MW / 44) a l
l 22
O e
p e
j z
H! 0.9 oE u.
W e
8 0.8 0 O z
O OF 0
I 0.7 a
gg a
g oEEO O
g 0.8 O. glass - H2 4
O A
glass - Ne
@ 0.6 O glass - N2 o
glass - 02 w
0.
E 0.4 m
H i
O I
I 100 200 300 W
TEMPERATURE (K)
Figure 6. Thermal Accommodation Coefficients for Various Gases Interacting with Glass Surfaces as Functions of Temperature.
l where f
MW = average molecular weight of the gas,
(
A = uncertain parameter with values uniformly distributed over the interval from 0 to 0.6, and AI = uncertain parameter with values uniformly distributed over the interval from 0 to 0.6.
This formulation makes the accommodation coefficients temperature-dependent and assures t < "m-a
[
The accommodation coefficients enter into the expressions for thermophoretic and diffusiophoretic deposition velocities. For instance, Talbot's model [4] of the thermophoretic deposition velocity is:
-2 p CC k
g 3
g + C Kn vinT t
px k
g p
VT" 2k
[
(1 + 3C Kn)1+
g + 2C Kn m
g P
1 r
where 1
= g s viscosity E
p
= gas density
(
g k = gas thermal conductivity g
k = effective particle thermal conductivity p
Kn = Knudsen number
{
C = slip correction factor
{
The " jump" coefficients C, C, and C in this expression are related to the thermal and 3
t m
momentum accommodation coefficients. The relationships between the accommodation coefficients and the parameters in the expression for the thermophoretic velocity is often
[
derived based on a hard-sphere potential particle surface and the gas. For the Monte Carlo analysis, a more realistic Lennard-Jones potential was between the assumed. Then, Cs = 0.75(1 - a ) + 3a &(s) m m
1 I
- Note that in Reference 12 describing the results of calculations with the NAUAHYGROS code C is referred to as the thermal accommodation coefficient and C is called the momentum r
t m
L accommodation coefficient. This is not standard nomenclature and these parameters are 1
certainly not the accommodation coefficients discussed here.
f L
24 r
C"715 (2 - a)
(I - "t) 3 b + "t((m) t 5
t q
(2 - a )
(I - "m) 6 + "m&(m) m Cm=
2 "m
where
((s) = uncertain parameter with values uniformly distributed over the range 0.35 to 0.383
((t) = uncertain parameter uniformly distributed over the range 1.263 to 1.296, and
((m) = uncertain parameter uniformly distributed over the range 0.996 to 1.02.
Accommodation coefficients also enter into the expression used here for the slip correction factor:
2 + 18C (C2 + 2)Kn 3
15 + 12C Kn + g C
+1 Kn i
2 2
15 - 3C Kn + C (8 + xa)C
+2 Kn i
2 t
where (2-a)and m
Ci=
"m C2* (2-a) m use of this expression for the slip correction factor provides a more realistic temperature dependence than do usual expressions of the form:
C = 1 + Kn[a + b exp(-c / Kn)]
Finally, accommodation coefficients enter into the expression for the diffusiophoresis scattering kernal described in subsection 7.
25
- 7. Diffusiophoretic Scattering Kernal P
The deposition velocity for aerosol particles due to diffusiophoresis is:
-C D(H O) 2 D*X
+ 012(1 - P(H O)/ P )
T - P(H O)%H O)
V 2
T 2
P 2
where P(H O) = PT x(H O) 2 2
x(H O) = mole fraction steam in the atmosphere, l
2 i
D(H O) = diffusion coefficient of steam in air = 0.3106 (T/373)l.82 cm /s, 2
2 PT i
PT = total pressure 12 = diffusiophoretic scattering kernal, 0
C = slip correction factor, and i
x = dynamic shape factor i
The diffusiophoretic scattering kernal is a source of uncertainty. Based on classic kinetic analysis treating gas molecules as hard spheres:
l I
m(H O) - m(air) 2 al2 (classic) =
m(air) + m(H O) + m(H O)m(air)'1/2 2
2 where m(i) is the mass of a molecule of species i. Unfortunately, this description does not yield results that always fit well experimental data. A variety of alternative expressions have been developed. One of the most complete derivations [4] yields:
m(H O)l/2 - m(air)1/2 Q(air) / Q(H O) 2 2
+ x(H O) m(H O)1/2 - m(air)1/2 Q(air) m(air)l/2 Q(air)-
2 2
Q(H O)
Q(H O) 2 2
26
where Q(i) = 1 + n / 8 - 0.5(1 - a fi)) '+ "(I - "t(i)) /16 m
a (i) = thermal accommodation coefHcient for species (i), and g
m(i) = momentum accommodation coefficient for species (i).
a Even this expression has not achieved widespread acceptance.
To account for the uncertainty in the diffusiophoretic scattering kernal, a parameter 6(o12) was defined to have values uniformly distributed over the interval 0 to 1, and al2(classic) for 6(o12) < 0.5 012
- al2(KC) for 6(o12) >_ 0.5 4
- 8. Natural Convection Length Scale A length scale, L, is required for the modeling of turbulent deposition of aerosol particles.
This scale should be related to the geometry of the containment. Here, it was assumed that the length scale was proportional to the specified equivalent height of the containment. The proportionality constant was taken to be log-uniformly distributed over the interval from 0.1 to 1.0.
- 9. Turbulent Energy Dissipation Rate The rate of turbulent energy dissipation enters into the calculation of particle coagulation by turbulent inertial processes and by turbulent diffusicn. The turbulent energy dissipation rate in reactor containment atmospheres is, hov/ever, quite uncertain. Here this energy dissipation ratb, c, was taken to be:
c = c(t) A H / V y
where A
vertical surface area of containment,
=
y H = effective height of containment, V = volume of containment, and j
c(t) is an uncertain parameter log-uniformly distributed over the interval from 2 to 23 20 cm /s,
27
1
- 10. Friction Velocity A friction velocity is used in the calculation of turbulent deposition of aerosol particles. This friction velocity is given by:
u
=&
where
& = uncertain parameter uniformly distributed over the range 0.1467 to 0.537, f = 0.045 ( g/ g[6)l/4 P
and [and 6 are dimensionless quantities calculated as described in Section I-8.
IIL RESULTS I
A. EXAMPLE CALCULATION l
Results of a single, typical calculation from the Monte Carlo uncertainty analysis of aerosol behavior in the AP600 reactor containment during the hypothesized 3BE accident are shown in Figures 7 and 8. These results were obtained using one particular set of values for the I
uncertain parameters discussed in the previous chapter. Some of the quantitative features of the predicted aerosol behavior are quite dependent on the selected values of these uncertain parameters. The results of this example calculations are, then, of only qualitative I
significance.
The overall decontamit ation coefficient is shown as a function of time in Figure 7. The I
variations of the overall decontamination coefficient with time parallel closely the variations with time of the rate of steam condensation from the containment atmosphere (see Figure 4).
I This suggests that aerosol deposition by diffusiophoresis is a dominant aerosol removal process.
I Deposition velocities for aerosol particles by diffusiophoresis, thermophoresis, gravitational settling and turbulent inertial processes are compared in Figure 8. Indeed, these results show that throughout the accident, diffusiophoresis is the dominant aerosol removal mechanism. It I
is generally true that gravitational settling grows in importance as aerosol mass continues to be added to the containment atmosphere and particles grow. Eventually, gravitational settling becomes comparable to diffusiophoresis as a decontamination mechanism.
Particle growth is not rapid at the low total aerosol concentrations involved in this design-basis accident (see Figure 7). Consequently, gravitational settling velocities increase even l
after release of aerosols to the containment atmosphere stops at 6480 seconds. Gravitational settling most efficiently removes larger aerosol particles. As decontamination progresses, aerosol concentrations fall and large particles removed from the containment atmosphere are i
28
- 3. 0
- 1. 0 m
i L
_C v
W E
3
- 2. 5 0.75 z
v w
~
o-U w
LL N
I--
w y
tt 4-1 w
s 0.50 0
2, 0 U
-a
's
\\
Z
-- - Q,j',
I
\\
+
o w
_J N
~
U N
1-oc s
<z
- 1. 5 s
O.25 s
's o
's I<
Ms I-
's Z
O U
w
,,,it i
i
. > > >>i g
100 1000 10000 100000 TIME (SECONDS)
Figure 7. Overall Decontamination Coefficient (solid line) and Median Aerosol Particle Size (dashed line) as Functions of time for the Example Calculation.
t
.E 1 o
o I
uma muu umu m
W
- 1. 0 3
W
- 0. 1 r
xg j
OIFFUSIOPHORESIS
~-
>- O. 01 r
i n
i i
U
~
SETTLING '
O
-3 3 10 r
w y
THERMOPHORESIS
....................................:.......l~--~,M.*Y---~.s-~_________:
2 y
o
-4 10 r
H
- _______________f_.,.___v._
,g._ g__,___.___:
m g
1
-5 w 10 TURBULENT O
i i
i i,,ii.:
, ii,iii 100 1000 10000 100000 1
TIME (SECONDS)
Figure 8. Deposition Velocities Due to Various Mechanisms as Functions of Time for the Example Calculation.
b
[
not rapidly replaced by aerosol growth. After some time, the rate of aerosol removal by
(
gravitational settling reaches a maximum and then begins to decrease.
Thermophoretic deposition of particles and turbulent deposition are smaller contributors to the
[.
total rate of aerosol removal throughout the accident. If the convoluted surfaces within the reactor containment are neglected as they were in the specification of this problem, these processes do not make significant contributions to the aerosol removal by natural processes.
[
Diffusiophoresis was found for these calculations of aerosol behavior in the AP600 containment to be an important aerosol removal mechanism at the start of the accident and to
(
remain important throughout the calculation. This contrasts with findings for analyses of aerosol behavior in the containments of existing light water reactors in which diffusiophoresis waned in importance as the accident progressed [4]. External cooling of the AP600
[
containment keeps steam condensation and, consequently, aerosol deposition by diffusiophoresis high throughout the accident. The rates of steam condensatH and diffusiophoretic deposition of aerosols are calculated to fall over the course of an accident in
[
an existing light water reactor as the containment surfaces rise in temperature.
[
B. MONTE CARLO UNCERTAINTY ANALYSIS Calculations similar to that described in the previous subsection were repeated using different
[
values of the uncertain parameters and the results accumulated to develop uncertainty distributions for the predicted aerosol behavior. Calculations, or sampling of the uncertainty distributions, was continued until there was a 99 percent confidence that 95 percent of the
[
range of predicted aerosol behavior had been sampled.
Uncertainty distributions were developed for the decontamination factors for both gap release
{
and in-vessel release materials at five selected times--1800, 6480,13600,49680 and 86450 seconds. The accumulated values of these decontamination factors were analyzed using nonparametric order statistics to duelop uncertainty distributions at selected levels of confidence. More details on the conctruction of these uncertainty distributions are presented in Appendix A of Reference 5. The uncertainty distributions consist of ranges of values that correspond to percentiles of the distribution. Percentiles so characterized are at 5 percent intervals from 5 percent to C5 percent. The widths of the ranges of values depend on the selected confidence level. Here, distributions were developed for confidence levels of 50 and 90 percent. That is. there is a 50 and a 90 percent confidence, respectively, that the true value of the decontamination factor corresponding to the specified percentile of the distribution falls within the indicated ranges and, consequently, a 50 and a 10 percent probability, respectively, that the true value is above or below the indicated range.
