The fuel-self-sustaining RBWR-Th core concept and parametric studies

The fuel-self-sustaining RBWR-Th core concept and parametric studies Phillip M. Gorman, Guanheng Zhang, Jeffrey E. Seifried, Christopher R. Varela, Jasmina L. Vujic, and Ehud Greenspan University of California, Berkeley 4155 Etcheverry Hall, MC 1730, Berkeley, CA, 94720-1730 Tel: (501) 642-4077, Fax: (501) 643-9685, Email: pmgorman@berkeley.edu Abstract This study searches for the optimal fuel assembly design for the RBWR-Th core -- a reduced-moderation BWR which is fuel-self-sustaining. Except for the initial fuel loading, it is charged with only thoria and discharges only fission products, recycling all actinides (with the exception of actinide impurities that end up in the waste streams). The design is a variant of the RBWR-AC core proposed by Hitachi, which arranges its fuel in a hexagonal tight-lattice, has a high outlet void fraction, axially segregates seed and blanket regions, and fits within the ABWR pressure vessel. The RBWR-Th shares these characteristics but replaces depleted urania with thoria as the primary fertile fuel, eliminates the internal blanket while axially elongating the seed region, and eliminates absorbers from the axial reflectors. The simulation is performed using MCNP6.1 for neutron transport, ORIGEN2.2 for transmutation, and a single-channel heat balance and void fraction correlation for a self-consistent neutronics thermal hydraulic solution. These three computational modules are iteratively executed by the MocDown driver code developed to automatically search for the equilibrium core composition and cycle length. The design variables of the parametric studies include the length of the seed and blanket zones, fuel rod diameter, lattice pitch, and concentration distribution of the recycled transfertile (TRF) isotopes in the seed. MocDown searches for the cycle length that will result in an end-of-cycle fissile inventory ratio of 1.0 along with estimated five batch core end-of-cycle keff value of 1.0. It was found that using thoria for the makeup fuel it is not possible to meet the shutdown margin constraint. Mixing in 25 to 30% depleted urania into the thoria makeup for the seed allows reduction of the magnitude of the negative void coefficient of reactivity so that adequate shutdown margin could be achieved along with adequate stability against two-phase coolant density oscillations. Promising designs arrived at so far are described. The performance of the RBWR-Th core is highly sensitive to modeling assumptions. Using the assumptions and correlations Hitachi used for the design of their RBWR-AC, the RBWR-Th average discharge burnup is 61 GWd/t versus 45 GWd/t of the depleted uranium fueled RBWR-AC. I. INTRODUCTION The RBWR-Th core design is based upon the RBWR- AC designed by Hitachi, 1 a Reduced-moderation BWR that employs axial seed and blanket segregation for fuel-selfsustaining operation within an ABWR pressure vessel. The RBWR-Th substitutes depleted urania with thoria as the primary makeup fuel, eliminates the internal blanket while elongating the seed region, and eliminates absorbers from the upper axial reflectors. A preliminary study of the RBWR-Th core concept feasibility was reported in reference 2 and results of a more thorough parametric study on the RBWR-Th core design were summarized in reference 3. The objective of the present study is to describe a couple of more recent parametric studies which sought to accommodate newly imposed coolant dryout and two-phase flow stability constraints while maximizing achievable burnup. The first of these parametric studies assumed that the makeup fuel is thoria; it was unable to identify a design that has an acceptable shutdown margin while meeting all the imposed design constraints. In the second parametric study depleted uranium was assumed to replace a fraction of the thorium for the makeup fuel of the seed in order to reduce the magnitude of the negative coolant void coefficient of reactivity and, thereby, to provide adequate shutdown margin. The parametric studies were subjected to the following mission constraints:

