1. Introduction
Recently, Hitachi developed a fuel-self-sustaining reduced moderation Boiling Water Reactor (BWR) core design that features a breeding ratio slightly above 1.0 when using depleted uranium for the makeup fuel; it is referred to as the RBWR-AC in which the “R” stands for “Resource Renewable” [
1,
2]. The discharged fuel is reprocessed to remove fission products and all the trans-uranium elements (TRU) are recycled back to the core along with the uranium. The RBWR-AC core can fit within the pressure vessel of the well proven Advanced BWR (ABWR) and deliver the same total power as the ABWR. Hence, the specific capital cost of the RBWR-AC is expected to be smaller than that of the presently available Sodium cooled Fast Reactor (SFR) core designs. Furthermore, it is reasonable to expect the RBWR-AC to have other cost advantages over the SFR because the Light Water Reactor (LWR) infrastructure required for RBWR-AC deployment is mostly in place and the utilities have extended experience in operating and maintaining light-water cooled reactors. On the other hand, the fuel cycle cost of the RBWR-AC is expected to be higher than that of the SFR because the discharge burnup of the RBWR is estimated to be only about half that of the SFR [
2].
Relative to conventional BWR (and ABWR), the RBWR-AC core design features a tighter fuel lattice, a shorter core, a smaller coolant mass flow-rate and pressure drop and a higher core void fraction.
Figure 1 shows the core layout of the RBWR-AC while
Table 1 compares selected design and performance characteristics of the RBWR-AC with the ABWR. The core average void fraction in the RBWR-AC is about 60% (closer to 65% in more recent designs) compared to about 36% in the ABWR (
Figure 2). The figures and table do not pertain to the latest designs but are representative; they are taken from open publications [
1,
2].
Figure 1.
Resource-Renewable Boiling Water Reactor (RBWR)-AC core layout (Note: fissile fuel is TRU, not Pu) [
1].
Figure 1.
Resource-Renewable Boiling Water Reactor (RBWR)-AC core layout (Note: fissile fuel is TRU, not Pu) [
1].
Table 1.
Comparison of performance characteristics of the fuel-self-sustaining RBWR-AC and Advanced BWR (ABWR) [
1].
Table 1.
Comparison of performance characteristics of the fuel-self-sustaining RBWR-AC and Advanced BWR (ABWR) [1].
Item | RBWR-AC | Item | ABWR |
---|
Thermal power, MWt | 3926 | Thermal power, MWt | 3926 |
Electrical power, MWe | 1356 | Electrical power, MWe | 1356 |
Number of fuel bundles | 720 | Number of fuel bundles | 872 |
Core height, mm | 1200 | Core height, mm | 3710 |
Core configuration | Parfait | | |
Coolant mass flow rate, kt/h | 22 | Coolant mass flow rate, kt/h | 58 |
Core exit quality, % | 41 | Core exit quality, % | 13 |
Core exit void fraction, % | 60 | Core exit void fraction, % | 36 |
Core pressure drop, MPa | 0.11 | Core pressure drop, MPa | 0.21 |
HM inventory, t | 131 | HM inventory, t | 151 |
Fissile Pu/HM in fissile zones, wt % | 18 | Uranium enrichment, % | 3.8 |
Fissile Pu inventory, t | 8.9 | | |
Burnup, GWd/tHM | 45 | Burnup, GWd/tHM | 45 |
MLHGR, kW/ft | 14.4 | MLHGR, kW/ft | 12 |
MCPR | 1.3 | MCPR | 1.3 |
Figure 2.
Axial distribution of coolant volume fraction in the RBWR-AC as compared to the ABWR [
1].
Figure 2.
Axial distribution of coolant volume fraction in the RBWR-AC as compared to the ABWR [
1].
The significantly smaller hydrogen-to-Heavy-Metal (HM) atom ratio and the high TRU loading makes the RBWR-AC spectrum quite hard. The neutron spectrum of the RBWR-AC is compared to the PWR and a BR = 1.0 SFR in
Figure 3. As indicated, the spectrum of the RBWR-AC is closer to that of a typical liquid metal cooled fast reactor (ARR in the figure) than it is to the spectrum of a conventional UO
2 fueled PWR. The RBWR-AC spectrum features a larger component of MeV neutrons and a larger component of epithermal neutrons than the SFR spectrum. The larger fraction of >1 MeV neutrons is due to the sharp drop of the energy-dependent hydrogen scattering cross section in this energy range. The hard spectrum of the RBWR-AC makes it possible to achieve a conversion ratio slightly higher than unity, which is similar to that of the ARR.