An example uncertainty distribution is shown in tabulated form in Table 3. Tabulations of
[
other distributions generated in this work are collected in Appendix B. Distributions for the decontamination factors for gap release material at various times are shown graphically in Figure 9.
31
{
Table 3. Uncertainty Distribution of the Decontamination Factor
{
for Gap Release Material at 86450 Seconds.
Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Confidence I2 vel, C, of Percentile C= 90%
C=50%
5 509.4 to 728.8 565.8 to 640.4 10 633.6 to 820.4 729.8 to 774.2 15 757.5 to 921.4 804.8 to 837.6
[
20 821.4 to 980.2 840.6 to 933.1 25 900.1 to 1029 933.1 to 992.3 30 951.0 to 1087 993.7 to 1062 35 1010 to 1165 1061 to 1117 40 1069 to 1418 1110 to 1278 45 1156 to 1554 1259 to 1465 50 1283 to 1622 1439 to 1568 55 1476 to 1746 1567 to 1651 60 1584 to 1897 1637 to 1748
[
65 1663 to 2145 1747 to 1964 70 1750 to 2319 1958 to 2198 75 1981 to 2560 2200 to 2394 f
80 2226 to 2673 2405 to 2604 85 2517 to 3118 2605 to 3002 90 2730 to 3816 3052 to 3488 95 3488 to 4515 3816 to 4011 f
32 W,
-a c
r m
r r
t__r m
r wj 95 l6480//
,H
,/
9 85
)l f
- V,h' HlW'
('H!
1
,y'
,i, ln
,i lw
?
13680 lI
/"!
~
p 75
~
M
?:
lW 3
65 W,
,4'
,!H!
cn n{
lnl h<l
,I '
8 55
,k' li 9
O h',i
,/d,
,/a,'
l Cr a-45
- n:
lH) g ji ini 49680
,Lj
,'i
,b//
lt' d
[
35 H
i
,4,
,M, a
25
,(
.4,,
jy c
D
,l
,t,
,n, i
xa 15
,4,
,1f
/I 86450 U
V],
,il lt' j w' 5
II
'l
,'H l
,,,,i
,,,,,,,i
- 1. 0 10 100 1000 10000 i
i DECONTAMINATION FACTOR 1
Figure 9. Uncertainty Distributions for the Gap Release Decontamination Factor at Selected Times.
The uncertainty distributions can be summarily described in terms of values for selected percentiles. Here the median or 50 percentile value is taken to be the "best estimate" of the decontamination factor. " Reasonable upper bound" and " reasonable lower bound" values are taken to be the 90 and 10 percentile values, respectively. These features of the various uncertainty distributions for the decontamination factors are summarized in Table 4. Also shown in the table are mean values which are of interest to some.
For some purposes, the effective decontamination coefficient is of more interest than the decontamination factor. Effective decontamination coefficients, A (t), are parameters that e
arise in the formal differential equation:
d DF(t) = A (t) DF(t) e dt where DF(O is the decontamination factor.
The effective decontamination coefficients are distinct from instantaneous decontamination coefficients, A(t), that are parameters in the formal differential equation:
= - A(t)M(t) + $(t) dt where M(t) = suspended aerosol mass, and
$(t) = aerosol source to the containment.
I The effective decontamination coefficient subsumes the effects of any aerosol source term.
Consequently, when a source is active the effective decontamination coefficient is less than l
the instantaneous decontamination coefficient. When there is no source term, the effective decontamination coefficient and the instantaneous decontamination coefficient are the same.
l Here, effective decontamination coefficients for selected time intervals from t(i) to t(0 were calculated from:
DF(t(0) = 1, gt(g _,(;))
In
(
DF(t(i))
l where DF(t) = decontamination factor at time t, and l
A, = effective decontamination coefficient.
These effective decontamination coefficients average over the substantial, transient variations in the decontamination coefficients shown in Figure 7 for an example calculation. Notice that this formulation for the effective decontamination coefficient subsumes that source rate as a process that mitigates decontamination. TF mfore, during periods of aerosol release, it is 1
E M
~
Table 4. Summary of Uncertainty Distributions of the Decontamination Factors at Selected Times Range of Values of DF(t) Corresponding to Various Percentiles, P, of the Uncertainty Distributions Best Estimate Upper Bound **
Lower Bound **
Time (s)
Mean (P=50%)
(P=90%)
(P=10%)
Gap Release 1800 1.2055 1.204 - 1.205 1.222 - 1.229 1.183 - 1.192 6480 2.0921 1.075 - 1.087 2.219 - 2.291 1.910 - 1.984 l
13680 5.3641 5.100 - 5.241 6.580 - 7.328 4.108 - 4.412 49680 74.27 65.99 - 72.22 108.2 - 131.1 39.74 - 44.8 86450 1740 1439 - 1568 2730 - 3816 633.6 - 820.4 In-Vessel Release 6480 1.2615 1.260 - 1.261 1.286 - 1.302 1.222 - 1.240 13680 3.227 3.096 - 3.145 4.217 - 4.295 2.583 - 2.719 49680 44.96 38.85 - 43.16 65.17 - 77.35 25.30 - 27.63 86450 1034 878.3 - 946.6 1600 - 21.67 399.5 - 507.5
- 0% confidence level.
5
- 90% confidence level.
l 35
possible to get decontamination coefficients that are not positive, though this did not occur in the calculations reported here. The formulation for the effective decontamination coefficients does mean that during the period of in-vessel release there are distinct values of the effective decontamination coefficient for gap release material and the effective decontamination coefficient for in-vessel release material. After 6480 seconds, the effective decontamination coefficients for these materials are the same.
Results of the Monte Carlo analyses were recalculated in terms of the effective decontamination coefficients for the time intervals 0-1800,1800-6480, 6480-13680,13680-49680,49680-86450 seconds. The uncertainty distribeSns for these effective decontamination coefficients are summarily desc' bed ii. Table 5. The detailed uncertainty distributions are listed in Appendix B. Uncertauty distributions for the effective decontamination coefficients for gap release material during selected time intervals are shown in Figure 10.
The distributions found for the decontamination factors and the effective decontamination coefficients for the 3BE accident in the AP600 reactor are narrower than distribution found in analysis of generalized accidents at existing light water reactors [4]. Typically, conservative, lower bound values of the effective decontamination coefficient are only 10 to 15 percent less than the median or best estimate values. This, of course, is because the accident boundary j
conditions have been fixed in the calculations for the AP600 reactor accident. Boundary conditions have such important effects on aerosol behavior that uncertainties in boundary 4
conditions during hypothesized accidents at existing light water reactors contribute significantly to uncertainties in predictions of aerosol behavior.
The effective decontamination coefficients found in the uncertainty analysis for the 3BE accident are compared in Table 6 to those found in the preliminary analysis. The effective decontamination coefficients found for the 3BE accident are substantially larger than values found in preliminary analyses. This is because continued cooling of the containment shell of the AP600 reactor maintains high rates of steam condensation. Consequently, there is a high rate of diffusiophoretic aerosol deposition from the containment atmosphere. In analyses of aerosol behavior in existing light water reactors, the containment boundary is heated so that diffusiophoresis makes a decreasing contribution to aerosol removal as an accident progress.
C. COMPARISON TO NAUAHYGROS RESULTS Predictions of acrosol behavior in the 3BE accident obtained with the NAUAHYGROS computer model are available m tabulated values of the instantaneous decontamination coefficient. These values are puted in Figure 11 against time. The decontamination coefficients shown in tN fqure have some qualitative similarity to the values shown in Figure 7 for an example calculation with the model used for the Monte Carlo uncertainty analysis. That is, there is a fairly smooth decrease in the decontamination coefficient over the interval 0 to 1800 seconds. After about 3500 seconds, there are sharp variations in the decontamination coefficient that parallel variations in the boundary conditions. The most striking difference in the variations of the decontamination coefficient with time calculated with the NAUAHYGROS code and values of the decontamination coefficients calculated for 36
Table 5. Summary of Uncertainty Distributions of the Effective Decontamination Coefficients Range of Values of A,(hr-I) Corresponding to Various Percentiles, P, of the Uncertainty Distributions Best Estimate Upper Bound **
Lower Bound **
Time interval (s)
Mean (P = 50%)
(P = 90%)
(P = 10%)
0-1800 0.374 0.371 to 0.373 0.402 to 0.413 0.336 to 0.351 1800-6480 0.423 0.419 to 0.422 0.458 to 0.479 0.368 to 0.392 (gap release) 1800 to 6480 0.178 0.178 to 0.178 0.193 to 0.203 0.154 to 0.166 (In-vessel release) 6480 to 13680 0.463 0.443 to 0.455 0.566 to 0.604 0.371 to 0.397 13680 to 49680 0.257 0.257 to 0.262 0.279 to 0.290 0.225 to 0.232 49680 to 86450 0.301 0.297 to 0.299 0.327 to 0.340 0.267 to 0.279
- at 50% confid:nce.
- at 90% confidence.
37
I I
I I
I I
95
,4
,1
/m
-m, ,-
lq ln' Q
85
- h
- kl fi,-v' kl 7,Ql kj&, /g f k
m,-
75 49680 to 86450il U
\\ 'N 1800
- d 65
- gi
?!/H,/
to 6480 'W IH/
m
/Hf 6480-13680 s _
55 j,E Hj
,k jfH/
c.
45 w
k,k I/
W
[
35 s
.g
/
a 25 4
,k' o
i x
o 15
'A',
u jj l
5 k'
I i
e i
i t
j O.1
- 0. 3
- 0. 5
- 0. 7 DECONTAMINATION COEFFICIENT (hr-1)
Figure 10. Uncertainty Distributions for the Effective Decontamination Ccefficients for Gap Release Material at Selected Times.
1
Table 6. Comparison of Effective Decontamination Coefficients Found for the 3BE Accident to those Found in the Preliminary Analysis l
l (hr-l) for 3BE Accident A (hr-I) from Preliminary Analysis e
e 10 to 90 Percentile Best 10 to 90 Percentile Time Interval (s)
Best Estimate Range Estimate Range 0-1800 0.372 i 0.001 0.336 to 0.413 0.0335 0.0245 to 0.0434 1800-6480 0.420 i 0.001 0.368 to 0.479 0.0383 0.0270 to 0.0517 a*
(gap release) 1800 to 6480 0.178 i 0.001 0.154 to 0.203 0.0733 0.054 to 0.102 (In-vessel release) i 6480 to 13680 0.449 i 0.006 0.371 to 0.604 0.170 0.0765 to 0.418 l
13680 to 49680 0.260 i 0.003 0.225 to 0.290 0.151 0.101 to 0.I89 49680 to 86450 0.298 0.001 0.267 to 0.340 0.0912 0.085 to 0.101
_o
l 1.00 m
~
UNCERTAINTY ANALYSIS - PART 1 I
t.
