1
2
3
Neutronic Evaluation of Using a Thorium Sulfate
4
Solution in an Aqueous Homogeneous Reactor
5 6
D. Pérez1,4*, D. Milian2, L. Hernández3, A. Gámez1,4, D. Lorenzo3, C. Brayner4
7
1Departamento de Energia Nuclear, Universidade Federal de Pernambuco (UFPE), Cidade Universitária,
8
Avenida Professor Luiz Freire 1000, Recife, PE, Brasil
9
2Departamento de Energía Renovable y Eficiencia Energética, Cubaenergía, Calle 20 No 4111 / 18a y 47, Playa, Habana, Cuba
10
3Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC), Universidad de La Habana, Avenida Salvador Allende y Luaces,
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Quinta de Los Molinos, Plaza de la Revolución, 10400, La Habana, Cuba
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4Centro Regional de Ciências Nucleares (CRCN-NE/CNEN), Cidade Universitária, Avenida Professor Luiz Freire 200,
13
Recife, PE, Brasil
14 15 16
A R T I C L E I N F O A B S T R A C T
17 18
Article history:
Received 24 September 2021
Received in revised form 10 February 2022 Accepted 16 February 2022
Keywords:
99Mo production
Aqueous Homogeneous Reactor Thorium fuel
MCNP Fuel solution Thorium sulfate
Radioisotope 99Mo is one of the most essential radioisotopes in nuclear medicine.
Its production in an Aqueous Homogeneous Reactor (AHR) could be potentially advantageous compared to the traditional technology, based on target irradiation in a heterogeneous reactor. An AHR conceptual design using low-enriched uranium for the production of 99Mo has been studied in depth. So far, the possibility of replacing uranium with a non-uranium fuel, specifically a mixture of 232Th and
233U, has not been evaluated in the conceptual design. Therefore, the studies conducted in this article aim to evaluate the neutronic behavior of the AHR conceptual design using thorium sulfate solution. Here, the 232Th-233U composition to guarantee ten years of operation without refueling, conversion ratio, medical isotopes production levels, and reactor kinetic parameters were evaluated, using the computational code MCNP6. It was obtained that 14 % 233U enrichment guarantees the reactor operation for ten years without refueling. The conversion ratio was calculated at 0.14. The calculated 99Mo production in the AHR conceptual design resulted in 24.4 % higher with uranium fuel than with thorium fuel.
© 2022 Atom Indonesia. All rights reserved
INTRODUCTION
19
Nowadays, radioisotopes are extensively
20
employed in nuclear medicine, with widespread
21
use in the diagnosis and treatment of diseases in
22
areas such as oncology, hematology, cardiology,
23
and neurology. One of those radioisotopes,
24
molybdenum-99 (99Mo) is used in hospitals to
25
generate technetium-99m (99mTc) employed in
26
around 80 % of nuclear imaging procedures.
27
Globally, a total of 30-40 million of these
28
procedures use 99mTc as a working substance.
29
Produced in research reactors, 99Mo has a half-life of
30
only 65.94 hours and cannot be stockpiled,
31
and security of supply is nowadays a key concern.
32
Most of the world's supply, to cover an estimated
33
demand of between 9,000 and 10,000 six-days
34
Corresponding author.
E-mail address: [email protected] DOI:
Ci per week, currently relies on a small group of
35
research heterogeneous reactors. Most of these
36
research reactors are more than 50 years old and
37
have an estimated production end date before or in
38
2030. Recent years have illustrated how unexpected
39
shutdowns at any of those reactors can quickly lead
40
to shortages. Furthermore, in some of these reactors,
41
99Mo is produced from high-enriched uranium
42
(HEU) targets, which are seen as a potential nuclear
43
proliferation risk [1-3].
