radiation shielding calculations for pakistan research reactor-1

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PINSTECH-I16 RADIATION SHIELDING CALCULATIONS FOR PAKISTAN RESEARCH REACTOR-1 NUCLEAR ENGINEERING DIVISION Pakistan Institute of Nuclear Science & Technology P. O. Nilore Islamabad. August, 1990

Transcript of radiation shielding calculations for pakistan research reactor-1

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PINSTECH-I16

RADIATION SHIELDING CALCULATIONS FOR

PAKISTAN RESEARCH REACTOR-1

NUCLEAR ENGINEERING DIVISION Pakistan Institute of Nuclear Science & Technology

P. O. Nilore Islamabad. August, 1990

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PINSTECH-116

RADIATION SHIELDING CALCULATIONS FOR

PAKISTAN RESEARCH REACTOR -1

S.SHOAIB RAZA ASIF SALAHUDDIN

Nuclear Engineering Division Pakistan Institute of Nuclear Science and Technology

Nilore, Islamabad August 1990

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ABSTRACT

Radiation shielding calculations have been performed for PARR-1 LEU (Low Enriched Uranium) core at 10 MW operation. The radiation include fast neutrons, fission gammas, fission products decay gammas and activation products decay gammas. Dose rates have been calculated at various locations, including pool water surface and around experimental facilities at beam port floor.

The results indicate that 2 4Na activity is the main contribution to the pool water surface dose. Its saturation activity came out to be 29 mR/hr, which is almost 85 % of the total activity. Dose rate at pool wall outer surface was found to be around 0.5mR/hr except at beam tube plug surface, where the dose rate was calculated to be 80 mR/hr.

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CONTENTS

ABSTRACT Page

1. INTRODUCTION 1

2. RADIATION SOURCES 2 2.1 Gamma Rays 2

2.1.1 Fission Gamma Rays 2 2.1.2 Fission-Product-Decay Gamma Rays 3 2.1.3 Capture Gamma Rays 4 2.1.4 Activation Product Gamma Rays 4

2. 2 Neutron Sources 5 2.2.1 Fission Neutrons 5

2.2.2 Activation Neutrons 5

2.2.3 Photoneutrons 6 2.2.4 Particle Reaction Neutrons 6

3. RADIATION TRANSPORT 6

4. APPLICATION OF THE POINT KERNEL TECHNIQUE 8

5. NEUTRON ATTENUATION 10

6. CALCULATIONS H

6.1 Exposure Rate from Direct Core Gammas 13 6.1.1 Exposure Rate at Pool Water Surface . . . .14 6.1.2 Exposure Rate at Pool Wall Outer Surface. . 14

24 16 6.2 Exposure Rates from Na and N 14

24 6.2.1 Na Activity 14

16 6.2.2 N Activity 16 6.2.3 Exposure Rate at Beam Tube Cover 17

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7 . RESULTS AND DISCUSSION 1 9

8 . REFERENCES 2 1

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1. INTRODUCTION

Reactor shielding is necessary to protect the personnel and equipment from exposure to radiation. The primary concern in reactor shield design is the provision of suitable barriers around the core to attenuate the neutrons and gamma rays emitted from it to a safe level. Both neutrons and gamma rays are sufficiently penetrating to be difficult to attenuate and sufficiently interacting to be damaging the human tissues and other materials.

Several other types of radiation arise from the fission event or from the interaction of fission neutrons with different nuclei. These include charged particles and neutrinos. Neutrinos, which posses no charge, mass or magnetic moment cannot interact with matter except through the very weak, purely nuclear forces. Thus despite the fact that they carry away 5% of the power of a reactor, they do not pose a shielding problem because they are incapable of causing damage [1].

Charged particles being highly interactive require relatively small amounts of shielding materials to stop them. The absorption of energy associated with charged particles may, however, be an important consideration in the thermal design of a system. The sources of radiation of primary interest i.e., gamma rays and neutrons are discussed in this report.