_r EFFECTIVE VALUES v
l g
O.75 0
TIME AVERAGED VALUE l
o L
]
s f
1 L
~
f u.
u-o 0
tu 8
0.50 Z
8 g
t O.25 NAUAHYGROS U
^ _
8 Z
x INSTANTANEOUS VALUES 0
TIME AVERAGED VALUES H
Z C3 U
y
...iii 100 1000 10000 100000 TIME (SECONOS)
Figure 11. Instantaneous Values of the Decontamination Coe.fficient Calculated with the NAUAHYGROS Computer Code. Time-average values of the decontamination coefficients are plotted as open symbols. Effective decontamination coefficients calculated in the uncertainty analysis are shown as filled symbols.
the example calculation shown in Figure 7 is that values calculated with NAUAHYGROS for times greater than about 6000 seconds are noticeably higher. Also, at late times, the decontamination coefficients calculated with.NAUAHYGROS vary less with variations in the boundary conditions than do values found in the uncertainty analysis calculations.
The tabu %ted values of the decontamination coefficients calculated with the NAUAHYGROS computer model reflect the significant variations with time in the boundary conditions including the transient spikes in these boundary conditions. To compare results obtained with the NAUAHYGROS computer code to the uncertainty distributions obtained here for the effective decontamination coefficients, the instantaneous values of the decontamination coefficients were time-averaged over the intervals 0-1800,1800-6480, 6480-13680, 13680-49680 and 49680-86450 seconds. These average values are plotted at the midpoint of their respective time intervals as open symbols in Figure 11. The values are compared to the medians, upper bounds and lower bounds of the uncertainty distributions for the effective decontamination coefficients in Table 7. Note that the comparison is not quite appropriate for the 0-1800 second interval. Values for the effective decontamination coefficient during this time interval include the effect of the gap release which is not included in the averaged values of the instantaneous decontamination coefficient. Other comparisons shown in the table including that for the 1800 to 6480 second time interval are not affected by the release.
l A second uncertainty analysis was done to compute the uncertainty distribution for the time-l averaged decontamination coefficient for the 0 to 1800 second period that could be directly compared to results of the NAUAHYGROS calculation. This second uncertainty analysis yielded a median time-averaged decontamination coefficient of 0.530 hr'I. The 10 percentile and 90 percentile values were found to be 0.488 and 0.585 hr-I, respectively. These values f
can be compared to 0.564 0.007 hr-I found for the 0 to 1800 second interval with the NAUAHYGROS computer code. This point value found with the NAUAHYGROS code falls at about the 80 percentile the uncertainty range found in the uncertainty analysis. It is evident then that the discrepancies between results obtained with the NAUAHYGROS computer code and results of the uncertainty analysis are not enormous at the beginning of the accident calculation, but these discrepancies increase as the accident calculation progresses.
Though the effective decontamination coefficients calculated in the Monte Carlo analysis of j
the 3BE accident are larger than what was calculated with general and uncertain boundary condition [4], they are not as large as values calculated with the NAUAHYGROS computer I
code [12]. In fact, values calculated with NAUAHYG)w or times after 1800 seconds exceed the 90 percentile of the uncertainty distributions calculated here.
The discrepancy between values calculated in the Monte Carlo uncertainty analysis and values calculated with the NAUAHYGROS code increases as the accident progresses until the last time interval considered here,49680 to 86450 seconds. Decontaminatior coefficients calculated with the NAUAHYGROS code remain high in the later phases of the accident. The
{
reasons for this are not yet known, but it is likely that gravitational settling makes a bigger predicted contribution to aerosol removal in the NAUAHYGROS calculations because a much larger nonradioactive source term of aerosols has been hypothesized for the NAUAHYGROS l
calculations than the range of nonradioactive source terms considered in the Monte Carlo uncertainty analysis. Calculations to confirm this speculation have been initiated.
(
41
l l
Table 7. Comparison of Effective Decontamination Coefficients to Averaged Values Obtained l
with the NAUAHYGROS Code i
Effective Decontamination Coefficient (hr-I)
Time-Averaged Instantaneous Values From MedianY Y
Y Upper Bound lower Bound Time Interval (s)
NAUAHYGROS* (hr-3)
(50 percentile)
(90 percentile)
(10 percentile) 0-1800**
0.5645 i 0.0074 0.372 i 0.001 0.408 i 0.006 0.344 i 0.008 1800-6480 0.5410 i 0.0091 0.420 i 0.002 0.468 1 0.010 0.380 i 0.012 6480-13680 0.6849 0.0152 0.449 i 0.006 0.585 i 0.019 0.384 0.013 13680-49680 0.5392 0.0082 0.260 1 0.003 0.284 0.006 0.228 i 0.004 49680-86450 0.4816 i 0.0032 0.298 i 0.001 0.334 i 0.006 0.273 i 0.005
, Standard deviation cited h:re is the_ square root of the time-weighted variance about the mean.
Effective decontamination coefficients for the 0-1800 s interval include the effect of gap release and are expected to be less
+than the time weighted average of instantaneous values.
Value is the midpoint of the range and the listed uncertainties define the range which is a 50 percent confidence interval for the median and a 90 percent confidence interval for the upper and lower bounds.
9
{
IV. CONCLUSIONS
{
Boundary conditions appropriate for accidents in the AP600 reactor significantly increase the predicted effective decontamination coefficients by natural aerosol processes from values
(
calculated in preliminary analyses. The increase is due to enhanced diffusiophoresis that is maintained throughout the accident by cooling the containment shell. Fixing the boundary conditions so that they do not vary in the Monte Carlo sampling to construct uncertainty distributions significantly narrows the distributions found for the effective decontamination coefficients.
Establishing the validity of the boundary conditions for the 3BE accident that produce the higher rates of aerosol removal is outside the domain of work considered here.
[
Though higher effective decontamination coefficients have been calculated using fixed boundary conditions for a particular, hypothetical accident, these decontamination coefficients are still smaller than decontamination coefficients calculated for the same accident with the NAUAHYGROS code. The decontamination coefficients calculated with the NAUAHYGROS code exceed the 90 percentiles of the uncertainty distributions for the effective decontamination coefficients calculated here. The cause of the remaining discrepancies has not been positively identified. The nature of the discrepancies suggests that NAUAHYGROS is predicting more aerosol removal by gravitational settling than is the model used for the Monte Carlo uncertainty analysis. A much larger source term of
[
nonradioactive aerosol mass has been hypothesized in the NAUAHYGROS analysis of the 3BE accident than that used in the Monte Carlo calculations. This larger, nonradioactive source term may be responsible for predictions of larger decontamination coefficients by the f
NAUAHYGROS code. An additional set of calculations to confirm this speculation l'as been initiated.
V. REFERENCES 1.
L. Soffer, et al., Accident Source Terms for Licht-Water Nuclear Power Plants,
' NUREG-1465, U.S. Nuclear Regulatory Commission, Washington, D.C. 1995.
[
2.
J. J. DiNunno, et al., Calculation of Distance Factors for Power and Test Reactor Sites, TID-14844, U.S. Atomic Energy Commission, Washington, D.C. 1962.
(
3.
D. A. Powers and S. B. Burson, A Simplified Model of Aerosol Removal by Containment Sorays, NUREG/CR-5966, SAND 92-2689, Sandia National Laboratories, Albuquerque, NM, June 1993.
f 4.
D. A. Powers, K. E. Washington, S. B. Burson, and J. L. Sprung, A Simplified Model of Aerosol Removal by Natural Processes in Reactor Containments, NUREG/CR-6189,
[
SAND 94-0407, Sandia National Laboratories, Albuquerque, NM.
L 43 r
5.
D. A. Powers and J. L. Sprung, A Simolified Model of Aerosol Scrubbine by a Water j
Pool Over1 vine Core Debris Interactine with Concrete, NUREG/CR-5901, SAND 92-l 1422, Sandia National Laboratories, Albuquerque, NM, August 1992.
6.
D. A. Powers, Source Term Attenuation by Water in The Mark I. Boiline Water Reactor Drvwell, NUREG/CR-5878, SAND 92-2688, Sandia National Laboratories, i
Albuquerque, NM, September 1993.
7.
R. S. Denning, et al., Radionuclide Release Calculations for Selected Severe Accident Scenarios. PWR. Subatmosoberic Containment Desien, NUREG/CR-4624, BMI-2139, Vol. 3, Battelle's Columbus Division, Columbus, Ohio, July 1986.
8.
R. S. Denning, et al., Radionuclide Release Calculations for Selected Severe Accident Scenarios. PWR Large Dry Containment Design. NUREG/CR-4624 BMI-2139, Vol. 5, Battelle's Columbus Division, Columbus. Ohio, July 1986.
9.
R. S. Denning, et al., Badionuchde Release Calculations for Selected Severe Accident Scenarios. Supplemental Calculations, NUREG/CR-4624, BMI-2139, Vol. 6, Battelle's Columbus Division, Columbus, Ohio, August 1990.
10.
M. T. Leonard, et al., Sunnlemental Radionuclide Release Calculations for Selected Severe Accident Scenarios, NUREG/CR-5062, BMI 2160, Battelle Columbus Division, Columbus, Ohio, February 1988.
- 11. J. A. Gieseke, et cl., Radionuclide Release Under Snecific LWR Accident Conditions Volume V. PWR-Large. Dry Containment Design (Surry Plant Recalculations) BMI-2104, Volume V, Battelle Columbus Iaboratories, Columbus, Ohio, July 1984.
- 12. I.etter from N. J. Liparulo to T. R. Quary, dated April 7,1995, entitled, "Information i
Requested by RAI 40.23 Regarding Input Parameters for the Calculation of Aerosol Removal Coefficients, NTD-NRC-95-4430, DCP/NRC0302, Docket No. STN-52003.
13.
R. Sher and J. Jokiniemi, NAUAHYGROS 1.0: A Code for Calculatine the Behavior of Hygroscopic and Nonhygrosconic Aerosols in Nuclear Power Plant Containments
]
Followine a Severe Accident, EPRI TR-102775, Electric Power Research Institute, Palo Alto, CA,1993.
14.
M. L. Corradini, Nuclear Technology 64 (1984) 186.
- 15. Office of Nuclear Regulatory Research, Severe Accident Risks: An Assessment for Five U. S. Nuclear Power Plants, NUREG-Il50, U.S. Nuclear Regulatory l
Commission, Washington, D.C., June 1989.
16.
R. J. Lipinski, et al., Uncertainty in Radionuclide Release Under Snecific LWR l
Accident Conditions, SAND 84-0410, Volume 2, Sandia National Laboratories, Albuquerque, NM, February 1985.
44
l APPENDIX A.
