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Dose Calculations
APPENDIX
DOSE CALCULATIONS
4
A4.1 INTRODUCTION This appendix gives some examples of dose calculations which have been used during discussions on conceptual designs of various plants. The dose calculations are of a simple type, suitable for indicative evaluations. More elaborate calculations are usually performed in the final phases of the safety analysis, when systems and components purchase specifications have already been defined.
A4.2 VIRTUAL POPULATION DOSE IN A SEVERE ACCIDENT The following sections describe the virtual population dose for a future reactor (an order of magnitude evaluation in the short term, at three days, and in the long term, several years).
A4.2.1 THE REACTOR AND THE RELEASED ISOTOPES The example is a passive type boiling water reactor of 600 MWe, provided with a double containment and a stack. The quantities of isotopes chosen as guide isotopes in the core (1800 MWt) are, at equilibrium: 131
I Cs 133 Xe 85 Kr 137
1.85 3 1018 Bq 148 3 1015 Bq 3.7 3 1018 Bq 12.95 3 1015 Bq
A4.2.2 SOURCE TERM AT THREE DAYS (I, CS, XE) •
•
The leakage rate assumed for the primary containment (taken into account the probability of leakage rates higher than the specified ones and possible damages to penetrations for severe accidents): 5%10% per diem. The leakage rate assumed for the secondary containment room (systems, collection room, or building): 1%10% per diem. (For this assumption to be valid extremely unlikely sequences are excluded, such as the rupture of a steam line with degraded core and valve leak proofing degraded.)
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The effective release height (e.g., passive routing of the leaks to a stack, collection of leaks in a leakproof room connected with the stack, leaks routed to a chimney through filters, etc.): 80 m. Iodine and cesium equivalent ground releases: n% of the core inventory w3x3y3z
(A4.1)
where n 5 20, w 5 10 for plateout and washout, x takes a value in the range 36 for leaks from primary containment in three days, y takes a value in the range 330 for leaks from the secondary containment in three days, and z 5 10 (a factor for elevated release). The iodine and cesium equivalent ground release range 5
0:2 3 core inventory 0:2 3 core inventory to 5 : 10 3 6 3 30 3 10 10 3 3 3 3 3 10
So for 131I, the range is (1.1 3 1025) (1.85 3 1018) to (2.2 3 1024) (1.85 3 1018) 5 20.35 3 101240.7 3 1013 Bq. (A realistic reference value 5 20.35 3 1012 Bq.) And for 137Cs, the range is 5 16.28 3 101132.56 3 1012 Bq. (A realistic reference value 5 18.5 3 1011 Bq.) For 133Xe, the equivalent ground release range [Eq. (A4.1)], calculated with n 5 80, w 5 0, x 5 36, y 5 330 and z 5 5, is 3.29 3 10156.58 3 1016 Bq. (A realistic reference value 5 1.85 3 1016 Bq.)
A4.2.3 DOSE AT THE FENCE AFTER THREE DAYS OF EXPOSURE I (effective dose for adults by inhalation) 5 (χ/Q) 3 dbf 3 grr, where χ (s/m3) is the cloud concentration at 1 km, Q (Bq) is the activity release, dbf (the dose biological factor) 5 10 and grr (the ground release range) 5 (20.35 3 1012)(40.7 3 1013) Bq. Assuming χ/Q at 1 km distance is 1 3 1024, then the effective iodine-131 dose for adults by inhalation is 5100 mSv. (A realistic value is 10 mSv.) 133 Xe (effective dose by cloud irradiation) 5 (χ/Q)(1/dcf) 3 grr, where dcf (dose conversion factor) (see Chapter 7: Health Consequences of Releases) 5 300 and grr 5 (3.29 3 1015) (6.58 3 1016) Bq. Assuming χ/Q is 1 3 1024, then the effective xenon-133 dose by cloud irradiation is 0.310 mSv. Calculations for all the noble gases give a dose at the fence after three days of 5120 mSv (about 10 times the value for 133Xe). An effective realistic value is 30 mSv.
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A4.2.4 GROUND SHINE LONG-TERM DOSE The integrated dose due to ground shine with absorption in the soil, corresponding to a ground initial concentration of 1 Bq/cm2 of cesium-137 (a contribution by other nuclides exists but is not evaluated here): First year Second year 050 years
120 μSv 80 μSv 1.6 mSv
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The initial concentration of cesium-137 corresponding to a realistic release of 1.85 3 1012 Bq is given by (1.85 3 1012) [Bq released] 3 1 3 1024[χ/Q], Bq s/m3 at 1 km] 3 (1 3 1022) [m/s: deposition velocity] 5 2 3 106 Bq/m2. Therefore the ground shine dose from cesium-137 is First year Second year 050 years (After 5 years this dose is 80 mSv.)
20 mSv 15 mSv 300 mSv
A4.3 EXPLORATIVE EVALUATION OF THE RADIOLOGICAL CONSEQUENCES OF A MECHANICAL IMPACT ON A SURFACE STORAGE FACILITY FOR CATEGORY 2 WASTE A4.3.1 TYPE OF REPOSITORY It is assumed that the disposal structure is similar to the French one at L’Aube or to the Spanish one in El Cabril. The waste is assumed to comply with the ANPA Technical Guide No. 26 (ANPA, 1985) and is, therefore, conditioned in a concrete matrix with compression strength of at least 500,000 kg m22.