Figure 3.
RBWR-AC, Pressurized Water Reactor (PWR) and Advanced Recycling Reactor (ARR) neutron spectrum [
2].
Figure 3.
RBWR-AC, Pressurized Water Reactor (PWR) and Advanced Recycling Reactor (ARR) neutron spectrum [
2].
However, the achievement of negative void reactivity coefficients in the RBWR-AC is very challenging because of the large increase, with coolant voiding induced spectrum hardening, in the η values of most of the TRU isotopes as well as of the 238U. To counteract that effect the coolant voiding has to substantially enhance the leakage probability of neutrons out from the fissile zones. (SFR cores usually feature positive void coefficient of reactivity which is compensated by, in addition to the fuel Doppler effect, the fuel axial expansion and core radial expansion—mechanisms that are not applicable in BWR type reactors using oxide fuel. The SFR power coefficient of reactivity is negative). The need for a large leakage-probability drove Hitachi to design a pancake shape small height core, to “lump” the fissile fuel into two axial zones, each approximately 20 cm in length, with depleted U blanket zones on both sides of each fissile zone, and to add B4C to the bottom and top reflectors. The resulting axial power distribution is quite sensitive to the TRU loading in the two axial fissile zones, to the Pu buildup in the three blanket zones surrounding the two fissile zones, to the axial void distribution, to the location and amount of boron in the reflectors and to the control rods insertion pattern.
In a recent EPRI-sponsored study, a team of researchers from the University of Michigan, MIT and the University of California at Berkeley performed an independent evaluation of the Hitachi RBWR-AC core design using largely independent computational methods [
2]. The independent evaluation concluded that the equilibrium-cycle breeding ratio is slightly above 1.0, thus providing for a self-sustaining fuel cycle in which depleted uranium is used for the makeup fuel. The fuel and power coefficients of reactivity were found to be negative under both beginning of equilibrium cycle and end of equilibrium cycle conditions. However, there is considerable uncertainty in the calculated void coefficient of reactivity, and it is not certain that the void coefficient is negative at all times, as presently required for BWR. The team has also expressed concerns that the Hitachi RBWR-AC core design may not have adequate thermal safety margin. In general the current Hitachi RBWR-AC design appears to be quite sensitive to small design variations and to perturbations in operating conditions, which could make it more difficult to for the RBWR-AC to meet the safety requirements for licensing than current BWRs. By slightly modifying the RBWR-AC core design, it may be possible to eliminate the concerns expressed above.
A different approach to the design of reduced moderation fuel-self-sustaining BWR cores that is based on the major ingredients of the Hitachi RBWR-AC core design has been recently proposed [
3,
4]. The objective of the present paper is to describe this alternative RBWR-AC design approach and to summarize results obtained from a very preliminary feasibility study. The differences between the proposed approach and the Hitachi design include: use of thorium instead of depleted uranium, elimination of the internal blanket and elimination of the B
4C or other parasitic absorbers from the axial reflectors, while increasing the length of the fissile zone (“seed”). As
232Th has a significantly smaller fast fission cross section than
238U and as the η(
233U) increase with neutron energy is significantly smaller than that of
239Pu and most other TRU in the relevant high energy range, it is possible to design a Th-based high void fraction water cooled core to have negative void reactivity coefficients without having to design the seed to have as high a leakage probability.
Many studies of thorium fueled LWRs had been performed in the past; [
5,
6,
7,
8,
9,
10,
11,
12,
13] is a very partial list of references. The closest to fuel-self-sustaining (breeding) designs arrived at in the past are the so called “seed-and blanket” designs in which the thorium and
233U fuels were radially segregated—the
233U fuel was loaded into “seed” fuel rods and/or fuel assemblies and most of the thorium was loaded into “blanket” fuel rods and/or fuel assemblies. In the Shippingport reactor [
5,
6] that demonstrated fuel-self-sufficiency the seed fuel assemblies had to be axially moved out and into the core in order to achieve sustainability. In more recent seed-and-blanket Th-based LWR core designs, such as those reported in [
7,
8], the radial segregation of seed and blanket results in power density mismatch that complicates the safety and fuel management. No such complications are needed for implementing the design presented in this work, which features radially uniform fuel rods and stationary fuel assemblies.