TABULATIONS OF BOUNDARY CONDITIONS INPUT TO TIIE MECIIANISTIC MODEL USED FOR TIIE MONTE CARLO UNCERTAINTY ANALYSIS Tabulated values for the 3BE accident boundary conditions:
containment pressure containment atmosphere temperature a
mole fraction steam in the containment atmosphere rate of steam condensation from the containment atmosphere a
rate of heat removal from the containment atmosphere e
were provided by Westinghouse Electric Corporation. These boundary condition specifications were input to the mechanistic model of aerosol behavior and held invariant during the uncertainty analyses. The tabulated values are reproduced from the mechanistic code so that they may be checked for accuracy.
The tabulated values were used in the units as provided except atmosphere temperatures were converted from celsius to Kelvin by adding 273.15 and heat removal rates were converted 7
from ergs /second to calories /second by dividing by 4.184 x 10.
Linear interpolation of the tabulated values was used to provide values for the fourth order Runge-Kutta routine with automatic step-size control used to solve the aerosol behavior equations. Plotted values in Figures 1 - 6 of the main text were also generated by the linear interpolation process.
i s
A-1
[
Table A-1. Containment Pressure TIME PRESSURE TIME PRESSURE (SECONDS)
(ata)
(SECONDS)
(at m) 1 0
2.293 41 5221 1.870 2
725 2.277 42 5631 1.899 3
930 2.255 43 5731 1.917 4
1034 2.241 44 5931 1.905
(
5 1140 2.226 45 6031 1.891 6
1243 2.212 46 7651 2.089
(-
7 1346 2.196 47 7761 2.010 8
1449 2.180 48 7861 1.968 9
1551 2.162 49 7971 1.942
(
10 1655 2.145 50 8081 1.925 11 1758 2.126 51 8281 1.912
(
12 1861 2.107 52 8891 1.898 13 1965 2.087 53 8991 1.882 14 2066 2.070 54 9091 1.866
[
15 2167 2.050 55 9191 1.851 16 2267 2.032 56 9291 1.836 17 2368 2.015 57 9391 2.029 18 2468 1.999 58 9491 1.941 19 2568 1.984 59 9591 1.888 20 2670 1.968 60 9691 1.855 21 2772 1.956 61 9791 1.872
[
22 2874 1.940 62 9891 1.900 23 2976 1.925 63 9991 1.936 24 3076 1.912 64 10090 1.975 25 3178 1.897 65 10190 1.998
{
26 3279 1.884 66 11100 1.988
(
27 3379 1.871 67 11500 1.974 28 3480 1.858 68 11700 1.958 29 3581 1.847 69 11800 1.946 30 3682 1.835 70 11910 1.931
{
31 3882 1.974 71 12010 1.915
(
32 3983 1.996 72 12110 1.897 33 4085 1.952 73 12210 1.881 34 4188 1.912 74 12310 1.865 35 4289 1.886 75 12410 1.851
{
36 4391 1.867 76 12510 1.838
(
37 4491 1.852 77 12710 1.816 38 4701 1.835 78 12810 1.989 i
39 4911 1.825 79 12910 1.911 r
40 5111 1.851 80 13010 1.859 L
A-2 c
1:
Table A-1. Containment Pressure (Continued) f TIME PRESSURE TIME PRESSURE (SECONDS)
(atm)
(SECONDS)
(ata) 81 13110 1.827 121 18750 1.424
{.
82 13210 1.799 122 19050 1.415 83 13310 1.777 123 19360 1.407 84 13420 1.762 124 19860 1.396 f
85 13520 1.903 125 20160 1.388 86 13623 1.831 126 20760 1.380
{
87 13720 1.787 127 21570 1.373 88 13820 1.752 128 22370 1.365 89.
13920 1.728 129 23670 1.358 f.
90 14020 1.710 130 24980 1.366
[
91 14120 1.697 131 25780 1.376 I
92 14220 1.678 132 25880 1.416 93
-14320 1.667 133 25980 1.497 94 14430 1.657 134 26080 1.564
{
95 14530 1.648 135 26180 1.596
[-
96 14630 1.639 136 26280 1.615 l
97 14730 1.920 137 26380 1.627 98 14830 1.796 138 26480 1.638 99 14930 1.724 139 26580 1.648 f.
100-15030 1.678 140 26680 1.660 101 15130 1.645 141 26780 1.673 102 15230 1.622 142 26880' 1.687 103 15330 1.604 143 26990 1.697 104 15430 1.588 144 27590 1.708 105 15530 1.576 145-27790 1.723 r.
106 15630 1.565 146 27990 1.735 t
107 15730 1.555 147 28290 1.744 108 15840 1.547 148 28700 1.755 109 15940 1.539 149 29800 1.745 110 16140 1.530 150 30000 1.734
[
111 16240 1.521 151 30200 1.720 r
[
112 16440 1.511 152 30400 1.705 113 16640 1.500 153 30600 1.692 114 16840 1.489 154 30800 1.679 115 17140 1.479 155 31000 1.667
{
116 17440 1.470 156 31200 1.655 117 17650 1.461 157 31410 1.643 j
118 17850 1.453 158 31610 1.633 1
119 18050 1.444 159 31810 1.623 120 18450 1.432 160 32110 1.611
. A-3 J
1
Table A-1. Containment Pressure (Concluded)
TIME PRESSURE (SECONDS)
(atn>
161 32410 1.600 162 32710 1.590 163 33010 1.582 164 33410 1.574 165 33910 1.566 i
166 34920 1.558 167 36120 1.550 168 37820 1.542 169 42940 1.550 170 44940 1.558 171 47150 1.566 172 49250 1.574 173 51460 1.582 174 53770 1.590 175 55980 1.598 176 58990 1.606 177 62800 1.615 178 67610 1.624 179 72830 1.633 180 78860 1.642 181 86490 1.649 i
1 A-4
[
Table A-2. Containment Atmosphere Temperature f
TIME TEMPERATURE TIME TEMPERATURE (SECONDS)
(K)
(SECONDS)
(K)
[
81 12110 381.1 121 18450 381.3 t
82 12210 380.3 122 18650 382.5 83 12310 379.6 123 18750 381.8 84 12410 379.0 124 18950 382.8 85 12810 415.9 125 19050
?82.0
[
86 12910 409.2 126 19260 382.8 87 13010 401.2 127 19360 381.9 88 13110 396.0 128 19860 380.9 89 13210 391.4 129 20160 379.8 90 13310 388.7 130 20360 379.1 r
91 13420 386.9 131 20760 378.5 l
92 13520 424.2 132 20860 379.1 93 13620 412.5 133 20960 378.2 94 13720 403.9 134 21070 378.9
[
95 13820 397.1 135 21170 378.0 96 13920 393.1 136 21270 378.7
(
97 14020 390.3 137 21370 377.8 98 14120 388.3 138 21470 378.5 99 14220 385.9 139 21570 377.6 100 14320 384,8 140 21670 378.2
[
101 14430 384,1 141 21770 377.3 f
102 14530 383.5 142 21870 378.0 103 14730 467.6 143 21970 377.2 104 14830 437.1 144 22570 376.4 105 14930 419.3 145 22670 377.0
[
106 15030 407.9 146 22770 376.3 107 15130 400.3 147 23170 377.2
(
108 15230 395.0 148 23270 376.3 109 15330 391.4 149 23370 377.0 110 15430 388.6 150 23470 376.2 111 15530 386.6 151 25180 375.2 112 15630 385.0 152 25280 375.9
[
113 15730 383.7 153 25380 375.3 114 15840 382.8 154 25480 376.2 115 15940 382.0 155 25580 375.5 116 16b40 381.2 156 25780 376.4 117 16340 380.3 157 25880 379.8
{
118 16540 381.0 158 25980 384.4 119 16640 380.4 159 26080 386.7 120 18250 382.3 160 26280 385.4 p
L A-5 f
Table A-2. Containment Atmosphere Temperature (Continued)
TIME TEMPERATURE TIME TEMPERATURE (SECONDS)
(K)
(SECONDS)
(K) 1 0
380.8 41 7651 429.8 2
621 380.1 42 7761 423.2 3
1140 379.5 43 7861 413.2 4
1551 378.7 44 7971 406.5 5
1758 377.7 45 8081 401.6 6
1965 376.6 46 8181 398.7 7
2167 374.8 47 8281 396.5 8
2976 374.2 48 8381 394.7 9
3581 373.6 49 8481 393.4 10 3782 375.5 50 8581 392.5 11 3882 406.4 51 8691 391.4 12 3983 417.9 52 8791 390.5 13 4085 411.6 53 8891 389.1 14 4188 404.7 54 8991 387.4 15 4289 400.6 55 9091 386.0 16 4391 397.8 56 9191 384.7 17 4491 395.9 57 9291 383.4 18 4701 394.4 58 9391 419.5 19 5011 396.6 59 9491 416.7 20 5111 402.2 60 9591 408.1 21 5221 407.6 61 9691 402.4 22 5531 408.3 62 9791 401.7 23 5631 415.5 63 9891 400.8 24 5731 420.7 64 10090 399.4 25 5931 416.7 65 10190 397.7 26 6031 411.6 66 10300 395.5 27 6131 407.8 67 10400 3o4.0 28 6231 404.8 68 10500 392.7 29 6341 402.7 69 10600 391.4 30 6441 401.2 70 10700 390.2 31 6541 399.8 71 10800 389.4 32 6641 398.4 72 10900 388.6 33 6741 397.2 73 11000 387.9 34 6841 396.4 74 11200 387.3 35 6941 395.6 75 11400 386.4 36 7041 394.5 76 11600 385.4 37 7141 393.5 77 11700 384.8 38 7241 392.6 78 11800 384.0 39 7341 391.9 79 11910 383.0
[
40 7451 391.3 80 12010 382.0 l
A6 l
Table A-2. Containment Atmosphere Temperature (Concluded)
TIME TEMPERATURE l
(SECONDS)
.(K) i i
161 26380 384.3 162 26480 383.4 163 26580 382.6 164 26780-381.8 165 27090 381.1 166 27190 380.4 167 27390 379.6 168 27790 380.3 169 28500 379.7 170 29400 378.9 171 29600 378.3 172 29900
' 377.6 173 30100 376.9 174 30300 376.3 175 30600 375.6 f
176 31000 374.9 177 31510 374.3 178 32310 373.7 179 34010 373.1 180 35720 372.6 181 37020 372.1 182 38630 371.6 183 43340 371.1 184 864900 371.1 f
l l
A-7
i t
i Table A-3. Mole Fraction Steam in the Containment Atmosphere TIME MOLE FRACTION TIME MOLE FRACTION (SECONDS)
STEAM (SECONDS)
STEAM l
1 0
0.5423 41 5011 0.3624 2
826 0.5384 42 5221 0.3596 3
1034 0.5331 43 5431 0.3575 4
1140 0.5301 44 6031 0.3600 5
1243 0.5270 45 6231 0.3623 6
1346 0.5238 46 6441 0.3654 l
7 1449 0.5204 47 6641 0.3684 8
1551 0.5169 48 6841 0.3726 9
1655 0.5132 49 6941 0.3753 l
10 1758 0.5094 50 7141 0.3780 l
11 1861 0.5054 51 7341 0.3800 l