1. Charge only fertile material 2. Recycle all transfertile (TRF) material 3. Maintain a fissile inventory ratio (FIR) of unity at equilibrium 4. Fit within an ABWR pressure vessel 5. Provide the full ABWR thermal power 6. Operate in cycles of at least 12 months 7. Discharge fuel at 25GWd t 8. Use light water as coolant The studies were also subjected to the following physical and operational constraints: 9. Pressure drop through core 0.25 MPa 10. Possess negative coefficients of reactivity for fuel temperature, coolant void, and power 11. Maintain criticality 12. Avoid coolant dryout: MCPR 1.5 13. Suppress density wave oscillations: DR 0.7 14. Have sufficient shutdown margin Here, MCPR is the minimum critical power ratio and DR is the decay ratio of the core response to two-phase density wave oscillation (DWO) perturbations. Constraints 12 and 13 were not accounted for in the 2011 design. 2 The pressure drop constraint was applied later in the study so not all the presented designs meet it. The study methodology is described in section II. Section III summarizes the core and fuel-cycle performance metrics of the 2013 reference and compares it with the 2011 variant. Section IV discusses the failure of this design to meet constraint 14. This failure motivates studies using a mixed thoria and depleted urania makeup, which is described in section V. Section VI summarizes the performance of this new mixed makeup reference and compares it to that of the thoria references. Section VII demonstrates the performance sensitivity to several uncertain modeling assumptions. Finally, Section VIII compares the effects of local coolant void perturbations upon reactivity for the ABWR, RBWR-AC, and RBWR- Th. II. PARAMETRIC STUDY METHODOLOGY A two-tiered approach was used for these studies. Coolant flow-rate and fuel residence time were chosen as the two primary design variables because for fixed power (constraint 5), constraint 12 is most sensitive to the former and constraint 11 is most sensitive to the latter. The effects of changes to the seed and blanket region axial lengths, axial isotopic charge distribution, inlet sub-cooling, fuel pin outer diameter, and fuel pin pitch-to-diameter ratio are multi-faceted, so these variables were selected as secondary design variables. Each set of secondary design variables uniquely determined the values of the coolant flow-rate and cyclelength required for attaining constraints 11 and 12 at the beginning and end of the cycle. Upon each choice of primary design variables, a new equilibrium core composition was calculated and the primary design variables were once again updated. A few iterations were required before a set of primary design variables leading to a design that meets constraints 11 and 12 could be found. Satisfaction of the remainder of the constraints was addressed by the adjustment of secondary design variables. The adjustments of the secondary design variables were guided by a sensitivity study, which estimated the effects of one-at-a-time variable change upon the MCPR, DR, and achievable discharge burnup (BU). These sensitivities are qualitatively tabulated in Table I. TABLE I Trends of the variation in primary and secondary design variables upon coolant dryout, two-phase flow stability, and achievable discharge burnup. Here, + s indicate improvement, s indicate deterioration, double symbols indicate large effects, and blank indicate no or ambiguous effects. Modification MCPR DR BU Increase of the coolant flow-rate + + Increase of the fuel residence time + Elongation of the seed + + Contraction of the blankets + + Axial variation of the TRF charge + + + Reduction of the inlet sub-cooling + + Decrease of the fuel pin outer diameter + Increase of the fuel pin P D + Elongation of the seed was found to improve MCPR due to a decreased linear heat generation rate (LHGR), to worsen DR due to increased two-phase pressure drop, and to improve core average BU due to a decreased blanket volume fraction. Contraction of the blankets improved DR due to a decreased two-phase pressure drop and improved BU due to a reduced blanket volume fraction with only small penalties in breeding. Charging TRF in axial grades with concentration increasing towards the top of the core improved MCPR by shifting the LHGR peaking towards the outlet and improved DR by reducing the two-phase pressure drop. 4 Reduction of the fuel pin outer diameter improved MCPR by reducing LHGR, but at the cost of worsening DR due to a shortened heat transfer timeconstant. An increase of the fuel pin pitch-to-diameter ratio improved MCPR performance by allowing for fuel wetting, but significantly penalized BU. The MocDown thermal/hydraulics-coupled depletion and core equilibrium search tool was used to simulate a single-pin unit cell of the 2013 thoria reference RBWR-Th core design. 5 Using MCNP6.1 for neutron transport and ORIGEN2.2 for transmutation, 55 axial fuel zones were depleted 10 lower blanket, 30 seed, and 15 upper blanket in 14 constant-power depletion steps. 6,7 Full-core reactivity metrics were derived from unit-cell results

