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| issue date = 05/06/1985
| issue date = 05/06/1985
| title = Monte Carolo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor
| title = Monte Carolo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor
| author name = Doster J M, Hey B E
| author name = Doster J, Hey B
| author affiliation = North Carolina State Univ
| author affiliation = North Carolina State Univ
| addressee name =  
| addressee name =  
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{{#Wiki_filter:Attachment 6 Monte Carlo Simulation of the Gamma Dose Rate in a Loss
{{#Wiki_filter:Attachment 6 Monte Carlo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor J.M. Doster and B.E. Hey
-of-Water Accident at the North Carolina State University Research Reactor J.M. Doster and B.E. Hey NUCLEAR SCIENCE AND ENGINEERING:
 
93, 1-12 (1986) Monte Carlo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor Joseph M. Doster and Brit E. Hey North Carolina State University, Department of Nuclear Engineering, Box 7909 Raleigh, North Carolina 27695-7909 Received May 6, 1985 Accepted November 11, 1985 Abstract-In pool-type research reactors, a sudden loss of all pool water can result in significant nal radiation dose. Of concern are fission product decay gamma rays emitted within the core, ing out of the biological shield producing unacceptable radiation exposure in and around the reactor building.
NUCLEAR SCIENCE AND ENGINEERING: 93, 1-12 (1986)
A Monte Carlo model was developed and used to generate dose maps for key access and traffic areas throughout the reactor facility at North Carolina State University.
Monte Carlo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor Joseph M. Doster and Brit E. Hey North Carolina State University, Department of Nuclear Engineering, Box 7909 Raleigh, North Carolina 27695-7909 Received May 6, 1985 Accepted November 11, 1985 Abstract-In pool-type research reactors, a sudden loss of all pool water can result in significant exter-nal radiation dose. Of concern are fission product decay gamma rays emitted within the core, stream-ing out of the biological shield producing unacceptable radiation exposure in and around the reactor building. A Monte Carlo model was developed and used to generate dose maps for key access and traffic areas throughout the reactor facility at North Carolina State University. It was found that several of these areas could be exposed to significant gamma radiation fields, ranging from 230 rem/h 20 ft directly over and in line of sight of the core to 4 mrem/h outside and adjacent to the reactor building. Expected dose rates were also computed for the reactor bay floor, control room, and offices.
It was found that several of these areas could be exposed to significant gamma radiation fields, ranging from 230 rem/h 20 ft directly over and in line of sight of the core to 4 mrem/h outside and adjacent to the reactor building.
The model was benchmarked against dose rates measured at the Lawrence Livermore National Lab-oratory pool-type reactor.
Expected dose rates were also computed for the reactor bay floor, control room, and offices. The model was benchmarked against dose rates measured at the Lawrence Livermore National oratory pool-type reactor. Simulation Monte-Carlo du taux de dose gamma dans un accident de perte d'eau intervenant dans le reacteur de recherche de la North Carolina State University Resume -Dans /es reacteurs piscines une perte brusque et complete de /'eau de piscine pourrait produire une dose de radiation externe significative.
Simulation Monte-Carlo du taux de dose gamma dans un accident de perte d'eau intervenant dans le reacteur de recherche de la North Carolina State University Resume - Dans /es reacteurs piscines une perte brusque et complete de /'eau de piscine pourrait produire une dose de radiation externe significative. On s'occupe particulierement du fait de la radi-ation gamma liberee dans le coeur suite a la desintegration des produits de fission, qui, en sortant de tecran biologique, cause une exposition intolerable dans le biitiment du reacteur ainsi que dans :ses environs. Un modele Monte-Carlo a ete mis au point et employe pour etablir des cartes de doses va-lables pour /es zones d'acces et de trafic /es plus importantes dans /'ensemble du biitiment du reacteur de la North Carolina State University. On a trouve qu'un nombre de ces zones pourraient etre exposees ii des champs significatifs de radiation gamma, s'elevant de 230 rem/h ii une distance de 20 pieds directement au-dessus du bfltiment de reacteur, sur la ligne de vue du coeur, jusqu'ii 4 mremlh au-dehors du et avoisinant le bfltiment du reacteur. Les taux de doses attendus ont ete ca/cutees ega/e-ment pour le sol de la baie du reacteur, la sal/e de commande et !es bureaux. Le modele fut repere en le comparant aux taux de doses mesures au "Lawrence Livermore National Laboratory pool-type reactor."
On s'occupe particulierement du fait de la ation gamma liberee dans le coeur suite a la desintegration des produits de fission, qui, en sortant de tecran biologique, cause une exposition intolerable dans le biitiment du reacteur ainsi que dans :ses environs.
Monte-Carlo-Simulation der bei einem Wasserverluststorfall im North Carolina State University Forschungsreaktor auftretenden Gamma-Dosisleistung Zusammenfassung- In Forschungsreaktoren in Pool-Bauweise kann ein p/Otzlicher Verlust des gesam-ten Beckenwassers zu einer betriichtlichen externen Strahlendosis fuhren. Sorge bereiten dabei die im Reaktor aufgrund des Spaltproduktzerfal/s emittierten Gammastrahlen; sie entweichen aus dem bio/ogischen Schild und verursachen im Reaktorgebiiude und in seiner Umgebung eine unannehmbar hohe Strahlenbelastung. Es wurde ein Monte-Carlo-Model/ entwickelt und eingesetzt, um Dosiskar-ten fur wichtige Zugangs- und Verkehrsbereiche in der ganzen Reaktoranlage der North Carolina State 1
Un modele Monte-Carlo a ete mis au point et employe pour etablir des cartes de doses lables pour /es zones d'acces et de trafic /es plus importantes dans /'ensemble du biitiment du reacteur de la North Carolina State University.
 
On a trouve qu'un nombre de ces zones pourraient etre exposees ii des champs significatifs de radiation gamma, s'elevant de 230 rem/h ii une distance de 20 pieds directement au-dessus du bfltiment de reacteur, sur la ligne de vue du coeur, jusqu'ii 4 mremlh dehors du et avoisinant le bfltiment du reacteur.
2                                                 DOSTER and HEY University erstellen zu konnen. Dabei stellte sich heraus, daj] eine Reihe dieser Bereiche starken Gam-mafeldern ausgesetzt werden konnte. Diese liegen zwischen 230 rem/h im Abstand von 20 Fuj] direkt iiber dem Reaktorgebiiude in Sichtlinie des Reaktorkerns und 4 mremlh auj]erhalb des Reaktorge-biiudes und in seiner unmittelbaren Umgebung. Die zu erwartenden Dosisleistungen wurden auch fiir den Boden des Arbeitsbereichs im Reaktor, die Warte und die Biiroriiume berechnet. Das Model!
Les taux de doses attendus ont ete ca/cutees ment pour le sol de la baie du reacteur, la sal/e de commande et !es bureaux. Le modele fut repere en le comparant aux taux de doses mesures au "Lawrence Livermore National Laboratory pool-type reactor." Monte-Carlo-Simulation der bei einem Wasserverluststorfall im North Carolina State University Forschungsreaktor auftretenden Gamma-Dosisleistung Zusammenfassung-In Forschungsreaktoren in Pool-Bauweise kann ein p/Otzlicher Verlust des ten Beckenwassers zu einer betriichtlichen externen Strahlendosis fuhren. Sorge bereiten dabei die im Reaktor aufgrund des Spaltproduktzerfal/s emittierten Gammastrahlen; sie entweichen aus dem bio/ogischen Schild und verursachen im Reaktorgebiiude und in seiner Umgebung eine unannehmbar hohe Strahlenbelastung.
wurde gegen die im "Lawrence Livermore National Laboratory pool-type reactor" gemessenen Dosis-leistungen abgeglichen.
Es wurde ein Monte-Carlo-Model/
INTRODUCTION                                 within the reactor bay requires dose determinations in several hundred locations. The need for a streamlined For a pool-type research reactor, the sudden loss           and very efficient model becomes immediately appar-of pool water is an accident considered for licensing             ent. Such a Monte Carlo model was developed specif-and emergency planning purposes. The PULST AR                     ically for the PULST AR facility. To decrease reactor located on the campus of North Carolina State             computer execution time and simplify the computa-University (NCSU) is considered susceptible to such an           tional algorithm, a number albedo approach was accident. The tank liner has several penetrations that           incorporated to calculate the dose from scattered radi-represent possible failure modes, permitting the tank             ation while eliminating the need for detailed tracking to drain into the reactor room basement. It is esti-              of radiation through concrete walls, ceilings, etc.
entwickelt und eingesetzt, um ten fur wichtige Zugangs-und Verkehrsbereiche in der ganzen Reaktoranlage der North Carolina State 1 2 DOSTER and HEY University erstellen zu konnen. Dabei stellte sich heraus, daj] eine Reihe dieser Bereiche starken mafeldern ausgesetzt werden konnte. Diese liegen zwischen 230 rem/h im Abstand von 20 Fuj] direkt iiber dem Reaktorgebiiude in Sichtlinie des Reaktorkerns und 4 mremlh auj]erhalb des biiudes und in seiner unmittelbaren Umgebung.
mated that the time required to drain the tank through           Though an approximation, this approach was consid-tank liner penetrations varies from 2.4 min for the               ered a reasonable compromise between accuracy and 12- x 12-in. beam tube to 12.3 min for the 6-in. beam           computational efficiency. Number as well as dose tube. 1 The power density of the core is sufficiently             albedos were used such that particle paths involving low to allow air cooling by natural circulation after a           multiple walls or structures could be simulated. A sec-sudden full-power shutdown. Fuel failure will, there-            ond Monte Carlo model was written to generate the fore, not result from inadequate core cooling. Of con-            necessary doubly differential number albedos used in cern, however, are fission product gamma rays emitted             this study. These albedos are supplied to the dose within the core escaping the biological shield with               model in tabular form and interpolated throughout the sufficient intensity to limit access to key maintenance           simulation.
Die zu erwartenden Dosisleistungen wurden auch fiir den Boden des Arbeitsbereichs im Reaktor, die Warte und die Biiroriiume berechnet.
and control areas. As the reactor building is centrally               A number of general purpose Monte Carlo codes located on the NCSU campus, of additional concern                 are available for photon and coupled neutron-photon is the potential radiation hazard in areas of high stu-          problems. 2 - 5 Although highly flexible, codes of this dent and personnel population. The areas of primary               type are not without their disadvantages. These codes interest are the reactor bay floor, reactor platform,             are very large in size and due to their generality, often control room, loading dock, offices, bay roof, and               less efficient in a particular application than a code campus areas outside the reactor building. These areas           developed specifically for that problem. In addition, were chosen due to their relative importance with                 a significant amount of work is involved in just install-regard to surveillance, reactor maintenance, and oper-            ing, checking, and learning to use these codes. For a ations. In addition, the loading dock is a high student           one-shot application, an alternate choice is the devel-and personnel traffic area connecting two wings of the           opment of a Monte Carlo model for the particular PULST AR facility. These locations are illustrated in             application at hand.
Das Model! wurde gegen die im "Lawrence Livermore National Laboratory pool-type reactor" gemessenen leistungen abgeglichen.
Fig. 1, with the exception of offices and campus areas.
INTRODUCTION For a pool-type research reactor, the sudden loss of pool water is an accident considered for licensing and emergency planning purposes.
The offices are located immediately adjacent to and north of the reactor building. The objective of this                 GAMMA-RAY NUMBER AND DOSE ALBEDOS study is to provide information regarding the poten-tial magnitude of these dose rates, their location, and               Albedo theory treats the interaction of gamma at what time these areas might be considered safe to             rays with a surface as a reflection phenomenon. The reenter. This study and its recommendations are to be             justification for this approach in our work is threefold.
The PULST AR reactor located on the campus of North Carolina State University (NCSU) is considered susceptible to such an accident.
incorporated into the PULSTAR Final Safety Analysis               First, the dimensions of the scattering surfaces mak-Report in support of current relicensing activities.             ing up the reactor shield, bay, and office rooms are The complicated geometry and number of mech-                very large and located at significant distances from the anisms by which radiation emitted within the core                 detection points. Under these circumstances, the dif-could arrive at a particular location within the facility         ference in location between incident and exit points effectively eliminate all computational techniques but           can be neglected. Second, the vast majority of the scat-the Monte Carlo method. Though extremely powerful,               tering surfaces is constructed of ordinary concrete.
The tank liner has several penetrations that represent possible failure modes, permitting the tank to drain into the reactor room basement.
the Monte Carlo method can require prohibitive                   This material is used in virtually every type of fixed amounts of computer time, particularly if not used               shield, and its albedo properties have been thoroughly efficiently. To adequately map the dose distribution             investigated. 6 Third, there are tremendous savings in
It is mated that the time required to drain the tank through tank liner penetrations varies from 2.4 min for the 12-x 12-in. beam tube to 12.3 min for the 6-in. beam tube. 1 The power density of the core is sufficiently low to allow air cooling by natural circulation after a sudden full-power shutdown.
 