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2. RADIATION SOURCES

2.1 Gamma Rays

A variety of sources such as prompt fission gamma rays, fission product gamma rays, capture gamma rays and activation products decay gamma rays contribute to the gamma radiation produced by the reactor. The relative importance of these sources to the total gamma-ray intensity vary with position of the detector and with reactor operating history. For example, at a point near the reactor core, the prompt fission gamma-rays may be most important during operation, the fission-product gamma rays may dominate for the first few hours after shut down. The gamma rays from activated materials in the coolant may be more important than the direct core gammas, at a point away from the reactor core.

2.1.1 Fission Gamma Rays

The discussion on gamma rays, from fission and fission 2'->5 235

products, is limited to those from U because U is the main source of fission in PARR. Gamma-ray energy released in fission is divided into four time ranges, the first and last contributing more than 90% of the total energy released as gamma rays. These time(t) ranges are:

prompt t •< 0.05 usee (7.2 MeV) Short life 0.05 < t ̂ 1.0 Msec (0.43 MeV) Intermediate-life l.Ousec < t 4 1.0 sec (0.55MeV) Delayed t > 1.0 sec (0.65 MeV)

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The values in parentheses are for the gamma energy 235

released per U fission and are taken from reference [2]. The spectrum of gamma rays produced simultaneously with the

235 fission of u may be approximated by the segmented fit [3],

r (E) = 6.6 0 . 1 < E < 0 - 6 MeV " =20.2 exp (-1.78E) 0.6 < E < 1.5 MeV " = 7.2 exp (-1.09E) 1.5 < E < 10.5 MeV

The above equation agrees with the experimental spectrum within about + 15%.

2.1.2 Fission Products Decay Gamma Rays

Most of the fission fragments or fission product isotopes, resulting from a fission event are radioactive and

-8 -3 decay by beta and/or gamma emission. Between 10 and 10

235 sec after fission of U the main contribution of decay gamma rays comes from decay of isomers in excited states to the ground state and afterward it comes from the beta decay of the unstable nuclei. Integration of fission product decay gammas over time gives a magnitude and shape of energy distribution which is close to the prompt fission gammas distribution and is given by [l],

N(E) = 7.4 Exp(-l.lOE) photons/fission/MeV 2.1

For calculation purpose this component is combined with the prompt fission gammas.

>

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2.1.3 Capture Gamma Rays

Radiative capture of neutrons at thermal and epi-thenna1 energies by nuclei of the materials present in the reactor produces secondary gamma rays commonly called capture gamma rays. They are emitted promptly from the compound nuclei formed due to neutron capture. The total energy available for gamma rays from capture is the sum of the kinetic energy of the incident neutron and its binding energy in the compound nucleus.

2.1.4 Activation Products Gamma Rays

Sometimes the nucleus formed by a neutron interaction may be radioactive and decays with certain half life, emitting photons and other radiations in the process. These activation-product gamma rays are important for shield design and are of particular concern after reactor shut down. A significant quantity of these are emitted from materials like irradiated samples, structural materials and reactor coolant which have been exposed to the high neutron flux in the core.

16 16 The 0(n,p) N reaction produced by fast-neutron activation of water emits gamma rays with energies of 6.1 and 7.1 MeV.

16 The half life of N is 7.4 sec, short enough to produce

24 high activities in irradiated-water-coolant streams. Na

23 24 27 24 produced by Na(n, v ) Na and Al(n,«c ) Na reactions, produce 1.3B and 2.76 Mev photons in cascade with a half-life of 14.8 hrs. Besides above mentioned gamma rays, there are some other gamma rays like reaction products gamma rays,

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annihilation and bremsstrahlung gamma rays. They are produced in very low quantities and hence are not important in shielding considerations.