Section 2 describes the reference thorium-based RBWR core examined while
Section 3 describes the methodology used for this preliminary feasibility study. The performance characteristics obtained for the reference core are summarized in
Section 4 (the analysis of this core was performed by the first author). An alternative thorium-based core design and its calculated performance characteristics are described in
Section 5 (the analysis of this core was performed by the second author).
Section 6 discusses issues of concern that will have to be addressed in the future.
4. Reference Case Results
Multi-recycling studies were performed to establish the equilibrium core composition and assess its neutronic performance. After each pass through the core, the fuel is cooled for 3 years and then reprocessed. All the actinides (up to 248Cm) are recycled and thorium oxide is added for makeup. Only ThO2 is loaded in the blankets. Reprocessing losses were ignored so as to obtain a theoretical upper bound on the Fissile Inventory Ratio (FIR).
Figure 5 shows that the
233U inventory increases rapidly in the first few recycles, in which the conversion ratio is larger than 1, before saturating at around recycle #15. The larger mass of
233U increases the value of k
eff with the number of recycles as shown in
Figure 6. After 7–8 recycles, k
eff gets close to the equilibrium core value. Since k
eff at the end of equilibrium cycle is larger than the design goal of 1.025, the cycle length could be extended or the core could be operated with a breeding gain: upon fuel recycling a fraction of the uranium (and, possibly, all trans-thorium actinides) would be removed so as to reduce the BOEC k
eff to the level that would result in an EOEC k
eff of 1.025. It should be realized, though, that in the real core the breeding ratio will be somewhat smaller than the one predicted from our single pin analysis, since there will be some fuel loss in the recycling/refabrication processes and neutron losses to radial leakage and to parasitic absorption in the control elements.
Figure 5.
Evolution of 233U and of total uranium mass per fuel pin.
Figure 5.
Evolution of 233U and of total uranium mass per fuel pin.
Figure 6.
Evolution of the unit cell keff for the first seven recycles along the fuel residence time (i.e., from loading in the 1st batch to discharge after the 5th batch).
Figure 6.
Evolution of the unit cell keff for the first seven recycles along the fuel residence time (i.e., from loading in the 1st batch to discharge after the 5th batch).
The primary conclusion from this preliminary analysis is that the neutron economy of the proposed system enables breeding. In the illustration provided in
Section 5 the EOEC k
eff is indeed, 1.025 and the system is fuel-self-sustaining.
Figure 7 shows the equilibrium concentration of the actinides other than U and
232Th;
i.e. of Np, Pu, Am, Cm, Pa and
230Th, as a fraction of the total HM mass. The equilibrium concentration of these actinides, to be referred to as Minor Actinides (MA), is 0.31%; it is reached after about 40 recycles. The evolution of the inventories of Pu, Am and Cm in the average fuel pin, relative to their equilibrium value, is shown in
Figure 8. As expected, each isotope reaches saturation after its predecessor does.
Figure 7.
Minor actinides concentration evolution as a fraction of total heavy-metal (HM).
Figure 7.
Minor actinides concentration evolution as a fraction of total heavy-metal (HM).
Figure 8.
Buildup of Pu, Am and Cm inventory.
Figure 8.
Buildup of Pu, Am and Cm inventory.
Table 2 gives the heavy metal composition in a fuel pin, including blanket zones, that is discharged from the equilibrium cycle and cooled for 3 years. The equilibrium composition in the loaded fuel pin can be inferred from the table data assuming that all the HM elements, except thorium, are loaded into the seed that makes 110/230 of the fuel pin volume and that 54 gm of thorium is added for makeup.
Table 2.
Heavy metal composition in a fuel pin discharged from the equilibrium core.
Table 2.
Heavy metal composition in a fuel pin discharged from the equilibrium core.
