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Progress in Nuclear Energy, Vol. 37, No. l-4, pp. 241-246.2000 0 2000 Elsevier Science Ltd. All rights reserved

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PII: SO149-1970(00)00053-6

EQUILIBRIUM CHARACTERISTICS OF TYPICAL FUEL CYCLES OF PWR

ABDUL WARIS and HIROSHI SEKIMOTO

Research Laboratory for Nuclear Reactors Tokyo Institute of Technology

2- 12- 1 0-okayama, Meguro-ku, Tokyo 152-8550 Japan Tel: +81-3-5734-2955; Fax: +81-3-5734-2959

e-mail: awaris@nr.titech.ac.jp

ABSTRACT

We have performed equilibrium analyses of light water reactor (LWR) with enriched uranium supply. In this study, five kinds of fuel cycles of 3000 MWt pressurized water reactor (PWR) were investigated, and a method to determine the uranium enrichment in order to achieve their criticality was presented. The results indicated that the enrichment decreases significantly with increasing number of confined heavy nuclides when U is discharged from the reactor. The required natural uranium was also evaluated for two different enrichment processes. The amount of required natural uranium also decreases as well, which may agree with the systematic comparison of typical fuel cycles of PWR on the same condition for resource requirements and discharged radioactive wastes. On the other hand, when U is totally confined, the enrichment becomes unacceptably high. 0 2000 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

Considering the limitation of the earth’s natural resources, it is expected that our society will be in an equilibrium condition, in which the energy consumption rate becomes constant. Assuming that the whole energy supply of the world can be secured by nuclear energy, each produced nuclide number density may also constant as well. We have called this situation as nuclear equilibrium society (Sekimoto and Takagi, 1991).

In the previous studies on the future nuclear equilibrium society (Sekimoto and Takagi, 1991; Mizutani and Sekimoto, 1997), only natural uranium and/or thorium were used as fuel supply. In such system, LWR can not be critical. Moreover, only one kind of fuel cycle was studied, in which all heavy metals (HMs) are confined. However, if enriched uranium is used, a light water reactor core can be critical and many kinds of fuel cycles are possible in LWRs.

241

242 A. Waris and H. Sekimoto

In this paper, PWR system fueled with enriched uranium for different fuel cycle cases are studied, and the required amount of enriched uranium and natural uranium are evaluated to show whether the system can perform Pu and minor actinides (MA) recycle efftciently or not.

2. REACTOR DESIGN AND FUEL CYCLE OPTIONS

In the present study, 3000 MWt PWR systems are investigated. The basic reactor core design parameters are shown in Table 1. The average power density of fuel pellet was fixed to 280 W/cc to satisfy 100 W/cc of cell average power density.

Table 1. Basic core design parameters of studied PWR

Power Output ( MW thermal ) Average power density of Pellet (W/cc) Fuel Pellet diameter (mm) Pin diameter (mm)

3000 280 8.0 9.6

Five kinds of fuel cycle cases are evaluated, where all fission products (FPs) and final products of HM natural decay chains (Tl - Fr) are discharged from the reactor at standard rate ,i.e., 33%/year:

Case 1: All HMs are discharged from the reactor at the standard rate. Case 2: All HMs except Pu are discharged from the reactor at the standard rate. Pu is discharged at the

rate of 16.5%/year (half of the other HM discharge constant). Case 3: All HMs except Pu are discharged from the reactor at the standard rate. Pu is confined in the

reactor. Case 4: All HMs except U are confined in the reactor. U is discharged from the reactor at the standard

rate. Case 5: All HMs are confined in the reactor.

