Ann. nucl. Energy, Vol. l I, No. 7, pp. 359 362, 1984 Printed in Great Britain. All rights reserved
0306-4549/84 $3.00 + 0.00 Copyright ~) 1984 Pergamon Press Ltd
TECHNICAL NOTE THE
A. YA. TEMKIN Department of Interdisciplinary Studies, School of Engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel
(Received 26 January 1984) The use of 232Th in nuclear reactors is considered and some recommendations concerning their design formulated. Abstract
loaded 2 3 5 U ; the ratio (Q3-QO/Q~ characterizes the utilization of loaded fissionable elements in general, and 235 U is considered simply as one of them; the ratio (Q3-Qz)/Q2 characterizes the transformation of the utilized 235U into the new fuel at the EOL. For the 3000 MW(t) (power density 200 W cm 3) reactor, described in the work of Radkowsky (Radkowsky et al, 1980), using 20% enriched U (without Th) as fuel and light water as moderator and coolant we found (we shall call it 'the standard reactor') :
Attempts to use the 233U breeding from 232Th in nuclear reactors began in the 1950s (see, for example, Sauteron, 1965) and are still being made (see, for example, Kamal et al., 1982 ; Schaeffer, 1981). In the present paper we formulate our conclusions and recommendations concerning the construction of nuclear reactors containing Th. They are based on general physical considerations and the results of numerical calculations of many different fuel moderator assemblies. We shall use three quantities QI, Q2 and Q3 --to characterize the effectiveness of the Th use :
Q1 = I/M235(0)
Q2 = I/[Mz35(O)--Mz35(tEoO]
Q3 : I / [ M 2 3 5 ( 0 ) - ~ Mi(tEoL)],
QI = 793,100 MWd/tonne, Q2 - 1,001,000 MWd/tonne and
(4) Q3 = 1,061,000 MWd/tonne ;
(Q2-Q,)/Q1 = 26%,
( Q 3 - QI)/Qa = 34%
where I is the total irradiation for the considered time tEOL,the time t = 0 corresponds to the BOL, Mz35(0)is the total mass of 235U loaded into the reactor, M~(tro 0 is the mass of a fissionable element i at the time tEOL.It was assumed that 135U is the only fissionable element loaded into the reactor. The summation in equation (3) must be done with respect to all fissionable elements contained in the reactor at the time t = tEoL. Strictly speaking, instead of
and (Q3 - Q2)/Qz = 6%. These values will be used to compare different kinds of Th-containing reactors with the 'standard' one to assess the effectiveness of the use of Th.
THE NEUTRON SPECTRUM
The main purpose of the design of Th-containing reactors is to make it possible to create at each moment in time, a neutron-spectrum shape, which ensures the maximum 233U breeding rate under the conditions of core criticality. It is a very difficult task because for breeding of new fuel from 232Th the spectrum should be hard, whilst for the fission it is best to make the neutron spectrum as thermal as possible. Resonance absorption of neutrons by 232Th nuclei, followed by nuclear transformations ending in the creation of 233U and 235U, occurs mainly within the energy interval 2(~ 370 eV. We shall call this interval the'232Th fertile interval'. At the BOL, when the basic fuel is not yet burned up, it would be reasonable to make the spectrum hard so that there would be as many neutrons as possible having energies inside the 232Th fertile interval. Then the new-fuel breeding rate would be as large as possible. At the same time, the increase of the neutron
we should use -1 -1 V O-fiss~ ffi,fissMi(tEOL)Yi, i
where tTi,fiss iS the microscopic fission cross-section of an element i averaged with respect to the slow-neutron spectrum O'fiss = ~ t~i,fiss~ i
vi is the average number of neutrons released at one fission, V=~V i
The meaning of Ql, Q2 and Q3 is obvious. The ratio (Q 2 - Q 1)/Q 1 characterizes the utilization of the 359
resonance capture by Th decreases the fission rate of the basic and new fuel and so it can be used to control the core criticality by regulation of the neutron spectrum (see, for example, Sauteron 1965, p. 447; Schaeffer, 1981). The advantage in this method is that neutrons captured by Th nuclei are not lost, but 'saved' for the future in the form of new fuel. The breeding of the new fuel does not completely compensate for the burnup of the loaded fuel, the total amount of fissionable elements decreases and so it must soften the neutron spectrum during the burnup process to maintain the fission rate at the necessary level for core criticality. The control of core (without Th) criticality by regulation of the neutron spectrum (spectrum shift control) was considered in detail by Galperin and Ronen (1983; Ronen and Galperin, 1980). It is possible to effect this control by changing the VF/VM ratio (VF and VMare the volumes of the fuel and moderator, respectively). But there is the relation (VT is the total volume of the core) VF/VT = (VdVM)(1 + VdVM)-1