2.2 Neutron Sources

2.2.1 Fission Neutrons

Neutrons are created in an operating reactor by the fission process, in which, alongwith the prompt gamma rays, free neutrons are released as a part of the fission event. Approximately 2.5 neutrons are emmited per fission event in " J U by thermal neutrons. The energy distribution of neutrons from fission may be represented by the empirical fit [4]:

N(E) = 1.75 Exp(-0.766E) neutrons/MeV/fission 2.2

The above expression is valid over entire energy range of fission neutrons within + 15%. For shielding purpose, fission neutrons may be assumed to be evolved simultaneously with the fission event. It may be mentioned here that neutron or gamma ray energy distribution depends on both, type of source and attenuation properties of the medium through which the radiations are transmitted, in fact, the spectrum of the neutrons and gamma rays emerging from reactor shield is determined by the shield moderator and structure layers and not by the type of fission.

2.2.2 Activation Neutrons

Decay of a daughter nucleus (formed after rte-exitation

s

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of compound nucleus) can be followed preferably by the emission of a neutron, when the excitation energy of the same is more than the binding energy of the last neutron in the nucleus. An example is the beta tlocay of N (half life 4.14 sec) to o nucleus which emits a neutron of energy around 1.0 MeV. 1 7 N is formed by the reaction 1 70(n,p) 1 7N.

2.2.3 Photoneutrons

A photon of energy greater than the neutron binding energy of a nucleus can cause ejection of a photoneutron from the nucleus. These are important, only if D, L-i, Be, 3C are present in the reactor.

2.2.4 Particle Reaction Neutrons

The interaction of alpha particles with the nuclei of Lithium, Beryllium, Oxygen, Boron and Flourine produces neutrons. Neutrons from these sources may be important to shielding and safety curing asseirbly or in the pre-start- up environment of reactors containing Beryllium in the fuel-element material. Similarly neutrons from (<*,n) reactions in Oxygen may be dominant in oxide fuel elements. Further incident neutrons with energies above 10 MeV can excite a compound nucleus sufficient to emit two or more neutrons. Such reactions are rr.rely of importance in reactor shield design.

3. RADIATION TRANSPORT

The principal task in shield design/analysis is to

(,

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develop and solve the radiation t ansport equation. The shield designer choose one out of several methods for solving the transport equation depending upon the nature of the problem, the accuracy required and time and funds available. One of the more widely used methods for the solution of both gamma ray and neutron shielding problems is the point kernel technique. In this technique the exponential attenuation law is used for calculating the uncollided flux at the surface of a spherical shield. For a mono-energetic point isotropic source S (Particles/sec), at the surface of a spherical shell of radius R the uncollided flux will be [5]:

0 U= S Exp(-Xt.R)/(4 * R 2) 3.1 where 2 t = the total macroscopic cross section evaluated at the initial energy of the source for the shell material, Exp(-2t.R) = material attenuation factor, which is the probability that a particle of energy E travels a distance R (cm) without suffering a collission, 1/(4 TV R 2) = geometric attenuation factor for a point source (cm - 2).

The collided/scattered particles are those which have undergone one or more interactions that have caused a change in direction or energy or both. Analysis of uncollided component is simpler although there are some complexities of spectra and geometry. Scattered component is important for thicker shields as ratio of scattered to unscattered/

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uncollided radiation increase with increasing shield thickness. For accurate analysis we must consider the scattered radiation and the secondary radiation produced in the shield. The scattered component is included by using a ^uild-up factor , which accounts for increase ( or build-up) in the flux density at some point, due to scattered gamma rays. This build-up factor at some point is defined as

B = Total (collided) flux / uncollided flux 3.2

A primary build-up data, obtained experimer.tly, is available in literature and a variety of functions have been derived to fit the data. The one which employs a summation of two exponents is due to Taylor [6]:

B(E, UR) - A.Exp (- <<1.UR) + (1-A) .Exp(-<* 2 .MP) 3.3

where A, «1 and <*-2 are the constants depending upon gamma ray initial energy and thickness (nean free path) of the shield material. An outstanding advantage of using this i*> that when it is multiplied by the point kernel for the uncollided flux the necessary integration over extended sources can be done analytically with ease and no new integral is involved in the calculations.