Fuel failure will, fore, not result from inadequate core cooling. Of cern, however, are fission product gamma rays emitted within the core escaping the biological shield with sufficient intensity to limit access to key maintenance and control areas. As the reactor building is centrally located on the NCSU campus, of additional concern is the potential radiation hazard in areas of high dent and personnel population.
LOSS-OF-WATER ACCIDENT                                                    3 LOADING DOCK Fig. 1. Reactor building.
The areas of primary interest are the reactor bay floor, reactor platform, control room, loading dock, offices, bay roof, and campus areas outside the reactor building.
machine time when using albedos over conventional                aD (EoJJo, 8, </>)
These areas were chosen due to their relative importance with regard to surveillance, reactor maintenance, and ations. In addition, the loading dock is a high student and personnel traffic area connecting two wings of the PULST AR facility.
methods of particle tracking and estimation between interaction points.                                                    = fo 00 a(Eo,80 ,E,8, </>)K(E) I K(E0) dE ,   (1)
These locations are illustrated in Fig. 1, with the exception of offices and campus areas. The offices are located immediately adjacent to and north of the reactor building.
Definitions                                                    where K(E) is the flux-to-dose conversion factor.
The objective of this study is to provide information regarding the tial magnitude of these dose rates, their location, and at what time these areas might be considered safe to reenter. This study and its recommendations are to be incorporated into the PULST AR Final Safety Analysis Report in support of current relicensing activities.
The differential gamma-ray number albedo                      Chilton and Huddleston 7 developed a semiempir-a(E0,00,E,0,</>) as defined here is the differential cur-      ical formula for this differential gamma-ray dose rent outward from a planar surface per incident cur-          albedo for ordinary concrete based on the Monte rent inward to that surface, where E0 is the incident          Carlo studies of Raso. 8 This formula has the form particle energy in mega-electron-volts, 00 is an inci-dent polar angle, Eis the exit particle energy, () is the aD(Eo,80,8, &#xa2;)    = [C(Eo)K(Eo,8s)      x 1026 exit polar angle, and</> is the exit azimuthal angle. Fig-                           + C' (&#xa3;0 )] / [I + cos00 secO] , (2) ure 2 illustrates this relationship. For situations where where the exit gamma-ray energy is not required, the differ-ential dose albedo can be useful. The dose albedo used            C(Eo), C ' (E0 ) =fitted parameters dependent only in this work is related to the number albedo by the                                   on incident energy E0 and mate-relationship                                                                          rial properties
The complicated geometry and number of anisms by which radiation emitted within the core could arrive at a particular location within the facility effectively eliminate all computational techniques but the Monte Carlo method. Though extremely powerful, the Monte Carlo method can require prohibitive amounts of computer time, particularly if not used efficiently.
 
To adequately map the dose distribution within the reactor bay requires dose determinations in several hundred locations.
4                                                    DOSTER and HEY TABLE I Incident Gamma-Ray Energies and Angles Eo                                                                Energy (MeV)                Direction &#xb5; 0 = (cos80 )
The need for a streamlined and very efficient model becomes immediately ent. Such a Monte Carlo model was developed ically for the PULST AR facility.
0.020                      0.000 0.050                      0.143 0.075                      0.286 0.100                      0.429 0.200                      0.571 0.500                      0.714 1.000                      0.857 1.250                      1.000 2.000 4.000 6.000 in solid angle. Figure 3 illustrates the divisions made Fig. 2. Geometry depicting particle reflection from a     in the emergent solid angle used in the albedo calcu-surface.                                                      lation. The physical model is simply a homogeneous laterally infinite 1-m-thick concrete slab. In accordance with usual practice, coherent scattering and multiple photon emission are ignored along with fluorescence Os= scattering angle as illustrated in Fig. 2                              radiation and bremsstrahlung, which are considered to be of little significance. 9 K(E0 , Os) :::: Klein-Nishina differential energy        A great deal of effort has been devoted to the scattering cross section per elec-  study of gamma rays backscattered from and transmit-tron per steradian.                 ted through concrete. Raso, 8 Berger and Raso, 10 and The dose albedos given by either Eq. (1) or (2) can be         Wells 11 amassed a considerable number of data on used in the Monte Carlo simulation as a means of esti-        differential and total albedos using the Monte Carlo method in the early 1960s. There have been numerous mating the dose from gamma-ray backscatter off ordi-nary concrete. The Chilton-Huddleston formula has the advantage of reduced run times and lower mem-ory requirements when calculating the backscattered dose from a single surface; however, it cannot be used exclusively to calculate the dose from higher order reflections as exit energy information has been lost.
To decrease computer execution time and simplify the tional algorithm, a number albedo approach was incorporated to calculate the dose from scattered ation while eliminating the need for detailed tracking of radiation through concrete walls, ceilings, etc. Though an approximation, this approach was ered a reasonable compromise between accuracy and computational efficiency.
Monte Carlo Simulation of Gamma-Ray Number Albedos The Monte Carlo method is used to generate a table of differential gamma-ray number albedos for ordinary concrete. 9 Values are computed for the 11 incident energies and 8 incident angles given in Ta-ble I. For each of these 88 incident conditions, 6 exit energy intervals, 6 exit polar angle intervals, and 6 exit azimuthal angle intervals are considered yielding
Number as well as dose albedos were used such that particle paths involving multiple walls or structures could be simulated.
-20 000 entries that must be stored and accessed. The 6 exit energy groups for each incident energy &#xa3; 0 and angle 00 evenly span the range 0.01 MeV to EMAX(E0 ,00 ), where EMAX is the maximum exit energy possible for the given incident conditions based on a single Compton scatter within the shield. The exit polar and azimuthal angular groups are evenly spaced                Fig. 3. Geometry used in albedo computations.
A ond Monte Carlo model was written to generate the necessary doubly differential number albedos used in this study. These albedos are supplied to the dose model in tabular form and interpolated throughout the simulation.
 
A number of general purpose Monte Carlo codes are available for photon and coupled neutron-photon problems.
LOSS-OF-WATER ACCIDENT                                                s attempts to fit this differential data to a semiempiri-        p(Eo,&#xb5; 0 ,E,&#xb5;,&#xa2;)   = a(E0 ,&#xb5; 0 ,E,&#xb5;,&#xa2;)/A(Eo,&#xb5;o)   ,
2-5 Although highly flexible, codes of this type are not without their disadvantages.
cal formula, such as that of Chilton and Huddleston                                                               (3) mentioned previously, or an exponential curve, such as that of Haggmark et al. 12 Results from the albedo      which are sampled for the energy and direction of the model developed in this work are compared to those          emergent reflected photons. The denominator from the literature in Tables II and Ill. The agreement is seen to be quite good. Material composition was            A(E0 ,&#xb5; 0 ) == lEMAX f a(E ,&#xb5; ,E,&#xb5;,&#xa2;)d0dE 0  0                (4) taken to be ordinary concrete 20 cm thick with a den-                                  0 sity of 2.35 g/cm 3
These codes are very large in size and due to their generality, often less efficient in a particular application than a code developed specifically for that problem. In addition, a significant amount of work is involved in just ing, checking, and learning to use these codes. For a one-shot application, an alternate choice is the opment of a Monte Carlo model for the particular application at hand. GAMMA-RAY NUMBER AND DOSE ALBEDOS Albedo theory treats the interaction of gamma rays with a surface as a reflection phenomenon.
* Total albedos were obtained by        is simply the total number albedo at the incident pho-numerically integrating the differential albedos over      ton energy and direction and also provides the weight exit polar and azimuthal angles.                            factor for the reflection.
The justification for this approach in our work is threefold.
The differential albedos are used to generate prob-ability distribution functions of the form MONTE CARLO MODEL OF FISSION PRODUCT GAMMA-RAY TRANSPORT TABLE II                                The computer code DOSE simulates the transport Total Number Albedo Comparison                  of delayed fission product gamma rays escaping from the NCSU PULSTAR. Dose rate information is cal-0                                                       culated in as many as 300 detector locations at once, (deg) Study 2.0 MeV        1.0 MeV 0.5 MeV 0.2 MeV        inside or out of the reactor building. The reactor core is treated as a volume source with gamma emission 0    pa      0.159      0.215      0.271    0.258    points distributed according to measured steady-state BRb      0.162      0.221      0.268    0.285 RC axial and radial flux distributions. PULSTAR fuel is 0.164      0.207      0.275    0.285 in the form of cylindrical rods containing 4% enriched 60    p        0.317      0.351      0.420    0.407    U0 2 pellets clad in Zircaloy-2. The core is approxi-BR      0.313      0.390      0.414    0.409    mated as homogeneous with the material volume frac-R        0.316      0.365      0.419    0.419    tions given in Table IV.
First, the dimensions of the scattering surfaces ing up the reactor shield, bay, and office rooms are very large and located at significant distances from the detection points. Under these circumstances, the ference in location between incident and exit points can be neglected.
90    p        0.717      0.733      0.752    0.703        Gamma rays emitted within the core are trans-BR      0.724      0.744      0.734    0.703    ported into the pool volume either directly or through d          d          d        d R                                                  scattering interactions with core materials. The biolog-ical shield is sufficiently thick at the base and top to ap = present paper: 1000 histories.                    effectively eliminate contributions to the dose from bBR = Berger and Raso. 9                              transmission through the shield. Gamma rays are, cR =Raso. 8                                            therefore, assumed to escape the biological shield and ctNumbers unavailable.
Second, the vast majority of the tering surfaces is constructed of ordinary concrete.
enter the bay through a series of reflections. This treat-ment models the biological shield as an oversized duct, for which albedos are ideally suited. The core and bio-TABLE III                          logical shield arrangement are illustrated in Fig. 4. Fis-sion product decay gammas are emitted isotropically; Total Dose Albedo Comparison however, from Fig. 4 it is apparent that photons emit-ted in the solid angle subtended by the biological shield 0
This material is used in virtually every type of fixed shield, and its albedo properties have been thoroughly investigated.
(deg) Study 2.0 MeV      1.0 MeV 0.5 MeV 0.2 MeV          opening have a much better chance of escape than those incident upon the shield walls. It is then advan-0    pa       0.017      0.037      0.071    0.139    tageous to place more importance on photons emitted BRb      0.020      0.040      0.074    0.138    in that direction. Similarly, photons emitted deep CHC      0.032      0.049      0.076    0.134    within the core have much less chance of escape than 60    p        0.057      0.099      0.143    0.211 BR      0.055      0.099      0.146    0.220 CH      0.063      0.094      0.136    0.214                            TABLE IV 90    p        0.302      0.347      0.387    0.463                      Core Volume Fractions BR      0.303      0.355      0.395    0.470 CH      0.322      0.388      0.456    0.580                  U02                      0.3823 Void                    0.0155 ap =present paper: 1000 histories.                                   Water                    0.4339 bBR =Berger and Raso. 9                                              Zircaloy-2              0.0802 ccH =Chilton and Huddleston, 10 numerically inte-                    Aluminum                0.0881 grated.
6 Third, there are tremendous savings in LOSS-OF-WATER ACCIDENT 3 LOADING DOCK Fig. 1. Reactor building.
 