A4.3.2 REFERENCE IMPACT It is assumed that the reference impact produces, on clear ground, a conical crater having an angle of 90 degrees and a depth of 4 m. Moreover, it is assumed that the cause of the impact is undefined, possibly to be identified with a plane crash, a launched projectile or a blast from an internal or external explosive charge. The 4 m deep crater has been chosen because it can be related to an explosive projectile of medium size (see a discussion at the Hanover Congress on the nuclear underground sites; Bender, 1982). The volume of material expelled from the crater would then be about 70 m3 corresponding to about 140 t. These values can be compared with the effects of mining explosives. The amount of rock (hard limestone rock) demolished in an open air mine is of the order of 710 t/kg explosive (Colombo, 1997). The rock in our example corresponds (in ideal conditions) to about 20 kg of explosive, an amount considered to be modest. The effect of an airplane crash, then, may cause, according to the usual assumptions, an impact load of about 10,000 t on a surface area of 7 m2, corresponding to about 150 kg/cm2. This load might cause the fall and the fragmentation of a column of structure, assumed to be 1015 m high with a volume of about 70 m3 (see Fig. A4.1).
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10 m
FIGURE A4.1 Fragmentation due to impact
Table A4.1 Fragmentation of Material Average Dimension of Blocks (m)
Layer Volume 1 mm (m3)
Layer Volume 3 mm (m3)
0.33 0.20
1.2 2.1
3.6 6.3
A4.3.3 FRAGMENTATION AND DISPERSION OF MATERIAL It is assumed that the material is fragmented into blocks 0.20.3 m in diameter and that a layer 13 mm thick of each block is pulverized into fragments ranging between 1 μm and 13 mm, with a uniform distribution between the two extremes (see Table A4.1). If an intermediate case is chosen (e.g., a volume equal to 2.5 m3), a weight of finely fractured material of 5 t is obtained, corresponding to a fraction of about 3% of the total. This percentage agrees with the values estimated, for example, for the Chernobyl accident (Vargo, 2000). It is possible to make an assumption, also on the basis of accident data, that the coarser part of the powder produced (from 10 μm to 1 mm), with an overall weight approximately equal to the total one (99%), is deposited over a radius of a few kilometers (2 km are assumed) from the release point, with an average concentration c5
5000 5 4 3 1024 kg=m2 π 3 20002
(A4.2)
This evaluation is not conservative as the effect of wind is completely disregarded. This effect causes the angular distribution of the particulate to be nonuniform. An estimate of the concentration of the deposited radioactivity can be made with the following assumptions: •
The complex of released radioisotopes is equivalent to an amount of 137Cs.
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Table A4.2 Soil Concentrations
•
Distance (km)
Soil Concentration (kBq/m2)
2 10
100 4
The equivalent value of 137Cs is equal to the value indicated in ANPA Technical Guide No. 26 (1985) as the limit for conditioned category 2, waste (3700 MBq/kg). The total radioactivity in the released particulate is, then R 5 5 ; 000; 000 3 3:7 3 1026 5 20 TBq
(A4.3)
With this assumption, the concentration on the soil is C 5 0:4 3 3:7 3 106 5 1500 kBq=m2
(A4.4)
The finest particles (110 μm), with an overall weight of about 50 kg and a total radioactivity of 0.2 TBq, can be assumed to be dispersed by diffusion and deposition (Pasquill model). Assuming a stability condition F with wind velocity of 2 m/s and a deposition velocity of 1022 m/s, the approximate soil concentrations shown in Table A4.2 are obtained. Indeed, the concentration, C, for example, at 1 km, is given by C
χ 3 Q 3 vd Q 5 2 3 1024 3 0:2 3 109 3 0:01 5 400 kBq=m2 5
(A4.5)
and decreases roughly with the 1.52 power of the ratio of distances for higher distances (concentrations of 100 and 4 kBq/m2 at 2 and 10 km, respectively, result). The levels of soil contamination calculated may be compared with the cesium-137 contamination in a generic European country after Chernobyl, equal on the average to 1020 kBq/m2 with peaks up to 100200 kBq/m2 (Vargo, 2000).
A4.3.3.1 Alternative Source Term A different approach to the previously considered accident can be pursued, along the following lines: • •
• •
To assume an applied force of 5000 t for the reference aircraft impact (as adopted in Italy for power plants), instead of the 10,000 t adopted in the previous evaluation. To allow for the dynamic character of the load applied by the impacting aircraft on the concrete. This would imply an increment in the limit load as allowed by the applicable regulations [e.g., American Concrete Institute ACI 349 (ACI, 2001)]. To evaluate the depth of the fractured material as a consequence of the impact by the penetration formulae adopted for nuclear plant evaluations such as the formula (17.2). To add to the aircraft impact a fire of the transported fuel. This could influence the dispersion of the released particulate. In particular, the coarse fraction could be transported and deposited further than the assumed 2 km.
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Taking into account the previous assumptions, the volume of fractured material would result in the order of 12 m3 instead of the 70 m3 assumed above. The coarse fraction of the release could be of the order of 860 kg instead of 5 t, whereas the fine fraction would turn out to be equal to 8.6 kg (instead of 50 kg). The uncertainty in the evaluation of the effect of the fire is rather high. Some indications could be obtained from the observation of the behavior of the Chernobyl release (Vargo, 2000). There, the large ( . 20 μm) particles were deposited within a radius of 5 km from the plant. With these assumptions, the following distribution of released material is obtained • • •
Coarse fraction: .20 μm: weight 5 860 kg. Ground concentration 5 1.1 3 1025 kg/m2, corresponding to 41 kBq/m2. Fine fraction: weight 5 17.2 kg.