Isotope | Mass per pin (gm) | Weight % of HM |
---|
Th-230 | 0.0386 | 0.0034 |
Th-232 | 1065.0412 | 92.9738 |
Pa-231 | 0.3018 | 0.0263 |
U-232 | 0.2706 | 0.0236 |
U-233 | 51.3227 | 4.4803 |
U-234 | 16.1287 | 1.4080 |
U-235 | 4.7991 | 0.4189 |
U-236 | 4.3508 | 0.3798 |
U-238 | 0.0309 | 0.0027 |
Np-237 | 1.2277 | 0.1072 |
Pu-238 | 1.2657 | 0.1105 |
Pu-239 | 0.3889 | 0.0339 |
Pu-240 | 0.1556 | 0.0136 |
Pu-241 | 0.0620 | 0.0054 |
Pu-242 | 0.0408 | 0.0036 |
Am-241 | 0.0419 | 0.0036 |
Am-242m | 0.0013 | 0.0001 |
Am-243 | 0.0261 | 0.0023 |
Cm-244 | 0.0176 | 0.0015 |
Cm-245 | 0.0094 | 0.0008 |
Cm-246 | 0.0056 | 0.0005 |
Cm-247 | 0.0010 | 8.63E-05 |
Cm-248 | 0.0005 | 3.95E-05 |
Total | 1145.5284 | 100.00 |
Makeup Th | 54.1705 | 4.515 |
Figure 9 shows a comparison of the mass of the transmutation products of
232Th and
233U that are downloaded after the 1st recycle and at the equilibrium recycle. It is observed that at the 1st recycle the vast majority of transmutation products is made of
231Pa, followed by
237Np and Pu—mostly
238Pu (see
Figure 10) and
230Th. At equilibrium the most abundant transmutation product is Pu—mostly
238Pu (
Figure 11), followed by
237Np and
231Pa. The mass of
230Th at equilibrium is similar to the mass of Cm.
The equilibrium isotopic composition of Am and Cm is shown in
Figure 12 and
Figure 13, respectively. The Am is made primarily of
241Am followed by
243Am, while
242mAm is present only in a relatively small amount.
244Cm is the most abundant Cm isotope, followed by Cm isotopes in order of increasing mass.
Figure 14 shows the isotopic composition of uranium, excluding
233U, after the 1st recycle and at equilibrium. In both cases the most abundant isotope is
234U, followed by
235U. At equilibrium,
236U is present in a similar amount to
235U, while
238U and
232U constitute a negligible fraction of the total U mass.
Figure 9.
Total mass of Minor Actinides (MA) per fuel pin after the 1st recycle and at equilibrium.
Figure 9.
Total mass of Minor Actinides (MA) per fuel pin after the 1st recycle and at equilibrium.
Figure 10.
Total mass of the Pu isotopes per fuel pin after the 1st recycle.
Figure 10.
Total mass of the Pu isotopes per fuel pin after the 1st recycle.
Figure 11.
Total mass of the Pu isotopes per fuel pin at equilibrium.
Figure 11.
Total mass of the Pu isotopes per fuel pin at equilibrium.
Figure 12.
Total mass per fuel pin for the equilibrium cycle of the Am isotopes.
Figure 12.
Total mass per fuel pin for the equilibrium cycle of the Am isotopes.
Figure 13.
Total mass per fuel pin for the equilibrium cycle of the Cm isotopes.
Figure 13.
Total mass per fuel pin for the equilibrium cycle of the Cm isotopes.
Figure 14.
Total mass per fuel pin for the equilibrium cycle of the U isotopes, excluding 233U.
Figure 14.
Total mass per fuel pin for the equilibrium cycle of the U isotopes, excluding 233U.
Figure 15 and
Figure 16 show how the concentration of
232Th and
233U is redistributed over the fuel residence time in the equilibrium core. By definition, the total core mass of each actinide, except thorium, is the same at the beginning (BOL) and at the end (EOL) of the fuel rod. The axial concentration distribution, though, varies over the fuel residence time because the BOL composition is not the equilibrium composition. The latter depends on the axial variation in the neutron spectrum and power density.
Figure 15.
232Th concentration distribution along the fuel pin at BOL and EOL in the equilibrium core (the vertical axis in the plot is by zone number and not by actual zone length: for this reason the segments are not in the correct proportions to each other).
Figure 15.
232Th concentration distribution along the fuel pin at BOL and EOL in the equilibrium core (the vertical axis in the plot is by zone number and not by actual zone length: for this reason the segments are not in the correct proportions to each other).
Figure 16.
233U concentration distribution along the fuel pin at BOL and EOL in the equilibrium core (the vertical axis in the plot is by zone number and not by actual zone length: for this reason the segments are not in the correct proportions to each other).
Figure 16.
233U concentration distribution along the fuel pin at BOL and EOL in the equilibrium core (the vertical axis in the plot is by zone number and not by actual zone length: for this reason the segments are not in the correct proportions to each other).
