Solving Advection Problems with Isotopic Evolution with SCALE/ORIGEN - Oak Ridge National Laboratory

Solving Advection Problems with Isotopic
 Evolution with SCALE/ORIGEN
 J.W. Bae
 B. Betzler
 W.Wieselquist

 Nuclear Energy and Fuel Cycle Division
 Oak Ridge National Laboratory
 SCALE Users’ Group Workshop
 August 4-6, 2021
ORNL is managed by UT-Battelle, LLC for the US Department of Energy

Two approaches for MSR simulation in SCALE
 • 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

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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 i Loss rate of nuclide i due Source of
 from decay and/or − to decay, irradiation, or + nuclide i
 irradiation of nuclide j other means (flow)

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Approach 1: TRITON-MSR
 Contributors: B. Betzler, K. Bekar, F. Bostelmann, W. A. Wieselquist, J. Powers, A. Worrall

 • 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 mix1  mix2
 – User specifies continuous removal rate
 233Pa concentration
 constant for Pa from mix 1 (core) to mix 2 (tank)
 , → • Th-based MSR unit cell
 – TRITON determines equivalent source for mix 2 model
 ≈ , → ( ) • Removal of Pa and Nd
 from irradiated mixture 1
 • Doing material transfer this way is stable as long as into initially empty
 , > 0 → > 0 mixtures 2 and 3

 • However, source is constant over a substep  users • Pa/Nd concentrations in
 must perform time step refinement study to ensure waste mixtures 2 and 3
 mass conservation reach equilibrium based
 on removal rate from
 mixture 1 and their decay
4
 rates

TRITON-MSR example

 Input Output Analysis
 • Define TRITON-NEWT 2D • Inventory of every “mixture” is • Outputs must be normalized
 model produced as a function of to provide total amount in
 • Define flow/removal rates time the system or relevant
 between “mixtures” • ORIGEN 1-group cross sections densities
 libraries for each “mixture” • Relate these trends in terms
 • New decay-only mixtures can of burnup or masses
 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
 MSBR

 233Pa concentration
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Approach 2: Follow a “slug” of fuel through the system
 Contributors: J.W. Bae, B. Betzler, W. A. Wieselquist
 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)

 • 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) ( ( )) = ( ) ( )
 Approximation of [138Xe] within the MSRE primary
 loop, showing generation within the core and
 removal in the pump

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

 • “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 Total delayed neutrons emitted for each flow rate
 perturbation
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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 Disadvantages
 Can provide more accurate isotope Does not adjust core flux with change in isotope
 concentrations, especially ex-core flows. (yet)
 Better tracking of in-core delayed neutron Must perform all substeps of depletion (can be
 precursors and signature isotopes 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

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