12 1965 0.5011 52 7651 0.3857 13 2066 0.4967 53 8181 0.3886 14 2167 0.4906 54 8481 0.3915 i
l 15 2267 0.4838 55 8691 0.3935 16 2368 0.4767 56 8991 0.3885 l
17 2468 0.4699 57 9091 9.3852 18 2568 0.4632 58 9191 u.3816 19 2670 0.4566 59 9291 0.3776 20 2772 0.4502 60 9491 0.3737 21 2874 0.4442 61 9591 0.3685 22 2976 0.4387 62 9691 0.3641 23 3076 0.4332 63 9791 0.3693 24 3178 0.4275 64 9891 0.3806 25 3279 0.4218 65 9991 0.3917 26 3379 0,.4162 66 10090 0.4014 l
27 3480 0.4107 67 10190 0.4090 28 3581 0.4053 68 10300 0.4139 29 3682 0.3999 69 10400 0.4186 30 3782 0.3947 70 10500 0.4219 31 3882 0.3917 71 10700 0.4243 f
32 3983 0.3879 72 11600 0.4211 i
33 4085 0.3832 73 11800 0.4166 34 4188 0.3792 74 11910 0.4134 35 4289 0.3763 75 12010 0.4096 36 4391 0.3738 76 12110 0.4053 37 4491 0.3715 77 12210 0.4008 38 4601 0.3694 78 12310 0.3963 39 4701 0.3670 79 12410 0.3919 l
40 4811 0.3651 80 12510 0.3875 l
A-8 l
f Table A-3. Mole Fraction Steam in the Containment Atmosphere (Continued)
TIME MOLE FRACTION TIME MOLE FRACTION (SECONDS)
STEAM (SECONDS)
STEAM
[
81 12610 0.3832 121 16840 0.2628 I
82 12710 0.3787 122 16940 0.2605 83 12910 0.3739 123 17040 0.2582 84 13010 0.3683 124 17140 0.2559 l
85 13110 0.3638 125 17240 0.2537 86 13210 0.3594 126 17340 0.2515 87 13310 0.3554 127 17440 0.2493 l
88 13420 0.3516 128 17540 0.2472 89 13620 0.3479 129 17650 0.2450 90 13720 0.3436-130 17750 0.2429 91 13820 0.3396 131 17850 0.2409 92 13920 0.3360 132 17950 0.2389 93 14020 0.3325 133 18050 0.2370 94 14120 0.3293 134 18150 0.2351 95 14220 0.3258 135 18250 0.2335 96 14320 0.3226 136 18350 0.2318 f
97 14430 0.3194 137 18450 0.2300 98 14530 0.3163 138 18550 0.2283 99 14630 0.3133 139 18650 0.2269 100 14730 0.3235 140 18750 0.2253
{
101 14860' O.3184 141 18850 0.2237 102 14930 0.3146 142 18950 0.2223 103 15030 0.3115 143 19050 0.2209 104 15130 0.3085 144 19150 0.2197 105 15230 0.3057 145 19260 0.2185 f
106 15330 0.3029 146 19360 0.2171 107 15430 0.3000 147 19560 0.2153 108 15530 0.2971 148 19760 0.2139 109 15630 0.2943 149 19960 0.2125 110 15730 0.2914 150 20160 0.2112 111 15840 0.2886 151 20460 0.2099 112 15940 0.2858 152 20960 0.2088 113 16040 0.2831 153 21670 0.2077 114 16140 0.2806 154 22270 0.2065 115 16240 0.2779 155 22970 0.2054 116 16340 0.2753 156 23970 0.2065 117 16440 0.2728 157 24370 0.2080 118 16540 0.2704 158 24680 0.2094 119 16640 0.2678 159 24880 0.2106 120 16740 0.2654 160 25080 0.2118 A-9
Table A-3. Mole Fraction Steam in the Containment Atmosphere (Continued)
TIME MOLE FRACTION TIME MOLE FRACTION (SEC0HDS)
STEAM (SECONDS)
STEAM 161 25280 0.2131 201 31510 0.3597 162 25480 0.2144 202 31610 0.3576 163 25680 0.2157 203 31710 0.3555 164 25780 0.2174 204 31810 0.3535 165 25880 0.2337 205 31910 0.3515 166 25980 0.2593 206 32010 0.3497 167 26080 0.2868 207 32110 0.3478 168 26180 0.3067 208 32310 0.3444 169 26280 0.3205 209 32510 0.3413 170 26380 0.3302 210 32710 0.3385 171 26480 0.3377 211 32910 0.3359 172 26580
~ 0.3442 212 33110 0.3336 173 26680 0.3506 213 33310 0.3315 174 26780 0.3568 214 33510 0.3297 175 26880 0.3633 215 33810 0.3274 176 26990 0.3693 216 34120 0.3255 177 27090 0.3712 217 34520 0.3237 178 27290 0.3733 218 35120 0.3220 179-27590 0.3781 219 35620 0.3203 180 27790 0.3833 220 36120 0.3186 181 27990 0.3878 221 36820 0.3169 182 28190 0.3913 222 37420 0.3152 183 28400 0.3935 223 38020 0.3136 184 28700 0.3969 224 42440 0.3152 185 29000 0.3991 225 43540 0.3168 186 29800 0.3970 226 44540 0.3184 187 30000 0.3944 227 45440 0.3200 188 30200 0.3906 228 46450 0.3217 189 30300 0.3883 229 47550 0.3235 190 30400 0.3860 230 48650 0.3252 191 30500 0.3835 231 49760 0.3270
)
192 30600 0.3811 232 50960 0.3287 I
193 30700 0.3787 233 52160 0.3304 194 30800 0.3762 234 53270 0.3322 195 30900 0.3737 235 54270 0.3340 19G 31000 0.3713 236 55270 0.3357 197 31100 0.3689 237 56380 0.3374 198 31200 0.3665 238 57680 0.3391 199 31300 0.3642 239 59190 0.3408 200 31410 0.3619 240 60890 0.3426 A-10 l
Table A-3. Mole Fraction Steam in the Containment Atmosphere (Concluded)
TIME MOLE FRACTION
~
(SECONDS)
STEAM 241 62700 0.3444 242 64600 0.3462 243 66810 0.3480 244 69320 0.3498 245 72230 0.3516 246 75040 0.3534 247 78760 0.3552 248 83580 0.3570 1
249 86490 0.3578 I
t i
I I
I I
I I
I
[
[
c L
A-ll E
l I
l Table A-4. Rate of Steam Condensation From the Containment Atmosphere l
TIME.
CONDENSATION TIME CONDENSRTION (SECONDS)
(S/s)
(SECONDS)
(9/s) 1 0
8302 41 4701 3677 i
2 521 8241 42 4811 3647 l
3 621 8137 43 5011 3710 l
4 725 8006 44 5111 3883-l 5
826 7889 45 5221 3990 l
l 6
930 7758 46 5321 3937 l
7 1034 7616 47 5431 3881 8
1140 7473 48 5531 3843 9
1243 7329 49 5631 4033 10 1346 7176 50 5731 4143 11 1449 7010 51 5831 4083 i
.12 1551 6849 52 5931 3980 l
13 1655 6673 53 6031 3873 i
l 14 1758 6493 54 6131 3831 15 1861 6303 55 6341 3854 16 1965 6119 56 6441 3894 17 2066 5951 57 6541 3926 l
18 2167
.5677 58 6641 3947 19 2267 5538 59 6741 3983 20 2368 5360 60 6841 4037 21 2468 5200 61 6941 4110 22 2568 5063 62 7241 4140 23 2670 4934 63 7451 4163 l
24 2772 4821 64 7651 7078 l
25 2874 4697 65 7761 5243 26 2976 4589 66 7861 4710 j
27 3076 4481 67 7971 4453 28 3178 4373 68 8081 4314 i
29 3279 4263 69 8181 4278 30 3379 4161 70 8581 4356 31 3480 4064 71 8791 4329 I
32 3581 3968 72 8891 4249 33 3682 3880 73 8991 4102 34 3882 5250 74 9091 3971 1
35 4085 4715 75 9191 3846 l
36
-4188 4287 76 9291 3724 37 4289 4010 77 9391 6237 i
38 4391 3860 78 9491 4611 39 4491 3764 79 9591 4041 l
40 4601 3729 80 9691 3708 4
A-12 I
[
Table A-4. Rate of Steam Condensation From the Containment Atmosphere (Continued)
[
TIME CONDENSATIDH TIME CONDENSATIOH l
(SECONDS)
(9/s)
(SECONDS)
(9/s) 81 9791 3867 121 14120 2576
(
82 9891 4255 122 14220 2487 83 9991 4750 123 14320 2437 84 10090 5266 124 14430 2392 85 10190 5613 125 14530 2350 86 10300 5641 126 14630 2307
[
87 10400 5594 127 14730 3945 88 10600 5599 128 14830 3011 89 10700 5488 129 14930 2503 90 10800 5417 130 15030 2232 91 10900 5344 131 15130 2075
{
92 11000 5290 132 15230 1980 93 11300 5240 133 15330 1920 94 11400 5176 134 15430 1876 95 11500 5103 135 15530 1845 96 11600 5016 136 15630 1818 97 11700 4911 137 15730 1794 98 11800 4772 138 15840 1772 99 11910 4603 139 15940 1750 100 12010 4420 140 16040 1729 101 12110 4238 141 16240 1699 102 12210 4095 142 16340 1670 103 12310 3973 143 16440 1660 104 12410 3865 144 16540 1647 105 12510 3761 145 16640 1610 106 12610 37S3 146 16740 1598 107 12710 3629 147 16840 1558
[
108 12810 5895 148 16940 1538 109 12910 4493 149 17040 1520 110 13010 3921 150 17140 1501
[
111 13110 3599 151 17240 1479 112 13210 3344 152 17340 1454 113 13310 3195 153 17440 1432 114 13420 3086 154 17540 1408 115 13520 4245 155 17650 1386 116 13620 3552 156 17750 1361 117 13720 3171 157 17850 1338
[
118 13820 2907 158 17950 1313 119 13920 2759 159 18050 1291 120 14020 2655 160 18150 1267
[
A-13 c
Table A-4. Rate of Steam Condensation From the Containment Atmosphere (Continued)
TIf1E CONDENSATION TIME CONDENSATION (SECONDS)
(9/s)
(SECONDS)
(9/s) 161 18250 1283 201 22770 1007 162 18350 1252 202 22870 1016 163 18450 1221 203 22970 1007 164 18550 1193 204 23070 1014 165 18650 1204 205 23170 1024 166 18750 1173 206 23270 1014 167 18850 1148 207 23370 1026 1
168 18950 1157 208 23470 1017 169 19050 1125 209 23570 1027 170 19150 1117 210 23670 1021 1
171 19360 1082 211 23770 1033 172 19460 1068 212 23970 1042 1
173 19660 1055 213 24170 1052 174 19760 1068 214 24370 1065 175 19860 1041 215 24580 1081 176 20160 1019 216 24780 1098 177 20360 1013 217 24980 1116 1
178 20460 1024 218 25280 1135 179 20560 1014 219 25480 1159 180 20660 1029 220 25780 1201 181 20760 1019 221 25880 1520 18-20860 1032 222 25980 2180 183 20960 1022 223 26080 2895 1
184 21070 1037 224 26180 3492 185 21170 1026 225 26280 3855 186 21270 1041 226 26380 4035 187 21370 1033 227 26480 4123 188 21470 1043 228 26580 4185 1
189 21570 1030 229 26680 4258 190 21670 1037 230 26780 4339 191 21770 1023 231 26880 4442 192 21870 1036 232 26990 4544 193 21970 1023 233 27090 4421 1
194 22070 1030 234 27190 4288 195 22170 1018 235 27290 4169 196 22270 1024 236 27390 4083 197 22370 1013 237 27490 4033 198 22470 1020 238 27590 4109 1