Although a larger fraction of the
232Th is converted to
233U at the lower part than at the upper part of the fissile zone (
Figure 15), the
233U EOL concentration is significantly smaller at the lower part than at the upper part of the fissile zone (
Figure 16). This is due to the fact that the spectrum is softer at the lower part of the core as a result of which the effective absorption cross section of
233U is larger and also because the power density tends to be skewed towards the bottom of the core (see below).
Figure 17 shows the redistribution of the
235U.
Figure 17.
235U concentration distribution along the fuel pin at Beginning of Cycle (BOL) and at End of Cycle (EOL) in the equilibrium core.
Figure 17.
235U concentration distribution along the fuel pin at Beginning of Cycle (BOL) and at End of Cycle (EOL) in the equilibrium core.
The linear heat generation rate axial distribution at the beginning, middle and end of the fuel life in the equilibrium core is given in
Figure 18. These distributions pertain to a radially infinite core made of fuel rods having the BOL, MOL and EOL composition. The axial power distribution in the actual core will be bounded by the BOL and EOL distributions shown in the figures; the MOL axial power distribution is expected to be the closest representation of the axial power distribution in the actual equilibrium core. However, the magnitude of the peak linear heat generation rate in the actual core will be higher by the radial power peaking factor. Assuming the radial peaking factor of ~1.25 (which is the case for the Hitachi RBWR core designs [
1,
2]), the peak linear heat generation rate of 280 W/cm of
Figure 18 corresponds to ~350 W/cm. This upper bound on the peak linear heat generation rate in the actual (finite) core is comfortably below the maximum acceptable value of 472 W/cm used by Hitachi for the RBWR-AC core design [
1,
2].
With burnup, the axial power shape flattens as the fissile concentration at the lower part of the fissile zone is depleted (
Figure 16) and as
233U and, hence, the fission rate, builds up in the blankets. If necessary, it is possible to significantly flatten the BOL axial power distribution by grading the initial fissile fuel concentration loaded onto the fuel rods—loading a smaller concentration in the lower part and a higher in the upper part of the core.
Figure 18.
Linear heat generation rate along the fuel pin at Beginning of Life (BOL), Middle of Life (MOL) and at End of Life (EOL) in the equilibrium core.
Figure 18.
Linear heat generation rate along the fuel pin at Beginning of Life (BOL), Middle of Life (MOL) and at End of Life (EOL) in the equilibrium core.
The calculated void reactivity effects at the beginning and end of each of the five batches of the equilibrium core are given in
Table 3. It is observed that the void coefficients of reactivity are negative and becoming less so with burnup. They are smaller in absolute value than for the initial core [
4] due to the difference in the seed composition. The less negative value of the void coefficient of reactivity at EOL relative to BOL is due, mostly, to the buildup of fissile isotopes in the blankets that increases the effective core height and reduces the voiding contribution to increase in the neutron leakage probability. The core average void reactivity effect will be a weighted average of the 5 batch values and, hence, will be negative. The void reactivity coefficients of the actual core are expected to be somewhat more negative than those given in
Table 3 due to the contribution of neutron leakage in the radial direction that is not accounted for in the unit cell model.
Table 3.
Unit cell reactivity effect of 5% coolant flow reduction (denoted by “f95”) in the equilibrium core of the reference design.
Table 3.
Unit cell reactivity effect of 5% coolant flow reduction (denoted by “f95”) in the equilibrium core of the reference design.
Fraction of residence time | Nominal keff | Nominal stdev | f95keff | f95stdev | Reactivity effect (pcm) | stdev (pcm) | 3 stdev (pcm) |
---|
0 (BOL) | 1.14168 | 5.9E-05 | 1.13863 | 5.7E-05 | -234.7 | 8.2 | 24.6 |
1/5 | 1.11048 | 5.7E-05 | 1.10832 | 5.6E-05 | -176.0 | 8.0 | 24.0 |
2/5 | 1.09335 | 5.7E-05 | 1.09092 | 5.6E-05 | -203.6 | 8.0 | 24.0 |
3/5 | 1.07737 | 5.7E-05 | 1.07544 | 5.7E-05 | -166.8 | 8.1 | 24.2 |
4/5 | 1.06363 | 5.6E-05 | 1.06234 | 5.5E-05 | -114.9 | 7.8 | 23.5 |
1.0 (EOL) | 1.05204 | 5.7E-05 | 1.05126 | 5.6E-05 | -70.6 | 8.0 | 24.0 |
Table 4 gives the k
eff value in the fully voided and cold zero power (CZP) conditions at BOL (Burnup Step 0) and at the end of each of the five batches of the equilibrium core, all without control rods insertion. The coolant density in the core (0 and 1 g/cm
3, respectively) is extended to the lower and upper reflectors. It is observed that in the voided conditions the core has lower reactivity than in the nominal condition, but is supercritical. However, the excess reactivity could be readily compensated by the control and/or safety rods. On the other hand, at CZP conditions the excess reactivity is very high and may be impractical to compensate with the control and safety rods. That is, it appears very challenging, if not impractical, to provide adequate shutdown safety margin in this point design.