during the five batches. Unit-cell multiplication factors were functionally fitted for interpolation and evaluated at five points along the burnup (according to the progression along the cycle), the harmonic mean of those five values was taken, and the full-core radial leakage probability was subtracted. The leakage probability was assumed to be invariant with fuel temperature and coolant void perturbations. Online coupling of a single-channel constant-pressure heat balance and void fraction correlation ensured selfconsistent neutronics (power distribution) and thermal/hydraulics (coolant density distribution) solutions to within 5%. Fuel passed through the system over 50 times before reaching an asymptotic equilibrium. Fuel was assumed to be at 90% of its nominal density. The void fraction was estimated with an MIT-modified LPG correlation and an MIT-modified CISE-4 correlation was used to estimate the critical power ratio while assuming a 25% inter-assembly power peaking and 5% coolant flowrate reduction. 8 The core radial leakage probability was assumed to be 2.5% and the density wave oscillate decay ration was estimated using the STAB frequency domain stability code using unit-cell VCRs. 9 III. PERFORMANCE OF THE THORIA MAKEUP RBWR-Th CORE DESIGN Based upon the trend sensitivity study described in the previous section, several design variable changes were made to the 2011 design 2, establishing a 2013 thoria makeup reference: the coolant flow-rate and fuel residence time were increased by 130%; the seed region was elongated by 170%; the total blanket length was contracted by a third; TRF loading into the seed was graded at three concentrations 75% of the average for the lower third, the average for the upper third, and 125% of the average for the upper third; and the inlet sub-cooling was reduced by 4.06 C. Table II provides the main design specifications which incorporate the changes resulted from the parametric studies. Table III compares the core and fuel cycle performance metrics for the new design with those of the 2011 design.compared to the 2011 reference, the 2013 thoria reference design offers approximately 20% smaller core average discharge burnup although nearly 30% longer cycle length. The 2013 design also features a flattened LHGR, as depicted in Fig. 1. Whereas the 2011 variant peaks at 280 W cm in the lower seed at the beginning of equilibrium fuel life (BOEL), the 2013 thoria variant peaks at only 100 W cm in the upper seed at EOEC. Also seen in Fig. 1 is buildup of a larger power in the blankets of the 2011 design. This is a result of enhanced breeding within the blankets of the 2011 design due to a shorter core with a higher probability of leakage from the seed into the blanket. Neither the 2011 nor the 2013 designs quite met the DR constraint (#13). TABLE II Main design specifications of the 2013 thoria reference RBWR- Th core design. Here, LB/S/UB refers to the lower blanket, seed, and upper blanket regions, and L/M/U are the lower, middle, and upper axial third of the seed region. Design variable Units Value Thermal power MW 3926 Coolant flow-rate kg s 8795 Fuel residence time EFPD 2300 Axial height (LB/S/UB) cm 40/300/40 Seed TRF loading (L/M/U) a / o of average 75/100/125 Fuel pin (OD/pitch) cm 1.005/1.135 Coolant inlet temperature C 282.56 Coolant inlet pressure MPa 7.25 TABLE III Core and fuel cycle performance metrics of the 2011 and 2013 thoria makeup reference RBWR-Th core designs. Here, FTCR and VCR are the fuel temperature and coolant void coefficients of reactivity, and B/E denote full-core conditions at the BOEC and EOEC states. A 34.5% thermodynamic efficiency is assumed for both variants. Performance metric Units 2011 2013 Core HM mass t 219 361 Core TRF mass t 27.8 33.2 TRF HM at BOEL w / o 12.7 9.2 Specific power MW e t 6 4 Active fuel length cm 111 300 Minimum CPR - 1.1 1.5 Outlet void fraction % 82 75 Maximum LHGR W th cm 300 100 DWO decay ratio - 1.23 1.08 Core volume m 3 56 93 Power density MW th m 3 70 42 Fissile inventory ratio - 1 1 # of batches # 5 5 Average discharge burnup GW th d t 32 25 Cycle length EFPD 356 460 Cycle reactivity swing %Δk 1.9 0.9 TRF loading t GW e 20 25 HM reprocessing t GW e y 33 42 TRF discharge t GW e y 2.1 4.0 FTCR (B/E) pcm K -4.2/-4.2-4.9/-4.8 VCR (B/E) pcm % -87/-63-145/-120 Void collapse worth (B/E) %Δk 19/17 22/20 Fig. 2 shows the evolution over a cycle of the axial distributions of 232 Th and 233 U. Apparent are the graded seed TRF charge concentration, the higher rate of gross breeding within the seed (proportional to the depression in thoria over the cycle), and the higher net rate of breeding within the blankets (due to a lower fissile content).