4. APPLICATION OP THi; POINT KERNEL TECHNIQUE

This technique provides means for solving a variety of problems which involve a distributed source. The point kernel is formally the solution to the unit point source problem and the desired answer to the problem is obtained by integrating

n

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ever the particular source geometry. The source geometry is modelled in such a way that this integral can be evaluated analytically, e.g., the flux density (#/cm2/sec) at the detector location R cm away from a line source (Fig. 1) emitting S photens/cm/sec in a medium having attenuation coefficient is given by [5]:

Flux = S/(4A R}JExp(-u R Bee 9) dO 4.1

Using the Sievert integral function F(0,x) and Taylors form of the build-up factor the above equation may be integrated to the form

Flux = S/(4ftR) 2An[F{0-l, (1+ 06n)uR}+F{e2, (1+ <*n)xiR}] 4.2

Similarly for a spherical source (Fig. 2) we use the relation [7]:

Flux - 0.666SV.R.3. [El (b2)-El (b2. sec©-) ] MeV/cm2/sec 4.3

where b2 = u.t + us.z s v = source strength in Mev/cm3/sec El = exponential integral of first order

«s = self attenuation coefficient of core (cm •*•) /U = attenuation coefficient of shield t = thickness of shield R = radiua of the spherical source B = build-up factor z = self aitenuation distance

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8 = angle (radians), see Figs. 1,2

5. NEUTRON ATTENUATION

The use of build-up factor in the attenuation kernel for neutrons has not developed to a large extent, primarily because neutron interactions are more complex than gamma-ray interactions. However a simple kernel is generally employed using neutron removal CVOSF sections for the shield materials, specially when other shield materials are used in conjunction with the hydrogenous medium. An adequate thickness of the hydrogenous material is required to moderate and absorb the scattered neutrons. Values of the macroscopic neutron removal cross sections for various shield materials are determined experimentally anc5 are generally used in the form of empirical function [8]:

E R/ e - 0.19 z " 0 , 7 4 3 cm2/g, for Z < 8 " = 0.125 z" 0- 5 6 5 cm2/g, for Z > 8

where Z is the atomic number of shield material and ? is the material density.

It may be pointed out thut the removal cross sections vary with source configuration and with shield thickness, specially when it increases beyond five relaxation lenghts. The removal cross section method described no far provides a method for calculating the dose rate due to high energy neutrons which penetrate a shield. However, this method can not be used for the neutrons moderated to epithermal and

V)

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thermal energies. The complexity arises from the emission of gamma rays from capture of thermal neutrons in the shield material. It becomes difficult to predict the thermal neutron flux density and hence the capture gamma ray source distribution within the shield, specially in case of laminated shields. However the energy distribution of the moderated neutrons throughout the shield can be calculated by using the elementry neutron diffusion and moderation theory. The neutron transport problem is, hence, solved in two steps. In first step high energy neutrons penetration, deep in the shield, is calculated where its energy degrades significantly. In second step the diffusion calculations of the resulting low energy neutrons are carried out. Characteristically, the distance travelled by the neutrons during the diffusion process is very much shorter than the distance it travelled as a fast neutron. This method of combining the fast-neutron removal concept and age-diffusion theory to carry out neutron attenuation calculations is failed as the spinney method [1.,.

6. CALCULATIONS

We have performed the calculations for LEU core, considering it tc be shielded by the same shield as was provided for the HEU core. The methodology adopted is the famous point kernel technique, which has been discussed (section 4) already in this report.

The new LEU core of PARR-1 (10 MW) comprises of 23

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Standard Fuel Elements (SFE) and 5 Control Fuel Elements (CFE) arranged in 6x3 matrix with two positions Left, vacant for use as flux trap. Its fuel is taken to be U 3Si2, and the uranium being 19.75% enriched. The core is considered to be a uniform, homogeneous spherical volume source of radiation although it is a parallclopipcd in its geometrical shape, so that eqn. 4.3 became applicable. This assumption is valid for large distances (more than a few mean free paths), as are encountered during this work. The LEU core of PARR-1 will replace the existing HEU core, where the following biological shield is already provided: a) On Top, 725 cm of light water [9] b) On sides, in stall end, 102 cm of light water and

180 cm of baryte concrete [9] and on one side 230 cm of graphite and 120 cm of baryte concrete [10]. In the open end the core shield comprise of 280 cm of light water and 180 cm or ordinary concrete [9], see Fig. 3. Beam tube shield comprise of 90 cm of water, 150 cm of baryte concrete and 2b cm of load [11], see Fig. 4.