machine time when using albedos over conventional methods of particle tracking and estimation between interaction points. Definitions The differential gamma-ray number albedo a(E 0 ,0 0 ,E,0,</>)
D 6                                                      DOSTER and HEY imation for the calculation of outside dose is made by CONTROL ROD                                      assuming the roof is a uniform thickness of 3 in.
as defined here is the differential rent outward from a planar surface per incident rent inward to that surface, where E 0 is the incident particle energy in mega-electron-volts, 0 0 is an dent polar angle, Eis the exit particle energy, () is the exit polar angle, and</> is the exit azimuthal angle. ure 2 illustrates this relationship.
ACTUATORS                                Gamma rays are tracked within the ceiling and, if scat-tered in an outward direction, forced to escape the roof into the atmosphere with weight reduced by the escape probability. There the photons undergo a series of scatters until termination criteria are met. Dose rate contributions are computed for all external detectors at each scatter within the atmosphere. Once the pho-TANK ton history in the atmosphere is terminated, the par-STANDARD                                                        ticle history is resumed at the point of scatter within CONCRETE                            11 ft,                    the ceiling.
For situations where the exit gamma-ray energy is not required, the ential dose albedo can be useful. The dose albedo used in this work is related to the number albedo by the relationship aD (EoJJo, 8, </>) = fo 00 a(Eo,8 0 ,E,8 ,</>)K (E)I K(E 0) dE , (1) where K(E) is the flux-to-dose conversion factor. Chilton and Huddleston 7 developed a
9 in.
ical formula for this differential gamma-ray dose albedo for ordinary concrete based on the Monte Carlo studies of Raso. 8 This formula has the form aD(Eo,80,8
COMPARISON TO THE LAWRENCE LIVERMORE NATIONAL LABORATORY
,&#xa2;) = [C(Eo)K(Eo,8s) x 10 26 + C' (&#xa3;0)] /[I + cos0 0 secO] , (2) where C(Eo), C'(E 0) =fitted parameters dependent only on incident energy E 0 and rial properties 4 DOSTER and HEY Eo Fig. 2. Geometry depicting particle reflection from a surface. Os= scattering angle as illustrated in Fig. 2 K(E 0 , Os) :::: Klein-Nishina differential energy scattering cross section per tron per steradian.
                                            - 6
The dose albedos given by either Eq. (1) or (2) can be used in the Monte Carlo simulation as a means of mating the dose from gamma-ray backscatter off nary concrete.
                                                    ~
The Chilton-Huddleston formula has the advantage of reduced run times and lower ory requirements when calculating the backscattered dose from a single surface; however, it cannot be used exclusively to calculate the dose from higher order reflections as exit energy information has been lost. Monte Carlo Simulation of Gamma-Ray Number Albedos The Monte Carlo method is used to generate a table of differential gamma-ray number albedos for ordinary concrete.
EXPERIMENT As a benchmark for the Monte Carlo model, dose
9 Values are computed for the 11 incident energies and 8 incident angles given in ble I. For each of these 88 incident conditions, 6 exit energy intervals, 6 exit polar angle intervals, and 6 exit azimuthal angle intervals are considered yielding -20 000 entries that must be stored and accessed.
          "*,. .. ~*
The 6 exit energy groups for each incident energy &#xa3;0 and angle 0 0 evenly span the range 0.01 MeV to EMAX(E 0 ,0 0), where EMAX is the maximum exit energy possible for the given incident conditions based on a single Compton scatter within the shield. The exit polar and azimuthal angular groups are evenly spaced TABLE I Incident Gamma-Ray Energies and Angles Energy (MeV) Direction
rates were calculated and compared with those mea-z~o
&#xb5;0 = ( cos8 0) 0.020 0.000 0.050 0.143 0.075 0.286 0.100 0.429 0.200 0.571 0.500 0.714 1.000 0.857 1.250 1.000 2.000 4.000 6.000 in solid angle. Figure 3 illustrates the divisions made in the emergent solid angle used in the albedo lation. The physical model is simply a homogeneous laterally infinite 1-m-thick concrete slab. In accordance with usual practice, coherent scattering and multiple photon emission are ignored along with fluorescence radiation and bremsstrahlung, which are considered to be of little significance.
        ~ *
9 A great deal of effort has been devoted to the study of gamma rays backscattered from and ted through concrete.
* 4                                              sured during the loss-of-water experiment conducted at Lawrence Livermore National Laboratory 13
Raso, 8 Berger and Raso, 10 and Wells 11 amassed a considerable number of data on differential and total albedos using the Monte Carlo method in the early 1960s. There have been numerous Fig. 3. Geometry used in albedo computations.
              )
LOSS-OF-WATER ACCIDENT s attempts to fit this differential data to a cal formula, such as that of Chilton and Huddleston mentioned previously, or an exponential curve, such as that of Haggmark et al. 12 Results from the albedo model developed in this work are compared to those from the literature in Tables II and Ill. The agreement is seen to be quite good. Material composition was taken to be ordinary concrete 20 cm thick with a sity of 2.35 g/cm 3* Total albedos were obtained by numerically integrating the differential albedos over exit polar and azimuthal angles. The differential albedos are used to generate ability distribution functions of the form TABLE II Total Number Albedo Comparison 0 (deg) Study 2.0 MeV 1.0 MeV 0.5 MeV 0 pa 0.159 0.215 BRb 0.162 0.221 RC 0.164 0.207 60 p 0.317 0.351 BR 0.313 0.390 R 0.316 0.365 90 p 0.717 0.733 BR 0.724 0.744 R d d ap = present paper: 1000 histories.
BARYTES CONCRETE                -    CORJ          --~
bBR = Berger and Raso. 9 cR =Raso. 8 ctNumbers unavailable.
(LLNL). Dose rates were measured at 10 min and 1 h after shutdown with 0 and 1 ft of water over the core.
TABLE III 0.271 0.268 0.275 0.420 0.414 0.419 0.752 0.734 d Total Dose Albedo Comparison 0 (deg) Study 2.0 MeV 1.0 MeV 0.5 MeV 0 pa 0.017 0.037 BRb 0.020 0.040 CHC 0.032 0.049 60 p 0.057 0.099 BR 0.055 0.099 CH 0.063 0.094 90 p 0.302 0.347 BR 0.303 0.355 CH 0.322 0.388 ap =present paper: 1000 histories.
Although this experiment is similar to the type of acci-
bBR =Berger and Raso.9 0.071 0.074 0.076 0.143 0.146 0.136 0.387 0.395 0.456 0.2 MeV 0.258 0.285 0.285 0.407 0.409 0.419 0.703 0.703 d 0.2 MeV 0.139 0.138 0.134 0.211 0.220 0.214 0.463 0.470 0.580 ccH =Chilton and Huddleston, 10 numerically grated. p(Eo,&#xb5;0 ,E,&#xb5;,&#xa2;) = a(E 0 ,&#xb5;0 ,E,&#xb5;,&#xa2;)/A(Eo,&#xb5;o) , (3) which are sampled for the energy and direction of the emergent reflected photons. The denominator A(E 0 ,&#xb5;0) == lEMAX f 0 a(E 0 ,&#xb5;0 ,E,&#xb5;,&#xa2;)d0dE (4) is simply the total number albedo at the incident ton energy and direction and also provides the weight factor for the reflection.
  ---------...--                  I 4 ft,  1-------            dent modeled for the PULSTAR, there are major dif-2 ft      6 in.                     ferences that warrant discussion. The LLNL reactor is a 2-MW reactor constructed of 90% enriched, Fig. 4. Geometry of the core and biological shield.
MONTE CARLO MODEL OF FISSION PRODUCT GAMMA-RAY TRANSPORT The computer code DOSE simulates the transport of delayed fission product gamma rays escaping from the NCSU PULSTAR. Dose rate information is culated in as many as 300 detector locations at once, inside or out of the reactor building.
plate-type, uranium-aluminum alloy fuel elements.
The reactor core is treated as a volume source with gamma emission points distributed according to measured steady-state axial and radial flux distributions.
The reactor building is a domed cylindrical structure constructed of steel plate as illustrated in Fig. 5. The biological shield is also cylindrical in shape. In order those emitted closer to the surface. Importance sam-            to simulate the LLNL facility with the PULST AR pling of both source position and direction is used to          model, the reactor building is approximated by a rec-enhance the number of photons emitted with a high              tangular steel structure of the same height and floor probability of escaping into the reactor bay. Upon              area. The cylindrical reactor pool is approximated by entering the reactor bay, the most likely point of inci-        a rectangular pool of equal height and volume. As the dence is the concrete bay roof. For a thick roof and           thermal flux distribution for this core was unavailable, detectors located within the reactor building, the              the shape is assumed to be the same as that of the escape of radiation through the ceiling is not treated.        PULSTAR. Fission product activity was estimated by The photon is instead forced to reflect off the ceiling        those performing the experiment to be 3.0 x 106 Ci.
PULST AR fuel is in the form of cylindrical rods containing 4% enriched U0 2 pellets clad in Zircaloy-2.
and other concrete structures until criteria for particle            Calculated and measured dose rates are given in history termination are met. Dose rate contributions            Table V for the numbered locations indicated in to all detectors are computed at each reflection. For          Fig. 5. The best agreement is obtained on the reactor thin roofs, there is a significant reduction in the dose        balcony out of direct line of sight with the reactor rate computed in the bay due to gamma rays escaping            core. Dose rates on the roof compare somewhat less through the ceiling. The use of albedos generated for          favorably with the discrepancy probably due to un-thick shields is overly conservative in the calculation        modeled attenuation from control rod actuators, struc-of reflected dose and cannot be used at all for the             tural beams, etc. The calculated dose rate 20 ft above determination of transmitted dose. Instead, statistical        and in line of sight of the core is 38% below the 4750 estimation is used to track photons within the ceiling          rem/h estimated in the experiment. The measured dose with the albedo treatment maintained for wall and sur-         rate at this same point 1 h after shutdown, however, face scatters within the reactor bay.                           was 2500 rad/h, as compared to the calculated value The dose at ground level detectors located outside          at 1 h of 2135 rad/h. This indicates the difference the reactor building is due almost entirely to backscat-        might result more from an error in the estimation tering in air. The reactor bay walls are constructed of        rather than in the calculated value. Dose rates on the 12-in.-thick concrete and allow negligible transmission.       bay floor were computed in two ways. The first allows The concrete ceiling, however, is catacombed with a            for the fact that many of the gamma rays escape minimum thickness of - 3 in. A conservative approx-            through the relatively thin steel roof. The second and
The core is mated as homogeneous with the material volume tions given in Table IV. Gamma rays emitted within the core are ported into the pool volume either directly or through scattering interactions with core materials.
 