Fig. 1. Linear heat generation rate of the (top) 2011 and (bottom) 2013 thoria makeup reference RBWR-Th core designs. The elongated active region and graded TRF concentration of the 2013 variant significantly flatten its power distribution. IV. SHUTDOWN MARGIN FOR THE THORIA MAKEUP RBWR-Th CORE DESIGN The void reactivity worths tabulated in Table III were derived from single-pin unit cell model that cannot model control elements. In order to quantify the shutdown margin, the assembly unit cell depicted in Fig. 3 was modeled with MCNP. Using this model, the reactivity worth of changing the core from hot full-power to cold zero-power states was found to be +13%Δk -- 4%Δk larger than the -9%Δk worth of the Hitachi-designed control elements. For sufficient shutdown margin, the system would have to overcome this deficit while accounting for ejection of the highest-worth control element and the decay of 135 Xe and 233 Pa. After determining that black control element worth is -32%Δk -- more than sufficient to provide adequate shutdown margin, increased control element worths were sought through modification of the Hitachi design. By swapping natural tungsten for the stainless steel clad, the worth increased to -10%Δk; by also doubling the B 4 C absorber density, the worth rose to -11%Δk. Usage of a Hf sheath increased the worth to -11%Δk. Using a AgInCd absorber (at 80, 15, and Fig. 2. Axial concentration of the (top) 232 Th and (bottom) 233 U along a cycle of the 2013 thoria makeup reference design. TRF is charged into graded enrichments within the seed. 5 w / o ) and a tungsten clad brought only -5.7%Δk and solid Gd and Hf control blades brought -5.8%Δk and -6.5%Δk, respectively all well below the original worth. These results are summarized in Table IV. Fig. 3. RBWR-Th assembly unit cell.

Although further improvement of control element worth could be achieved by increasing the ratio of control to fuel elements, most approaches would tend to increase the fractional volume of assembly bypass and penalize achievable burnup through spectrum softening and enhanced parasitic absorptions. Instead, the desirable shutdown worth was pursued by reducing the void reactivity worth by loading an adequate amount of depleted uranium to the thorium feed fuel. It was found that the larger the fraction of depletion uranium, the larger becomes the amount of plutonium and minor actinides bred, and the less negative the void reactivity worth is. The reduction in the VCR also improves two-phase flow stability. TABLE IV Summary of control element design study. Only the black control element was able to meet the non-conservative 13%Δk shutdown requirement. Variations of Hitachi control element Shutdown worth [%Δk] Original (SS sheath; B 4 C absorber) -9 W sheath -10 Hf sheath -11 W sheath + 2 B 4 C absorber -11 W sheath + AgInCd absorber -5.7 Gd sheath + Gd absorber -5.8 Hf sheath + Hf absorber -6.5 Black sheath + black absorber -32 V. DESIGN IMPROVEMENT THROUGH USE OF A MIXED THORIA-DEPLETED URANIUM MAKEUP A new series of design studies sought to reduce the void reactivity worth by breeding plutonium and minor actinides into the equilibrium core composition. This was achieved by replacement of a fraction of the thoria makeup with depleted urania. By adjusting this fraction, the void reactivity worth could be tuned to as small a negative value as required to provide an adequate shutdown margin. Depleted urania was mixed with thoria for the seed makeup fuel only; the makeup fuel for the blankets was thoria. This avoided the need to isotopically separate the 233 U bred from thorium from the 238 U of the depleted uranium. The primary design variable was the DU makeup fraction. For each DU makeup fraction, the axial enrichment distribution that would maximize the MCPR by optimizing the axial power and water density distributions was found. As with the thoria parametric study, the selection of the coolant mass flow rate and fuel residence time was uniquely defined to meet constraints 11 and 12. Adequate shutdown reactivity margin was also verified for each design at core-averaged beginning of equilibrium cycle (BOEC) and end of equilibrium cycle (EOEC) conditions using the Hitachi design for the control blades and taking into account the 135 Xe and 233 Pa decay. VI. PERFORMANCE OF THE MIXED MAKEUP RBWR-Th CORE DESIGN The same approach