Dose rates hrivr> bRon cnl.cu.l rited at the following locatit iis:

1. Pool water surface (directly above core), 2. Concrete wall outer surface at core level (beam

port floor), 3. Outer face of che thermal column door, 4. Outer face of the beam tube plug.

As neutrons do not contribute much towards the dose

1 •:

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rates at locations considered [12], so only gamma rays have been considered for the calculations. Calculations have been done separately for the two groups of gamma rays i.e., direct core gammas and activation products decay gammas. The direct core gammas include prompt fission gammas and fission products decay gammas. The activation products decay gammas include the gamma rays from 2 4Na and * 6N.

6.1 Exposure Rate from Direct Core Gammas

As a total energy of 200 MeV is released per fission, it may be shown that 3.l*lo10 fissions will take place per watt-sec of energy. If core active volume is represented by V (cmJ) then total fissions per unit volume occuring in the reactor operating at 10 MW power will be

Sv = 3.1*1017/V (#/cc/sec) 6.1

Knowing the gamma spectrum per fission in 5 energy groups, each of energy 1 MeV, 2 MeV, 4 MeV, 6 MeV, 8 MeV, as shown in Table-1 [13], energy source term (MeV/cc/sec) was calculated by multiplying Sv with total core gamma ray sources for each group of energy. Then we can find the energy flux corresponding to each group by using the methodology for core modelling, already described in section 4. The total attenuation coefficients (cm - 1) of materials present in the configuration are given in Table-2 [14]. To include the scattered component of gamma rays, the Taylor build-up factor was employed. The coefficients A, - oCl and °C2 used

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in the calculat ion of the same are 1isted in Table-3 [14 ].

6.1.1 Exposure Rate at Pool water surface

Flux at pool water surf i CG was calculated by using eqn. 4.3. To convert this flux in exposure rate, appropriate dose conversion factors were applied, which were calculated for each of the gamma energy groups using the relation [14].

1 mR/hr = 0.02/ua MeV/cm2/sec 6.2

where u a is the energy absorption coefficient (cm-1)off air.

6.1.2 Exposure Rate at Pool Wall outer surface

The flux at pool wall outer surface was also calculated by using eqn. 4.3, with the only difference here, from previous case, that now the shield materials and their thicknesses were different. To get the exposure rate corresponding dose conversion factors calculated frozj eqn. 6.2 were applied to the flux values for each energy group. Exposure rates at thermal column door outer surface and beam tube cover were also calculated similarly.

6.2 Exposure Rate from 2 4Na ana 16v

Exposure rates due to 2 4Na and 1 6 N activity dispersed in pool water was calculated separately as given below:

6.2.1 2 4 Activity

Most of the 2 4Na activity is formed by (n,ec) reaction of fast neutrons with the 2 7 A 1 present in cladding and

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structural parts of the core, AS already mentioned in section 2.1.3 threshold for the reaction is 3.1 MeV and cross-section for the same averaged over fast neutron spectrum is 0.6mb. The saturation activity due to 2 4Na in the pool water is calculated using the relation (based on the assumption that only 1/4 of the 2 4 produced enter into pool water) given below [13],

N 6 $ R S Act = atoms/cc/sec 6.3

4 VPool where N = Number density of 2 7A1 (#/cc) tf = Effective reaction cross-section (era ) 0 = Fast neutron flux (#/cm2/sec) R = Range of 2 4Na in 2 7A1 (2.4*10_4cm) S = Surface area of £ /Al (target) exposed to fast

neutrons (cm2) V p o o l = Total pool water volume (cm3)

Number density of 2 7A1 was calculated by

N - C A v/ A 6.4

Taking \= material density of 2 7A1 (2.7 g/cc), A v= Avagadro's number (6.02252*1023) and A = atomic weight of 2 7A1 (26.98)

the surface area of the target was calculated to be 5.8*105cm2. This includes the surface area of all the fuel plates, side plates (both faces) of 28 fuel elements in the

l'»

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core, and an additional 10 % of this area to account for the presence of aluminum in the form of grid plate, supporting tower, casings and guides of various instruments, thermal column extension and beam tubes etc., around the core. Total volume of pool water was taken to be 4.8*10 cm 3.