The ical shield is sufficiently thick at the base and top to effectively eliminate contributions to the dose from transmission through the shield. Gamma rays are, therefore, assumed to escape the biological shield and enter the bay through a series of reflections.
LOSS-OF-WATER ACCIDENT                                            7
This ment models the biological shield as an oversized duct, for which albedos are ideally suited. The core and logical shield arrangement are illustrated in Fig. 4. sion product decay gammas are emitted isotropically; however, from Fig. 4 it is apparent that photons ted in the solid angle subtended by the biological shield opening have a much better chance of escape than those incident upon the shield walls. It is then tageous to place more importance on photons emitted in that direction.
            . , . - - - - - - 6 0 - f t diam -------------------1~
Similarly, photons emitted deep within the core have much less chance of escape than TABLE IV Core Volume Fractions U0 2 Void Water Zircaloy-2 Aluminum 0.3823 0.0155 0.4339 0.0802 0.0881 6 DOSTER and HEY STANDARD CONCRETE "*,. .. *
fu-in. STEEL ACTUATORS 52 ft 39 ft 26 ft, 6 in.
* 4 ) . BARYTES CONCRETE CONTROL D ROD ACTUATORS TANK 11 ft, 9 in. -CORJ -6 . _,.,. ---------...--
4
I 4 ft, 1-------2 ft 6 in. Fig. 4. Geometry of the core and biological shield. those emitted closer to the surface. Importance pling of both source position and direction is used to enhance the number of photons emitted with a high probability of escaping into the reactor bay. Upon entering the reactor bay, the most likely point of dence is the concrete bay roof. For a thick roof and detectors located within the reactor building, the escape of radiation through the ceiling is not treated. The photon is instead forced to reflect off the ceiling and other concrete structures until criteria for particle history termination are met. Dose rate contributions to all detectors are computed at each reflection.
_i_                CORE
For thin roofs, there is a significant reduction in the dose rate computed in the bay due to gamma rays escaping through the ceiling. The use of albedos generated for thick shields is overly conservative in the calculation of reflected dose and cannot be used at all for the determination of transmitted dose. Instead, statistical estimation is used to track photons within the ceiling with the albedo treatment maintained for wall and face scatters within the reactor bay. The dose at ground level detectors located outside the reactor building is due almost entirely to tering in air. The reactor bay walls are constructed of 12-in.-thick concrete and allow negligible transmission.
                                                      -a
The concrete ceiling, however, is catacombed with a minimum thickness of -3 in. A conservative approx-imation for the calculation of outside dose is made by assuming the roof is a uniform thickness of 3 in. Gamma rays are tracked within the ceiling and, if tered in an outward direction, forced to escape the roof into the atmosphere with weight reduced by the escape probability.
                                                              *.* ~
There the photons undergo a series of scatters until termination criteria are met. Dose rate contributions are computed for all external detectors at each scatter within the atmosphere.
BAY FLOOR
Once the ton history in the atmosphere is terminated, the ticle history is resumed at the point of scatter within the ceiling. COMPARISON TO THE LAWRENCE LIVERMORE NATIONAL LABORATORY EXPERIMENT As a benchmark for the Monte Carlo model, dose rates were calculated and compared with those sured during the loss-of-water experiment conducted at Lawrence Livermore National Laboratory 13 (LLNL). Dose rates were measured at 10 min and 1 h after shutdown with 0 and 1 ft of water over the core. Although this experiment is similar to the type of dent modeled for the PULSTAR, there are major ferences that warrant discussion.
                        &#xa9;          4 ft~
The LLNL reactor is a 2-MW reactor constructed of 90% enriched, plate-type, uranium-aluminum alloy fuel elements.
60 ft 12\~
The reactor building is a domed cylindrical structure constructed of steel plate as illustrated in Fig. 5. The biological shield is also cylindrical in shape. In order to simulate the LLNL facility with the PULST AR model, the reactor building is approximated by a tangular steel structure of the same height and floor area. The cylindrical reactor pool is approximated by a rectangular pool of equal height and volume. As the thermal flux distribution for this core was unavailable, the shape is assumed to be the same as that of the PULST AR. Fission product activity was estimated by those performing the experiment to be 3.0 x 10 6 Ci. Calculated and measured dose rates are given in Table V for the numbered locations indicated in Fig. 5. The best agreement is obtained on the reactor balcony out of direct line of sight with the reactor core. Dose rates on the roof compare somewhat less favorably with the discrepancy probably due to modeled attenuation from control rod actuators, tural beams, etc. The calculated dose rate 20 ft above and in line of sight of the core is 38% below the 4750 rem/h estimated in the experiment.
                                                                      ~          90ft
The measured dose rate at this same point 1 h after shutdown, however, was 2500 rad/h, as compared to the calculated value at 1 h of 2135 rad/h. This indicates the difference might result more from an error in the estimation rather than in the calculated value. Dose rates on the bay floor were computed in two ways. The first allows for the fact that many of the gamma rays escape through the relatively thin steel roof. The second and LOSS-OF-WATER ACCIDENT .,.------60-ft diam fu-in. STEEL ACTUATORS
                                                                            @~
_i_ 4 &#xa9; BAY FLOOR CORE -a 4 *.* "'' .. 39 ft 26 ft, 6 in. 60 ft 90ft 52 ft @ 120 ft " 150 ft @---"' Fig. 5. Lawrence Livermore reactor building.
120 ft
TABLE V Dose Rate Comparison to Measured Values Location Measured Dose Rate 1 (reactor platform) 195 mrem/h 2a (bay roof) 105 mrem/h 2b 46.5 mrem/h 2c 0.58 mrem/h 2d 0.84 mrem/h 3 (line of sight) 4750 rem/ha 2500 rad/hb 4 (bay floor) 370 mrem/hc 5a (outside) 80 to 60 mrem/h 5b 55 to 40 mrem/h 5c 35 to 30 mrem/h 5d 30 mrem/h aEstimated value. bMeasured 1 h after loss of water. cMaximum dose rate measured on bay floor. ctunconservative case (allows for escape through roof). econservative case (no gamma rays escape bay). Computed Dose Rate 220 +/- 60/o mrem/h 290 +/- 40/o mrem/h 24 +/- 20/o mrem/h 0.27 +/- 70/o mrem/h 0.67 +/- 80/o mrem/h 2925 +/- 40/o rem/h 2135 +/- 40/o rad/h 70 +/- 60/o mrem/hct 720 +/- 80/o mrem/he 72.3 +/- 18 O/o mrem/h 33.2 +/- 17 O/o mrem/h 18. 7 +/- 15 O/o mrem/h 12.8 +/- 15 O/o mrem/h 7 8 DOSTER and HEY more conservative is to assume that there is sufficient unmodeled structure in the bay to significantly increase the amount of backscattered radiation.
                                                                                @          "  150 ft Fig. 5. Lawrence Livermore reactor building.
The control rod actuators, for instance, are located directly above the core and will tend to backscatter gamma rays escaping the biological shield. A conservative estimate of the bay floor dose is therefore obtained by ing none of the photons escape the building.
TABLE V Dose Rate Comparison to Measured Values Location                          Measured Dose Rate                      Computed Dose Rate 1 (reactor platform)                      195 mrem/h                            220    +/-  60/o  mrem/h 2a (bay roof)                              105 mrem/h                            290    +/-  40/o  mrem/h 2b                                          46.5 mrem/h                          24    +/-  20/o  mrem/h 2c                                          0.58 mrem/h                          0.27 +/-  70/o  mrem/h 2d                                          0.84 mrem/h                          0.67 +/-  80/o  mrem/h 3 (line of sight)                        4750 rem/ha                          2925    +/-  40/o  rem/h 2500 rad/hb                          2135    +/-  40/o  rad/h 4 (bay floor)                              370 mrem/hc                            70    +/-  60/o  mrem/hct 720    +/-  80/o  mrem/he 5a (outside)                                80 to 60 mrem/h                      72.3  +/- 18 O/o mrem/h 5b                                          55 to 40 mrem/h                      33.2  +/- 17 O/o mrem/h 5c                                          35 to 30 mrem/h                      18. 7 +/- 15 O/o mrem/h 5d                                          30 mrem/h                            12.8  +/- 15 O/o mrem/h aEstimated value.
The true value for the dose should lie somewhere in between as evidenced by Table V. As a final comparison, dose rates were computed 3 ft above ground level outside of the reactor building.
bMeasured 1 h after loss of water.
Good agreement is obtained between calculated and measured values. In summary, the calculated and measured values are in reasonable agreement, especially considering the approximations necessary to apply the PULST AR model to the LLNL experiment.
cMaximum dose rate measured on bay floor.
The results further indicate realistic dose rates can be expected when the model is applied to the PULST AR facility.
ctunconservative case (allows for escape through roof).
NORTH---100 to 125 +/- 8% 125 to 150 +/- 6% 1 50 to 1 7 5 +/- 7 %
econservative case (no gamma rays escape bay).
0 2 3 4 5 SCALE (ml NORTH BAY DOOR 50to75+/-10%
 