was used to determine equilibrium performance with the mixed thoria-du makeup as with the thoria makeup. The optimal design arrived at replaces 28 atom-percent of the makeup thoria with depleted urania. Table VI summarizes the fuel performance metrics and compares them with the 2013 thoria cycle. The axial power shape with the mixed thoria-du makeup fuel is significantly more central-peaked than for the reference design. This mitigated the need for axially varying transfertile concentration. Additionally, since the VCR became nearly zero, though negative, throughout the cycle, the new design has a significant margin for two-phase flow stability. This was used to increase the number of fuel pins per assembly from 271 to 547 while maintaining the same P/D ratio. The assembly can dimensions were kept constant. This improved the MCPR, allowing a lower flow rate, a harder spectrum and a larger discharge burnup. The design specifications for the mixed fertile feed design are compared against the reference thoria feed design in Table V, and the performance metrics are compared in Table VI. TABLE V Main design specifications of the 2013 thoria makeup reference RBWR-Th core design and the mixed thoria-du design. Here, LB/S/UB refers to the lower blanket, seed, and upper blanket regions, and L/M/U are the lower, middle, and upper axial third of the seed region. Design variable Units Thoria Mixed Thermal power MW 3926 3926 Coolant flow-rate kg s 8795 8428 Axial height (LB/S/UB) cm 40/300/40 40/300/40 Seed TRF loading (L/M/U) a / o of avg. 75/100/125 95/100/105 Fuel pin (OD/pitch) cm 1.005/1.135 0.707/0.799 Coolant inlet temperature C 282.56 282.56 Coolant inlet pressure MPa 7.25 7.25 Fuel pins per assembly # 271 547 Number of assemblies # 720 720 Compared to the thoria design, the mixed thoria-du design features a 28% higher core-averaged discharge burnup and cycle length. The increased number of pins per assembly significantly lowered the peak LHGR, although it is somewhat less flat than that of the 2013 thoria design variant (Fig. 1 bottom). The VCR is an order of magnitude lower with the mixed variant, which provides an adequate shutdown margin and enables meeting the DR constraint. The pressure drop of the mixed thoria-du design is 0.314 MPa -- higher than the limit of 0.25 MPa imposed after this design was completed. Design modifications are being worked out to meet the pressure drop constraint. They are not expected to effect the study conclusions.

Table VII shows the equilibrium discharge compositions after the three-year cooling period from the seed for the 2013 thoria reference design and the mixed thoria-du design. 238 U is excluded from the results in Table VII because its amount in the mixed makeup fuel is greater than the amount of transfertile material. 233 U and 235 U make up 19.5% and 2.7% of the total mass of uranium in the mixed design. While the mixed thoria-du design reduces the fissile U/total U fraction significantly, it falls short of the LEU limit of 12% 233 U. Furthermore, within the blankets of both designs, nearly all of the transfertile material is pure 233 U. TABLE VI Core and fuel cycle performance metrics of the 2013 thoria and mixed makeup reference RBWR-Th core designs. A 34.5% thermodynamic efficiency is assumed for both variants. Performance metric Units Thoria Mixed Core HM mass t 361 364 Core TRF mass t 33.2 41.8 Pin TRF HM at BOEL w / o 9.2 11.5 Specific power MW e t 4 4 Seed length cm 300 300 Combined blanket length cm 80 80 Minimum CPR - 1.5 1.5 Outlet void fraction % 75 78 DWO decay ratio - 1.08 0.45 Core pressure drop MPa 0.268 0.314 Maximum LHGR W th cm 100 50 Core volume m 3 93 93 Power density MW th m 3 42 42 Fissile inventory ratio - 1 1 # of batches # 5 5 Average discharge burnup GW th d t 25 32 Cycle length EFPD 460 600 Fuel residence time EFPD 2300 3000 Cycle reactivity swing %Δk 0.85 0.88 Specific TRF loading t GW e 25 31 HM reprocessing rate t GW e y 42 32 TRF discharge rate t GW e y 4.0 3.8 FTCR (BOC/EOC) pcm K -4.9/-4.8-4.4/-4.3 VCR (BOC/EOC) pcm % -145/-120-11.1/-8.4 Void collapse worth (B/E) % 13/11 3.5/3.0 Shutdown reactivity (B/E) % 3.9/2.3-0.9/-1.4 Fig. 4. LHGR of the mixed thoria-du core. The larger number of fuel pins per assembly significantly reduced the LHGR relative to the 2013 reference case (Fig. 1, bottom). TABLE VII Comparison of the