Table 4.
Unit cell keff and standard deviation (stdev) in fully voided and Cold Zero Power (CZP) conditions in equilibrium core of reference design.
Table 4.
Unit cell keff and standard deviation (stdev) in fully voided and Cold Zero Power (CZP) conditions in equilibrium core of reference design.
Fraction of residence time | BU step | Nominalkeff | Nominalstdev | CZP keff | CZP stdev | Full void keff | Full void stdev |
---|
0 (BOL) | 0 | 1.141693 | 6.1E-05 | 1.43 | 6.8E-05 | 1.08201 | 4.9E-05 |
1/5 | 1 | 1.109711 | 5.5E-05 | 1.34 | 6.4E-05 | 1.06288 | 4.5E-05 |
2/5 | 2 | 1.09157 | 6.1E-05 | 1.29 | 6.5E-05 | 1.05343 | 5.0E-05 |
3/5 | 3 | 1.076256 | 5.7E-05 | 1.26 | 5.9E-05 | 1.04530 | 4.9E-05 |
4/5 | 4 | 1.063234 | 5.7E-05 | 1.23 | 6.1E-05 | 1.03810 | 5.2E-05 |
1.0 (EOL) | 5 | 1.051665 | 5.7E-05 | 1.21 | 6.7E-05 | 1.03199 | 5.1E-05 |
The core average k
eff values will be a weighted average of the 5 batch values.
Table 5 gives a rough estimate of the k
eff value of the reference core at beginning (BOEC), middle (MOEC) and end (EOEC) of the equilibrium cycle obtained by applying the linear reactivity model to the averaging of the 5-batch data of
Table 4. As the linear reactivity model gives an equal weight to the 5 batches and as in the real core the 4th and 5th batches are located near the core radial periphery where the power density is lower and the importance function is lower, it is expected that the linear reactivity averaging underestimates the expected real core value. As the nominal EOEC k
eff is larger than the design objective of 1.025 this core should have been calculated to higher discharge burnup or, else, should be operated with a small breeding gain—a small fraction of the uranium (and, possibly, trans-thorium elements) should be removed from the reprocessed fuel so as to reduce the BOEC (and, therefore, also EOEC) k
eff.
Table 5 also gives k
eff values that are adjusted to EOEC k
eff of 1.025 by subtracting (1.078 – 1.025 = ) 0.053 from all the k
eff values. Although not exact, the adjusted k
eff values well represent the values expected from a well converged and consistent design.
Table 5.
Average keff at nominal and CZP condition of the reference core.
Table 5.
Average keff at nominal and CZP condition of the reference core.
Time in Cycle | Nominal keff | CZPkeff | Adjusted Nominal keff | Adjusted CZP keff |
---|
BOEC | 1.096 | 1.306 | 1.043 | 1.253 |
MOEC | 1.087 | 1.284 | 1.034 | 1.231 |
EOEC | 1.078 | 1.264 | 1.025 | 1.211 |
It is concluded that it is possible to obtain a fuel-self-sustaining boiling-water-cooled core based on thorium-dioxide-fuel. The core features stationary fuel and relatively uniform fuel assemblies. It uses the tight lattice, radial dimensions and coolant outlet void fraction of the Hitachi RBWR-AC core [
1,
2] and could fit within an ABWR pressure vessel. The core analyzed is made of a ~1 m long zone initially loaded with a mixture of
233UO
2 and ThO
2 with a ThO
2 blanket on top and bottom of it. The peak linear heat generation rate is significantly smaller than that of the RBWR-AC core that is designed to have a power level of 4000 MW
th. All the reactivity coefficients, including the void reactivity coefficient, are negative throughout the fuel life. However, a safety issue that has not been resolved yet is the insufficient shutdown reactivity margin at cold zero power conditions. Design modifications that will provide adequate shutdown margin are required. One possible design recently identified is described in the following section.