25 to 50 +/- 10% Fig. 6. Computed dose rates on bay floor (mrem/h).
8                                              DOSTER and HEY more conservative is to assume that there is sufficient                          RESULTS unmodeled structure in the bay to significantly increase the amount of backscattered radiation. The control            Detectors were located in and around the PUL-rod actuators, for instance, are located directly above  STAR facility such that isodose lines could be estab-the core and will tend to backscatter gamma rays          lished as illustrated in Figs. 6 through 11. This escaping the biological shield. A conservative estimate  required approximately one point detector per square of the bay floor dose is therefore obtained by assum-     metre of analyzed surface. Does rates were obtained ing none of the photons escape the building. The true    10 min after shutdown assuming an infinite operating value for the dose should lie somewhere in between as    time at 1 MW.
RESULTS Detectors were located in and around the ST AR facility such that isodose lines could be lished as illustrated in Figs. 6 through 11. This required approximately one point detector per square metre of analyzed surface. Does rates were obtained 10 min after shutdown assuming an infinite operating time at 1 MW. Figure 6 illustrates the computed dose rates on the bay floor. The hottest spots are located east and south of the reactor with dose rates ranging from 150 to 175 mrem/h. Local variations in the dose lines are duced by the off-center location of the core within the biological shield and by the asymmetric nature of the bay walls. The least exposed area is adjacent to the biological shield with dose rates ranging from 25 to 50 mrem/h. Approximately 75% of the dose on the floor NORTH----10 to 50 +/- 4% 50 to 230 +/- 4% 0.3 to 0.5 +/- 5% 0 2 3 4 5 SCALE (m) Fig. 7. Computed dose rates on the reactor platform (mrem/h).
evidenced by Table V. As a final comparison, dose            Figure 6 illustrates the computed dose rates on the rates were computed 3 ft above ground level outside      bay floor. The hottest spots are located east and south of the reactor building. Good agreement is obtained      of the reactor with dose rates ranging from 150 to 175 between calculated and measured values.                  mrem/h. Local variations in the dose lines are pro-In summary, the calculated and measured values      duced by the off-center location of the core within the are in reasonable agreement, especially considering the   biological shield and by the asymmetric nature of the approximations necessary to apply the PULST AR            bay walls. The least exposed area is adjacent to the model to the LLNL experiment. The results further        biological shield with dose rates ranging from 25 to 50 indicate realistic dose rates can be expected when the   mrem/h. Approximately 75% of the dose on the floor model is applied to the PULST AR facility.
LOSS-OF-WATER ACCIDENT 9 is due to backscatter directly from the ceiling; the logical shield tends to shadow areas immediately rounding it, producing the lower dose rates. Dose rates on the reactor platform are shown in Fig. 7. Detector locations are -9 m above the bay floor and 6 ft (approximately head high) above the platform itself. As expected, the computed dose rates are substantially higher than those on the bay floor. Much of the interior surface of the biological shield is visible from the platform, leading to significant tributions to the dose rate due to direct gamma-ray reflections from these surfaces.
NORTH----
This accounts for the rapidly increasing dose rate as detectors are placed closer to the pool edge. The platform extends up to the pool edge providing detector locations in direct line of sight of the core. These locations experience the greatest exposure to the gamma field with maximum dose rates on the order of 230 rem/h. Figure 8 illustrates the expected dose rates in the control room. The two control room windows are ordinary glass and the door is wood. Gamma rays stream in through the windows and door much as the sun shines in a window. This results in dose rates on ,......-.....
NORTH---
50 to 100 +/- 6% (/\ \ 1 00 to 1 50 +/- 5 % \\ 1 50 to 200 +/- 4% DOOR the order of 250 mrem/h next to the windows and door, decreasing rapidly to a minimum of 5 mrem/h in the northeast corner of the control room. Note that dose rates could be cut dramatically by the placement of temporary shields in front of these openings.
100 to 125 +/- 8%                NORTH BAY DOOR 125 to 150 +/- 6%
This is of particular importance considering the console location.
50to75+/-10%
A similar effect is seen due to the doors opening from the reactor bay into the loading dock area as illustrated in Fig. 9. The projection is a small landing 12 ft above the bay floor and on the same level as the loading dock. An equipment room is located neath. The loading dock is a nonradiation area quently used as a passageway between buildings.
25 to 50 +/- 10%                                            10 to 50 +/- 4%
Dose rates as high as 175 mrem/h tapering off to a fraction of a millirem per hour are encountered in this area. Other areas of interest are the offices of the health physicist and nuclear reactor operations located cent to and north of the reactor building.
50 to 230 +/- 4%
Due to the attenuation provided by the concrete bay wall, dose rates in these areas are on the order of 10-6 rem/h. This is comparable to the present background and is considered negligible.
0.3 to 0.5 +/- 5%
... *---NORTH CONTROL ROOM WINDOWS 0 2 3 SCALE (m) Fig. 8. Computed dose rates in the control room (mrem/h).
1 50 to 1 7 5 +/- 7 %
10 DOSTER and HEY 1 to 5 +/- 18% NORTH 0 2 SCALE (m) 3 10to25+/-12%
                ~
25 t012'5'+/- 10% / --------125 to 150 +/- 5% Fig. 9. Computed dose rates in the loading dock (mrem/h).
0      2 3 4     5 0      2    3  4   5                                          SCALE (m)
Dose rates found on the bay roof range from a few rems per hour to 25 rem/h 16 m directly above the core midplane as shown in Fig. 10. Outside the tor building, the isodose lines form concentric circles around the facility with the reactor core at the center as illustrated in Fig. 11. These dose rates are computed using dry air as the scattering medium. Ground effects are neglected.
SCALE (ml Fig. 7. Computed dose rates on the reactor platform Fig. 6. Computed dose rates on bay floor (mrem/h).   (mrem/h).
Dose rates reach a maximum of 4 mrem/h immediately adjacent to the building, ping to <0.3 mrem/h at distances
 
>80 m from the core. Natural background outside the building ages 200 mrem/yr.  
LOSS-OF-WATER ACCIDENT                                                  9 is due to backscatter directly from the ceiling; the bio-        the order of 250 mrem/h next to the windows and logical shield tends to shadow areas immediately sur-            door, decreasing rapidly to a minimum of 5 mrem/h rounding it, producing the lower dose rates.                     in the northeast corner of the control room. Note that Dose rates on the reactor platform are shown in              dose rates could be cut dramatically by the placement Fig. 7. Detector locations are -9 m above the bay                of temporary shields in front of these openings. This floor and 6 ft (approximately head high) above the                is of particular importance considering the console platform itself. As expected, the computed dose rates            location.
are substantially higher than those on the bay floor.                 A similar effect is seen due to the doors opening Much of the interior surface of the biological shield is          from the reactor bay into the loading dock area as visible from the platform, leading to significant con-           illustrated in Fig. 9. The projection is a small landing tributions to the dose rate due to direct gamma-ray              12 ft above the bay floor and on the same level as the reflections from these surfaces. This accounts for the            loading dock. An equipment room is located under-rapidly increasing dose rate as detectors are placed              neath. The loading dock is a nonradiation area fre-closer to the pool edge. The platform extends up to the          quently used as a passageway between buildings. Dose pool edge providing detector locations in direct line of          rates as high as 175 mrem/h tapering off to a fraction sight of the core. These locations experience the                of a millirem per hour are encountered in this area.
greatest exposure to the gamma field with maximum                Other areas of interest are the offices of the health dose rates on the order of 230 rem/h.                            physicist and nuclear reactor operations located adja-Figure 8 illustrates the expected dose rates in the           cent to and north of the reactor building. Due to the control room. The two control room windows are                    attenuation provided by the concrete bay wall, dose ordinary glass and the door is wood. Gamma rays                  rates in these areas are on the order of 10- 6 rem/h.
stream in through the windows and door much as the               This is comparable to the present background and is sun shines in a window. This results in dose rates on            considered negligible.
50 to 100 +/- 6%
(/\
1 00 to 1 50 +/- 5 %
                                \
              \\ ~\I 1 50 to 200 +/- 4%
DOOR CONTROL ROOM
                    *---NORTH                          WINDOWS 0              2      3 SCALE (m)
Fig. 8. Computed dose rates in the control room (mrem/h).
 
10                                                DOSTER and HEY 1 to 5 +/- 18%
10to25+/-12%
125
                                                                            / --------
25 t012'5'+/- 10%
to 150 +/- 5%
              ~          NORTH 0                2      3 SCALE (m)
Fig. 9. Computed dose rates in the loading dock (mrem/h).
Dose rates found on the bay roof range from a            istic dose rates for the PULST AR facility. Computed few rems per hour to 25 rem/h 16 m directly above the       dose rates for the PULST AR 10 min following a full-core midplane as shown in Fig. 10. Outside the reac-          power shutdown range from 230 mrem/h on the reac-tor building, the isodose lines form concentric circles      tor platform in direct line of sight of the core to 0.3 around the facility with the reactor core at the center        mrem/h outside the reactor building 80 m from the as illustrated in Fig. 11. These dose rates are computed      core. Maximum dose rates in key access areas through-using dry air as the scattering medium. Ground effects        out the facility were 175 mrem/h on the reactor bay are neglected. Dose rates reach a maximum of 4                floor, 250 mrem/h in the control room adjacent to the mrem/h immediately adjacent to the building, drop-            control room windows, and 150 mrem/h on the load-ping to <0.3 mrem/h at distances >80 m from the               ing dock adjacent to the bay access door. Dose rates core. Natural background outside the building aver-           in offices separated from the reactor bay by thick con-ages 200 mrem/yr.                                             crete walls were on the order of background and con-sidered negligible.


==SUMMARY==
==SUMMARY==
A Monte Carlo model has been developed and used to generate expected dose rates in and around the reactor facility at NCSU for a postulated accident involving sudden loss of all pool water. Benchmark comparisons with the measured dose rates from a of-water experiment at the LLNL pool-type reactor indicates the model can be expected to produce real-istic dose rates for the PULST AR facility.
 
Computed dose rates for the PULST AR 10 min following a power shutdown range from 230 mrem/h on the tor platform in direct line of sight of the core to 0.3 mrem/h outside the reactor building 80 m from the core. Maximum dose rates in key access areas out the facility were 175 mrem/h on the reactor bay floor, 250 mrem/h in the control room adjacent to the control room windows, and 150 mrem/h on the ing dock adjacent to the bay access door. Dose rates in offices separated from the reactor bay by thick crete walls were on the order of background and sidered negligible.
REFERENCES A Monte Carlo model has been developed and used to generate expected dose rates in and around the         1. "NCSU PULSTAR Safety Analysis Report," Copy reactor facility at NCSU for a postulated accident            Number 80, North Carolina State University, Department involving sudden loss of all pool water. Benchmark            of Nuclear Engineering, Raleigh, North Carolina (1967).
REFERENCES
comparisons with the measured dose rates from a loss-          2. W.-C. TUNG, "A Guide to Computer Code MORSE-of-water experiment at the LLNL pool-type reactor            CG: General-Purpose Monte Carlo Multigroup Neutron indicates the model can be expected to produce real-          and Gamma-Ray Transport Code with Combinatorial
: 1. "NCSU PULSTAR Safety Analysis Report," Copy Number 80, North Carolina State University, Department of Nuclear Engineering, Raleigh, North Carolina (1967). 2. W.-C. TUNG, "A Guide to Computer Code CG: General-Purpose Monte Carlo Multigroup Neutron and Gamma-Ray Transport Code with Combinatorial NORTH-----
 