199 22570 1009 239 27790 4217 200 22670 1017 240 27990 4284 L-A-14
Table A-4. Rate of Steam Condensation From the Containment Atmosphere (Continued)
TIf1E CONDEt1 SAT 10t1 T I(1E CollDEl4S AT10t1 (SEC0t4DS)
(9/s)
(SEC0t4DS)
(9/s) 241 28400 4249 281 32910 2571 242 28500 4220 282 33010 2557 1
243 28700 4270 283 33110 2544 244 28900 4247 284 33310 2522 245 29300 4214 285 33510 2508 246 29400 4150 286 33910 2494 247 29500 4086 287 35720 2481 1
248 29600 4029 288 36120 2467 249 29700 3975 289 37020 2450 250 29800 3921 290 37320 2434 251 29900 3868 291 37620 2422 252 30000 3789 292 38330 2409 253 30100 3703 293 39230 2423 1
254 30200 3619 294 39730 2437 255 30300 3537 295 40230 2452 1
256 30400 3461 296 40730 2464 257 30500 3389 297 41330 2479 258 30600 3322 298 41830 2494 1
259 30700 3256 299 42340 2506 260 30800 3196 300 42840 2521 261 30900 3145 301 43340 2535 262 31000 3095 302 43740 2548 263 31100 3047 303 44240 2562 1
264 31200 3009 304 44740 2575 265 31300 2969 305 45240 2589 266 31410 2934 306 45740 2603 267 31510 2900 307 46250 2616 268 31610 2866 308 46850 2633 l
269 31710 2835 309 47350 2646 270 31810 2804 310 47950 2661 271 31910 2777 311 48550 2676 272 32010 2750 312 49150 2692 273 32110 2724 313 49760 2705 1
274 32210 2699 314 50260 2719 275 32310 2676 315 50860 2733 276 32410 2656 316 51560 2749 277 32510 2637 317 52260 2764 278 32610 2618 318 52860 2779 279 32710 2602 319 53370 2794 280 32810 2586 320 53870 2809 A-15
Table A-4. - Rate of Steam Condensation From the Containment Atmosphere (Concluded)
TIME CONDENSATION (SECONDS)
(s/s) 321 54470 2826 322 54970 2841 323 55570 2856 324 56180 2871 325 57080 2887 326 57880 2902 327 58780 2917 328 59690 2932 329 60590 2947 330 61490 2962 331 62500 2978 332 63500 2993 333 64500 3009 334 65710 3025 335 66910 3041 336 68320 3057 337 69820 3073 338 73340 3088 339 75140 3105 340 76950 3121 341 79160 3136 342 81570 3152 343 84380 3168 344 86490 3177
(
A-16
Table A-5. Rate of Heat Removal From the Containment Atmosphere TIME HEAT REMOVAL TIME HEAT REMOVAL (SECONDS)
(J/s)
(SECONDS)
(J/s) 1 0
2.0480E 07 41 4289 1.2900E 07 2
104 2.0750E 07 42 4391 1.2280E 07 3
206 2.0470E 07 43 4491 1.1900E 07 4
521 2.0340E 07 44 4601 1.1820E 07 5
621 2.0110E 07 45 4701 1.1600E 07 6
725 1.9800E 07 46 4811 1.1720E 07 7
826 1.9520E 07 47 4911 1.1530E 07 I
8 930 1.9170E 07 48 5011 1.1740E 07 9
1034 1.8860E 07 49 5111 1.2940E 07 10 1140 1.8520E 07 50 5221 1.3510E 07 11 1243 1.8190E 07 51 5321 1.3610E 07 12 1346 1.7850E 07 52 5431 1.3300E 07 13 1449 1.7450E 07 53 5631 1.4490E 07 I
14 1551 1.7100E 07 54 5731 1.5190E 07 15 1655 1.6660E 07 55 5831 1.4980E 07 16 1758 1.6220E 07 56 5931 1.4470E 07 17 1861 1.5750E 07 57 6031 1.3730E 07 18 1965 1.5310E 07 58 6131 1.3270E 07 I
19 2066 1.4910E 07 59 6231 1.2990E 07 20 2167 1.4220E 07 60 6341 1.2860E 07 21 2267 1.3930E 07 61 6541 1.2760E 07 22 2368 1.3530E 07 62 6641 1.2690E 07 23 2468 1.3180E 07 63 6941 1.3170E 07 I
24 2568 1.2880E 07 64 7041 1.2790E 07 25 2670 1.2590E 07 65 7241 1.2670E 07 26 2772 1.2380E 07 66 7341 1.2530E 07 27 2874 1.2120E 07 67 7451 1.2660E 07 28 2976 1.1880E 07 68 7651 2.6880E 07 29 3076 1.1660E 07 69 7761 1.8730E 07 30 3178 1.1410E 07 70 7861 1.6090E 07 31 3279 1.1190E 07 71 7971 1.4520E 07
{
32 3379 1.0940E 07 72 8081 1.3690E 07 33 3480 1.0760E 07 73 8181 1.3390E 07 34 3581 1.0540E 07 74 8281 1.3250E 07 35 3682 1.0380E 07 75 8381 1.3090E 07 36 3782 1.0440E 07 76 8791 1.2780E 07 37 3882 1.6270E 07 77 8891 1.2600E 07 38 3983 1.7560E 07 78 8991 1.2110E 07 39 4085 1.5720E 07 79 9091 1.1690E 07 40 4188 1.4030E 07 80 9191 1.1300E 07 A-17 1
Table A-5. Rate of Heat Removal From the Containment Atmosphere (Continued)
TIME HEAT REMOVAL TIME HEAT REMOVAL (SECONDS)
(J/s)
(SECONDS)
(J/s) 81 9291 1.0890E 07 121 13820 1.0200E 07 82 9391 2.3860E 07 122 13920 9.4940E 06 83 9491 1.6430E 07 123 14020 8.9950E 06 84 9591 1.3950E 07 124 14120 8.6360E 06 85 9691 1.2500E 07 125 14220 8.2710E 06 86 9791 1.2880E 07 126 14320 8.0850E 06 87 9891 1.3720E 07 127 14430 7.9370E 06 88 9991 1.4850E 07 128 14530 7.8140E 06 89 10090 1.59.90E 07 129 is630 7.6890E 06 90 10190 1.6610E 07 130 14730 2.0880E 07 91 10300 1.6430E 07 131 14830 1.4660E 07 92 10500 1.6130E 07 132 14930 1.1360E 07 93 10600 1.5880E 07 133 15030 9.5410E 06 94 10700 1.5500E 07 134 15130 8.4470E 06 95 10800 1.5190E 07 135 15230 7.7580E 06 96 11000 1.4820E 07 136 15330 7.5160E 06 i
97 11300 1.4610E 07 137 15430 7.2010E 06 98 11400 1.4420E 07 138 15530 6.9780E 06 99 11500 1.4210E 07 139 15630 6.8050E 06 100 11600 1.3970E 07 140 15730 6.6730E 06 101 11700 1.3680E 07 141 15640 6.5630E 06 102 11800 1.3300E 07 142 15940 6.4690E 06 103 11910 1.3030E 07 143 16040 6.3860E 06 104 12010 1.2340E 07 144 16140 6.4300E 06 105 12110 1.1980E 07 145 16240 6.3340E 06 106 12210 1.1600E 07 146 16340 6.2340E 06 107 12310 1.1280E 07 147 16640 6.1400E 06 108 12410 1.1000E 07 148 16840
.6.0210E 06 109 12510 1.0740E 07 149 17040 5.9800E 06 110 12710 1.0470E 07 150 17240 5.9270E 06 111 12810 2.1090E 07 151 17340 5.8700E 06 112 12910 1.5480E 07 152 17440 5.8290E 06 113 13010 1.3030E 07 153 17540 5.7890E 06 114 13110 1.1730E 07 154 17650 5.7540E 06 l
115 13210 1.0700E 07 155 17750 5.7010E 06 116 13310 1.0130E 07 156 17850 5.6590E 06 117 13420 9.7270E 06 157 17950 5.6060E 06 4
118 13520 1.6850E 07 158 18050 5.5580E 06 119 13620 1.3340E 07 159 18150 5.5030E 06 120 13720 1.1480E 07 160 18250 5.6520E 06 A-18 l
Table A-5. Rate of Heat Removal From the Containment Atmosphere (Continued)
TIME HEAT REMOVAL TIME-HERT REMOVAL (SECONDS)
(J/s)
(SECONDS)
(J/s) 161 18350 5.5890E 06 201 22670 4.9200E 06 162 18450 5.4900E 06 202 22770 4.8530E 06 163 18550 5.3960E 06 203 22870 4.9140E 06 164 18650 5.5410E 06 204 22970 4.8520E 06 165 18750 5.4340E 06 205 23070 4.9010E 06 166 18850 5.3500E 06 206 23170 4.9440E 06 167 18950 5.4700E 06 207 23270 4.8920E 06 168 19050 5.3640E 06 208 23370 4.9560E 06 169 19260 5.3960E 06 209 23470 4.8930E 06 170 19360 5.2730E 06 210 23570 4.9530E 06 171 19460 5.2190E 06 211 23670 4.8980E 06
[
172 19560 5.2630E 06 212 23770 4.9630E 06 173 19660 5.1930E 06 213 23870 4.9120E 06 174 19760 5.2740E 06 214 23970 4.9860E 06 175 19860 5.1350E 06 215 24070 4.9380E 06 176 20160 5.0070E 06 216 24170 5.0040E 06
[
177 20260 5.0430E 06 217 24270 4.9570E 06 178 20360 4.9600E 06 218 24370 5.0360E 06 179 20460 5.0110E 06 219 24480 4.9960E 06 180 20560 4.9450E 06 220 24580 5.0790E 06 181 20660 5.0080E 06 221 24680 5.0360E 06 182 20760 4.9530E 06 222 24780 5.1220E 06
[
183 20860 4.9980E 06 223 24880 5.0790E 06 184 20960 4.9530E 06 224 24980 5.1600E 06 185 21070 5.0050E 06 225 25080 5.1270E 06
{
186 21170 4.9560E 06 226 25180 5.0980E 06 187 21270 5.0160E 06 227 25280 5.1900E 06
[
188 21370 4.9720E 06 228 25380 5.1570E 06 189 21470 5.0160E 06 229 25480 5.2440E 06 190 21570 4.9560E 06 230 25680 5.1910E 06 191 21670 4.9860E 06 231 25780 5.3620E 06 192 21770 4.9250E 06 232 25880 6.4230E 06 193 21870 4.9890E 06 233 25980 8.4250E 06 194 21970 4.9250E 06 234 26080 1.0340E 07 195 22070 4.9660E 06 235 26180 1.1700E 07 196 22170 4.9020E 06 236 26280 1.2410E 07 197 22270 4.9480E 06 237 26380 1.2670E 07 198 22370 4.8800E 06 238 26580 1.2760E 07 199 22470 4.9310E 06 239 26680 1.2830E 07 200 22570 4.8630E 06 240 26780 1.2950E 07
(
A-19 r
Table A-5. Rate of Heat Removal From the Containment Atmosphere (Continued)
TIME HEAT REMOVAL TIME HEAT REMOVAL (SECONDS)
(J/s)
(SECONDS)