This would be dispersed under the influence of the buoyancy effect of the fire. In the case of Chernobyl, the thermal elevation of the plume caused by the fire was of the order of 1000 m (Vargo, 2000) and this figure can be assumed to be valid also for this example. In order to get an idea of the characteristics of a (presumed) fire in a reference plane crash, it is assumed that the full fuel load charge of the aircraft is equal to 10 m3, corresponding roughly to 7 t. This amount of fuel, with a conservative assumption, can be considered to form a square pool with 10-m long sides. The burning velocity of a pool of kerosene of this size is roughly 170 kg/m2/h (Lees, 1996). The fuel would be completely burnt in about 25 min. The flame height would be equal to about twice its width, namely 20 m. The usual thermal-elevation formulae can be used to perform a further evaluation of the height to which the radioactive release will be brought by the flame. The Stu¨mke formula [see Eq. (6.7)] can be used to indicate a plume rise of .1000 m. The uncertainty of this evaluation is, however, high as both the wind velocity field and the atmospheric turbulence have a strong influence on the phenomenon. It has to be noted that the presence of a fuel fire should not significantly increase the amount of radioactive particulate released. Indeed, the duration of the fire is short and the radioactive waste packaging is made of “fire resistant” and “nonflame propagating” materials (ANPA, 1985).
A4.3.4 DOSES On the assumption that in the vicinity of the plant there is no intake of cesium through the food chain, the doses to the population can be caused by ground shine (on the assumption the population have not been evacuated). The doses at 1 year and at 50 years can be calculated on the basis of the factors shown in Table A4.3, corresponding to a contamination of 1 kBq/m2 (Ferreli and Bologna, 1991). Table A4.3 Dose Factors Time After Accident (Years)
Effective Dose (mSv)
1 50
0.012 0.16
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Table A4.4 Doses Time After the Accident (Years)
Effective Dose (mSv)
1 50
18 (5) 240 (65)
The inhalation dose gives a negligible contribution. Therefore within a radius of 1 km from the site, multiplying the values in Table A4.3 by 1500 or 400, the doses shown in Table A4.4 are obtained. At 10 km from the plant, with the above-evaluated contamination figures, about 0.05 and 0.65 mSv can be obtained at 1 and at 50 years, respectively.
A4.3.5 CONCLUSIONS Although these evaluations are inevitably subjective and need further reflection, the consideration of a severe impact accident seems opportune, taking into account the long life of a repository (centuries). Technical solutions incorporating a special technological protection from the aircraft crash and from explosive events or solutions in which the disposal structure is located at a depth in the ground of at least 20 m should be considered among the alternatives to be examined. The subsurface solution would offer better protection during the phases of construction and of filling up of the repository.
A4.4 EXPLORATIVE EVALUATION OF THE RADIOLOGICAL CONSEQUENCES OF A MECHANICAL IMPACT ON A TRANSPORT/STORAGE CASK CONTAINING SPENT FUEL A4.4.1 CHARACTERISTICS OF THE CASK The cask complies with the international requirements for fuel transportation and, therefore, it resists the fall, punching, and submersion. Moreover, the cask will be designed to protect it from aircraft impact and consequent fire. The cask considered has two independent leakproof lids, each one equipped with metallic seals. It is assumed that the cask contains 50 fuel elements of the type used at the Caorso plant and that the maximum temperature of the cladding is 200 C. The interior of the cask is normally kept at negative pressure and in an inert atmosphere.
A4.4.2 REFERENCE IMPACT It is assumed that the cause of the impact is undefined, possibly to be identified but assumed to be due to a plane crash, the launch of a projectile or the blast of an internal or external explosive charge. The effect of a plane crash may cause, according to the usual assumptions, a load of about 10,000 t on a surface area of 7 m2, corresponding to about 1.43 3 106 kg m2.
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Notwithstanding the strength characteristics of the cask and its leakproof seals against impact and other conceivable external loads, it is assumed that in the accident considered, both seals are damaged, allowing a certain communication between its internal and the outside atmosphere and a gas flow dependent on the pressure difference between the inside and outside. Immediately after the deterioration of the seals, the external air will flow into the cask because of the internal underpressure. Subsequently, as a consequence of the lowering of external atmospheric pressure, part of the gas contained inside the cask might escape to the outside. If it is assumed that the variation of the atmospheric pressure in one day is 1000 Pa (normal variation), the percentage of the internal atmosphere escaped to the outside will be in the same period of time 10/1000 5 1%. It is assumed here that after one day, steps have been taken to stop the release.