...
N O R T H - - - - -...
* D <1+/-10% ._____ 0 2 3 4 5 SCALE (m) Fig. 10. Computed dose rates on the bay roof (mrem/h).
* WEST BROUGHTON DRIVE w
w > a: 0 I (.'.) ::J 0 a: 0 al a: <! >-WEST BROUGHTON DRIVE EAST BROUGHTON DRIVE 0 1 to 2 +/- 7% 0.5 to 1 +/- 7% 10 20 SCALE (ml 30 Fig. 11. Computed dose rates outside the reactor building (mrem/h).  
a:
.... ....
0 I
12 DOSTER and HEY Geometry," INER-0409/MN-80, Institute of Nuclear Energy Research (1981). 3. E. D. CASHWELL, J. R. NEERGAARD, C. J. EVERETT, R. G. SCHRANDT, W. M. TAYLOR, and G.D. TURNER, "Monte Carlo Photon Codes: MCG and MCP," USAEC Report LA-5157-MS, Los Alamos National Laboratory (1973). 4. Los Alamos Radiation Transport Group (X-6), "MCNP-A General Monte Carlo Code for Neutron and Photon Transport," LA-7396-M, Los Alamos National Laboratory (1981 ). 5. J. W. KIMLINGER, E. F. PLECHATY, and J. R. TERRALL, "SORS Monte Carlo Photon-Transport Code for the CDC 6600," USAEC Report UCRL-50358, sity of California, Livermore, Lawrence Livermore tion Laboratory (1967). 6. N. M. SCHAEFFER, "Reactor Shielding for Nuclear Engineers," U.S. Department of Energy (1973). 7. A. B. CHILTON and C. M. HUDDLESTON, Nucl. Sci. Eng., 17, 419 (1963). 8. D. J. RASO, Nucl. Sci. Eng., 17, 411 (1963). 9. E. M. FOURNIE and A. B. CHILTON, Nucl. Sci. Eng., 76, 66 (1980). 10. M. J. BERGER and D. J. RASO, Radial. Res., 12, 20 (1960). 11. M. B. WELLS, "Differential Dose Albedos for lations of Gamma-Ray Reflection from Concrete," USAEC Report RRA-T56, Radiation Research Associates, Inc. (1964). 12. S. GLASSTONE, Principles of Nuclear Reactor neering, p. 120, Van Nostrand Reinhold Company (1955). 13. M. KNEZEVICH, R. L. KATHREN, 0. K. FERICH, and K. R. KASE, Health Phys. J., 11, 481 (1965).}}
(.'.)
::J 0
a:
0 al a:
D
                                                      >-                                           1 to 2 +/- 7%
                      <1+/-10%
0.5 to 1 +/- 7%
EAST BROUGHTON DRIVE 0      10       20     30 0          2    3    4    5 SCALE (ml SCALE (m)
Fig. 10. Computed dose rates on the bay roof (mrem/h).      Fig. 11. Computed dose rates outside the reactor building (mrem/h).
 
12                                               DOSTER and HEY Geometry," INER-0409/MN-80, Institute of Nuclear           7. A. B. CHILTON and C. M. HUDDLESTON, Nucl.
Energy Research (1981).                                   Sci. Eng., 17, 419 (1963).
: 3. E. D. CASHWELL, J. R. NEERGAARD, C. J.                 8. D. J. RASO, Nucl. Sci. Eng., 17, 411 (1963).
EVERETT, R. G. SCHRANDT, W. M. TAYLOR, and G.D. TURNER, "Monte Carlo Photon Codes: MCG and           9. E. M. FOURNIE and A. B. CHILTON, Nucl. Sci.
MCP," USAEC Report LA-5157-MS, Los Alamos                 Eng., 76, 66 (1980).
National Laboratory (1973).
: 10. M. J. BERGER and D. J. RASO, Radial. Res., 12, 20
: 4. Los Alamos Radiation Transport Group (X-6),         (1960).
"MCNP-A General Monte Carlo Code for Neutron and Photon Transport," LA-7396-M, Los Alamos National         11. M. B. WELLS, "Differential Dose Albedos for Calcu-Laboratory (1981 ).                                       lations of Gamma-Ray Reflection from Concrete," USAEC Report RRA-T56, Radiation Research Associates, Inc.
: 5. J. W. KIMLINGER, E. F. PLECHATY, and J. R.           (1964).
TERRALL, "SORS Monte Carlo Photon-Transport Code for the CDC 6600," USAEC Report UCRL-50358, Univer-       12. S. GLASSTONE, Principles of Nuclear Reactor Engi-sity of California, Livermore, Lawrence Livermore Radia-  neering, p. 120, Van Nostrand Reinhold Company (1955).
tion Laboratory (1967).
: 13. M. KNEZEVICH, R. L. KATHREN, 0. K. HEL-
: 6. N. M. SCHAEFFER, "Reactor Shielding for Nuclear      FERICH, and K. R. KASE, Health Phys. J., 11, 481 Engineers," U.S. Department of Energy (1973).            (1965).}}

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Monte Carolo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor
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Attachment 6 Monte Carlo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor J.M. Doster and B.E. Hey

NUCLEAR SCIENCE AND ENGINEERING: 93, 1-12 (1986)

Monte Carlo Simulation of the Gamma Dose Rate in a Loss-of-Water Accident at the North Carolina State University Research Reactor Joseph M. Doster and Brit E. Hey North Carolina State University, Department of Nuclear Engineering, Box 7909 Raleigh, North Carolina 27695-7909 Received May 6, 1985 Accepted November 11, 1985 Abstract-In pool-type research reactors, a sudden loss of all pool water can result in significant exter-nal radiation dose. Of concern are fission product decay gamma rays emitted within the core, stream-ing out of the biological shield producing unacceptable radiation exposure in and around the reactor building. A Monte Carlo model was developed and used to generate dose maps for key access and traffic areas throughout the reactor facility at North Carolina State University. It was found that several of these areas could be exposed to significant gamma radiation fields, ranging from 230 rem/h 20 ft directly over and in line of sight of the core to 4 mrem/h outside and adjacent to the reactor building. Expected dose rates were also computed for the reactor bay floor, control room, and offices.

The model was benchmarked against dose rates measured at the Lawrence Livermore National Lab-oratory pool-type reactor.

Simulation Monte-Carlo du taux de dose gamma dans un accident de perte d'eau intervenant dans le reacteur de recherche de la North Carolina State University Resume - Dans /es reacteurs piscines une perte brusque et complete de /'eau de piscine pourrait produire une dose de radiation externe significative. On s'occupe particulierement du fait de la radi-ation gamma liberee dans le coeur suite a la desintegration des produits de fission, qui, en sortant de tecran biologique, cause une exposition intolerable dans le biitiment du reacteur ainsi que dans :ses environs. Un modele Monte-Carlo a ete mis au point et employe pour etablir des cartes de doses va-lables pour /es zones d'acces et de trafic /es plus importantes dans /'ensemble du biitiment du reacteur de la North Carolina State University. On a trouve qu'un nombre de ces zones pourraient etre exposees ii des champs significatifs de radiation gamma, s'elevant de 230 rem/h ii une distance de 20 pieds directement au-dessus du bfltiment de reacteur, sur la ligne de vue du coeur, jusqu'ii 4 mremlh au-dehors du et avoisinant le bfltiment du reacteur. Les taux de doses attendus ont ete ca/cutees ega/e-ment pour le sol de la baie du reacteur, la sal/e de commande et !es bureaux. Le modele fut repere en le comparant aux taux de doses mesures au "Lawrence Livermore National Laboratory pool-type reactor."

Monte-Carlo-Simulation der bei einem Wasserverluststorfall im North Carolina State University Forschungsreaktor auftretenden Gamma-Dosisleistung Zusammenfassung- In Forschungsreaktoren in Pool-Bauweise kann ein p/Otzlicher Verlust des gesam-ten Beckenwassers zu einer betriichtlichen externen Strahlendosis fuhren. Sorge bereiten dabei die im Reaktor aufgrund des Spaltproduktzerfal/s emittierten Gammastrahlen; sie entweichen aus dem bio/ogischen Schild und verursachen im Reaktorgebiiude und in seiner Umgebung eine unannehmbar hohe Strahlenbelastung. Es wurde ein Monte-Carlo-Model/ entwickelt und eingesetzt, um Dosiskar-ten fur wichtige Zugangs- und Verkehrsbereiche in der ganzen Reaktoranlage der North Carolina State 1

2 DOSTER and HEY University erstellen zu konnen. Dabei stellte sich heraus, daj] eine Reihe dieser Bereiche starken Gam-mafeldern ausgesetzt werden konnte. Diese liegen zwischen 230 rem/h im Abstand von 20 Fuj] direkt iiber dem Reaktorgebiiude in Sichtlinie des Reaktorkerns und 4 mremlh auj]erhalb des Reaktorge-biiudes und in seiner unmittelbaren Umgebung. Die zu erwartenden Dosisleistungen wurden auch fiir den Boden des Arbeitsbereichs im Reaktor, die Warte und die Biiroriiume berechnet. Das Model!

wurde gegen die im "Lawrence Livermore National Laboratory pool-type reactor" gemessenen Dosis-leistungen abgeglichen.

INTRODUCTION within the reactor bay requires dose determinations in several hundred locations. The need for a streamlined For a pool-type research reactor, the sudden loss and very efficient model becomes immediately appar-of pool water is an accident considered for licensing ent. Such a Monte Carlo model was developed specif-and emergency planning purposes. The PULST AR ically for the PULST AR facility. To decrease reactor located on the campus of North Carolina State computer execution time and simplify the computa-University (NCSU) is considered susceptible to such an tional algorithm, a number albedo approach was accident. The tank liner has several penetrations that incorporated to calculate the dose from scattered radi-represent possible failure modes, permitting the tank ation while eliminating the need for detailed tracking to drain into the reactor room basement. It is esti- of radiation through concrete walls, ceilings, etc.

mated that the time required to drain the tank through Though an approximation, this approach was consid-tank liner penetrations varies from 2.4 min for the ered a reasonable compromise between accuracy and 12- x 12-in. beam tube to 12.3 min for the 6-in. beam computational efficiency. Number as well as dose tube. 1 The power density of the core is sufficiently albedos were used such that particle paths involving low to allow air cooling by natural circulation after a multiple walls or structures could be simulated. A sec-sudden full-power shutdown. Fuel failure will, there- ond Monte Carlo model was written to generate the fore, not result from inadequate core cooling. Of con- necessary doubly differential number albedos used in cern, however, are fission product gamma rays emitted this study. These albedos are supplied to the dose within the core escaping the biological shield with model in tabular form and interpolated throughout the sufficient intensity to limit access to key maintenance simulation.

and control areas. As the reactor building is centrally A number of general purpose Monte Carlo codes located on the NCSU campus, of additional concern are available for photon and coupled neutron-photon is the potential radiation hazard in areas of high stu- problems. 2 - 5 Although highly flexible, codes of this dent and personnel population. The areas of primary type are not without their disadvantages. These codes interest are the reactor bay floor, reactor platform, are very large in size and due to their generality, often control room, loading dock, offices, bay roof, and less efficient in a particular application than a code campus areas outside the reactor building. These areas developed specifically for that problem. In addition, were chosen due to their relative importance with a significant amount of work is involved in just install-regard to surveillance, reactor maintenance, and oper- ing, checking, and learning to use these codes. For a ations. In addition, the loading dock is a high student one-shot application, an alternate choice is the devel-and personnel traffic area connecting two wings of the opment of a Monte Carlo model for the particular PULST AR facility. These locations are illustrated in application at hand.

Fig. 1, with the exception of offices and campus areas.

