DOPPLER COEFFICIENT OF REACTIVITY BENCHMARK CALCULATIONS FOR DIFFERENT ENRICHMENTS OF UO 2

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1 Supercomputing in Nuclear Applications (M&C + SNA 2007) Monterey, California, April 15-19, 2007, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2007) DOPPLER COEFFICIENT OF REACTIVITY BENCHMARK CALCULATIONS FOR DIFFERENT ENRICHMENTS OF UO 2 L. Thilagam, C. Sunil Sunny and K.V. Subbaiah Safety Research Institute Atomic Energy Regulatory Board Kalpakkam, India thilagam@igcar.gov.in; ssunil@igcar.gov.in; kvs@igcar.gov.in K. Devan Indira Gandhi Centre for Atomic Research Kalpakkam, India devan@igcar.gov.in Lee,Young-Seok Center for High Energy Physics, Kyungpook National University Daegu , South Korea leeyngsk@yahoo.co.kr V. Jagannathan LWRPS, RPDD, Bhabha Atomic Research Centre Trombay, Mumbai, India, v_jagan1952@rediffmail.com ABSTRACT Continuous-energy Monte Carlo code, MCNP along with its cross section data library in ACE format based on ENDF/B-V &VI has been used to analyze a new computational benchmark circulated by LANL (LA-UR ) on Doppler coefficient for different types UO 2. Doppler coefficient has been computed by calculating the eigen values of some selected idealized PWR fuel pin cell configurations with seven different fuel enrichments of UO 2. Even though the benchmark contained configurations for different kinds of mixed oxide fuel configurations, the same could not be analyzed for evaluating the Doppler coefficient due to lack of nuclear data with us for some of the isotopes. The pin cell configuration is modeled in 3-D geometry by assuming an infinite dimension instead of reflecting boundary conditions in the axial direction and reflective boundary conditions are assumed on all other four sides of the pin cell. With this geometry model of the pin cell, first an initial criticality run is made with 1.0 million active histories (i.e active and 50 skipped cycles with 1000 histories per cycle). The fission source file (SRCTP) from the last cycle of this run is then used as converged input source for the final run with 14 million histories (3500 active cycles and 500 skipped with 4000 histories per cycle). The intermediate MCNP run confirmed the sampling of fission sites in the entire fuel cell region modeled. Thermal Author for communication

2 Thilagam et al. treatment (S αβ ) option is used to take care of binding effect of hydrogen in water. The corresponding light water S αβ cross-section treatments for temperature 600K (HZP) is used. Doppler coefficients for all the UO 2 cases are estimated using two different cross-section sets: Case-I based on ENDF/B-VI and Case II based on ENDF/B-V. In Case-I, fuel temperature changes from 600K (Hot Zero Power) to 900K (Hot Full Power) but in Case-II due to lack of data in the MCNP data library available, fuel temperature change assumed is from 587K (Hot Zero Power) to 881K (Hot Full Power). The maximum decrease in reactivity (Doppler defect) in going from HZP to HFP is found to be pcm for Case-I and pcm for Case-II. These maximum reactivity changes are observed for natural enrichment of UO 2. Key Words: Reactivity, UO 2, Doppler Coefficient, MCNP5, ENDF-B/V & VI 1. INTRODUCTION The interaction probability (cross sections) of neutrons with fuel nuclei in a reactor depends on the temperature at which the system exists. The resonance behavior of neutron interaction cross section can change due to the change in relative motion between the neutron and fuel nuclei in thermal motion. The thermal motion of fuel nuclei changes due to the change in fuel temperature. It is observed that as fuel temperature increases, the resonance in the interaction cross section broadens while its peak magnitude decreases. This phenomenon is known as Doppler effect or Doppler broadening of cross section [2]. Doppler broadening of resonances in the cross section of fuel nuclei leads to change in the neutron multiplication factor (k eff ) in a reactor. Therefore, the assessment of fuel temperature coefficient of reactivity (Doppler coefficient) is an important aspect in any reactor core physics evaluation. Doppler coefficient evaluation involves the study of reactivity change with respect to change in fuel temperature by keeping other parameters like moderator temperature, moderator density, boron concentration, xenon poisoning, burn-up etc., constant, while changing fuel temperature from one to another. The data on Doppler coefficient generated is required in the analysis of nuclear reactor transients. This report deals with such an evaluation of Doppler coefficient proposed as a benchmark [5]. Benchmark data is given for seven different fuel enrichments of a typical pressurized water reactor (PWR) UO 2 lattice, five different mixed oxide (MOX) concentrations of reactor-recycle fuel and four different MOX concentrations of weapons-grade fuel. This benchmark is based on previous benchmark studies [3, 4] but extended to higher enrichments of UO 2 as well as two different types of MOX fuels. The objective of this benchmark exercise is to calculate the Doppler coefficient between hot full power (HFP) and hot zero power (HZP) temperature conditions of the fuel. The benchmark computational details and the analysis performed for evaluating Doppler coefficient is presented here. In the analysis reported here only UO 2 benchmark is attempted. Monte Carlo transport code MCNP5 [1] employing both ENDF/B- V & ENDF/B-VI cross section data is used for the assessment of Doppler coefficient in the present study. The following sections describe benchmark specifications, Monte Carlo methodology employed and the results obtained in sequel. 2/10