A4.4.3 AMOUNT OF SIGNIFICANT FISSION PRODUCTS IN THE INTERNAL ATMOSPHERE OF THE CASK AND EXTERNAL RELEASE IN ONE DAY Only cesium-137 and krypton-85 are considered significant. Indeed, the other isotopes (such as xenon and iodine) normally considered in explorative evaluations like this one are either completely decayed 15 years after the removal of the fuel from the reactor, or are not volatile enough to be released at relatively low temperature and through narrow and tortuous leak paths (e.g., imperfections in the metallic seals). In the first place it can be assumed that the amount of the fission products in the gap between the fuel and the cladding is the same as that which was there when the fuel was discharged from the reactor, except for the effects of radioactive decay. Indeed, the phenomenon of diffusion from the fuel to the gap is governed by a diffusion coefficient, D0Cs , which depends on the temperature (in kelvin) according to an Arrhenius type law (ANS, 1984): D0Cs 5 1:22eð272300=RTÞ 3 100ðBu=28000Þ
(A4.6)
where R is the gas constant 5 1.987 cal/mol/K (8.3143 J/mol/K), T is the temperature (K), and Bu is the fuel burn-up (MWD/t). The ratio between the diffusion coefficient at the average operating temperature of the fuel (roughly 1300 K) and at the fuel temperature after shutdown and during the storage (some hundreds of kelvin, typically 500 K) is practically infinite. The inventory of radioactive isotopes in the gap is, then, practically equal to that at the discharge from the reactor. Therefore for the Caorso reactor (860 MWe) and on the basis of the data on the content of fission products in a 1000-MWe reactor, the following evaluation can be made. In all the fuel (560 elements), after 15 years decay:
860 5 17 585 000 Cið650 600 TBqÞ 1000 3 2ð15=10:82Þ 860 137 5 2 924 533 Cið108 208 TBqÞ Cs: 4:7 3 106 1000 3 2ð15=30:13Þ 85
Kr:5:6 3 107
In the gap of 50 elements, assumed equal to 1% of the gap itself: 85
Kr:
17 585 000 50 3 5 15 700 Cið580 TBqÞ 100 560
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137
Cs:
381
2 924 553 50 3 5 2611 Cið97 TBqÞ 100 560
Assuming, moreover, that five fuel elements leak as a result of the event, corresponding to 10% of the total (therefore equal to 10 times the percentage of fissured rods normally assumed in safety analyses for the normal operation of a reactor), then values available for release are obtained that are equal to one tenth of those indicated above. The external release in one day will be, for the considerations made above on the consequence of the variation of the atmospheric pressure, equal to one hundredth of the available activity values: 85
Kr:0:6 TBq Cs:0:1 TBq
137
The release is assumed to be at ground level in cases where no accompanying fuel failure is postulated and at hundreds of meters high in the case where a fire occurs. A fire of short duration (,1 hour), such as one resulting from a plane crash or a manually extinguished fire could have a limited influence on the amount of the release as the thermal time constant of the cask wall ( . 0.3 m of steel or cast iron) should be higher than the fire duration. In these conditions, the increase in the internal cask pressure caused by the fire could be high enough to change the amount (but not the order of magnitude) of the previously described release assumptions. A simple thermal analysis shows that a conservative estimate of the internal pressure increase caused by the fire in half an hour could be of the order of 3000 Pa (namely a factor of three over the above-described assumptions). In conclusion, the release in a fire could be of the order of three times the one assumed above, in a time frame of ,1 hour. The two releases should not be combined.
A4.4.4 EFFECTIVE COMMITTED DOSES A4.4.4.1 Cesium Doses The cloud resulting from the release can be considered dispersed by diffusion and deposition (Pasquill model). If a stability condition, F, is assumed with a 2 m/s wind velocity and a deposition velocity of 0.01 m/s, the ground concentrations shown in Table A4.5 (roughly) result. The ground concentration (e.g., at 1 km) is C 5 2 3 1024 3 0.1 3 109 3 0.01 5 200 kBQ/m2 (see Eq. A4.5) and roughly decreases with the 1.52 power of the ratio of distances (resulting in concentrations of 50 and 2 kBq/m2 at 2 and 10 km, respectively).
Table A4.5 Ground Concentrations Distance (km)
Soil Concentrations (kBq m2)
1 2 10
200 50 2
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The levels of ground contamination calculated above, can be compared with the contamination levels in a generic European country after Chernobyl, on the average equal to 1020 kBq/m2 with peaks of 100200 kBq/m2 (Vargo, 2000). On the assumption that the food chain is controlled after the accident and so the cesium intake is zero, the doses to the population can be due only to ground shine (if the population has not been evacuated). The doses at one year and at 50 years can be calculated on the basis of the factors shown in Table A4.6 corresponding to a contamination of 1 kBq/m2 (Vargo, 2000). The inhalation dose gives a negligible contribution. Therefore within a radius of 1 km from the site, multiplying the figures of the preceding table by 200, the results shown in Table A4.7 are obtained. At 2 km from the site, the doses are shown in Table A4.8. At 10 km, the doses are shown in Table A4.9.
Table A4.6 Unit Doses Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.012 0.16
Table A4.7 Doses at 1 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
2.5 30
Table A4.8 Doses at 2 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.6 8
Table A4.9 Doses at 10 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.025 0.3
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A4.4.4.2 Krypton-85 Effective Doses The krypton-85 doses are due to immersion in a finite dimension cloud. For a diffusion category F and at a distance of 1 km, the conversion coefficient between the effective dose and cloud concentration (Vargo, 2000) is 3.6 3 1025 rem per Ci s/m3 (2.7 3 10213 Sv per Bq s/m3). Therefore for a cloud concentration of 2 3 1024 3 0.6 TBq s/m3, the following effective dose results: 1 3 1029 Sv, which is practically zero.
A4.4.5 CONCLUSIONS The preceding evaluations, despite the high level of protection already incorporated in the casks, support the need for technological solutions which offer special protection against aircraft crash and against explosive events or solutions such as where the storage structure is located at least 20 m below ground level.
REFERENCES ACI, 2001. Code Requirements for Nuclear Safety Related Concrete Structures and Commentary. ACI 349, American Concrete Institute, USA. ANPA, 1985. Gestione dei rifiuti radioattivi. Guida Tecnica 26. ANS, 1984. Report of the Special Committee on Source Terms. American Nuclear Society, September. Bender F., Herausgegeber, 1982. Underground Siting of Nuclear Power plants. Hanover Symposium, Stuttgart. Colombo, G., 1997. Manuale dell’Ingegnere. Nuovo Colombo, L-37 (83a), Ulrico Hoepli Editore, Milano. Ferreli, A., Bologna, L., 1991. Reattori nucleari: Termine di sorgente e piani di emergenza, Commissione Tecnica. Vargo, G.J., 2000. The Chernobyl Accident: A Comprehensive Risk Assessment. Battelle Press, Columbus.