44
The use of Aqueous Homogeneous Reactors
45
(AHR) for producing 99Mo could be a promising
46
technology, compared to the traditional method of
47
irradiating targets in heterogeneous reactors, due to
48
their expected low cost (up to US$ 30 million per
49
unit), small critical mass ( 10 kg of Uranium),
50
low thermal power (50-300 kWth), low operating
51
pressure (slightly below atmospheric pressure)
52
and temperature (up to 90 °C), inherent safety,
53
and simplified fuel handling, processing and
54
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purification characteristics [1,4,5]. An AHR
55
conceptual design, based on the Russian reactor
56
ARGUS, was developed for the production of 99Mo
57
and other medical isotopes [6-14]. Presently,
58
the ARGUS reactor stands out as the only large-
59
scale successful experiment on the use of an AHR in
60
steady-state operation. This reactor, a 20 kWth,
61
HEU fuel solution reactor is in operation at
62
the “Kurchatov Institute” since 1981 with
63
great economic and safety aspects. In July 2014,
64
after feasibility calculations and a conversion period,
65
the ARGUS reactor reached the first criticality with
66
low-enriched uranium (LEU) fuel. This conversion
67
to LEU fuel meets the purposes of the Reduced
68
Enrichment for Research and Test Reactor (RERTR)
69
program, which aims to replace HEU into LEU or
70
with non-uranium targets/fuels [15].
71
The flexibility of the AHR parameters
72
variation, specifically the fuel selection, allows the
73
use of various mixtures of uranium salts (uranyl
74
sulfate, nitrate, etc.) and various levels of
75
enrichment in 235U [1]. Although there seems to be
76
no evidence against the viability of using an AHR
77
with an aqueous solution of thorium salts for the
78
production of 99Mo, the possibility of replacing the
79
enriched uranium with a non-uranium fuel,
80
specifically a mixture of 232Th and 233U, has not been
81
evaluated in the conceptual design. Few articles
82
dealing with this issue are identified in the scientific
83
literature, specifically concerning the production
84
levels of 99Mo and other radioisotopes when the
85
fuel/target is a mixture of 232Th and 233U. The use of
86
thorium could be potentially advantageous
87
considering the benefits of this fertile material over
88
the use of uranium. Therefore, the primary objective
89
of this paper is to evaluate the neutronic viability of
90
using an AHR with an aqueous solution of thorium
91
salts for the production of 99Mo. For this, different
92
232Th-233U mixtures will be evaluated to guarantee
93
10 years of normal operation without refueling.
94
In addition, the reactor conversion ratio (CR) will be
95
calculated as well as the production levels of 99Mo,
96
89Sr, 131I, and 133Xe. In the same way, the effective
97
delayed neutron fraction (βeff) and mean
98
neutron generation time (Λ) will be calculated.
99
All computational calculations will be carried out
100
using the computational code MCNP6.
101 102 103
METHODOLOGY
104
The AHR conceptual design (Fig. 1)
105
previously studied in [6-11,14] using LEU fuel,
106
consists of an aqueous solution located in a steel
107
cylindrical vessel (wall thicknesses of 0.5 cm) with a
108
hemispherical bottom. Placed inside the vessel are
109
two coiled-tube heat exchangers and three channels.
110
The central channel has an experimental purpose,
111
while the other two channels are intended for poison
112
rods, with sufficient reactivity worth to compensate
113
the reactivity reserve and to be able to shut down the
114
reactor. The steel channels are 4.8 cm in outer
115
diameter, and their wall thickness is 0.2 cm. The two
116
coiled-tube heat exchangers use 34.5 m of tubing,
117
0.60 cm inner diameter, and 1.0 cm outer diameter.
118
Side and bottom graphite reflectors surround the
119
reactor vessel. The main reactor core parameters are
120
shown in Table 1.
121 122
123
Fig. 1. AHR conceptual design model.
124 125
Table 1. The reactor core parameters.
126 127
Parameter Value
Fuel solution Thorium sulfate solution
233U in the mixture (%) 14
Heavy metal concentration (g/liter) 380 Inner core diameter (cm) 30.5
Reactor height (cm) 65.6
Reactor vessel Stainless steel
Vessel thickness (cm) 0.5
Reflector (radial) Graphite – 60 cm
Solution Density (g/cm3) 1.67084 Fuel solution height (cm) 52.94*
Total 233U mass (kg) 1.74
Total 232Th mass (kg) 10.63
Cold solution volume with no voids
(liter) 29.50*
Thermal power (kWth) 50
Power density (kWth/liter of solution) 1.70
Operating temperature less than 90 °C 128
* Considering the effects of the fuel thermal expansion (20 to 70 °C) and 129
the radiolytic gas bubble formation, the fuel solution height and volume 130
increase to 54.45 cm to 30.50 liters, respectively.