equilibrium compositions, 3 years after discharge, of the 2013 thoria and mixed makeup reference RBWR-Th core designs. Fissile TRF includes 233,235 U, 237 Np, 239,241 Pu, and 241,243 Am. Unless noted, values are for the seed. Mass fraction [%] Thoria Mixed TRF HM 12.1 15.0 Fissile TRF HM 6.6 9.4 Th HM 87.9 66.3 238 U HM 0 18.7 Non-fertile U* TRF 90.6 63.2 Np TRF 2.3 1.5 Pu TRF 6.2 30.7 Am TRF 0.3 3.3 Cm TRF 0.2 0.8 232 U non-fertile U 0.8 0.4 233 U non-fertile U 47.7 58.0 234 U non-fertile U 32.6 26.3 235 U non-fertile U 8.8 8.0 236 U non-fertile U 10.2 7.4 fissile U non-fertile U 56.5 66.0 238 Pu Pu 73.6 10.9 239 Pu Pu 16.5 48.0 240 Pu Pu 4.3 30.5 241 Pu Pu 3.7 5.9 242 Pu Pu 1.9 4.3 fissile Pu total Pu 20.2 53.9 blanket 233 U blanket HM 0.3 0.4 blanket 233 U blanket TRF 97.8 97.7 * Excluding U-238

TABLE VIII Comparison of the equilibrium BOEL compositions between the 2013 thoria and mixed makeup reference RBWR-Th core designs. Fissile TRF includes 233,235 U, 237 Np, 239,241 Pu, and 241,243 Am. All values are for the seed BOEL composition. Mass fraction [%] Thoria Mixed TRF HM 11.8 14.5 Fissile TRF HM 6.5 9.2 Th HM 88.2 66.4 238 U HM 0.0 19.1 Non-fertile U* TRF 90.7 63.5 Np TRF 2.3 1.5 Pu TRF 6.1 30.5 Am TRF 0.3 3.3 Cm TRF 0.2 0.8 232 U non-fertile U 0.8 0.3 233 U non-fertile U 48.1 58.4 234 U non-fertile U 32.3 26.0 235 U non-fertile U 8.7 8.0 236 U non-fertile U 10.1 7.3 fissile U non-fertile U 56.8 66.3 238 Pu Pu 73.6 10.9 239 Pu Pu 16.5 48.0 240 Pu Pu 4.3 30.9 241 Pu Pu 3.7 5.9 242 Pu Pu 1.9 4.3 fissile Pu total Pu 20.2 53.9 * Excluding U-238 VII. SENSITIVITY OF PERFORMANCE TO MODELING ASSUMPTIONS RBWR-Th performance is highly sensitive to the void fraction, critical power, and core radial leakage probability. The first two are estimated by correlations that have large experimental uncertainties 8 and the third requires a fullcore model. The impact of these uncertain modeling assumptions upon performance is quantified by relaxing the assumptions in turn and re-optimizing the design variables. 10 Key results are summarized in Table IX. The MIT-modified LPG correlation 8 is assumed to offer a best-estimate of the RBWR-Th coolant void fraction which is conservatively lower than that predicted by the RELAP correlation, used by Hitachi to model the RBWR-AC. Upon switching to the RELAP correlation, the estimated coolant void fraction increases, system slowingdown power decreases, flux spectra harden, fissile breeding improves, equilibrium fissile content increases, and higher discharge burnup along with longer cycle lengths can be achieved 10. The MIT-modified CISE-4 correlation 8 offers a bestestimate of the RBWR-Th critical power and recommends a conservative limit of 1.5. Hitachi uses their own modified CISE-4 correlation and a 1.3 limit, which permits less wetting of the fuel before dryout. Upon switching to the Hitachi-modified correlation and limit, a reduced coolant flow and shortened active fuel length can be accommodated, which, when combined, improves both burnup and stability. The former does so by increasing coolant void fraction and the latter does so by reducing the heavy metal loading and reducing the two-phase pressure drop. This switch, in addition to the usage of the RELAP void fraction correlation, more than doubles the achievable burnup 32 to 61 GWd/t and drops the DWO decay ratio from 0.45 to 0.16. The EOEC VCR for the selected design is slightly positive; however, for a full-core model, leakage effects are expected to bring this value negative. VIII. LOCAL VOID PERTURBATIONS IN THE ABWR, RBWR-AC, AND RBWR-Th Fig. 5. Axial concentration of the (top) fertile and (bottom) fissile isotopes along a cycle of the mixed thoria-du reference design. Here, fissile TRF includes 233,235 U, 237 Np, 239,241 Pu, and 241,243 Am, and fertile isotopes includes 232 Th and 238 U. Coefficients of reactivity are typically determined by calculating the multiplication factor of a system at nominal and perturbed conditions; for example with a voided coolant density due to a coolant flow-rate reduction or an elevated fuel temperature. These global perturbations can be considered as the simultaneous occurrence of multiple local perturbations which are independent of one another. It is possible for some of these local perturbations to have positive reactivity worth, even when the global set has a negative worth.

