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Solving Advection Problems with Isotopic Evolution with SCALE/ORIGENJ.W. BaeB. BetzlerW.Wieselquist

Nuclear Energy and Fuel Cycle DivisionOak Ridge National Laboratory

SCALE Users’ Group Workshop

August 4-6, 2021

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• TRITON-MSR (new in SCALE 6.3 currently in beta)– Ability to account for flowing fuel materials in a liquid-fueled system

• Material feeds and removal with specific rates to and from depleted materials• Tracking of removed materials that are not irradiated

– Draws on reactor physics tools within the SCALE code system• Neutron transport and depletion• Strong quality assurance program

• ORIGEN (available in SCALE 6.2 from RSICC)– Investigate inventory throughout system following “slugs” of fuel– Uses standard ORIGEN input (with transformation from time length

coordinates) – Requires knowledge of core neutron spectrum cannot easily take into

account changes in inventory that greatly affect spectrum

Two approaches for MSR simulation in SCALE

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Challenges in depletion modeling and simulation• Consider reaction/advection on fixed-in-space volumes as ideal

starting point

• For NRC confirmatory analysis with SCALE, we are more interested in high-fidelity inventory than detailed flow characteristics

• Existing ORIGEN framework includes continuous feed & removal terms

Production of nuclide ifrom decay and/or irradiation of nuclide j

Source of nuclide i

Loss rate of nuclide i due to decay, irradiation, or other means (flow)

𝑑𝑑𝑁𝑁𝑖𝑖𝑑𝑑𝑡𝑡

= �𝑗𝑗≠𝑖𝑖

𝑀𝑀

𝑙𝑙𝑖𝑖𝑗𝑗𝜆𝜆𝑗𝑗 + 𝑓𝑓𝑖𝑖𝑗𝑗𝜎𝜎𝑖𝑖𝜙𝜙 𝑁𝑁𝑗𝑗(𝑡𝑡) − 𝜆𝜆𝑖𝑖 + �𝑘𝑘

𝑊𝑊

𝜆𝜆𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖𝑘𝑘 + 𝜎𝜎𝑖𝑖𝜙𝜙 𝑁𝑁𝑖𝑖 𝑡𝑡 + 𝑆𝑆𝑖𝑖(𝑡𝑡)

− +

𝑑𝑑𝑁𝑁(𝒙𝒙, 𝑡𝑡)𝑑𝑑𝑡𝑡

= 𝑨𝑨 𝒙𝒙, 𝑡𝑡 𝑁𝑁 𝒙𝒙, 𝑡𝑡 − 𝒖𝒖 𝒙𝒙, 𝑡𝑡 � 𝜵𝜵𝑁𝑁 𝒙𝒙, 𝑡𝑡 + 𝑺𝑺(𝒙𝒙, 𝑡𝑡)

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Approach 1: TRITON-MSR• Based on ChemTriton development for Molten Salt Reactors

Benjamin R. Betzler, Jeffrey J. Powers, Andrew Worrall, “Molten salt reactor neutronics and fuel cycle modeling and simulation with SCALE”, Annals of Nuclear Energy, Volume 101, (2017).

• Remove/add isotopes from/to material with user-specified rates

• Example for mix1mix2– User specifies continuous removal rate

constant for Pa from mix 1 (core) to mix 2 (tank)

– TRITON determines equivalent source for mix 2

• Doing material transfer this way is stable as long as𝜆𝜆𝑟𝑟𝑟𝑟𝑟𝑟,𝑖𝑖𝑘𝑘 > 0 → 𝑆𝑆𝑖𝑖 > 0

• However, source is constant over a substep users must perform time step refinement study to ensure mass conservation

233Pa concentration• Th-based MSR unit cell

model

• Removal of Pa and Nd from irradiated mixture 1 into initially empty mixtures 2 and 3

• Pa/Nd concentrations in waste mixtures 2 and 3 reach equilibrium based on removal rate from mixture 1 and their decay rates

Contributors: B. Betzler, K. Bekar, F. Bostelmann, W. A. Wieselquist, J. Powers, A. Worrall