3 Doppler coefficient of reactivity - Benchmark 2. BENCHMARK SPECIFICATIONS The geometry for this benchmark corresponds to an infinite array of identical, infinitely long PWR fuel pin cells. Such an array can be modeled as a single rectangular pin cell with reflecting boundary conditions on the top, bottom, and four sides. A pin cell consists of fuel, clad and moderator region. The pin cells are based on optimized fuel assembly design that has been used in both initial and reload cycles of several PWRs. The schematic of the benchmark geometry is given in Fig.1 and pin cell dimensions are listed in Table-I. Table I. Pin cell dimensions for different temperatures DIMENSIONS (CM) 600K 900K/600K Radius of Fuel Inner Radius of Clad GAP Outer Radius of Clad Pitch GAP CLAD FUEL BORATED H 2 O Figure.1 MCNP Model of Benchmark Geometry 3/10

4 Thilagam et al. Doppler coefficient evaluations are done by changing fuel temperature alone from 600K to 900K, which are respectively hot zero power (HZP) and hot full power (HFP) temperatures in the first case using ENDF/B-VI cross section data. As a second case Doppler coefficient evaluations are done by changing fuel temperature from 587K to 881K using ENDF/B-V cross section data also (data library available with MCNP5 code does not have data at 600K and 900K using ENDF/B-V). Moderator temperature, moderator density and clad temperature correspond to 600K, which enables to study the effect of change in fuel temperature alone on reactivity. Coolant pressure assumed is 2250psia for both HZP and HFP. The moderator is borated light water and contains 1400ppm (by weight) of natural boron concentration Fuel Benchmark specifications provided for conventional UO2 with seven different enrichments spanning from natural uranium to 5 wt.% enriched in U 235 are analysed for Doppler reactivity estimations. Fuel density assumed is g/cm 3 at room temperature. The change in fuel density with temperature is given in Table-IA of the Appendix. The number densities of each fuel type of UO 2 for different U 235 enrichments are given in Table-IIA and Table-IIB of the Appendix Clad At room temperature, the nominal density of Zircaloy is assumed as 6.56g/cm 3. Removal of materials other than Zirconium (Tin, Chromium, Iron & Nickel) reduces the density to g/cm 3. At 600K, the density is reduced further to g/cm 3 due to thermal expansion. The number densities of clad material at 600K and 900K are given in Table-IIIA of the Appendix Moderator At the operating pressure of 2250psia and hot zero power temperature 600K, the density of unborated water is approximately g/cm 3. Retaining that density and adding 1400ppm of boron (and assuming negligible displacement of water), the number densities at 600K and 900K are given in Table-IIIA of the Appendix. The presence of trace isotopes of oxygen ( 17 O, 18 O) is ignored. 3. MONTE CARLO MODEL The pin cell configuration as described in section 2 is modeled in 3-D geometry using MCNP code. An infinite dimension is assumed instead of reflecting boundary conditions in the axial 4/10