TABLE IX Core and fuel cycle performance metrics of the 2013 mixed makeup RBWR-Th core design using different modelling assumptions. LPG and RELAP are drift-flux correlations for void fraction and M-CISE and H-CISE are correlations for critical power. A 34.5% thermodynamic efficiency is assumed for both variants. Performance metric Units LPG & M- RELAP & CISE H-CISE Core HM mass t 364 225 Core TRF mass T 41.8 23.2 Pin TRF HM at BOEL w / o 11.5 10.3 Specific power MW e t 4 6 Depleted uranium fraction of makeup a / o 28 25 Seed length cm 300 155 Combined blanket length cm 80 80 Minimum CPR - 1.5 1.3 Outlet void fraction % 78 85 DWO decay ratio - 0.45 0.16 Maximum LHGR W th cm 50 82 Core volume m 3 93 57 Power density MW th m 3 42 69 Fissile inventory ratio - 1 1 # of batches # 5 5 Average discharge burnup GW th d t 32 61 Cycle length EFPD 600 700 Cycle reactivity swing %Δk 0.88 1.79 Specific TRF loading t GW e 30.9 17.1 HM reprocessing rate t GW e y 31.7 16.3 TRF discharge rate t GW e y 3.8 1.8 FTCR (BOC/EOC) pcm K -4.4/-4.3-3.7/-3.7 VCR (BOC/EOC) pcm % -11.1/-8.4-6.45/+0.5 Void collapse worth (B/E) % 3.5/3.0 3.3/3.0 Shutdown reactivity (B/E) % -0.9/-1.4-0.3/-1.1 The KPERT tool in MCNP6.1 was used to estimate the local void coefficient of reactivity for the ABWR, 2011 reference RBWR-Th, and Hitachi RBWR-AC. 11 Examining the results in Fig. 6, one finds that the ABWR and 2011 reference RBWR-Th share many characteristics: both are negative for virtually the extent of the active length; both are most negative near the coolant inlet, where coolant and power densities are highest; and both trend towards zero near the coolant outlet. Overall, the RBWR- Th local VCRs are more negative. The RBWR-AC contrasts with both, exhibiting a local VCR which alternates in sign, depending on the axial region: it peaks positively within the upper and internal blankets; it drifts between positive and negative within the seeds; and it remains around zero within the lower blanket. The physics phenomena responsible for the widely varying VCR(z) are being investigated. constraints. By elongating the seed and flattening the LHGR profile, shortening the blankets, axially varying the transthoria seed charge, and reducing the inlet subcooling, the constraints were met with only modest penalties on the fuel discharge burnup. All coefficients of reactivity are negative, but the void coefficient of reactivity is too negative to allow for safe shutdown at cold zero-power conditions. Mixing in depleted urania into the thoria makeup for the seed allows reduction of the magnitude of the negative void coefficient of reactivity so that adequate shutdown margin could be achieved along with adequate stability against two-phase coolant density oscillations. The significant improvement in flow stability shifted the optimal design to larger number of pins of a smaller diameter. The mixed thoria-depleted urania design therefore halved the peak linear heat generation rate of the thoria design thus enabling meeting the MCPR constraint using smaller coolant flow rate. The resulting harder spectrum enabled a 28% increase in the discharge burnup. The performance of the RBWR-Th core is highly sensitive to modeling assumptions. Using the assumptions and correlations Hitachi used for the design of their RBWR-AC, the RBWR-Th average discharge burnup is 61 GWd/t versus 45 GWd/t of the depleted uranium fueled RBWR-AC. On-going studies search for small design modifications that will enable to meet the pressure drop constraint with minimal penalty on the core performance. ACKNOWLEDGMENTS This research was performed using funding received from the U.S. Department of Energy Office of Nuclear Energy s Nuclear Energy University Programs. This research is based upon work partially supported by the U.S. Department of Energy National Nuclear Security Administration under Award Number DE-NA0000979. IX. CONCLUSIONS The RBWR-Th core design was improved to accommodate coolant dryout and two-phase flow stability

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