From this activity, exposure rate at pool water surface was obtained by assuming the whole pool to be a thick uniform slab source of radiation and using the following relation:

X = Act/2(Ml-Dl + U2.D2) 6.5

where Act = Activity calculated by eqn. 6.3, ul and u2 are total linear attenuation coefficients of water for gamma energies of 1.38 and 2.76 MeV, Dl and D2 are the dose conversion factors for both the gamma energies.

The result came out to be 29 mR/hr. It may be mentioned here that this exposure is due to the saturation activity of 2 4Na, which is achieved after n continuous operation of the reactor at full power, for many hours ( > 80 hours) . A graph has been plotted which shows the relative increase in exposure rate due to 2 4Ma with time (Fig. 5) .

6.2.2 1 6 N Actvity

1 f ,H is produced in the reactor core by the interaction of fast neutrons (having energy above 10 MeV) with oxygen atoms present in the molecules of water. This reaction has a

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cross section of 0.0185 mb averaged over fission neutron spectrum. 1 6 N produced in the core flows out due to forced convection and stays in the hold-up tank for about 250 sec, where this activity decays to a large extent [12], and no significant dose is recieved at pool water surface due to this activity.

At pool wall and at thermal column door outer surface the exposure rate due to 2 Na anu 1 6 N activity was found to be negligible, as compared to that from other sources.

6.2.3 Exposure Rate at Beam Tube cover

As beam tubes are generally filled with water, this stagnant water in them, if not flushed intermittently, becomes a large source of 2 Na and 1 6 N activity.

Activity due to 2 4Na produced by 2 7A1 (n,oc)24Na reaction occuring in the aluminum structure of the tube was calculated by the same method as described in section 6.2.1. The only difference here is that now the target area S was replaced by the surface area of only 10 cm length of beam tube (outer side only) , which is in the vicinity of the core. The 10 cm of the length was taken by considering the inverse of the removal cross-section of fast neutrons (0.103 cm - 1 ) . Only this amount of water, which is contained in 10 cm length of the beam tube, was considered for activation. To be on the conservative side, it was assumed that neutron flux remains the same as at the face of the core, throughout this length.

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Exposure rate due to this activity was calculated to be 20 mR/hr.

1 6 N activity produced in the stagnant water of beam tube was calculated by:

Act = N<r<{>/v 6.6 where

N = number density of oxygen in water, <*" = microscopic cross section for the reaction, <f> = fast neutron flux, V = volume of water.

Exposure rate at beam tube cover due to this activity was calculated by using the above equation and was found to be 60 mR/hr. Hence the total exposure rate due to both of the activities is 80 mR/hr.

IK

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7 . RESULTS AMD DISCUSSION

The r e s u l t s o b t a i n e d f o r t h e t o t a l d o s e r a t e s a t

d i f f e r e n t l o c a t i o n s are mentioned b e l o w :

1 - Pool w a t e r s u r f a c e 35 mR/hr.

2 - Pool w a l l ( o u t e r s u r f a c e )

stall end 0.5 mR/hr. open end 0.5 mR/hr.

3- Thermal column door (outer surface) 0.5 mR/hr. 4- Beam tube cover (outer surface) 80 mR/hr.

A comparison of the results for pool water surface and beam tube cover, with those quoted from the measured data for HEU core of PARR-l operating at 5 MW [9] i.e., 75 mR/hr and 300 mR/hr shows that we have under predicted thr dose rates. The reasons for these differences may be:

1. Contribution from activated impurities towards dose rates at pool water surface has not been included in the calculations.

2. Presence of the convection water currents, which may be responsible for carrying some of the pool water activity, directly towards the pool surface.