𝑑𝑑𝑁𝑁𝑖𝑖𝑑𝑑𝑡𝑡

= �𝑗𝑗≠𝑖𝑖

𝑀𝑀

𝑙𝑙𝑖𝑖𝑗𝑗𝜆𝜆𝑗𝑗 + 𝑓𝑓𝑖𝑖𝑗𝑗𝜎𝜎𝑖𝑖𝜙𝜙 𝑁𝑁𝑗𝑗(𝑡𝑡) − 𝜆𝜆𝑖𝑖 + �𝑘𝑘

𝑊𝑊

𝜆𝜆𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟,𝑗𝑗𝑘𝑘 + 𝜎𝜎𝑖𝑖𝜙𝜙 𝑁𝑁𝑖𝑖 𝑡𝑡 + 𝑆𝑆𝑖𝑖(𝑡𝑡)

𝜆𝜆𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑖𝑖𝑚𝑚𝑚→𝑟𝑟𝑖𝑖𝑚𝑚𝑚

𝑆𝑆𝑖𝑖 𝑡𝑡 ≈ 𝜆𝜆𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑖𝑖𝑚𝑚𝑚→𝑟𝑟𝑖𝑖𝑚𝑚𝑚𝑁𝑁𝑖𝑖(𝑡𝑡)

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Input

• Define TRITON-NEWT 2D model

• Define flow/removal rates between “mixtures”

• New decay-only mixtures can be defined to represent out-of-core inventory, e.g. tanks

• Must scale down power to adjust for out-of-core salt in the main loop

Output

• Inventory of every “mixture” is produced as a function of time

• ORIGEN 1-group cross sections libraries for each “mixture”

Analysis

• Outputs must be normalized to provide total amount in the system or relevant densities

• Relate these trends in terms of burnup or masses

TRITON-MSR example

MSBR

233Pa concentration

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Approach 2: Follow a “slug” of fuel through the system

• Leverages standard SCALE/ORIGEN simulations

• Helps understand inventory and gamma emissions at various points in the salt loop

• Relies on recasting the equation

For a moving slug (no mixing/diffusion of slug)

𝑑𝑑𝑁𝑁(𝒙𝒙, 𝑡𝑡)𝑑𝑑𝑡𝑡 = 𝑨𝑨 𝒙𝒙, 𝑡𝑡 𝑁𝑁 𝒙𝒙, 𝑡𝑡 − 𝒖𝒖 𝒙𝒙, 𝑡𝑡 � 𝜵𝜵𝑁𝑁 𝒙𝒙, 𝑡𝑡 + 𝑺𝑺(𝒙𝒙, 𝑡𝑡)

Contributors: J.W. Bae, B. Betzler, W. A. Wieselquist

𝑑𝑑𝑁𝑁(𝒙𝒙(𝑡𝑡))𝑑𝑑𝑡𝑡 = 𝑨𝑨 𝒙𝒙(𝑡𝑡) 𝑁𝑁 𝒙𝒙(𝑡𝑡) Approximation of [138Xe] within the MSRE primary

loop, showing generation within the core and removal in the pump

Bae, J.W., Betzler, B.R., Wieselquist, W.A., n.d. Characteristic Solutions for Advection Problems with Isotopic Evolution with SCALE/ORIGEN, in: 04/11/2021. Presented at the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering 2021 (M&C 2021), Raleigh, NC. (Accepted)

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Approach 2 (ORIGEN “slug flow”) versus Approach 1 (TRITON-MSR)

Total delayed neutrons emitted for each flow rate perturbation

• “Non-scaled” result is an assumption that most impacts short-lived radionuclides (assumes power generated throughout the flow loop)

• “scaled” result uses TRITON-MSR and generates a reasonable average

• Slug flow model results at different flow speeds

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Flow Rate Perturbation• The equilibrium maximum value has a linear relationship with flow rate • Isotopes with shorter half lives (e.g., 135Te) are more severely affected

by flow rate

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Advantages vs. Disadvantages of Approach 2

Advantages DisadvantagesCan provide more accurate isotope concentrations, especially ex-core flows.

Does not adjust core flux with change in isotope (yet)

Better tracking of in-core delayed neutron precursors and signature isotopes

Must perform all substeps of depletion (can be alleviated with hybrid method)

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Conclusions

• Slug flow method can model equilibrium isotope flow pattern in an MSR– Fluctuations of short-lived fission products

• Ex-core signatures for safeguards• Delayed neutron precursor drift• Sensitive to flow rate

– Drawbacks• Time-consuming• Can be mitigated with hybrid method