DOSE CALCULATIONS
4
A4.1 INTRODUCTION This appendix gives some examples of dose calculations which have been used during discussions on conceptual designs of various plants. The dose calculations are of a simple type, suitable for indicative evaluations. More elaborate calculations are usually performed in the final phases of the safety analysis, when systems and components purchase specifications have already been defined.
A4.2 VIRTUAL POPULATION DOSE IN A SEVERE ACCIDENT The following sections describe the virtual population dose for a future reactor (an order of magnitude evaluation in the short term, at three days, and in the long term, several years).
A4.2.1 THE REACTOR AND THE RELEASED ISOTOPES The example is a passive type boiling water reactor of 600 MWe, provided with a double containment and a stack. The quantities of isotopes chosen as guide isotopes in the core (1800 MWt) are, at equilibrium: 131
I Cs 133 Xe 85 Kr 137
1.85 3 1018 Bq 148 3 1015 Bq 3.7 3 1018 Bq 12.95 3 1015 Bq
A4.2.2 SOURCE TERM AT THREE DAYS (I, CS, XE) •
•
The leakage rate assumed for the primary containment (taken into account the probability of leakage rates higher than the specified ones and possible damages to penetrations for severe accidents): 5%10% per diem. The leakage rate assumed for the secondary containment room (systems, collection room, or building): 1%10% per diem. (For this assumption to be valid extremely unlikely sequences are excluded, such as the rupture of a steam line with degraded core and valve leak proofing degraded.)
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The effective release height (e.g., passive routing of the leaks to a stack, collection of leaks in a leakproof room connected with the stack, leaks routed to a chimney through filters, etc.): 80 m. Iodine and cesium equivalent ground releases: n% of the core inventory w3x3y3z
(A4.1)
where n 5 20, w 5 10 for plateout and washout, x takes a value in the range 36 for leaks from primary containment in three days, y takes a value in the range 330 for leaks from the secondary containment in three days, and z 5 10 (a factor for elevated release). The iodine and cesium equivalent ground release range 5
0:2 3 core inventory 0:2 3 core inventory to 5 : 10 3 6 3 30 3 10 10 3 3 3 3 3 10
So for 131I, the range is (1.1 3 1025) (1.85 3 1018) to (2.2 3 1024) (1.85 3 1018) 5 20.35 3 101240.7 3 1013 Bq. (A realistic reference value 5 20.35 3 1012 Bq.) And for 137Cs, the range is 5 16.28 3 101132.56 3 1012 Bq. (A realistic reference value 5 18.5 3 1011 Bq.) For 133Xe, the equivalent ground release range [Eq. (A4.1)], calculated with n 5 80, w 5 0, x 5 36, y 5 330 and z 5 5, is 3.29 3 10156.58 3 1016 Bq. (A realistic reference value 5 1.85 3 1016 Bq.)
A4.2.3 DOSE AT THE FENCE AFTER THREE DAYS OF EXPOSURE I (effective dose for adults by inhalation) 5 (χ/Q) 3 dbf 3 grr, where χ (s/m3) is the cloud concentration at 1 km, Q (Bq) is the activity release, dbf (the dose biological factor) 5 10 and grr (the ground release range) 5 (20.35 3 1012)(40.7 3 1013) Bq. Assuming χ/Q at 1 km distance is 1 3 1024, then the effective iodine-131 dose for adults by inhalation is 5100 mSv. (A realistic value is 10 mSv.) 133 Xe (effective dose by cloud irradiation) 5 (χ/Q)(1/dcf) 3 grr, where dcf (dose conversion factor) (see Chapter 7: Health Consequences of Releases) 5 300 and grr 5 (3.29 3 1015) (6.58 3 1016) Bq. Assuming χ/Q is 1 3 1024, then the effective xenon-133 dose by cloud irradiation is 0.310 mSv. Calculations for all the noble gases give a dose at the fence after three days of 5120 mSv (about 10 times the value for 133Xe). An effective realistic value is 30 mSv.
131
A4.2.4 GROUND SHINE LONG-TERM DOSE The integrated dose due to ground shine with absorption in the soil, corresponding to a ground initial concentration of 1 Bq/cm2 of cesium-137 (a contribution by other nuclides exists but is not evaluated here): First year Second year 050 years
120 μSv 80 μSv 1.6 mSv
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375
The initial concentration of cesium-137 corresponding to a realistic release of 1.85 3 1012 Bq is given by (1.85 3 1012) [Bq released] 3 1 3 1024[χ/Q], Bq s/m3 at 1 km] 3 (1 3 1022) [m/s: deposition velocity] 5 2 3 106 Bq/m2. Therefore the ground shine dose from cesium-137 is First year Second year 050 years (After 5 years this dose is 80 mSv.)
20 mSv 15 mSv 300 mSv
A4.3 EXPLORATIVE EVALUATION OF THE RADIOLOGICAL CONSEQUENCES OF A MECHANICAL IMPACT ON A SURFACE STORAGE FACILITY FOR CATEGORY 2 WASTE A4.3.1 TYPE OF REPOSITORY It is assumed that the disposal structure is similar to the French one at L’Aube or to the Spanish one in El Cabril. The waste is assumed to comply with the ANPA Technical Guide No. 26 (ANPA, 1985) and is, therefore, conditioned in a concrete matrix with compression strength of at least 500,000 kg m22.