3. Leakage of some of the fission products from the failed cladding of the fuel elements which have undergone high burnup or stayed for a long time in the core.

4. Assumption in calculating the 2 4Na activity(eqn.6.3), that only 1/4 of its production enter into water. This may

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however increase under actual conditions jf the cladding and other targets surfaces.

5. While calculating the dose rate at beam tube cover, contribution from activation of some of the constituents of concrete in the plugs has been ignored.

6. As beam tube plugs do not r.pal the tube tightly, some of the activated water may come in direct contact with the cover, hence contributing to the surface dose significantly. Presence of this fact hat also been ignored in the calculations.

AKMOWLEDGEKEHTS

Thanks are due to Mr. Khalid Mahmood Akhtar, Head NED, for his useful suggestions and encouragement during this work.

Authors want to pay their gratitude to Dr. Nasir Ahmad, PSO Cits, for providing help in calculating the recoil activity of ̂ 4Na.

Authors are also thankful to Mr. Tariq Mahmood, SO CD, for his contribution in writing the computer program used in dose rate calculations due to direct core gammas.

/(">

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8. REFERENCES

1 : N.M.Schaeffer. " Reactor shielding for nuclear engineers," TID-25951 (1973).

2 : N.E. Holden et al. , " Total gamma energy release due to thermal neutron fission in 2 3 5 u , " Nucl. Sci. Engg., 30: 461 (1967).

3 : R.w. Peelle and F.C. Maienscein," Prompt gamma rays from thermal-neutron fission of 2 3 5 u , " Nucl. Sci. Eng., 40: 485 (1970).

4 : E. P. Blizard, Reactor Handbook , 2nd ed. , Vol. Ill, Part B, Interscience Publishers, New York (1962).

5 : John R. Lamursh, Introduction to Nuclear Engineering, Addison- Wesley Publishing Company, New York (197 5).

6 : J.J. Taylor," Application of Gamma Ray Build-up Data to shield design," USAEC Report WAPD-RM-217 (1954).

7 : T. Rockwell, Shielding Design Manual, D. Von Nostrand, New York (1956).

8 : L.K. Zoller, "Fast-neutron Removal Cross-sections," Nucleonics, 22(8): 128 (1964).

9 : Khalid Mahmud Akhtar, Mohammad Azim, "Pakistan Research Reactor Safety Analysis Report," (1982).

10: M. N. Qazi et al., "Neutron Flux Measurements in the Experimental Facilities of the Pakistan Research Reactor," PINSTECH/PHY-7 (1967).

11: L. A. Khan et al., "Pakistan Research Reactor

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Operating Manual," (1984). M. U. Shaikh, G. M. Asaf, " Shielding Calculations for Uprating PARR," PINSTECH/NED-7 (1974). R. G. Jaeger et al., Engineering Compendium on Radiation Shielding, Vol. 1-3 , Springer-Verlag, New York (1968). H. Ethirington, Nuclear Engineering Handbook. McGraw-Hill Book Company, Inc. (1958) .

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Table l: core Gamma Ray Sources (Energy Released Per Fission)

Gamma ray energies

1 MeV ! 2 MeV ! 4 MeV ! 6 MeV 8 MeV !

! Prompt Fission 3.46 3.09 ! 1.04 ! 0.26 J

I Fission Product ! Decay Gammas

5.16 ! 1.74 i 0.322 I - • j

!

! Aluminum Capture - - ! 0.288 ! 0.132 I 0.176 !

i Water Capture 1 . 0.58 ! - ! !

I " -tal (MeV/f isson) • 8.61 1 5.41 ! 1.65 i 0.392 0.176 !

Table 2: Total Linear Attenuation Coefficients for Different Materials

! Materials ! Gamma ray energies

! Materials ! 1 MeV ! 2 MeV ! 4 MeV ! 6 KeV ! 8 MeV

! Water ! 0.0705 ! 0.0493 ! 0.0339 ! 0.0275 ! 0.024

! Aluminum ! 0.1653 ! 0.1166 . 0.0837 ! 0.0713 ! 0.0651 ! Uranium 1.416 0.9051 0.8228 0.8509 ! 0.8957 i

i i « * 1 Core 0.1079 0.0754 0.0537 0.0453 ! 0.0410 i

t Lead 0.776 . 0.513 . 0.476 . 0.498 ! 0.5?0 !