3. CALCULATION METHOD

The equilibrium calculation, where all nuclides in the reactor core are in an equilibrium-state, is performed. The nuclear equilibrium-state has the following characteristics: - number density of each nuclide, except fuel nuclides and discharged stable products is constant, and - refueling process is supposed as a continuous process. The nuclide densities obey the equilibrium equation. These densities should be also consistent with the power density and flux level. However, in this basic study, we employed the same microscopic cross sections and neutron spectrum for all cases. These spectrum and cross sections are the neutron spectrum and microscopic cross sections of fresh fuel of 3.5% U-235, which have been generated by using SRAC code (Tsuchihashi, et al., 1986). Nuclear data are prepared from JENDL-2, -3.1, -3.2 and ENDF/B-IV, -V, -VI. The neutron spectrum used in this study is shown in Figure 1.

The uranium enrichment for the criticality of reactor core for each case is determined as follows. The equilibrium calculation is performed to determine a flux level. Then we calculate a neutron production importance and a neutron absorption importance of nuclide fuel U-234, U-235 and U-238 (Sekimoto and Nemoto, 1997). We can evaluate an h-value of each system from the number densities of nuclide fuel and their importances. The h-value, which is a ratio of the number of produced neutron and the number of absorbed neutron in the system can be written as the following equation (1).

Equilibrium characteristics 243

(1)

Where, f : vector of neutron production importance, a : vector of neutron absorption importance, and s : vector of nuclide fuel density.

In our calculation, the systems can attain their criticality if h-value equal to or more than 1.06. In other word, if the h-value becomes 6% higher than an infinite multiplication factor, the reactor core can be critical. The relation among the nuclide densities of U-234, U-235, and U-238 satisfy a condition given by the enrichment process. Finally, from these relations we can determine the required enrichment of the charged fuel.

Based on the uranium enrichment calculation we calculated the total enriched uranium supply and the required amount of natural uranium for each fuel cycle.

0.024

0.016

Figure 1. Neutron spectrum used in this study

4. RESULTS AND DISCUSSION

The required enrichment and amount of charged fuel to achieve the criticality of the reactor are shown in Table 2. For calculating the amount of required natural uranium, two different enrichment processes were adopted. The first process corresponds to 0.1% of U-235 concentration in the tail. The second one for 0.3% of U-235 in the tail. These results are also shown in Table 2. As can be seen in this table, for case 1 through 4, where uranium is not confined, the enrichment decreases significantly with the increasing number of confined nuclides in the reactor. Moreover, the quantity of charged fuel also reduces little. On the top of that, the amount of required natural uranium decreases as well, which may agree with the systematic comparison

244 A. Waris and H. Sekimoto

of typical fuel cycles of PWR on the same condition for resource requirements and discharged radioactive wastes.

Table 2 Required enrichment and fuel amount for criticality

Case 1 2 3 4 5

Enrichment (w%) 4.0 3.7 3.4 3.2 70.2

Charged fuel (ty-‘) 29.2 29.0 28.8 28.5 1.2

Natural Uranium (ty-‘) tail 0.1% 188 170 156 144 134

Natural Uranium (ty-‘) tail 0.3% 265 238 218 201 199

These facts probably due to the changing of the neutron production and neutron absorption importances, denoted by f and a, respectively. The neutron production importance expresses the number of neutrons produced from fission of one nucleus of the studied nuclide during its residence in the reactor core. While the neutron absorption importance explains the number of neutrons absorbed by one nucleus of the studied nuclide in the reactor (Sekimoto and Nemoto, 1997). The values of these two parameters of some important nuclides for each case are shown in Table 3. Generally, f and a become higher for the confined nuclides because their lifetime in reactor are longer than of the discharged nuclides. For the cases 1 through 4, where U is discharged from the reactor, the f value of U-235 decreases with the increasing number of confined nuclides, but the f value of other HMs, especially Pu-239 and Pu-241, increase significantly. Taken together with these increments, the number densities of most of transuranic nuclides also increase considerably as shown in Figure 2. These all facts may play important role in the reduction of the uranium enrichment in case 2 to case 4. Consequently, the amount of required natural uranium reduces as well.