A4.3.2 REFERENCE IMPACT It is assumed that the reference impact produces, on clear ground, a conical crater having an angle of 90 degrees and a depth of 4 m. Moreover, it is assumed that the cause of the impact is undefined, possibly to be identified with a plane crash, a launched projectile or a blast from an internal or external explosive charge. The 4 m deep crater has been chosen because it can be related to an explosive projectile of medium size (see a discussion at the Hanover Congress on the nuclear underground sites; Bender, 1982). The volume of material expelled from the crater would then be about 70 m3 corresponding to about 140 t. These values can be compared with the effects of mining explosives. The amount of rock (hard limestone rock) demolished in an open air mine is of the order of 710 t/kg explosive (Colombo, 1997). The rock in our example corresponds (in ideal conditions) to about 20 kg of explosive, an amount considered to be modest. The effect of an airplane crash, then, may cause, according to the usual assumptions, an impact load of about 10,000 t on a surface area of 7 m2, corresponding to about 150 kg/cm2. This load might cause the fall and the fragmentation of a column of structure, assumed to be 1015 m high with a volume of about 70 m3 (see Fig. A4.1).
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10 m
FIGURE A4.1 Fragmentation due to impact
Table A4.1 Fragmentation of Material Average Dimension of Blocks (m)
Layer Volume 1 mm (m3)
Layer Volume 3 mm (m3)
0.33 0.20
1.2 2.1
3.6 6.3
A4.3.3 FRAGMENTATION AND DISPERSION OF MATERIAL It is assumed that the material is fragmented into blocks 0.20.3 m in diameter and that a layer 13 mm thick of each block is pulverized into fragments ranging between 1 μm and 13 mm, with a uniform distribution between the two extremes (see Table A4.1). If an intermediate case is chosen (e.g., a volume equal to 2.5 m3), a weight of finely fractured material of 5 t is obtained, corresponding to a fraction of about 3% of the total. This percentage agrees with the values estimated, for example, for the Chernobyl accident (Vargo, 2000). It is possible to make an assumption, also on the basis of accident data, that the coarser part of the powder produced (from 10 μm to 1 mm), with an overall weight approximately equal to the total one (99%), is deposited over a radius of a few kilometers (2 km are assumed) from the release point, with an average concentration c5
5000 5 4 3 1024 kg=m2 π 3 20002
(A4.2)
This evaluation is not conservative as the effect of wind is completely disregarded. This effect causes the angular distribution of the particulate to be nonuniform. An estimate of the concentration of the deposited radioactivity can be made with the following assumptions: •
The complex of released radioisotopes is equivalent to an amount of 137Cs.
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Table A4.2 Soil Concentrations
•
Distance (km)
Soil Concentration (kBq/m2)
2 10
100 4
The equivalent value of 137Cs is equal to the value indicated in ANPA Technical Guide No. 26 (1985) as the limit for conditioned category 2, waste (3700 MBq/kg). The total radioactivity in the released particulate is, then R 5 5 ; 000; 000 3 3:7 3 1026 5 20 TBq
(A4.3)
With this assumption, the concentration on the soil is C 5 0:4 3 3:7 3 106 5 1500 kBq=m2
(A4.4)
The finest particles (110 μm), with an overall weight of about 50 kg and a total radioactivity of 0.2 TBq, can be assumed to be dispersed by diffusion and deposition (Pasquill model). Assuming a stability condition F with wind velocity of 2 m/s and a deposition velocity of 1022 m/s, the approximate soil concentrations shown in Table A4.2 are obtained. Indeed, the concentration, C, for example, at 1 km, is given by C
χ 3 Q 3 vd Q 5 2 3 1024 3 0:2 3 109 3 0:01 5 400 kBq=m2 5
(A4.5)
and decreases roughly with the 1.52 power of the ratio of distances for higher distances (concentrations of 100 and 4 kBq/m2 at 2 and 10 km, respectively, result). The levels of soil contamination calculated may be compared with the cesium-137 contamination in a generic European country after Chernobyl, equal on the average to 1020 kBq/m2 with peaks up to 100200 kBq/m2 (Vargo, 2000).
A4.3.3.1 Alternative Source Term A different approach to the previously considered accident can be pursued, along the following lines: • •
• •
To assume an applied force of 5000 t for the reference aircraft impact (as adopted in Italy for power plants), instead of the 10,000 t adopted in the previous evaluation. To allow for the dynamic character of the load applied by the impacting aircraft on the concrete. This would imply an increment in the limit load as allowed by the applicable regulations [e.g., American Concrete Institute ACI 349 (ACI, 2001)]. To evaluate the depth of the fractured material as a consequence of the impact by the penetration formulae adopted for nuclear plant evaluations such as the formula (17.2). To add to the aircraft impact a fire of the transported fuel. This could influence the dispersion of the released particulate. In particular, the coarse fraction could be transported and deposited further than the assumed 2 km.
378
APPENDIX 4 DOSE CALCULATIONS
Taking into account the previous assumptions, the volume of fractured material would result in the order of 12 m3 instead of the 70 m3 assumed above. The coarse fraction of the release could be of the order of 860 kg instead of 5 t, whereas the fine fraction would turn out to be equal to 8.6 kg (instead of 50 kg). The uncertainty in the evaluation of the effect of the fire is rather high. Some indications could be obtained from the observation of the behavior of the Chernobyl release (Vargo, 2000). There, the large ( . 20 μm) particles were deposited within a radius of 5 km from the plant. With these assumptions, the following distribution of released material is obtained • • •
Coarse fraction: .20 μm: weight 5 860 kg. Ground concentration 5 1.1 3 1025 kg/m2, corresponding to 41 kBq/m2. Fine fraction: weight 5 17.2 kg.