! Ordinary ! Concrete ! (2.35 g/cc)

! 0.149 ! 0.105 ! 0.0745 1 0.0658 • 0.057

! Baryte ! Concrete S (3.49 g/cc)

! 0.213 I 0.180 ! 0.120 1 0.110 ! 0.075

* T!ie core (of volume l.l6E+05cc) is assumed to comprise of the following materials

water = C4.7 vol% aluminum - 3 5.0 vol% uranium = 0.3 vol%

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Page 29: radiation shielding calculations for pakistan research reactor-1

Table 3: Taylor Build-up Factor Coefficients

! ! Gamma m y e n e r g i e s I

! ! 1 MeV ! 2 MeV ! 4 MeV ! 6 MeV ! 8 MeV !

1 ! A ! 11 I 6 . 4 ! 4 . 5 ! 3 . 6 5 ! 3 . 0 5 !

• W a t e r ! -<*i i 0 . 1 0 4 I 0 . 0 7 6 1 0 . 0 5 5 ! 0 . 0 4 9 5 ! 0 . 0 4 5 !

! ! <*,! 0 . 0 2 8 I 0 . 0 9 2 I 0 . 1 1 6 5 ! 0 .12 .4 I 0 . 1 2 8 I

I ! A ! 2 . 4 5 ! 2 . 6 0 ! 1 . 6 5 ! 0 . 9 6 ! 0 . 6 7 !

! Lead 1-<K.,1 0 . 0 4 5 ! 0 . 0 7 1 ! 0 . 1 2 3 I 0 . 1 7 5 ! 0 . 2 0 4 1

I i oc, ! 0 . 1 7 8 ! 0 . 1 0 3 ! 0 . 0 6 4 ! 0 . 0 5 9 ! 0 . 0 6 7 !

! ! A ! 9 . 9 ! 6 . 3 ! U .9 ! 3 . 1 ! 2 . 7 !

• O r d . C o n c . !-<*. ! 0 . 0 8 8 • 0 . 0 6 8 ! 0 . 0 5 9 ! 0 . 0 5 8 5 ! 0 . 0 6 7 ! 1 ( 2 . 3 5 g / c c ) ! ! I I ! ! ! ! oix I 0 . 0 2 9 ! 0 . 0 5 8 ! 0 . 0 7 9 I 0 . 0 8 3 1 0 . 0 8 5 5 !

2-i

Page 30: radiation shielding calculations for pakistan research reactor-1

UNE SOURCE

S PI lOTON/CM/SEC

SHIELD

FIG. 1:- GEOMETRY FCR A LINL SOURCE IN A CYLINDRICAL SHIELD

25

Page 31: radiation shielding calculations for pakistan research reactor-1

SPHERICAL SOURCE

S PHOTON/CM3/SEC

SHIELD

r*BH k M

h H

FIG. 2:- GEOMETRY FOR A SPHERICAL SOURCE SHIELDED BY A SLAB SHIELD

20

Page 32: radiation shielding calculations for pakistan research reactor-1

T

o

• £ 1 £

i- z i- —" 9 0k

Hi

ac •t <

£ 2

I- O w i z O Ul

s S o

*t -1

i § 1

1}

Page 33: radiation shielding calculations for pakistan research reactor-1

. - H A D PLUS

NOTES =

* 1 . FINAL AUoSVSNT & FIK'.SW'.NO AT RSACTOR r*C = ACCORCiNG TO THE POSITION 0? 7 r e BEAM TJSE .

CO

FIGURED BEAM TUBE SKETCH

Page 34: radiation shielding calculations for pakistan research reactor-1

0 20 40 60 Time (hr)

BO

2 * i , . Fig. 5: RELATIVE INCREASE IN Na

ACTIVITY WITH TIME

100