Table 3. Importance values of some important nuclides

Case Case 1 Case 2 Case 3 Case 4 Case 5

f a f a f a f a f a

U-234 0.518 0.726 0.483 0.684 0.437 0.629 0.421 0.612 2.529 3.118

U-235 1.233 0.788 1.200 0.761 1.158 0.728 1.157 0.745 2.527 2.166

U-236 0.146 0.494 0.180 0.509 0.260 0.567 0.550 0.959 2.929 5.105

U-238 0.067 0.079 0.069 0.079 0.072 0.081 0.074 0.082 2.933 3.284

Np-237 0.565 1.156 0.766 1.355 1.249 1.859 2.873 4.115 2.941 4.244

Pu-239 2.030 1.625 2.280 1.841 2.673 2.214 2.945 2.437 2.949 2.508

Pu-240 1.604 1.985 1.877 2.281 2.326 2.830 3.071 3.458 3.081 3.493

Pu-24 1 1.839 1.284 2.025 1.467 2.324 1.835 3.071 2.465 3.082 2.500

Pu-242 0.390 1.144 0.484 1.471 0.706 2.243 3.471 4.527 3.504 4.472

Am-243 0.753 1.326 0.715 1.295 0.671 1.261 3.476 3.579 3.510 3.523

Cm-244 0.970 0.744 0.938 0.734 0.903 0.734 3.477 2.595 3.511 2.540

f: neutron production importance, a: neutron absorption importance

Equilibrium characteristics 245

This basic study shows that Pu and MA recycle can significantly reduce the required nuclear fuel resources. Furthermore, this reduction will become larger when U is perfectly confined in the reactor, but the required enrichment becomes inevitably very high. The accumulation of large amount of U-236 in the reactor core when uranium is totally confined could be the reason why the required enrichment for criticality becomes unacceptably high. U-236 is produced mostly from (n,$ reaction of U-235. According to Figure 2, the number density of U-236 accumulated in reactor core is very large for case 5, and almost same as the amount of U-235 in the core. As a result, we need very high uranium enrichment to overcome this problem. This neutron economic characteristic of U-236 is easy to see in Table 3, which indicated by the neutron absorption importance equal to 5.105. This characteristic is also mentioned in reference (Sekimoto and Nemoto, 1997).

It should be noted that the present tendency is attributed to the use of the same microscopic cross sections for all cases instead of using the microscopic cross sections of each case itself.

Figure 2. Number density of some important HM in reactor core

5. CONCLUSION

Five important refueling schemes of 3000 MWt PWR were investigated and a method to determine the uranium enrichment in order to achieve their criticality was presented. The results show that the enrichment decrease significantly with the increasing number of confined heavy nuclides when U is discharged from the reactor. The required amount of natural uranium also decreases as well, which may agree with the common expected idea. However, when U is totally confined in the reactor, the enrichment becomes unacceptably high.

This basic study shows that Pu and MA recycle can significantly reduce the required nuclear fuel resources.

246 A. Waris and H. Sekimoto

ACKNOWLEDGMENT

The authors would like to acknowledge Dr. Naoyuki Takaki, Dr. Akihiko Mizutani and Mr. Atsushi Nemoto. Without their pioneering works, this study would not have been performed.

REFERENCES

Mizutani A. and Sekimoto H. (1997) Calculational Method of One-Group Nuclear Constants in Nuclear Equilibrium State, J. Nucl. Sci. Technol., 34, 6.

Sekimoto H. and Nemoto A. (1997), Importance Vectors for Some Characteristic Values of Equilibrium Systems, Proc. of GLOBAL’97, Vol. I, p. 198. Yokohama, 5-10 October.

Sekimoto H. and Takagi N. (1991), Preliminary study on Future Society in Nuclear Quasi-Equilibrium, J. Nucl. Sci. Technol., 28, 10.

Tsuchihashi K., et. al. (1986) Revised SRAC Code System, Japan Atomic Energy Research Institute, JAERI-1302.