to consider, which results from the equality Vr = Vv+ VM
Case 1 (6)
(we do not take into account the volume of the clad). We cannot therefore change VF/VMwithout a change of Vv/VT. To overcome this limitation we must replace the equality (6) by the inequality VT >~ lie + VM,
fuel assembly. The solution of this problem depends on our requirements. If we want only one cycle, AQ1 = Q ~ - Q ] (where Q] is Q~ for the standard reactor) should be as large as possible, while (Q2 - Q1)/Q1, (Q3 -Q1)/Q1 should be as small as possible. If we want (n + l) cycles, then (Q3 - Q 1)/Q1 should be as large as possible and AQ3 = Q3 - Q ~ should be large at the end of the nth cycle. If we also require that the 235U utilization remains good to the end of the nth cycle, (Q3 - Qz)/Q2 should not be small. The conditions at the end of (n + 1) cycles have the same form as the ones at t = tEOL for the case of the once-through cycle considered above. It should be recommended that the construction of each fuel assembly is such that fuel rearrangements during its lifetime would be possible to replace the more or less burned up fuel rods. Some calculations made using the 1-D WIMS-D code can illustrate the above. These calculations were made for a PWR with total power 3000 MW(t), specific power 200 W cm a and total volume Vr = 1.5.107 cm 3.
SOthat VMcan be changed and Vv/Vx will remain constant. This can be done by the insertion of hollow tubes into the moderator region. By moving them in and out we can regulate the hardness of the neutron spectrum in the active zone of the reactor. Rods made of practically non-moderating and nonabsorbing material can also be used for this purpose to avoid mechanical problems in PWRs.
THE CASE OF IDENTICAL FUEL REGIONS Consider the nuclear reactor where all the fuel regions are identical and each contains a mixture of 232Th ' 235U, 238U and some other non-fissionable and non-fertile elements. In this case fissionable and fertile elements are under the same conditions of irradiation, so it is impossible to create a thermal neutron spectrum for fissionable elements and a hard one for fertile elements. So the optimal shape of the neutron spectrum must be found at each moment in time which keeps the core critical and produces enough new fuel. The solution of this problem depends on the construction of the core and for different constructions the effectiveness of the use of fissionable and fertile elements will vary. Firstly, it should be recommended to use relatively big fuel assemblies practically without a moderator, with the purpose of increasing the neutron resonance capture probability (by Th nuclei) and therefore the 233Ubreeding. For example, fuel rods of such an assembly can be inserted very close to one another so that there remains only a small part of the assembly volume for the moderator. The moderator will be in the main between fuel assemblies. However, the dimensions of this assembly should be limited as the increase of the resonance absorption by the peripheral area of the fuel assembly makes its central region inaccessible to neutrons coming from the moderator. Thus, one problem is to find the optimal size of the
The above-mentioned fuel assembly represents a cylinder with a radius of l0 cm. The materials inside this cylinder were homogenized for the calculation and represent a mixture containing 40 vol% of 232Th, 25 vol% of UO2 (20% 235U + 80%0023su) and 35 vol% of BeO. For this concentration of BeO the slowing-down length of fission neutrons to the upper bound of the 2a2Th fertile interval is about 43 cm. Therefore, the slowing-down inside the fuel assembly may be important for neutrons entering from the moderator having energies higher than this upper bound, but lower than the average energy of fission neutrons; a fission neutron will most probably leak from the fuel assembly before it reaches the 232Th fertile interval. The described cylindrical rod is surrounded by Zr clad and light water. The outer radius of this cell is 13 cm. It is supposed that hollow tubes are inserted into the moderator region-- represented in our 1-D calculations by the diminishing water density. The temperature of the fuel was taken as 1100 K, and that of the clad and the water to be 550 K. At the BOL the hollow tubes occupied 66% of the moderator volume. During the cycle this value was reduced in several steps with the aim of keeping the core critical. It was possible to keep it critical up to irradiations of about 50,000 MWd/tonne (of loaded heavy elements, i.e. all isotopes of Th and U). We found for this reactor : Q1 = 770,900 MWd/tonne, Q2 = 1,202,000 MWd/tonne and Q3 = 2,039,000 MWd/tonne.