5. Alternative Core Design
An approach explored for reducing the magnitude of the coolant void reactivity effect and, thus, reducing the CZP k
eff, is to add to the seed a small amount of plutonium from LWR used nuclear fuel, thus making the resulting core a LWR plutonium transmuter while generating most of the energy from a self-sustaining thorium-based fuel cycle. A parametric search was made to identify the maximum amount of Pu that can be added before turning the void reactivity effect at the EOL from negative to positive. The amount of Pu addition found optimal was 1.2 weight percent. The core performance is estimated from a single pin-cell burnup analysis assuming a 5-batch fuel-management scheme as done for the reference case analysis described above. The pin power assumed for this analysis is 40KW
th—twice the value assumed for the reference unit cell analysis (
Section 4).
Figure 19 shows the k
eff evolution of a unit cell in the equilibrium cycle. The EOEC 5-batch core average k
eff design objective is 1.025, as in
Section 4. The burnup achieved in one cycle is 14.98 GWD per metric ton of all the heavy-metal (HM), including that in the blankets and the cycle length is 1.22 full power years. The average discharge burnup is 74.9 GWD/MTiHM after 5 cycles in the core, for a total fuel life of 6.12 years. The core is featuring a Fissile Inventory Ratio (FIR) of 1.01 accounting for
233U,
235U,
239Pu and
241Pu at the end of a 3-years cooling/recycling time. The variation of the axial dependent concentration of selected isotopes from BOL to EOL in the alternative design is shown in
Figure 20 through
Figure 22.
Figure 19.
keff evolution of the unit cell of the equilibrium cycle of the alternative design.
Figure 19.
keff evolution of the unit cell of the equilibrium cycle of the alternative design.
Figure 20.
232Th concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
Figure 20.
232Th concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
Figure 21.
233U concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
Figure 21.
233U concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
Figure 22.
239Pu concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
Figure 22.
239Pu concentration distribution along the fuel pin at BOL and EOL in the equilibrium core of the alternative design.
The BOL isotopic distribution of selected elements is given in
Figure 23 to
Figure 25. All these compositions pertain to the equilibrium cycle. The overall trends are similar to those displayed in
Section 4 for the reference pin cell.
Figure 23.
Amount of uranium isotopes in a fuel pin of the alternative core design at equilibrium.
Figure 23.
Amount of uranium isotopes in a fuel pin of the alternative core design at equilibrium.
Figure 24.
Amount of plutonium isotopes in a fuel pin at the beginning and end of life in the alternative core design at equilibrium.
Figure 24.
Amount of plutonium isotopes in a fuel pin at the beginning and end of life in the alternative core design at equilibrium.
Figure 25.
Amount of Np, Am and Cm isotopes in a fuel pin of the alternative core design at equilibrium.
Figure 25.
Amount of Np, Am and Cm isotopes in a fuel pin of the alternative core design at equilibrium.
The amount of
233U is slightly smaller than in the reference core (
Figure 5) but the amount of plutonium is higher (
Figure 24 versus Figure 11). However, the amount of plutonium in the alternative core is only 0.5% of the HM—even less than in typical LWR Used Nuclear Fuel (UNF). Nearly 60% of the loaded
239Pu is transmuted over the equilibrium cycle so that the fissile plutonium isotopes constitute only 27.6% of the total plutonium discharged—less than half the fraction in LWR UNF. The discharged
238Pu concentration is very high—about 40%
versus approximately 1% in LWR UNF. Hence, the plutonium in this RBWR discharged fuel will probably not be of proliferation concerns. The fissile uranium concentration is of significantly more proliferation concern and it may be desirable to denature the uranium by adding some depleted uranium to the thorium. This option will be explored in the future.
The axial power profile of the unit cell having the composition of the equilibrium core are shown for BOL, MOL and EOL in
Figure 26. The total pin power assumed is 40 kW
th—twice that assumed for the reference pin design. The peak pin linear heat generation rate is close to 450 W/cm. Assuming, as in
Section 4, a core radial power peaking factor of 1.25, the peak core linear heat generation rate is estimated to be 562 W/cm—significantly larger than the Hitachi design constraint of 472 W/cm. Nevertheless, a core based on the alternative fuel design could possibly safely operate at ~75% of the assumed power level; that is, at ~6000 MW
th or ~150% of the nominal ABWR power level. This is because the axial power peaking factor of the alternative design is significantly smaller than that of the reference unit cell (
Figure 18); if normalized to the same total pin power of 20 kW
th, the peak linear heat generation rate is 225 W/cm
versus 280 W/cm of
Figure 18.