131 132
Neutronic calculations have been carried out
133
using the computational code MCNP6 with the
134
ENDF/B-VII.1 library, evaluated at 70 °C (fuel
135
solution average temperature determined in a
136
previous study [11]). MCNP is a general-purpose,
137
continuous-energy, generalized-geometry, time-
138
dependent, Monte Carlo radiation-transport code
139
designed to track many particle types over broad
140
Cooling pipes
Core channels Vessel
Fuel solution
ranges of energies. The MCNP version used in this
141
work offers a group of new capabilities beyond its
142
predecessors used in this work such as the
143
depletion/burnup and the FMESH card, which
144
enables to determine the energy deposition and
145
neutrons flux profiles [16]. Figure 2 shows the
146
geometrical model of the AHR conceptual design on
147
the MCNP Visual Editor. As the helical pipes cannot
148
exactly be modeled in MCNP, they were represented
149
by equally spaced toroids.
150 151
152 153
Graphite reflector Stainless steel Air Distilled water Thorium sulfate solution 154
Fig. 2. Longitudinal section of the AHR geometrical model in
155
the MCNP Visual Editor.
156 157
Four studies were conducted during the
158
investigation:
159
First, the determination of the keff dependence
160
on various enrichments in 233U. The objective of this
161
study was to determine the 233U fraction in the initial
162
mixture (233U + 232Th) which allows the reactor
163
to operate without refueling for at least ten years.
164
The five enrichments in 233U that were evaluated
165
were 12, 14, 16, 18, and 20 %. The calculations were
166
carried out without control rods during ten full-
167
power years.
168
The second was the determination of the
169
reactor conversion ratio (CR). This parameter,
170
as defined in Eq. (1), measures the ability to convert
171
fertile isotopes into fissile isotopes. In the fuel
172
solution, the fissile atoms (233U) are produced
173
by neutron capture in fertile atoms (232Th) as
174
indicated in Eq. (2), while the consumption includes
175
fission and capture.
176 177
(1)
178 179
(2)
180
181
Third, the determination of the production
182
levels of medical isotopes. This study was carried
183
out considering fresh fuel and an operating time
184
of ten days.
185
Four, the determination of the most important
186
kinetic parameters in a nuclear reactor, which are the
187
effective delayed neutron fraction (βeff) and the mean
188
neutron generation time (Λ). The βeff for the AHR
189
conceptual design was calculated with MCNP code
190
using the prompt method [8]. The procedure of the
191
prompt method includes the calculation of the
192
multiplication factor with delayed neutron (keff) and
193
without delayed neutron (kp), then approximating
194
the βeff according to in Eq. (3).
195 196
(3)
197
198
The mean neutron generation time was
199
determined using the pulsed neutron technique.
200
In this method, a burst of neutrons is injected into a
201
slightly subcritical system and the decay of the
202
neutron population is observed as a function of time.
203
Figure 3 shows the location of the two detectors
204
used to evaluate the decay of the neutron population
205
as a function of time. A neutron source with a fission
206
spectrum was placed at the center of the reactor
207
core, inside the central experimental channel.
208
A detailed description of the pulsed neutron technique
209
for the mean neutron generation time calculation with
210
MCNP in an AHR can be found in [8].
211 212
213 214
Graphite reflector Stainless Steel Air Distilled water Thorium sulfate solution 215
Fig. 3. Location of the two detectors used to evaluate the decay
216
of the neutron population.
217
218
To conduct these studies, two types of MCNP
219
calculations were performed, namely KCODE
220
and NPS calculations. The KCODE criticality
221
calculations were performed using 50 and 3,000
222
inactive and active cycles respectively, with 10,000
223
neutron histories per cycle. In the other type of
224
calculation, the NPS history cutoff card was used to
225
run 30,000,000 neutron histories using the SDEF
226
card to define the neutron source. Tally F5 was used
227
to determine the neutron flux. Both prompt and
228
delayed neutrons were taken into account for
229
criticality and NPS calculations using the TOTNU
230
card. Benchmarking exercises to evaluate the
231
1
2
prediction capability of the developed models of
232
AHR with MCNP code and the available libraries
233
have been carried out in previous works [8,11].