The differences from their corresponding values (4) are: AQ 1 = -2.80%, AQ2 = 20.1% and AQ3 = 92.2%. We obtain from the above values (8): (Q2-QI)/Q1 = 56%, (Q3-QO/Q1 = 164% and (Q3 - Q2)/Q2 = 70%. This means the use of Th in this case cannot be recommended for the once-through cycle because it leads to a certain increase in the amount of 235U necessary for loading to obtain the same Q 1 as for the standard reactor. But the value of 164% shows that there is an appreciable amount of fissionable materials remaining at the end of the first cycle and so it is reasonable to assume that two or more cycles should be profitable, i.e. AQ ~at the EOL should
Technical Note be positive and big enough to justify the use of Th in such an arrangement. The m a x i m u m variation of kerr in this case was about 0.1%. It is thought that using a more sophisticated computer code it would be possible to determine the optimal strategy of the neutron spectrum regulation by hollow tubes necessary to keep the core strictly critical. The contribution of thermal fissions to the total fission rate changed from 44% at the B O L to 68% at the EOL. By the EOL 54% of the produced 233U had been burned up. The contributions of different fission elements to the total number of fissions for the whole cycle were : 233U, 22.3%; 235U,65.9%; and Pu, 11.8%. If the fuel rods of the described assembly are cylindrical, then free space remains in the fuel region even with the most compact arrangement of the rods. We have considered the case when this free space is filled by light water--performed in the framework of the described 1-D model with homogenization of the fuel assembly. The total irradiation for the first cycle was 42,082 M W d / t o n n e (of loaded heavy elements), 50.6% of the produced 233U was used during the first cycle. We obtained : Qx = 649,400 MWd/tonne, Q2 = 1,098,000 M W d / t o n n e and Q3 - 1,799,000 MWd/tonne.
The differences from their corresponding values (4) are: AQ~ = -18.12%, AQ2 = 9.69% and AQ3 = 69.6%. We obtain from the above values (9): (Q2-QO/Q1 = 69%, (Q3 -QI)/Q1 = 177% and (Q3-Q2)/Q2 = 64.0%. Comparison of these results with those for the same case, but without the light water inside the fuel assembly, shows that light water only impairs the results.
361 THE CASE OF IDENTICAL CELLS
Let each cell consist of U rods and rods containing Th and U together. In this case it is possible to obtain only a small difference between neutron spectra in basic fuel rods and in those containing Th. N u m e r o u s burnup calculations for different fuel arrangements in such a cell (for PLWRs) allow us to conclude that it is necessary to surround Th-containing rods by burnable poisons to reduce the keff variation during the cycle and to, a certain degree, protect 233U from fission in the first period of the cycle when there is enough fuel in the basic fuel rods to keep the core critical. The most promising were the results of the calculations for the following system : (1) one rod placed in the centre of the cell contains 40 vol% of 232Th, 35 vol% of BeO and 25 vol% o f U O 2 (20% 235U-~-80%235U),the radius of the rod was 0.5 cm; (2) the central rod surrounded by two concentric layers containing 0.733 vol% and 9 vol% of l°B in Zr and having outside radii of 0.544 and 0.545 cm, respectively ; (3) the lightwater moderator maintained at 550 K with four uranium rods [16.3 vol% of UO2 (enriched to 20% of 235U) and 83.7 vol% of Zr] of radius 0.321 cm. The radius of the cell is 1.3 cm. At the end of the first cycle the irradiation was about 90,000 M W d / tonne (of the loaded heavy elements). The m a x i m u m variation of keff during the cycle was 19%. At the B O L the ratio of the 15th WlMSgroup flux to the thermal one was 4.205 for the central rod and 3.138 for the whole cell ; after an irradiation of 22,700 M W d / t o n n e (of the loaded heavy elements) the abovementioned value for the central rod became 2.727 because of the l°B burnup. 62% Of the produced 233U was burned up during the first cycle. We found for this case : Q1 = 833,200 MWd/tonne, Q2 = 1,057,000 M W d / t o n n e and
Case 2 Each fuel element has the shape of the cylindrical layer with an inner radius of 1.5 cm and an outer one of 4.65 cm. The hole inside and the space outside of this layer are filled with light water. Hollow tubes are supposed to be placed only into the outside region. The radius of the cell was 5.3 cm. The composition of the fuel elements was the same as in the first case. The irradiation during the first cycle was about 43,600 M W d / t o n n e (of the loaded heavy elements). At the B O L there are 44.4% of thermal fissions, rising to 50.9% at the EOL. 50.2% of the produced 233U was burned during the cycle. We found: Q1 = 672,300 MWd/tonne, Q2 = 1,198,000 M W d / t o n n e and Q3 = 2,735,000 MWd/tonne.