Figure 26.
Axial variation of the linear heat generation rate along the fuel pin at BOL, MOL and EOL of the equilibrium cycle of the alternative core design. Total pin power is 40 kWth.
Figure 26.
Axial variation of the linear heat generation rate along the fuel pin at BOL, MOL and EOL of the equilibrium cycle of the alternative core design. Total pin power is 40 kWth.
Table 6 gives the k
eff value in the nominal, voided, and cold zero power (CZP) conditions at BOL (Burnup Step 0) and at the end of each of the five batches of the equilibrium core of the alternative design, all without control rods insertion. The voiding considered is an arbitrary 20% reduction from the nominal water density in each of the axial zones from the bottom of the seed and upward.
Table 6.
Unit cell keff in nominal, 20% voided and CZP conditions in the equilibrium core of the alternative design.
Table 6.
Unit cell keff in nominal, 20% voided and CZP conditions in the equilibrium core of the alternative design.
Fraction of residence time | BU step | Nominal keff | 20% voided keff | CZP Keff |
---|
0 (BOL) | 0 | 1.10 | 1.09 | 1.20 |
1/5 | 1 | 1.06 | 1.05 | 1.12 |
2/5 | 2 | 1.03 | 1.03 | 1.06 |
3/5 | 3 | 1.01 | 1.01 | 1.03 |
4/5 | 4 | 0.99 | 0.99 | 1.01 |
1.0 (EOL) | 5 | 0.97 | 0.98 | 0.99 |
Table 7 gives an estimate of the core average CZP k
eff and void reactivity effect at BOEC, MOEC and EOEC values obtained using the linear reactivity approximation. The actual value of the void coefficient of reactivity is expected to be somewhat more negative than that given in the table because the effect of radial neutron leakage is not accounted for. This radial leakage effect is likely to make the EOEC void reactivity effect—slightly positive in
Table 7, negative. If not, slight design modifications could do so.
Table 7.
Core average reactivity effect of 20% voiding and CZP keff of the alternative core design equilibrium core.
Table 7.
Core average reactivity effect of 20% voiding and CZP keff of the alternative core design equilibrium core.
Time in Cycle | kvoid-knominal (pcm) | CZP keff |
---|
BOEC | -166.2 | 1.079 |
MOEC | -66.9 | 1.056 |
EOEC | +4.6 | 1.039 |
Figure 27 compares the core CZP k
eff over the equilibrium cycle for the reference and alternative designs. It is seen that the alternative design CZP k
eff is significantly smaller and is likely manageable.
Figure 27.
Core average CZP keff values at the beginning, middle and end of the equilibrium cycle of the reference and alternative cores.
Figure 27.
Core average CZP keff values at the beginning, middle and end of the equilibrium cycle of the reference and alternative cores.
However, a preliminary analysis performed for the equilibrium core composition indicates that the axial variation of the reactivity effect of local voiding of the coolant has a wavy behavior with positive in addition to negative components, as illustrated in
Figure 28. The axially integrated change in k
∞ is consistent with the results reported in
Table 7. The axial zone dependent void reactivity effect was calculated using a methodology similar to that described in detail in reference [
14]. Briefly, the method calculates the contribution of a given axial zone to the k
∞ of the unit cell for the reference under perturbed conditions, and takes the difference between the perturbed and reference values to represent the reactivity effect of the perturbation.
Figure 28.
Axial distribution of the effect of voiding 20% of the coolant in the seed, upper blanket and upper reflector zones on the zone contribution to the unit cell k∞. Alternative core at equilibrium.
Figure 28.
Axial distribution of the effect of voiding 20% of the coolant in the seed, upper blanket and upper reflector zones on the zone contribution to the unit cell k∞. Alternative core at equilibrium.
A wavy trend quite similar to that displayed in
Figure 28 was more recently obtained using a couple of different methodologies—the, so called, PERT and KPERT options provided by the Monte-Carlo code MCNP6 for the calculation of the effect of perturbation on the system multiplication factor [
15]. The results provided by these two perturbation effect calculation options were found [
15] consistent with the value inferred from k
eff (perturbed)-k
eff (reference) in which the perturbation consists of 10% reduction of the reference water density in a single axial zone and each of the k
eff values was calculated with MCNP to have a standard deviation that is significantly smaller than the k
eff difference value.