234 235 236
RESULTS AND DISCUSSION
237
As a first step, the dependence of keff on
238
various 233U enrichments was studied. Figure 4
239
shows the keff evolution over ten full-power years,
240
reaching a discharge fuel burnup of 14.76
241
GWd/tonU. As seen in Fig. 4, 233U enrichment of 14
242
% is sufficient for the reactor to operate without
243
refueling for ten years.
244 245
246 247
Fig. 4. Keff vs. fuel burnup for five 233U enrichments.
248 249
The next step was the determination of the
250
reactor conversion ratio. For that, the masses of the
251
fertile and fissile isotopes obtained from the burnup
252
calculation after ten full-power years were used.
253
ACR of 0.14 was determined, which is consistent
254
with values reported in the literature for this type of
255
system using thorium fuel [17,18].
256
The third study consisted of determining the
257
production levels of medical isotopes using thorium
258
fuel. For quantifying the production levels, a
259
comparison was made against the isotope production
260
in the same AHR using uranium fuel. Figures 5 to 8
261
show the comparison for the isotopes 99Mo, 89Sr, 131I,
262
and 133Xe, respectively, and demonstrate how the
263
choice of fuel affects the isotope production. In the
264
case of 99Mo, it is observed that its production
265
is 24.4 % higher with uranium fuel than with
266
thorium fuel. This behavior is a result of the
267
differences between the thermal and fast fission
268
yields. A 232Th-233U fuel, in comparison with a
269
standard uranium fuel, produces approximately
270
18 % and 53 % less 99Mo due to the thermal and fast
271
fission yield in 233U and 232Th, respectively (Table 2)
272
[19]. Therefore, an AHR with thorium fuel needs to
273
work at a power level 1.244 times higher than an
274
AHR with Uranium fuel, to produce the same
275
amount of 99Mo. This implies that the heat removal
276
system must be improved to take into account the
277
increase in thermal power.
278
279
Fig. 5. Accumulation of 99Mo for ten days of reactor operation.
280 281
282
Fig. 6. Accumulation of 89Sr for ten days of reactor operation.
283 284
285
Fig. 7. Accumulation of 131I for ten days of reactor operation.
286 287
288
Fig. 8. Accumulation of 133Xe for ten days of reactor operation.
289 290
Table 2. Thermal and fast fission yields for 99Mo.
291 292
Isotope Thermal fission yield (% per fission)
Fast fission yield (% per fission)
232Th - 2.919
238U - 6.181
233U 5.03 4.85
235U 6.132 5.80
0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25
0.00 3.00 6.00 9.00 12.00 15.00
Keff
Fuel burnup (GWd/tonU)
12%
14%
16%
18%
20%
0 0.001 0.002 0.003 0.004 0.005 0.006
0 1 2 3 4 5 6 7 8 9 10
Isotope mass (grams)
Time (days) Uranium sulphate fuel Thorium sulphate fuel
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014
0 1 2 3 4 5 6 7 8 9 10
Isotope mass (grams)
Time (days) Uranium sulphate fuel Thorium sulphate fuel
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
0 1 2 3 4 5 6 7 8 9 10
Isotope mass (grams)
Time (days) Uranium sulphate fuel Thorium sulphate fuel
0.000 0.002 0.004 0.006 0.008 0.010 0.012
0 1 2 3 4 5 6 7 8 9 10
Isotope mass (grams)
Time (days) Uranium sulphate fuel Thorium sulphate fuel
As observed in Figs. 6 and 7, the production
293
of 89Sr and 131I is higher with thorium fuel than
294
with uranium fuel. Meanwhile, in the case of
295
133Xe, its production with uranium fuel is higher.
296
As with the 99Mo, the thermal fission yields of the
297
233U and 235U are the main responsible for
298
these behaviors.
299
The final study was the determination of the
300
most important kinetic parameters in a nuclear
301
reactor, which are βeff and Λ. Table 3 shows the keff,
302
kp, and the result of βeff calculations. The βeff with the
303
thorium fuel represents only 45 % of the effective
304
delayed neutron fraction determined for the same
305
system using uranium fuel (726 pcm) [20].
306 307
Table 3. Total (keff) and prompt (kp) multiplication factors and
308
effective delayed neutron fraction (βeff).