5 Doppler coefficient of reactivity - Benchmark direction and reflective boundary conditions are assumed on all other four sides of the pin cell. With this geometry model of the pin cell, first an initial criticality run is made with 1.0 million active histories (i.e active and 50 skipped cycles with 1000 histories per cycle). The fission source file (SRCTP) from the last cycle of this run is then used as converged input source for the final run with 14 million histories (3500 active cycles and 500 skipped with 4000 histories per cycle). The intermediate MCNP run confirmed the sampling of fission sites in the entire fuel cell region modeled. Thermal treatment (S αβ ) option is used to take care of binding effect of hydrogen in water. The corresponding light water S αβ cross-section treatments for temperature 600K (HZP) is used. The respective values of k eff are obtained at two fuel temperatures 600K (HZP) and 900K (HFP) for all the fuel types in the first case and fuel temperatures 587K and 881K in the second case. The isotope cross-section evaluations and temperatures used are shown in Table-II. A diagram showing the behavior of number of histories (active neutrons) as a function of active cycles is shown in Fig E+7 1.6E+7 Number of Active Neutrons 1.2E+7 8.0E+6 4.0E+6 600UO2 2.4 wt% 600UO2 3.1 wt% 900UO2 2.4 wt% 900UO2 3.1 wt% 0.0E Number of Active Cycles Figure.2 Neutron Source Generated for the MCNP Active Cycles 5/10

6 Thilagam et al. Table II. MCNP Cross Section Data and Evaluated Temperatures CASE-I Isotope Temperature Cross Section ZAID No. of CXS data Evaluation Borated Water c 587K c 587K c 587K c 294K ENDF-B/VI.0 LWTR.04t 600K TMCCS Clad c 587K ENDF- B/V:XTM Fuel c c c c c c c c 600K 294K 600K 587K 900K 294K 900K 881K ENDF-B/VI.2 ENDF-B/VI.0 ENDF-B/VI.2 ENDF-B/VI.2 ENDF-B/VI.0 ENDF-B/VI.2 CASE-II Isotope Temperature Cross Section ZAID No. of CXS data Evaluation Borated Water c 587K c 587K c 587K c 294K ENDF-B/VI.0 LWTR.04t 600K TMCCS Clad c 587K ENDF- B/V:XTM Fuel c c c c c c c c 587K 294K 587K 587K 881K 294K 881K 881K ENDF-B/VI.0 ENDF-B/VI.0 The equation (1) is used to calculate the reactivity change ( ρ) ρ = k k HFP eff HFP eff k k HZP eff HZP eff (1) HZP HFP Where, k eff & keff are the effective multiplication factors corresponding to HZP and HFP conditions. The Doppler coefficient (D C ) is then estimated as the change in reactivity per degree change in fuel temperature using equation (2) and is expressed in percent millik eff (pcm) ρ D C = T ( 2) Where, T is the change in fuel temperature (300K for case I and 294K for case II). 6/10

7 Doppler coefficient of reactivity - Benchmark 4. RESULTS AND DISCUSSIONS 1. The calculated values of neutron multiplication factor (k eff ), Doppler defect ( ρ) and the Doppler coefficient (D C ) for seven different enrichments of UO 2 mentioned in the benchmark specifications are presented in Table-III and Table-IV. 2. The statistical uncertainty in the computed k eff values for each calculation is determined as standard deviation (σ), which are also presented in the respective Tables. 3. The neutron multiplication factor (k eff ) values are found to increase with increase in fissile content, which is an expected behavior. 4. The maximum decrease in reactivity (Doppler defect) in going from HZP to HFP is found to be pcm in the first case and pcm in the second case. These maximum reactivity changes are observed for natural enrichment of UO 2. This may be because of the more number of resonances in U 238 compared to U 235 and also due to the neutron spectral change. 5. The computed value of Doppler coefficient (D C ) lies in the range of pcm/k to pcm/k for the first case and pcm/k to pcm/k in the second case. Table III. Results for Case-I (UO 2 with ENDF/B-VI Data) Enrichment (wt.%) HFP k eff ± σ HZP k eff ± σ Doppler Defect ( ρ)(pcm) Doppler Coefficient ( ρ/ T) (pcm/k) ± ± ± ± ± ± ± ± ± ± ± ± ± ± /10