(J/s) 241 26880 1.3140E 07 281 31710 8.5420E 06 242 26990 1.3340E 07 282 31810 8.4750E 06 243 27090 1.2940E 07 283 31910 8.4150E 06 244 27190 1.2530E 07 284 32010 8.3560E 06 245 27290 1.2170E 07 285 32110 8.2990E 06 246 27390 1.1910E 07 286 32210 8.2480E 06 247 27490 1.1760E 07 287 32310 8.2000E 06 248 27590 1.1960E 07 288 32410 8.1590E 06 249 27790 1.2220E 07 289 32610 8.0820E 06 250 27890 1.2150E 07 290 32810 8.0210E 06 251 27990 1.2350E 07 291 33010 7.9650E 06 252 28290 1.2270E 07 292 33210 7.9200E 06 253 28400 1.2170E 07 293 33510 7.8790E 06 254 28500 1.2070E 07 294 35920 7.8330E 06 255 28700 1.2190E 07 295 36920 7.7890E 06 256 28900 1.2100E 07 296 37220 7.7460E 06 257 29200 1.2020E 07 297 37620 7.7000E 06 258 29400 1.1790E 07 298 39930 7.7410E 06 259 29500 1.1610E 07 299 40730 7.7830E 06 260 29600 1.1460E 07 300 41530 7.8220E 06 261 29700 1.1320E 07 301 42340 7.8630E 06 262 29800 1.1170E 07 302 43040 7.9030E 06 263 29900 1.1030E 07 303 43740 7.9430E 06 264 30000 1.0830E 07 304 44540 7.9840E 06 265 30100 1.0600E 07 305 45340 8.0270E 06 266 30200 1.0390E 07 306 46250 8.0700E 06 267 30300 1.0180E 07 307 47050 8.1110E 06 268 30400 9.9980E 06 308 47850 8.1540E 06 269 30500 9.8230E 06 309 48750 8.1960E 06 270 30600 9.6610E 06 310 49560 8.2380E 06 271 30700 9.5030E 06 311 50560 8.2860E 06 272 30800 9.3600E 06 312 51560 8.3290E 06 273 30900 9.2410E 06 313 52560 8.3730E 06 274 31000 9.1240E 06 314 53370 8.4180E 06 275 31100 9.0160E 06 315 54170 8.4630E 06 276 31200 8.9270E 06 316 54970 8.5080E 06 277 31300 8.8380E 06 317 55880 8.5530E 06 278 31410 8.7590E 06 318 57080 8.5960E 06 279 31510 8.6830E 06 319 58340 8.6400E 06 280 31610 8.6090E 06 320 59890 8.6840E 06 A-20
[
Table A-5. Rate of Heat Removal From the Containment Atmosphere (Concluded) r TIME HEAT REMOVAL i
(SECONDS)
(J/s) 321 61290 8.7280E 06
[L 322 62700 8.7720E 06 L
323 64200 8.8180E 06 324 66110 8.8640E 06 325 68020 8.9090E 06 326 70520 8.9560E 06 327 75950 9.0030E 06
[
328 79460 9.0490E 06 329 83580 9.0960E 06 330 86490 9.1140E 06
(
[
[
[
[
[
[-
[
{
{
(
A-21
l l
APPENDIX B. TABULATED UNCERTAINTY DISTRIBUTIONS The tables in this appendix provide detailed uncertainty distributions calculated in this work for decontamination factors at 1800, 6480,13680, 49680, and 86450 seconds as well as for the effective decontamination coefficients for the time intervals 0-1800,1800-6480, 6480-13680,13680-49680,49680-86450 seconds, Uncerta'mty distributions were constructed at two levels of confidence-50 and 90 percent. The distributions are given as the range of values that characterize percentiles of the distribution at 5 percent intervals from 5 to 95 percent.
e i
l l
l B-1 l
W M
M M
M M
Table B-1. Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 1800 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
l 5
1.180 to 1.185 1.181 to 1.183 10 1.183 to 1.192 1.185 to 1.192 15 1.190 to 1.195 1.192 to 1.194 20 1.192 to 1.197 1.194 to 1.196 25 1.195 to 1.199 1.196 to 1.198 e
30 1.197 to 1.201 1.198 to 1.199 h
35 1.198 to 1.202 1.199 to 1.202 40 1.200 to 1.204 1.201 to 1.203 45 1.202 to 1.204 1.203 to 1.204 50 1.203 to 1.205 1.204 to 1.205 55 1.204 to 1.207 1.2048 to 1.2054 60 1.205 to 1.210 1.205 to 1.207 65 1.206 to 1.212 1.207 to 1.210 70 1.206 to 1.212 1.210 to 1.213 75 1.207 to 1.215 1.213 to 1.215 80 1.214 to 1.221 1.215 to 1.217 85 1.216 to 1.227 1.219 to 1.224 90 1.222 to 1.229 1.225 to 1.228 95 1.228 to 1.233 1.229 to 1.232 Mean = 1.2055 4
Table B-2. Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 6480 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a -
Percentile Confidence Ixvel, C, of C = 90%
C = 50%
5 1.898 to 1.934 1.903 to 1.910 10 1.910 to 1.984 1.936 to 1.978 15 1.966 to 2.017 1.981 to 1.999 20 1.986 to 2.022 2.000 to 2.022 25 2.011 to 2.036 2.022 to 2.025 30 2.022 to 2.057 2.026 to 2.042 cn 35 2.028 to 2.064 2.042 to 2.058 6
40 2.046 to 2.074 2.058 to 2.066 45 2.060 to 2.082 2.066 to 2.075 50 2.067 to 2.095 2.075 to 2.087 55 2.076 to 2.102 2.083 to '2.096 60 2.088 to 2.124 2.096 to 2.108 65 2.098 to 2.149 2.108 to 2.127 70 2.116 to 2.160 2.127 to 2.151 75 2.142 to 2.176 2.151 to 2.165 80 2.159 to 2.210 2.165 to 2.180 85 2.172 to 2.264 2.I88 to 2.235 90 2.219 to 2.291 2.258 to 2.283 95 2.283 to 2.309 2.290 to 2.303 i
Mean = 2.0921
r Table B-3. Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 13680 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
5 3.905 to 4.222 3.926 to 4.I18 10 4.108 to 4.412 4.222 to 4.345 15 4.308 to 4.493 4.388 to 4.424 20 4.415 to 4.652 4.439 to 4.548 j
25 4.475 to 4.683 4.556 to 4.672 30 4.582 to 4.766 4.672 to 4.702 t?
35 4.673 to 4.902 4.702 to 4.835 40 4.706 to 5.084 4.805 to 4.947 45 4.840 to 5.218 4.908 to 5.128 50 4.979 to 5.293 5.100 to 5.241 55 5.156 to 5.413 5.220 to 5.300 60 5.260 to 5.628 5.295 to 5.440 65 5.317 to 5.734 5.420 to 5.654 70 5.482 to 5.935 5.651 to 5.829 75 5.694 to 6.115 5.830 to 6.006 80 5.870 to 6.518 6.045 to 6.245 85 6.107 to 6.860 6.402 to 6.623 90 6.580 to 7.328 6.814 to 7.191 95 7.213 to 8.147 7.326 to 7.582 Mean = 5.3641
mw f,
e-t m
_c,
e-,
e, r,
Table B-4. Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 4%80 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
5 33.75 to 42.41 34.06 to 39.74 10 39.74 to 44.80 42.75 to 43.70 15 43.19 to 48.69 43.82 to 47.16 20 44.96 to 50.81 47.81 to 50.07 25 48.53 to 52.83 50.13 to 51.49 30 50.26 to 54.50 51.52 to 53.64 tp 35 52.15 to 60.29 53.63 to 56.31 40 53.70 to 65.49 56.30 to 61.19 45 56.76 to 71.33 61.09 to 66.66 50 61.57 to 74.66 65.99 to 72.22 55 66.66 to 76.49 72.09 to 75.36 60 72.36 to 81.21 75.36 to 77.61 65 75.d4 to 85.21 77.48 to 81.81 70 78.41 to 92.89 81.67 to 86.83 75 82.49 to 95.83 87.08 to 93.74 80 90.26 to 107.9 94.22 to 98.38 85 95.56 to 118.1 99.59 to 111.6 90 108.2 to 131.1 116.90 to 124.8 95 124.8 to 153.3 130.1 to 149.3 Mean = 74.272
Table B-5. Uncertainty Distribution of the Decontamination Factor for Gap Release Material at 86450 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence level, C, of C = 90%
C = 50%
5 509.4 to 728.8 565.8 to 640.4 10 633.6 to 820.4 729.8 to 774.2 15 757.5 to 921.4 804.8 to 837.6 20 821.4 to 980.2 840.6 to 933.1 25 900.1 to 1029 933.1 to 992.3 30 951.0 to 1087 993.7 to 1062 e
35 1010 to 1165 1061 to 1117 6
40 1069 to 1418 1110 to 1278 45 1156 to 1554 1259 to 1465 50 1283 to 1622 1439 to 1568 55 1476 to 1746 1567 to 1651 60 1584 to 1897 1637 to 1748 65 1663 to 2145 1747 to 1964 70 1750 to 2319 1958 to 2198 75 1981 to 2560 2200 to 2394 80 2226 to 2673 2405 to 2604 85 2517 to 3118 2605 to 3002 90 2730 to 3816 3052 to 3488 95 3488 to 4515 3816 to 4011 Mean = 1740
Table B-6. Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 6480 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a i
Percentile Confidence level, C, of C = 90%
C = 50%
4 5
1.218 to 1.228 1.220 to 1.222 10 1.222 to i.240 1.229 to 1.235 15 1.232 to 1.244 1.237 to 1.242 20 1.241 to 1.245 1.242 to 1.245 i
25 1.243 to 1.249 1.245 to 1.247 j
30 1.245 to 1.254 1.247 to 1.250 35 1.248 to 1.258 1.250 to 1.255 m
O 40 1.251 to 1.260 1.255 to 1.258 45 1.255 to 1.260 1.258 to 1.260 50 1.258 to 1.263 1.260 to 1.261 55 1.260 m 1.266 1.261 to 1.264 60 1.261 to 1.270 1.264 to 1.268 65 1.265 to 1.275 1.267 to 1.272 70 1.268 to 1.277 1.272 to 1.276 75 1.273 to 1.279 1.276 to 1.279 80 1.276 to 1.285 1.277 to 1.279 85 1.278 to 1.297 1.282 to 1.291 90 1.286 to 1.302 1.2 6 to 1.301 95 1.301 to 1.305 1.302 to 1.304 Mean = 1.2615 l
t
s Table B-7. Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 13680 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
1 5
2.4% to 2.640 2.515 to 2.587 10 2.583 to 2.719 2.642 to 2.700 15 2.674 to 2.766 2.717 to 2.741 20 2.720 to 2.831 2.742 to 2.786 25 2.759 to 2.859 2.797 to 2.843 i
tp 30 2.822 to 2.896 2.844 to 2.863 35 2.848 to 2.995 2.860 to 2.913 40 2.876 to 3.096 2.908 to 3.026 45 2.914 to 3.142 3.022 to 3.098 50 3.033 to 3.177 3.096 to 3.145 55 3.117 to 3.216 3.145 to 3.191 60 3.156 to 3.327 3.183 to 3.258 65 3.191 to 3.370 3.255 to 3.341 70 3.267 to 3.440 3.338 to 3.390 75 3.343 to 3.663 3.394 to 3.484 80 3.413 to 3.928 3.511 to 3.716 85 3.626 to 4.101 3.727 to 3.983 90 3.976 to 4.295 4.004 to 4.207 95 4.217 to 4.772 4.294 to 4.450
' Mean = 3.227
Table B-8. Uncertainty Distribution of the Decontamination Factor for In-Vessel Release Material at 4%80 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
5 21.577 to 26.422 21.815 to 25.338 10 25.295 to 27.629 26.628 to 26.960 15 26.866 to 29.823 27.083 to 29.084 20 27.738 to 31.036 29.495 to 30.344 25 29.807 to 32.314 30.437 to 31.493 30 30.572 to 33.578 31.510 to 32.586 t?