Q3 = 1,200,000 MWd/tonne.
The differences from their corresponding values (4) are: AQ1 = 5.06%, AQ2 = 5.59% and AQ3 = 15.0%. F r o m the above values (11) we obtain: (Q2-QO/Q1 = 27%, (Qa-QI)/Q1 = 46% and (Qa-QE)/Q2 = 15.4%. Thus, the use of Th allows us to save 5% of the U in the first cycle and to reduce the necessary control from 70 to 19%. It is reasonable to expect that more U can be saved by the use of two or more cycles because the value of 46% indicates that there is an appreciable a m o u n t of fissionable materials remaining in the reactor at the end of the first cycle. For a rough estimation we have performed calculations under the condition that at a particular m o m e n t in time all the U rods were replaced by new rods containing 17.87 vol% of U O 2 enriched only to 12.05% of 235U. The complete irradiation for these two cycles was 120,467 M W d / t o n n e (of the loaded heavy elements) and Qt = 889,100 MWd/tonne,
The differences from their corresponding values (4) are: AQ~ = - 15.23%,AQ2 = 19.7% andAQ3 = 158%. From theabove values (10) we found: (Q2-QO/QI =78%, (Qa-QO/Q1 = 306.8% and (Qa - Q2)/Q2 = 128.3%. As in the first case, we cannot recommend the use of this reactor for the oncethrough-cycle process, but it should be suitable, even better than the first one, for n-cycle processes. The numbers 306.8 and 128.3%, compared to 164 and 70% from the first case, indicate that the a m o u n t of new fuel produced is greater than in the first case.
Q2 = 1,021,000 M W d / t o n n e and Q3 = 1,135,000 MWd/tonne.
The differences from their corresponding values (4) are: AQt = 12.1%,AQ2 = 2%andAQ3 = 6.97%.Fromthevaluesgiven above (12) we obtain: (Q2-QO/Q1 = 15%, (Qa-Q1)/Q1 = 28% and (03-Q2)/Q2 = 11%. Thus, in a two-cycle period we can save-about 12% of the U, and at the same time there is a
sufficient amount of fissionable materials (see the values 28 and 11%) remaining to expect that the next cycle will also be profitable. Comparing the corresponding values for the oneand two-cycle periods, it can be concluded that only the addition of one more (maximum two) cycle is viable: the creation of new fuel decreases from the one-cycle period to the two-cycle period and this trend renders the use of m a n y cycles unprofitable.
In the present paper the use of 232Th in nuclear reactors was considered. The following conclusions and recommendations are made as a result of our findings.
would be in the lower part. Thus, the Th will be in the region with the hard neutron spectrum, because there are many more bubbles than in the lower part. If regulation of the neutron spectrum is not used, fuel assemblies or fuel elements containing Th should be surrounded by layers of burnable poisons to reduce the necessary criticality control and to improve conditions for the 233U breeding during the first part of the cycle. If the core consists of identical fuel elements (or assemblies) containing Th and U together, we recommend the use of large-size fuel elements (or assemblies) on the grounds that, from the results obtained here, it is expected that a certain a m o u n t of U can be saved in such a reactor after a number of cycles.
1. The neutron spectrum must be hard in all regions of the core so that there will be more neutrons having energy values within the 232Th fertile interval. 2. Use ofregulation ofthe neutron spectrum for the control of the core criticality is recommended. 3. It is proposed to use hollow tubes (or rods of practically non-absorbing and non-slowing-down material) for the regulation of the neutron spectrum by manipulating the Vv/VM ratio. 4. For BWRs containingTh we propose the use ofchanging the boiling regime to regulate the neutron spectrum. In such reactors it would be reasonable to put the Th only into the upper part of fuel region, and hence more U
Galperin A. and Ronen Y. (1983) Nucl. TechnoL 62, 238. Kamal A., Driscoll M. J. and Lanning D. D. (1982) Report MIT-EL-82-033, MIT, Cambridge, Mass. Radkowsky A., Dayan A., Temkin A. Ya and Green L. (1980) Nucl. Sci. Engn9 75, 265. Ronen Y. and Galperin A. (1980) Ann. nucl. Energy 7, 59. Sauteron J. (1965) Les Combustibles Nuclbaires. Hermann, Paris. Schaeffer H. (1981) Report FRNC-TH-1157, Orsay, France.