8 Thilagam et al. Table IV. Results for Case-II (UO 2 with ENDF/B-V Data) Enrichment (wt.%) HFP k eff ± σ HZP k eff ± σ Doppler Defect ( ρ)(pcm) Doppler Coefficient ( ρ/ T) (pcm/k) ± ± ± ± ± ± ± ± ± ± ± ± ± ± CONCLUSIONS In this report, a new benchmark on fuel Doppler coefficient assessment is presented. Monte Carlo transport code employing continuous energy nuclear data library ENDF/B-VI and ENDF/B-V are used for the computations. The neutron multiplication factor (k eff) is determined for a typical PWR UO 2 fuel pin cell at two different temperatures 600K & 900K in case I and 587K and 881K in case II. Subsequently the Doppler coefficient (D C ), that is the change in reactivity for unit change in fuel temperature are estimated and presented. The maximum decrease in reactivity (Doppler defect) in going from hot zero power (HZP) to hot full power (HFP) is found to be pcm in the first case and pcm in the second case. These maximum reactivity changes are observed for natural enrichment of UO 2. This may be because of the more number of resonances in U 238 compared to U 235 and also due to the neutron spectral change. The computed value of Doppler coefficient (D C ) lies in the range of pcm/k to pcm/k for the first case and pcm/k to pcm/k in the second case. It is concluded that Doppler feedback in going from HZP to HFP in a light water reactor produces a reactivity decrease of about 1000 pcm. 6. REFERENCES 1. X-5 Monte Carlo Team, MCNP- a General Monte Carlo n-particle Transport Code, Version-5 Volume-I, Volume-II, Volume-III, LA-CP , LA-CP , LA-CP , Los Alamos National Laboratory Report, (2003). 8/10

9 Doppler coefficient of reactivity - Benchmark 2. James J. Duderstadt, Louis J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, Russel D. Mosteller, Eisenhart L.D, Little R.C, Eich W.J, and Chao.J, "Benchmark Calculations for the Doppler Coefficient of Reactivity", Nuclear Science and Engineering, 107, pp (March 1991). 4. Russel D. Mosteller, Holly J.T, and Mott L. A, "Benchmark Calculations for the Doppler Coefficient of Reactivity in Mixed-Oxide Fuel", Proceedings of the International Topical Meeting on Advances in Mathematics, Computations, and Reactor Physics, CONF , pp , Pittsburgh, Pennsylvania (April 1991). 5. Russel D. Mosteller, Computational Benchmarks of Doppler Coefficient of Reactivity, LA- UR , (JUNE 2006) 9/10

10 Thilagam et al. APPENDIX Table-IA Fuel density for Different Temperatures S.NO Temperature (in K) Density of fuel (in g/cc) Table-IIA Number Density of UO 2 Fuel at 600K for different Enrichments (atoms/barn-cm) Enrichment (wt.%) 16 O 234 U 235 U 238 U x x x x x x x x x x x x x x x x x x x x x x x x x x x 10-2 Table-IIB Number Density of UO 2 Fuel at 900K for different Enrichments (atoms/barn-cm) Enrichment (wt.%) 16 O 234 U 235 U 238 U x x x x x x x x x x x x x x x x x x x x x x x x x x x 10-2 Table-IIIA Number Densities of Clad & Moderator for various temperatures Material Isotope Number density in atoms/barn-cm 600K 900K Cladding Zr E E-02 1 H E E-02 Moderator 10 B E E-05 B E E O E E-02 10/10