This would be dispersed under the influence of the buoyancy effect of the fire. In the case of Chernobyl, the thermal elevation of the plume caused by the fire was of the order of 1000 m (Vargo, 2000) and this figure can be assumed to be valid also for this example. In order to get an idea of the characteristics of a (presumed) fire in a reference plane crash, it is assumed that the full fuel load charge of the aircraft is equal to 10 m3, corresponding roughly to 7 t. This amount of fuel, with a conservative assumption, can be considered to form a square pool with 10-m long sides. The burning velocity of a pool of kerosene of this size is roughly 170 kg/m2/h (Lees, 1996). The fuel would be completely burnt in about 25 min. The flame height would be equal to about twice its width, namely 20 m. The usual thermal-elevation formulae can be used to perform a further evaluation of the height to which the radioactive release will be brought by the flame. The Stu¨mke formula [see Eq. (6.7)] can be used to indicate a plume rise of .1000 m. The uncertainty of this evaluation is, however, high as both the wind velocity field and the atmospheric turbulence have a strong influence on the phenomenon. It has to be noted that the presence of a fuel fire should not significantly increase the amount of radioactive particulate released. Indeed, the duration of the fire is short and the radioactive waste packaging is made of “fire resistant” and “nonflame propagating” materials (ANPA, 1985).
A4.3.4 DOSES On the assumption that in the vicinity of the plant there is no intake of cesium through the food chain, the doses to the population can be caused by ground shine (on the assumption the population have not been evacuated). The doses at 1 year and at 50 years can be calculated on the basis of the factors shown in Table A4.3, corresponding to a contamination of 1 kBq/m2 (Ferreli and Bologna, 1991). Table A4.3 Dose Factors Time After Accident (Years)
Effective Dose (mSv)
1 50
0.012 0.16
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Table A4.4 Doses Time After the Accident (Years)
Effective Dose (mSv)
1 50
18 (5) 240 (65)
The inhalation dose gives a negligible contribution. Therefore within a radius of 1 km from the site, multiplying the values in Table A4.3 by 1500 or 400, the doses shown in Table A4.4 are obtained. At 10 km from the plant, with the above-evaluated contamination figures, about 0.05 and 0.65 mSv can be obtained at 1 and at 50 years, respectively.
A4.3.5 CONCLUSIONS Although these evaluations are inevitably subjective and need further reflection, the consideration of a severe impact accident seems opportune, taking into account the long life of a repository (centuries). Technical solutions incorporating a special technological protection from the aircraft crash and from explosive events or solutions in which the disposal structure is located at a depth in the ground of at least 20 m should be considered among the alternatives to be examined. The subsurface solution would offer better protection during the phases of construction and of filling up of the repository.
A4.4 EXPLORATIVE EVALUATION OF THE RADIOLOGICAL CONSEQUENCES OF A MECHANICAL IMPACT ON A TRANSPORT/STORAGE CASK CONTAINING SPENT FUEL A4.4.1 CHARACTERISTICS OF THE CASK The cask complies with the international requirements for fuel transportation and, therefore, it resists the fall, punching, and submersion. Moreover, the cask will be designed to protect it from aircraft impact and consequent fire. The cask considered has two independent leakproof lids, each one equipped with metallic seals. It is assumed that the cask contains 50 fuel elements of the type used at the Caorso plant and that the maximum temperature of the cladding is 200 C. The interior of the cask is normally kept at negative pressure and in an inert atmosphere.
A4.4.2 REFERENCE IMPACT It is assumed that the cause of the impact is undefined, possibly to be identified but assumed to be due to a plane crash, the launch of a projectile or the blast of an internal or external explosive charge. The effect of a plane crash may cause, according to the usual assumptions, a load of about 10,000 t on a surface area of 7 m2, corresponding to about 1.43 3 106 kg m2.
380
APPENDIX 4 DOSE CALCULATIONS
Notwithstanding the strength characteristics of the cask and its leakproof seals against impact and other conceivable external loads, it is assumed that in the accident considered, both seals are damaged, allowing a certain communication between its internal and the outside atmosphere and a gas flow dependent on the pressure difference between the inside and outside. Immediately after the deterioration of the seals, the external air will flow into the cask because of the internal underpressure. Subsequently, as a consequence of the lowering of external atmospheric pressure, part of the gas contained inside the cask might escape to the outside. If it is assumed that the variation of the atmospheric pressure in one day is 1000 Pa (normal variation), the percentage of the internal atmosphere escaped to the outside will be in the same period of time 10/1000 5 1%. It is assumed here that after one day, steps have been taken to stop the release.