309 310
Keff Kp βeff
βeff
(pcm) 1.07934
±0.00014
1.07579
±0.00014
0.00329
±0.00018 329 ±18 311
Figure 9 shows the averaged neutron flux in
312
relative units, over the two detectors, after thirty
313
million source pulses. Figure 9 also shows the
314
exponential fitting used. The decay constant (α0) was
315
obtained by fitting the prompt drop with the first-order
316
exponential decay function, ( ) ;
317
where n denotes the average number of neutrons
318
tallied and N is a constant. As the parameters
319
reactivity (ρ), α0, and βeff are known, the mean
320
neutron generation time can be determined by solving
321
in Eq. (4).
322 323
(4)
324 325
Table 4 shows the results of the Λ calculations
326
(for each detector and the average value).
327
As expected, the Λ was found to be relatively
328
independent of the location in which the neutron
329
flux was measured. Combining βeff and Λ, a βeff/Λ
330
ratio of 40.21 s-1 was obtained.
331 332
333
Fig. 9. Averaged neutron flux as a function of time.
334
Table 4. Mean neutron generation time (Λ) results.
335
Parameter Value
Λ1 (µs) 87.97
Λ2 (µs) 88.02
Λave (µs) 88.00
βeff/Λ (s-1) 40.21
336
The calculated average effective neutron
337
generation time (including the delayed ones - Λeff) is
338
0.063 seconds. This demonstrates the effect that
339
delayed neutrons have on neutron generation time
340
and thus on reactor control. If the AHR conceptual
341
design were operated in a self-sustained chain
342
reaction using only prompt neutrons (βeff = 0),
343
the generation time would be 8.8*10-5 seconds
344
(Table 4). On the other hand, when operating
345
the reactor so that a fraction of 0.00329 neutrons
346
is delayed, the generation lifetime is extended to
347
0.063 seconds (more than 700 times higher). The
348
average effective neutron generation time
349
determined with the thorium fuel represent
350
s 66 % of the Λeff determined for the same
351
system using uranium fuel (0.096 seconds) [20].
352
Therefore, from the point of view of these kinetic
353
parameters of the conceptual design (βeff and Λeff),
354
the use of uranium fuel seems to be safer.
355 356 357
CONCLUSION
358
The primary objective of this paper was to
359
evaluate the neutronic viability of using AHR with
360
an aqueous solution of thorium salts for the
361
production of 99Mo. The neutronic calculations
362
demonstrated that 14 % 233U enrichment in the
363
mixture of 232Th-233U is sufficient for the reactor
364
to operate without refueling for ten years.
365
The discharge burnup after ten years reaches
366
14.76 GWd/tonU. The conversion ratio calculated
367
(0.14) is consistent with values reported by other
368
authors for this type of system using thorium fuel.
369
It was determined that 99Mo production in the AHR
370
conceptual design is 24.4 % higher with uranium
371
fuel than with thorium fuel. Therefore, an AHR
372
with thorium fuel needs to work at a power level
373
1.244 times higher than an AHR with uranium fuel,
374
to produce the same amount of 99Mo. The effective
375
delayed neutron fraction, the average mean neutron
376
generation time, and the average effective neutron
377
generation time were 329 pcm, 88.00 µs, and
378
0.063 seconds, respectively. In conclusion, based
379
only on the neutronic factors studied, the use of
380
uranium fuel in AHR seems more advantageous
381
and safer than a mixture fuel of 232Th-233U.
382
However, many other physical, economic, and safety
383
factors need to be studied and analyzed for a more
384
complete conclusion.
385 y = 4.4060e-132.8987x
R² = 0.9951
0.00 0.20 0.40 0.60 0.80 1.00 1.20
0.008 0.013 0.018 0.023 0.028 0.033 0.038
Neutron flux (relative units)
Time (seconds)
ACKNOWLEDGMENT
386
This research was partially supported by
387
the Coordination for the Improvement of
388
Higher Education Personnel (CAPES), project
389
No. 88887.518186/2020-00 and the Brazilian
390
National Nuclear Energy Commission (CNEN),
391
project no: 01341.011318/2021-51.
392 393 394
AUTHOR CONTRIBUTION
395
D. Pérez conceived the presented idea,
396
developed the theory, and wrote the manuscript.
397
D. Milian, L. Hernández, and A. Gámez performed
398
the computational calculations. D. Lorenzo and
399
C. Brayner supervised the findings of this work.
400
All authors read and approved the final version
401
of the paper.
402 403 404
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