The offices are located immediately adjacent to and north of the reactor building. The objective of this GAMMA-RAY NUMBER AND DOSE ALBEDOS study is to provide information regarding the poten-tial magnitude of these dose rates, their location, and Albedo theory treats the interaction of gamma at what time these areas might be considered safe to rays with a surface as a reflection phenomenon. The reenter. This study and its recommendations are to be justification for this approach in our work is threefold.

incorporated into the PULSTAR Final Safety Analysis First, the dimensions of the scattering surfaces mak-Report in support of current relicensing activities. ing up the reactor shield, bay, and office rooms are The complicated geometry and number of mech- very large and located at significant distances from the anisms by which radiation emitted within the core detection points. Under these circumstances, the dif-could arrive at a particular location within the facility ference in location between incident and exit points effectively eliminate all computational techniques but can be neglected. Second, the vast majority of the scat-the Monte Carlo method. Though extremely powerful, tering surfaces is constructed of ordinary concrete.

the Monte Carlo method can require prohibitive This material is used in virtually every type of fixed amounts of computer time, particularly if not used shield, and its albedo properties have been thoroughly efficiently. To adequately map the dose distribution investigated. 6 Third, there are tremendous savings in

LOSS-OF-WATER ACCIDENT 3 LOADING DOCK Fig. 1. Reactor building.

machine time when using albedos over conventional aD (EoJJo, 8, </>)

methods of particle tracking and estimation between interaction points. = fo 00 a(Eo,80 ,E,8, </>)K(E) I K(E0) dE , (1)

Definitions where K(E) is the flux-to-dose conversion factor.

The differential gamma-ray number albedo Chilton and Huddleston 7 developed a semiempir-a(E0,00,E,0,</>) as defined here is the differential cur- ical formula for this differential gamma-ray dose rent outward from a planar surface per incident cur- albedo for ordinary concrete based on the Monte rent inward to that surface, where E0 is the incident Carlo studies of Raso. 8 This formula has the form particle energy in mega-electron-volts, 00 is an inci-dent polar angle, Eis the exit particle energy, () is the aD(Eo,80,8, ¢) = [C(Eo)K(Eo,8s) x 1026 exit polar angle, and</> is the exit azimuthal angle. Fig- + C' (£0 )] / [I + cos00 secO] , (2) ure 2 illustrates this relationship. For situations where where the exit gamma-ray energy is not required, the differ-ential dose albedo can be useful. The dose albedo used C(Eo), C ' (E0 ) =fitted parameters dependent only in this work is related to the number albedo by the on incident energy E0 and mate-relationship rial properties

4 DOSTER and HEY TABLE I Incident Gamma-Ray Energies and Angles Eo Energy (MeV) Direction µ 0 = (cos80 )

0.020 0.000 0.050 0.143 0.075 0.286 0.100 0.429 0.200 0.571 0.500 0.714 1.000 0.857 1.250 1.000 2.000 4.000 6.000 in solid angle. Figure 3 illustrates the divisions made Fig. 2. Geometry depicting particle reflection from a in the emergent solid angle used in the albedo calcu-surface. lation. The physical model is simply a homogeneous laterally infinite 1-m-thick concrete slab. In accordance with usual practice, coherent scattering and multiple photon emission are ignored along with fluorescence Os= scattering angle as illustrated in Fig. 2 radiation and bremsstrahlung, which are considered to be of little significance. 9 K(E0 , Os) :::: Klein-Nishina differential energy A great deal of effort has been devoted to the scattering cross section per elec- study of gamma rays backscattered from and transmit-tron per steradian. ted through concrete. Raso, 8 Berger and Raso, 10 and The dose albedos given by either Eq. (1) or (2) can be Wells 11 amassed a considerable number of data on used in the Monte Carlo simulation as a means of esti- differential and total albedos using the Monte Carlo method in the early 1960s. There have been numerous mating the dose from gamma-ray backscatter off ordi-nary concrete. The Chilton-Huddleston formula has the advantage of reduced run times and lower mem-ory requirements when calculating the backscattered dose from a single surface; however, it cannot be used exclusively to calculate the dose from higher order reflections as exit energy information has been lost.

Monte Carlo Simulation of Gamma-Ray Number Albedos The Monte Carlo method is used to generate a table of differential gamma-ray number albedos for ordinary concrete. 9 Values are computed for the 11 incident energies and 8 incident angles given in Ta-ble I. For each of these 88 incident conditions, 6 exit energy intervals, 6 exit polar angle intervals, and 6 exit azimuthal angle intervals are considered yielding

-20 000 entries that must be stored and accessed. The 6 exit energy groups for each incident energy £ 0 and angle 00 evenly span the range 0.01 MeV to EMAX(E0 ,00 ), where EMAX is the maximum exit energy possible for the given incident conditions based on a single Compton scatter within the shield. The exit polar and azimuthal angular groups are evenly spaced Fig. 3. Geometry used in albedo computations.

LOSS-OF-WATER ACCIDENT s attempts to fit this differential data to a semiempiri- p(Eo,µ 0 ,E,µ,¢) = a(E0 ,µ 0 ,E,µ,¢)/A(Eo,µo) ,

cal formula, such as that of Chilton and Huddleston (3) mentioned previously, or an exponential curve, such as that of Haggmark et al. 12 Results from the albedo which are sampled for the energy and direction of the model developed in this work are compared to those emergent reflected photons. The denominator from the literature in Tables II and Ill. The agreement is seen to be quite good. Material composition was A(E0 ,µ 0 ) == lEMAX f a(E ,µ ,E,µ,¢)d0dE 0 0 (4) taken to be ordinary concrete 20 cm thick with a den- 0 sity of 2.35 g/cm 3

  • Total albedos were obtained by is simply the total number albedo at the incident pho-numerically integrating the differential albedos over ton energy and direction and also provides the weight exit polar and azimuthal angles. factor for the reflection.

The differential albedos are used to generate prob-ability distribution functions of the form MONTE CARLO MODEL OF FISSION PRODUCT GAMMA-RAY TRANSPORT TABLE II The computer code DOSE simulates the transport Total Number Albedo Comparison of delayed fission product gamma rays escaping from the NCSU PULSTAR. Dose rate information is cal-0 culated in as many as 300 detector locations at once, (deg) Study 2.0 MeV 1.0 MeV 0.5 MeV 0.2 MeV inside or out of the reactor building. The reactor core is treated as a volume source with gamma emission 0 pa 0.159 0.215 0.271 0.258 points distributed according to measured steady-state BRb 0.162 0.221 0.268 0.285 RC axial and radial flux distributions. PULSTAR fuel is 0.164 0.207 0.275 0.285 in the form of cylindrical rods containing 4% enriched 60 p 0.317 0.351 0.420 0.407 U0 2 pellets clad in Zircaloy-2. The core is approxi-BR 0.313 0.390 0.414 0.409 mated as homogeneous with the material volume frac-R 0.316 0.365 0.419 0.419 tions given in Table IV.

90 p 0.717 0.733 0.752 0.703 Gamma rays emitted within the core are trans-BR 0.724 0.744 0.734 0.703 ported into the pool volume either directly or through d d d d R scattering interactions with core materials. The biolog-ical shield is sufficiently thick at the base and top to ap = present paper: 1000 histories. effectively eliminate contributions to the dose from bBR = Berger and Raso. 9 transmission through the shield. Gamma rays are, cR =Raso. 8 therefore, assumed to escape the biological shield and ctNumbers unavailable.

enter the bay through a series of reflections. This treat-ment models the biological shield as an oversized duct, for which albedos are ideally suited. The core and bio-TABLE III logical shield arrangement are illustrated in Fig. 4. Fis-sion product decay gammas are emitted isotropically; Total Dose Albedo Comparison however, from Fig. 4 it is apparent that photons emit-ted in the solid angle subtended by the biological shield 0

(deg) Study 2.0 MeV 1.0 MeV 0.5 MeV 0.2 MeV opening have a much better chance of escape than those incident upon the shield walls. It is then advan-0 pa 0.017 0.037 0.071 0.139 tageous to place more importance on photons emitted BRb 0.020 0.040 0.074 0.138 in that direction. Similarly, photons emitted deep CHC 0.032 0.049 0.076 0.134 within the core have much less chance of escape than 60 p 0.057 0.099 0.143 0.211 BR 0.055 0.099 0.146 0.220 CH 0.063 0.094 0.136 0.214 TABLE IV 90 p 0.302 0.347 0.387 0.463 Core Volume Fractions BR 0.303 0.355 0.395 0.470 CH 0.322 0.388 0.456 0.580 U02 0.3823 Void 0.0155 ap =present paper: 1000 histories. Water 0.4339 bBR =Berger and Raso. 9 Zircaloy-2 0.0802 ccH =Chilton and Huddleston, 10 numerically inte- Aluminum 0.0881 grated.

D 6 DOSTER and HEY imation for the calculation of outside dose is made by CONTROL ROD assuming the roof is a uniform thickness of 3 in.

ACTUATORS Gamma rays are tracked within the ceiling and, if scat-tered in an outward direction, forced to escape the roof into the atmosphere with weight reduced by the escape probability. There the photons undergo a series of scatters until termination criteria are met. Dose rate contributions are computed for all external detectors at each scatter within the atmosphere. Once the pho-TANK ton history in the atmosphere is terminated, the par-STANDARD ticle history is resumed at the point of scatter within CONCRETE 11 ft, the ceiling.

9 in.

COMPARISON TO THE LAWRENCE LIVERMORE NATIONAL LABORATORY

- 6

~

EXPERIMENT As a benchmark for the Monte Carlo model, dose

"*,. .. ~*

rates were calculated and compared with those mea-z~o

~ *

  • 4 sured during the loss-of-water experiment conducted at Lawrence Livermore National Laboratory 13

)

BARYTES CONCRETE - CORJ --~

(LLNL). Dose rates were measured at 10 min and 1 h after shutdown with 0 and 1 ft of water over the core.

Although this experiment is similar to the type of acci-


...-- I 4 ft, 1------- dent modeled for the PULSTAR, there are major dif-2 ft 6 in. ferences that warrant discussion. The LLNL reactor is a 2-MW reactor constructed of 90% enriched, Fig. 4. Geometry of the core and biological shield.

plate-type, uranium-aluminum alloy fuel elements.

The reactor building is a domed cylindrical structure constructed of steel plate as illustrated in Fig. 5. The biological shield is also cylindrical in shape. In order those emitted closer to the surface. Importance sam- to simulate the LLNL facility with the PULST AR pling of both source position and direction is used to model, the reactor building is approximated by a rec-enhance the number of photons emitted with a high tangular steel structure of the same height and floor probability of escaping into the reactor bay. Upon area. The cylindrical reactor pool is approximated by entering the reactor bay, the most likely point of inci- a rectangular pool of equal height and volume. As the dence is the concrete bay roof. For a thick roof and thermal flux distribution for this core was unavailable, detectors located within the reactor building, the the shape is assumed to be the same as that of the escape of radiation through the ceiling is not treated. PULSTAR. Fission product activity was estimated by The photon is instead forced to reflect off the ceiling those performing the experiment to be 3.0 x 106 Ci.

and other concrete structures until criteria for particle Calculated and measured dose rates are given in history termination are met. Dose rate contributions Table V for the numbered locations indicated in to all detectors are computed at each reflection. For Fig. 5. The best agreement is obtained on the reactor thin roofs, there is a significant reduction in the dose balcony out of direct line of sight with the reactor rate computed in the bay due to gamma rays escaping core. Dose rates on the roof compare somewhat less through the ceiling. The use of albedos generated for favorably with the discrepancy probably due to un-thick shields is overly conservative in the calculation modeled attenuation from control rod actuators, struc-of reflected dose and cannot be used at all for the tural beams, etc. The calculated dose rate 20 ft above determination of transmitted dose. Instead, statistical and in line of sight of the core is 38% below the 4750 estimation is used to track photons within the ceiling rem/h estimated in the experiment. The measured dose with the albedo treatment maintained for wall and sur- rate at this same point 1 h after shutdown, however, face scatters within the reactor bay. was 2500 rad/h, as compared to the calculated value The dose at ground level detectors located outside at 1 h of 2135 rad/h. This indicates the difference the reactor building is due almost entirely to backscat- might result more from an error in the estimation tering in air. The reactor bay walls are constructed of rather than in the calculated value. Dose rates on the 12-in.-thick concrete and allow negligible transmission. bay floor were computed in two ways. The first allows The concrete ceiling, however, is catacombed with a for the fact that many of the gamma rays escape minimum thickness of - 3 in. A conservative approx- through the relatively thin steel roof. The second and

LOSS-OF-WATER ACCIDENT 7

. , . - - - - - - 6 0 - f t diam -------------------1~

fu-in. STEEL ACTUATORS 52 ft 39 ft 26 ft, 6 in.