35 31.785 to 37.455 32.568 to 34.758 40 32.697 to 39.510 34.429 to 38.297 45 34.999 to 42.788 37.907 to 40.368 50 38.823 to 44.506 39.946 to 43.164 55 40.930 to 45.784 42.905 to 44.828 60 43.517 to 47.18' 44.624 to 46.174 65 45.351 to 50.696 46.087 to 48.688 70 46.407 to 54.269 48.408 to 51.000 75 49.028 to 57.028 51.025 to 54.615 80 53.052 to 64.887 54.813 to 58.212 85 56.456 to 71.613 59.169 to 67.024 90 65.171 to 77.349 67.065 to 73.026 95 73.277 to 88.873 76.970 to 86.498 Mean = 44.461
L Table B-9. Uncertainty Distributio[1 of the Decontamination Factor for In-Vessel Release Material at 86450 Seconds Values of the Decontamination Factor Characteristic of the Indicated Percentile at a Confidence Level, C, of l
Percentile C = 90%
C = 50%
5 323.6 to 455.5 361.4 to 403.0 10 399.5 to 507.5 456.7 to 487.I 15 471.3 to 566.3 497.0 to 529.7 20 511.6 to 597.9 544.2 to 575.8 25 553.5 to 629.7 576.0 to 615.2 30 585.7 to 669.2 615.4 to 647.0 to 35 616.5 to 715.2 646.8 to 679.8 40 648.6 to 857.7 679.8 to 774.7 45 700.9 to 941.8 767.4 to 895.0 50 779.2 to 983.2 898.3 to 946.6 55 895.4 to 1040 946.1 to 989.6 60 946.8 to 1143 989.0 to 1045 65 995.2 to 1257 1041 to 1148 70 1054 to 1378 1147 to 1314 75 1164 to 1484 1316 to 1400 80 1363 to 1572 1410 to 1519 85 1475 to 1822 1534 to 1702 90 1600 to 2167 1739 to 2072 95 2072 to 2578 2167 to 2317 Mean = 1034'
m m
m m Table B-10. Uncertainty Distribution of Gap Release Effective Decontamination Coefficient, A,,
Over the Period 0 - 1800 Seconds j
Values of Effective 6 (hr-I) Characteristic of the Indicated Percentile at a Percentile Confidence Ixvel, C, of C = 90 %
C = 50%
5 0.331 to 3.339 0.333 to 0.336 10 0.336 to 0.351 0.339 to 0.350 3
15 0.347 to 0.356 0.351 to 0.354 1
20 0.352 to 0.360 0.354 to 0.358 25 0.356 to 0.362 0.359 to 0.362 l
t?
30 0.360 to 0.367 v.362 to 0.363 C
35 0.362 to 0.368 0.363 to 0.367 40 0.364 to 0.371 0.367 to 0.369 45 0.367 to 0.372 0.369 to 0.371 50 0.369 to 0.373 0.371 to 0.373 l
55 0.371 to 0.376 0.373 to 0.374 60 0.373 to 0.381 0.373 to 0.376 I
65 0.374 to 0.384 0.376 to 0.382 70 0.377 to 0.390 0.382 to 0.386 75 0.384 to 0.391 0.386 to 0.390 80 0.388 to 0.400 0.390 to 0.393 85 0.390 to 0.409 0.396 to 0.404 90 0.402 to 0.413 0.406 to 0.411 95 0.411 to 0.418 0.413 to 0.417 i
Mean = 0.3736 hr-I
r Table B-11. Uncertainty Distribution of the Gap Release Effective Decontamination Coefficient, A,,
Over the Period 1800 - 6480 Seconds l
t Values of Effective 6 (hr-I) Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
(
5 0.365 to 0.377 0.367 to 0.368 10 0.368 to 0.392 0.378 to 0.390 15 0.385 to 0.401 0.391 to 0.396
+
20 0.393 to 0.403 0.398 to 0.402 25 0.399 to 0.408 0.402 to 0.404 30 0.403 to 0.413 0.404 to 0.409 35 0.405 to 0.417 0.409 to 0.414 I
40 0.410 to 0.419 0.414 to 0.417 45 0.415 to 0.422 0.417 to 0.420 50 0.417 to 0.424 0.419 to 0.422 55 0.420 to 0.429 0.422 to 0.425 60 0.423 to 0.434.
0.425 to 0.430 i
65 0.426 to 0.440 0.430 to 0.435 70 0.431 to 0.444 0.435 to 0.441 75 0.438 to 0.447 0.441 to 0.444 1
i 80 0.442 to 0.456 0.444 to 0.449 85 0.446 to 0.471 0.450 to 0.464 i
90 0.458 to 0.479 0.470 to 0.477 95 0.477 to 0.483 -
0.478 to 0.482 Mean = 0.4231 hr-I i
- - -.. -. - - -.. - -. -. - ~ - -
-n a.
~
Table B-12. Uncertainty Distribution of the In-Vessel Release Effective Decontamination Coefficient, A,,
Over the Period 1800 - 6480 Seconds Values of Effective 6 (hr-I) Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
5 0.152 to 0.159 0.153 to 0.154 10 0.154 to 0.166 0.158 to 0.162 15 0.161 to 0.168 0.163 to 0.167 20 0.166 to 0.169 0.167 to 0.168 25 0.168 to 0.172 0.169 to 0.170
?
30 0.169 to 0.174 0.170 to 0.172 C
35 0.170 to 0.176 0.172 to 0.175 40 0.172 to 0.177 0.175 to 0.177 45 0.175 to 0.178 0.177 to 0.178 50 0.177 to 0.180 0.178 to 0.178 55 0.178 to 0.182 0.178 to 0.180 60 0.178 to 0.184 0.180 to 0.182 65 0.181 to 0.I87 0.I82 to 0.I85 70 0.183 to 0.188 0.185 to 0.187 75 0.186 to 0.189 0.187 to 0.188 80 0.188 to 0.193 0.188 to 0.189 85 0.189 to 0.200 0.191 to 0.196 90 0.193 to 0.203 0.199 to 0.203 95 0.203 to 0.205 0.203 to 0.204 Mean = 0.1785 hr-I
~
Table B-13. Uncertainty Distribution of the Effective Decontamination Coefficient,1,,
Over the Period 6480 - 13680 Seconds Values of Effective 6 (hr-I) Characteristic of the indicated Percentile at a Percentile Confidence Ixvel, C, of C = 90%
C = 50%
5 0.358 to 0.379 0.360 to 0.372 10 0.371 to 0.390 0.379 to 0.388 -
15 0.384 to 0.397 0.390 to 0.393 20 0.391 to 0.407 0.394 to 0.403 25 0.397 to 0.410 0.404 to 0.408
?
30 0.406 to 0.417 0.409 to 0.412 E
35 0.409 to 0.428 0.412 to 0.419 40 0.413 to 0.441 0.419 to 0.433 45-0.419 to 0.452 0.432 to 0.446 50 0.434 to 0.461 0.443 to 0.455 55 0.446 to 0.468 0.454 to 0.462 60 0.457 to 0.474 0.462 to 0.469 65 0.463 to 0.487 0.469 to G.476 70 0.471 to 0.505 0.476 to 0.491 75 0.484 to 0.521 0.491 to 0.508 80 0.497 to 0.555 0.511 to 0.539 -
85 0.520 to 0.585 0.543 to 0.575 90 0.566 to 0.604 0.576 to 0.588 95 0.591 to 0.658 0.604 to 0.633 Mean = 0.4629 hr-I
i Table B-15. Uncertainty Distribution of the Effective Decontamination Coefficient, A,,
Over the Period 49680 - 86450 Seconds Values of Effective 6 (hr-I) Characteristic of the Indicated Percentile at a Percentile Confidence Level, C, of C = 90%
C = 50%
5 0.262 to 0.274 0.252 to 0.267 10 0.267 to 0.279 0.275 to 0.277 15 -
0.276 to 0.285 0.279 to 0.280 20 0.280 to 0.289 0.281 to 0.286 25 0.284 to 0.291 0.286 to 0.289 30 0.287 to 0.293 0.289 to 0.291 35 0.290 to 0.295 0.291 to 0.294 40 0.292 to 0.297 0.294 to 0.296 45 0.294 to 0.298 0.295 to 0.297 50 0.296 to 0.300 0.297 to 0.299 55 0.297 to 0.304 0.299 to 0.301 60 0.299 to 0.306 0.300 to 0.305 65 0.301 to 0.310 0.305 to 0.307 70 0.305 to 0.314 0.307 to 0.311 75 0.308 to 0.317 0.311 to 0.314 80 0.312 to 0.325 0.314 to 0.319 85 0.317 to 0.335 0.321 to 0.330 90 0.327 to 0.340 0.332 to 0.338 95 0.338 to 0.344 0.340 to 0.343 Mean = 0.3007 hr-I i
_ _. _