A4.4.3 AMOUNT OF SIGNIFICANT FISSION PRODUCTS IN THE INTERNAL ATMOSPHERE OF THE CASK AND EXTERNAL RELEASE IN ONE DAY Only cesium-137 and krypton-85 are considered significant. Indeed, the other isotopes (such as xenon and iodine) normally considered in explorative evaluations like this one are either completely decayed 15 years after the removal of the fuel from the reactor, or are not volatile enough to be released at relatively low temperature and through narrow and tortuous leak paths (e.g., imperfections in the metallic seals). In the first place it can be assumed that the amount of the fission products in the gap between the fuel and the cladding is the same as that which was there when the fuel was discharged from the reactor, except for the effects of radioactive decay. Indeed, the phenomenon of diffusion from the fuel to the gap is governed by a diffusion coefficient, D0Cs , which depends on the temperature (in kelvin) according to an Arrhenius type law (ANS, 1984): D0Cs 5 1:22eð272300=RTÞ 3 100ðBu=28000Þ
(A4.6)
where R is the gas constant 5 1.987 cal/mol/K (8.3143 J/mol/K), T is the temperature (K), and Bu is the fuel burn-up (MWD/t). The ratio between the diffusion coefficient at the average operating temperature of the fuel (roughly 1300 K) and at the fuel temperature after shutdown and during the storage (some hundreds of kelvin, typically 500 K) is practically infinite. The inventory of radioactive isotopes in the gap is, then, practically equal to that at the discharge from the reactor. Therefore for the Caorso reactor (860 MWe) and on the basis of the data on the content of fission products in a 1000-MWe reactor, the following evaluation can be made. In all the fuel (560 elements), after 15 years decay:
860 5 17 585 000 Cið650 600 TBqÞ 1000 3 2ð15=10:82Þ 860 137 5 2 924 533 Cið108 208 TBqÞ Cs: 4:7 3 106 1000 3 2ð15=30:13Þ 85
Kr:5:6 3 107
In the gap of 50 elements, assumed equal to 1% of the gap itself: 85
Kr:
17 585 000 50 3 5 15 700 Cið580 TBqÞ 100 560
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137
Cs:
381
2 924 553 50 3 5 2611 Cið97 TBqÞ 100 560
Assuming, moreover, that five fuel elements leak as a result of the event, corresponding to 10% of the total (therefore equal to 10 times the percentage of fissured rods normally assumed in safety analyses for the normal operation of a reactor), then values available for release are obtained that are equal to one tenth of those indicated above. The external release in one day will be, for the considerations made above on the consequence of the variation of the atmospheric pressure, equal to one hundredth of the available activity values: 85
Kr:0:6 TBq Cs:0:1 TBq
137
The release is assumed to be at ground level in cases where no accompanying fuel failure is postulated and at hundreds of meters high in the case where a fire occurs. A fire of short duration (,1 hour), such as one resulting from a plane crash or a manually extinguished fire could have a limited influence on the amount of the release as the thermal time constant of the cask wall ( . 0.3 m of steel or cast iron) should be higher than the fire duration. In these conditions, the increase in the internal cask pressure caused by the fire could be high enough to change the amount (but not the order of magnitude) of the previously described release assumptions. A simple thermal analysis shows that a conservative estimate of the internal pressure increase caused by the fire in half an hour could be of the order of 3000 Pa (namely a factor of three over the above-described assumptions). In conclusion, the release in a fire could be of the order of three times the one assumed above, in a time frame of ,1 hour. The two releases should not be combined.
A4.4.4 EFFECTIVE COMMITTED DOSES A4.4.4.1 Cesium Doses The cloud resulting from the release can be considered dispersed by diffusion and deposition (Pasquill model). If a stability condition, F, is assumed with a 2 m/s wind velocity and a deposition velocity of 0.01 m/s, the ground concentrations shown in Table A4.5 (roughly) result. The ground concentration (e.g., at 1 km) is C 5 2 3 1024 3 0.1 3 109 3 0.01 5 200 kBQ/m2 (see Eq. A4.5) and roughly decreases with the 1.52 power of the ratio of distances (resulting in concentrations of 50 and 2 kBq/m2 at 2 and 10 km, respectively).
Table A4.5 Ground Concentrations Distance (km)
Soil Concentrations (kBq m2)
1 2 10
200 50 2
382
APPENDIX 4 DOSE CALCULATIONS
The levels of ground contamination calculated above, can be compared with the contamination levels in a generic European country after Chernobyl, on the average equal to 1020 kBq/m2 with peaks of 100200 kBq/m2 (Vargo, 2000). On the assumption that the food chain is controlled after the accident and so the cesium intake is zero, the doses to the population can be due only to ground shine (if the population has not been evacuated). The doses at one year and at 50 years can be calculated on the basis of the factors shown in Table A4.6 corresponding to a contamination of 1 kBq/m2 (Vargo, 2000). The inhalation dose gives a negligible contribution. Therefore within a radius of 1 km from the site, multiplying the figures of the preceding table by 200, the results shown in Table A4.7 are obtained. At 2 km from the site, the doses are shown in Table A4.8. At 10 km, the doses are shown in Table A4.9.
Table A4.6 Unit Doses Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.012 0.16
Table A4.7 Doses at 1 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
2.5 30
Table A4.8 Doses at 2 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.6 8
Table A4.9 Doses at 10 km Time After the Accident (Years)
Effective Dose (mSv)
1 50
0.025 0.3
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A4.4.4.2 Krypton-85 Effective Doses The krypton-85 doses are due to immersion in a finite dimension cloud. For a diffusion category F and at a distance of 1 km, the conversion coefficient between the effective dose and cloud concentration (Vargo, 2000) is 3.6 3 1025 rem per Ci s/m3 (2.7 3 10213 Sv per Bq s/m3). Therefore for a cloud concentration of 2 3 1024 3 0.6 TBq s/m3, the following effective dose results: 1 3 1029 Sv, which is practically zero.
A4.4.5 CONCLUSIONS The preceding evaluations, despite the high level of protection already incorporated in the casks, support the need for technological solutions which offer special protection against aircraft crash and against explosive events or solutions such as where the storage structure is located at least 20 m below ground level.
REFERENCES ACI, 2001. Code Requirements for Nuclear Safety Related Concrete Structures and Commentary. ACI 349, American Concrete Institute, USA. ANPA, 1985. Gestione dei rifiuti radioattivi. Guida Tecnica 26. ANS, 1984. Report of the Special Committee on Source Terms. American Nuclear Society, September. Bender F., Herausgegeber, 1982. Underground Siting of Nuclear Power plants. Hanover Symposium, Stuttgart. Colombo, G., 1997. Manuale dell’Ingegnere. Nuovo Colombo, L-37 (83a), Ulrico Hoepli Editore, Milano. Ferreli, A., Bologna, L., 1991. Reattori nucleari: Termine di sorgente e piani di emergenza, Commissione Tecnica. Vargo, G.J., 2000. The Chernobyl Accident: A Comprehensive Risk Assessment. Battelle Press, Columbus.