Pin Cell Results (TRITON & KENO-V.a/KENO-VI). Assembly Results (POLARIS). ⢠Typical PWR pin-cell and lattice were selected from Uncertainty Analysis in.
Sampling-based Uncertainty Quantification of Kinetic Parameters for PWRs Majdi I. Radaideh – The University of Illinois at Urbana Champaign Mentor: W. Wieselquist With: T. Kozlowski Program: NESLS Reactor and Nuclear Systems Division
Introduction • Delayed neutrons are significant for nuclear reactor operation and safety analysis as they make nuclear reactors controllable. • Most of the neutrons ( ~ 99%) are emitted immediately after fission: these are called prompt neutrons • A small fraction (~1 %) is released later: these neutrons are called delayed neutrons [1]. • In general, reactor kinetics are described by two major kinetic parameters related to neutron precursors groups: delayed neutron fraction (β) and decay constant (λ). • Consequently, evaluation of kinetic parameters’ uncertainties due to nuclear data uncertainties is important for accurate reactor kinetics modeling.
• Sampling-based uncertainty quantification using Sampler code of the SCALE code system to develop an approach for uncertainty quantification of kinetic parameters. • Fundamental nuclear data —including nuclear cross sections, fission yield, and decay data— were statistically sampled using random perturbation factors. Kinetic parameters were calculated using these samples. • Two levels of kinetic parameters’ uncertainty quantification haven been considered: pin-cell and lattice levels. • Two methods for βeff calculations were explored: 1. Adjoint-weighted: (
' 𝛽"## = & 𝛽"## ')*
,,0,1 ∑, 𝛽, ∑0 ∑1 𝜈𝛴# 𝜑0,1 𝑉0 ' 𝛽"## = ∑, ∑0 ∑1 𝜈𝛴#,,0,1 𝜑0,1 𝑉0
Assembly Results (POLARIS)
Methodology • Sampler code in SCALE was used in conjunction with different codes within SCALE to conduct sampling-based uncertainty quantification: 1. TRITON for pin-cell calculations 2. KENO-V.a and KENO-V.I for pin-cell calculations 3. Polaris for lattice calculations Main Code Input
Model Input
Nuclear Data with Uncertainty
Output
ENDF/B-VII – Sample 1
β1, λ1
ENDF/B-VII – Sample 2
β2, λ2
ENDF/B-VII – Sample 3
SAMPLER
TRITON or POLARIS
β3, λ3
β ± σβ , λ ± σλ βN, λN
ENDF/B-VII – Sample N
Problem Statements
Test Models • Typical PWR pin-cell and lattice were selected from Uncertainty Analysis in Modeling Benchmark [2].
Results Summary
Results Pin Cell Results (TRITON & KENO-V.a/KENO-VI)
∗ ∑18 𝜒718 𝜑18 × ∗ ∑18 𝜒 18 𝜑18
2. k-ratio:
𝑘> 𝛽"## ≅ 1 − 𝑘 • For decay constant: ∑, 𝜆',, 𝛽',, ∑0 ∑1 𝜈𝛴#,,0,1 𝜑0,1 𝑉0 𝜆' = ,,0,1 𝛽' ∑, ∑0 ∑1 𝜈𝛴# 𝜑0,1 𝑉0 where i, is the precursor group, j is the nuclide in each precursor group, m is the cell node, and g refers to the energy group indices.
Results (Cont.)
Materials and Methods
Group
Delayed Neutron Fraction (𝜷)
𝑫𝒆𝒄𝒂𝒚 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 (λ)
1
2.118 ×10RS ± 8.747×10R( (4%)
1.249 ×10RY ± 1.928×10RZ (0.1%)
2
1.412 ×10R[ ± 7.421×10RZ (5%)
3.080 ×10RY ± 5.590×10RZ (0.2%)
3
1.295 ×10R[ ± 8.129×10RZ (6%)
1.145 ×10R* ± 1.361×10R[ (1%)
4
2.689 ×10R[ ± 1.887×10RS (7%)
3.093 ×10R* ± 3.121×10R[ (1%)
5
8.880 ×10RS ± 1.022×10RS (11%)
1.232 ± 2.020×10RY (2%)
6
2.985 ×10RS ± 3.411×10RZ (11%)
3.289 ± 8.213×10RY (3%)
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒
6.795 ×10R[ ± 4.844×10RS (7%)
8.119 ×10RY ± 2.038×10R[ (3%)
Conclusions • This study found that fundamental nuclear data libraries contributed significantly to kinetic parameters’ uncertainties. • Uncertainties were 4-11% for the delayed neutron precursor fractions and 0.13% for delayed neutron precursor decay constants. • It should be noted that this study did not include the direct impact of uncertainty in nuclide-dependent precursor data on the six-group formulation. • Future work should add uncertainty of nuclide-dependent precursor data to Sampler’s nuclear data uncertainty library and give users the ability to easily perform kinetics’ parameter uncertainty propagation.
References [1] Keepin, G. R. et al., (1957). “Delayed neutrons from fissionable isotopes of uranium, plutonium and thorium.” Journal of Nuclear Energy, 6, pp. 1-21. [2] Ivanov, K. et al., (2013). “Benchmark for uncertainty analysis in modeling (UAM) for design, operation and safety analysis of LWRs,” Vol. 1. OECD Nuclear Energy Agency.