4

_i_ CORE

-a

  • .* ~

BAY FLOOR

© 4 ft~

60 ft 12\~

~ 90ft

@~

120 ft

@ " 150 ft Fig. 5. Lawrence Livermore reactor building.

TABLE V Dose Rate Comparison to Measured Values Location Measured Dose Rate Computed Dose Rate 1 (reactor platform) 195 mrem/h 220 +/- 60/o mrem/h 2a (bay roof) 105 mrem/h 290 +/- 40/o mrem/h 2b 46.5 mrem/h 24 +/- 20/o mrem/h 2c 0.58 mrem/h 0.27 +/- 70/o mrem/h 2d 0.84 mrem/h 0.67 +/- 80/o mrem/h 3 (line of sight) 4750 rem/ha 2925 +/- 40/o rem/h 2500 rad/hb 2135 +/- 40/o rad/h 4 (bay floor) 370 mrem/hc 70 +/- 60/o mrem/hct 720 +/- 80/o mrem/he 5a (outside) 80 to 60 mrem/h 72.3 +/- 18 O/o mrem/h 5b 55 to 40 mrem/h 33.2 +/- 17 O/o mrem/h 5c 35 to 30 mrem/h 18. 7 +/- 15 O/o mrem/h 5d 30 mrem/h 12.8 +/- 15 O/o mrem/h aEstimated value.

bMeasured 1 h after loss of water.

cMaximum dose rate measured on bay floor.

ctunconservative case (allows for escape through roof).

econservative case (no gamma rays escape bay).

8 DOSTER and HEY more conservative is to assume that there is sufficient RESULTS unmodeled structure in the bay to significantly increase the amount of backscattered radiation. The control Detectors were located in and around the PUL-rod actuators, for instance, are located directly above STAR facility such that isodose lines could be estab-the core and will tend to backscatter gamma rays lished as illustrated in Figs. 6 through 11. This escaping the biological shield. A conservative estimate required approximately one point detector per square of the bay floor dose is therefore obtained by assum- metre of analyzed surface. Does rates were obtained ing none of the photons escape the building. The true 10 min after shutdown assuming an infinite operating value for the dose should lie somewhere in between as time at 1 MW.

evidenced by Table V. As a final comparison, dose Figure 6 illustrates the computed dose rates on the rates were computed 3 ft above ground level outside bay floor. The hottest spots are located east and south of the reactor building. Good agreement is obtained of the reactor with dose rates ranging from 150 to 175 between calculated and measured values. mrem/h. Local variations in the dose lines are pro-In summary, the calculated and measured values duced by the off-center location of the core within the are in reasonable agreement, especially considering the biological shield and by the asymmetric nature of the approximations necessary to apply the PULST AR bay walls. The least exposed area is adjacent to the model to the LLNL experiment. The results further biological shield with dose rates ranging from 25 to 50 indicate realistic dose rates can be expected when the mrem/h. Approximately 75% of the dose on the floor model is applied to the PULST AR facility.

NORTH----

NORTH---

100 to 125 +/- 8% NORTH BAY DOOR 125 to 150 +/- 6%

50to75+/-10%

25 to 50 +/- 10% 10 to 50 +/- 4%

50 to 230 +/- 4%

0.3 to 0.5 +/- 5%

1 50 to 1 7 5 +/- 7 %

~

0 2 3 4 5 0 2 3 4 5 SCALE (m)

SCALE (ml Fig. 7. Computed dose rates on the reactor platform Fig. 6. Computed dose rates on bay floor (mrem/h). (mrem/h).

LOSS-OF-WATER ACCIDENT 9 is due to backscatter directly from the ceiling; the bio- the order of 250 mrem/h next to the windows and logical shield tends to shadow areas immediately sur- door, decreasing rapidly to a minimum of 5 mrem/h rounding it, producing the lower dose rates. in the northeast corner of the control room. Note that Dose rates on the reactor platform are shown in dose rates could be cut dramatically by the placement Fig. 7. Detector locations are -9 m above the bay of temporary shields in front of these openings. This floor and 6 ft (approximately head high) above the is of particular importance considering the console platform itself. As expected, the computed dose rates location.

are substantially higher than those on the bay floor. A similar effect is seen due to the doors opening Much of the interior surface of the biological shield is from the reactor bay into the loading dock area as visible from the platform, leading to significant con- illustrated in Fig. 9. The projection is a small landing tributions to the dose rate due to direct gamma-ray 12 ft above the bay floor and on the same level as the reflections from these surfaces. This accounts for the loading dock. An equipment room is located under-rapidly increasing dose rate as detectors are placed neath. The loading dock is a nonradiation area fre-closer to the pool edge. The platform extends up to the quently used as a passageway between buildings. Dose pool edge providing detector locations in direct line of rates as high as 175 mrem/h tapering off to a fraction sight of the core. These locations experience the of a millirem per hour are encountered in this area.

greatest exposure to the gamma field with maximum Other areas of interest are the offices of the health dose rates on the order of 230 rem/h. physicist and nuclear reactor operations located adja-Figure 8 illustrates the expected dose rates in the cent to and north of the reactor building. Due to the control room. The two control room windows are attenuation provided by the concrete bay wall, dose ordinary glass and the door is wood. Gamma rays rates in these areas are on the order of 10- 6 rem/h.

stream in through the windows and door much as the This is comparable to the present background and is sun shines in a window. This results in dose rates on considered negligible.

50 to 100 +/- 6%

(/\

1 00 to 1 50 +/- 5 %

\

\\ ~\I 1 50 to 200 +/- 4%

DOOR CONTROL ROOM

  • ---NORTH WINDOWS 0 2 3 SCALE (m)

Fig. 8. Computed dose rates in the control room (mrem/h).

10 DOSTER and HEY 1 to 5 +/- 18%

10to25+/-12%

125

/ --------

25 t012'5'+/- 10%

to 150 +/- 5%

~ NORTH 0 2 3 SCALE (m)

Fig. 9. Computed dose rates in the loading dock (mrem/h).

Dose rates found on the bay roof range from a istic dose rates for the PULST AR facility. Computed few rems per hour to 25 rem/h 16 m directly above the dose rates for the PULST AR 10 min following a full-core midplane as shown in Fig. 10. Outside the reac- power shutdown range from 230 mrem/h on the reac-tor building, the isodose lines form concentric circles tor platform in direct line of sight of the core to 0.3 around the facility with the reactor core at the center mrem/h outside the reactor building 80 m from the as illustrated in Fig. 11. These dose rates are computed core. Maximum dose rates in key access areas through-using dry air as the scattering medium. Ground effects out the facility were 175 mrem/h on the reactor bay are neglected. Dose rates reach a maximum of 4 floor, 250 mrem/h in the control room adjacent to the mrem/h immediately adjacent to the building, drop- control room windows, and 150 mrem/h on the load-ping to <0.3 mrem/h at distances >80 m from the ing dock adjacent to the bay access door. Dose rates core. Natural background outside the building aver- in offices separated from the reactor bay by thick con-ages 200 mrem/yr. crete walls were on the order of background and con-sidered negligible.

SUMMARY

REFERENCES A Monte Carlo model has been developed and used to generate expected dose rates in and around the 1. "NCSU PULSTAR Safety Analysis Report," Copy reactor facility at NCSU for a postulated accident Number 80, North Carolina State University, Department involving sudden loss of all pool water. Benchmark of Nuclear Engineering, Raleigh, North Carolina (1967).

comparisons with the measured dose rates from a loss- 2. W.-C. TUNG, "A Guide to Computer Code MORSE-of-water experiment at the LLNL pool-type reactor CG: General-Purpose Monte Carlo Multigroup Neutron indicates the model can be expected to produce real- and Gamma-Ray Transport Code with Combinatorial

N O R T H - - - - -...

  • WEST BROUGHTON DRIVE w

a:

0 I

(.'.)

J 0

a:

0 al a:

D

>- 1 to 2 +/- 7%

<1+/-10%

0.5 to 1 +/- 7%

EAST BROUGHTON DRIVE 0 10 20 30 0 2 3 4 5 SCALE (ml SCALE (m)

Fig. 10. Computed dose rates on the bay roof (mrem/h). Fig. 11. Computed dose rates outside the reactor building (mrem/h).

12 DOSTER and HEY Geometry," INER-0409/MN-80, Institute of Nuclear 7. A. B. CHILTON and C. M. HUDDLESTON, Nucl.

Energy Research (1981). Sci. Eng., 17, 419 (1963).

3. E. D. CASHWELL, J. R. NEERGAARD, C. J. 8. D. J. RASO, Nucl. Sci. Eng., 17, 411 (1963).

EVERETT, R. G. SCHRANDT, W. M. TAYLOR, and G.D. TURNER, "Monte Carlo Photon Codes: MCG and 9. E. M. FOURNIE and A. B. CHILTON, Nucl. Sci.

MCP," USAEC Report LA-5157-MS, Los Alamos Eng., 76, 66 (1980).

National Laboratory (1973).

10. M. J. BERGER and D. J. RASO, Radial. Res., 12, 20
4. Los Alamos Radiation Transport Group (X-6), (1960).

"MCNP-A General Monte Carlo Code for Neutron and Photon Transport," LA-7396-M, Los Alamos National 11. M. B. WELLS, "Differential Dose Albedos for Calcu-Laboratory (1981 ). lations of Gamma-Ray Reflection from Concrete," USAEC Report RRA-T56, Radiation Research Associates, Inc.

5. J. W. KIMLINGER, E. F. PLECHATY, and J. R. (1964).

TERRALL, "SORS Monte Carlo Photon-Transport Code for the CDC 6600," USAEC Report UCRL-50358, Univer- 12. S. GLASSTONE, Principles of Nuclear Reactor Engi-sity of California, Livermore, Lawrence Livermore Radia- neering, p. 120, Van Nostrand Reinhold Company (1955).

tion Laboratory (1967).

13. M. KNEZEVICH, R. L. KATHREN, 0. K. HEL-
6. N. M. SCHAEFFER, "Reactor Shielding for Nuclear FERICH, and K. R. KASE, Health Phys. J., 11, 481 Engineers," U.S. Department of Energy (1973). (1965).