1. Modeling MSRs in DYMOND
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20 min total
Bo Feng
Ed Hoffman
Florent Heidet
Fuel Cycle Systems Modeling
MSR Modeling and Simulation
Fuel Cycle Transition Analysis
MSR Modeling and Simulation
3rd Technical Workshop on Fuel Cycle Simulation
Paris, France, July 9-11, 2018

2. Overview Introduction DYMOND, System Dynamics Fast Chloride MSR Core
Modeling Methodology
Mass Flow Equations, Inputs
Results
Fuel Cycle Transition Results
Approximations, Future Work
State “the focus of this presentation is more on the fuel cycle modeling methodology rather than the results”

3. DyMOND A Dynamic Model of Nuclear Development DYMOND
Nuclear fuel cycle systems code (fleet-based) based on system dynamics (an approach to understanding the nonlinear behavior of complex systems over time using stocks, flows, internal feedback loops, table functions, and time delays)
DYMOND provides time-dependent mass flows and reactor/facility profiles for future deployment scenarios  identifies bottlenecks and resource shortages
System dynamics or fleet-based codes inherently model fuel loading and discharge at each time step (annual mass flow divided by time steps per year)  This approximation is actually more appropriate for MSRs that employ online refueling than for reactors with batches
Simplified Example

4. Code features and approximations
Dynamic Resource Allocation Model (DREAM) – Resource (e.g., Pu) allocation at each time-step based on user-assigned priority levels for each reactor type
Resource Prediction Model (optional) – Automated reactor construction based on prediction of future resource availability
Models energy shortage and unfueled reactors – if automation turned off
Can switch between different fuel types within same reactor type
Reprocessing throughput can be based on need or capacity
Currently, no direct isotopic tracking or decay (Pu vectors are implicitly tracked)
Lumped compositions (U, Pu, MA, FP) depend on accuracy of user-input charge/discharge fuel recipes
Code development philosophy: quick, clean, and simple
Don’t read everything here (no time), just focus on the first one and last one.

5. Running DYMOND Excel + Stella Architect
All input and output in Excel, model and programming in Stella Architect platform
Almost instant data import/export from Excel (user decides which outputs)
Run time = 10 seconds per century (1 month time steps on 3.4 GHz CPU)

6. molten salt reactors
One of Argonne’s activities for the U.S. Department of Energy was to investigate the differences in fuel cycle transition performance between different technologies (e.g., Sodium-cooled Fast Reactors versus Molten Salt Fast Reactors) operating in continuous U/TRU recycle mode.
Traditional MSRs are designed to have online fission product (FP) removal and online refueling with make-up materials
For the U/TRU continuous recycle fuel cycle, this implies virtually zero recycling time (versus several years for batch-wise fuel management used in SFRs)
However, since the fuel salt flows through not only the core, but also the heat removal and salt processing loops, additional fuel (heavy metal) inventory outside of the active core is required to start up each MSR
Fuel composition evolution is also very slow  many exciting challenges for fuel cycle systems modeling!

7. Fast Spectrum MSR Specific example to be modeled in DYMOND
Starting point was a design based on a fast spectrum MSR [1] using sodium and magnesium chlorides (40UCl3-35.1NaCl-24.9MgCl2) at 3.87 g/cm3 density
Reactor starts up with 15% enr. LEU (no Pu) and is refueled with NU to replace removed FPs
Equilibrium core model of fast MSR was developed using MCODE (MCNP + ORIGEN coupled depletion code) with fuel management script for “continuous” fuel loading and FP removal
Parameter
Value
Core Thermal Power, GWt
1.528
Core HM Mass, tHM
50.90
Core Radius, cm
163.5
Core Height, cm
300
Fuel Salt Volume (ignoring both holes), cm3
2.519E+07
Fuel Salt Mass, t
97.50
HM + FP Flow Rate, tIHM/s
2.32
Top and Bottom Hole Radius, cm 30
FP Removal Efficiency*, % 50
FP removal (U addition) per energy gen., tU/GWt-y
0.37
Refueling Rate (U mass per burnup), kgU/(MWd/kg) 52
Initial Core U Enrichment, wt% 15
Chlorine-37 Enrichment (nat. is 24 wt%), wt% 90
Isotope
First Core,
wt% (15% enr)
Reload Fuel,
wt% (NU)
Na-23
4.441%
Mg-24
2.631%
Mg-25
0.333%
Mg-26
0.366%
Cl-35
0.400%
Cl-37
39.558%
U-235
7.756%
0.372%
U-238
44.515%
51.899%
This is way too much detail, mention that all the specific details are here, but the main takeaway is that it’s a FAST spectrum MSR started up on 15% LEU and continuously refueled with NU only. No surplus Pu – breakeven breeding. 50% of all FPs are removed through each pass (major approximation)
[1] Heidet, Florent, Bo Feng, T.K. Kim, and Temitope Taiwo, “Transmutation Scoping Studies for a Chloride Molten Salt Reactor,” 14IEMPT, San Diego, CA, October (2016).

8. Fission Product Concentration
In a simplified case in which a fixed fraction of all fission products are removed during salt processing, the equilibrium concentration of fission products (CFP) in the salt can be easily calculated:
Pd is the power density, in GWth/tHM
Tc is the fuel residence time in the core, in days
FB is the fraction of fuel being bled
FFP is the fraction of fission products removed from the bled fuel
1.015x10-3 is the factor to convert burnup from GWd/t to %FIMA
This equation is derived based on setting FP generation rate = FP removal rate
Based on the salt bleed fraction (1E-5), FP removal efficiency (0.5), and fuel in- core residence time (22 seconds), the fast MSR has an equilibrium FP concentration of wt% of iHM
𝐶 𝐹𝑃 =1.015× 10 −3 × 𝑃 𝑑 × 𝑇 𝑐 × 1 𝐹 𝐵 × 𝐹 𝐹𝑃 −1

9. Mass Flow Equations
How DYMOND calculates mass flows for each reactor type
Annual Loading [tHM/y] = Core Power [GWt] x Capacity Factor x [d/y]
Burnup [GWt-d/tHM]
Core Mass [tHM] = Annual Loading [tHM/y] x Cycle Length [CY] x Batches
Annual refueling rate of 0.51 tHM/y was calculated based on core parameters and confirmed via MCODE assuming 100% fission product removal efficiency with equilibrium FP concentration of wt%
Plug into first equation  “burnup” of 987 MWd/kg (matches 100% FIMA)
This burnup is non-physical unless reactor has infinite lifetime, but it is a necessary input to calculate mass flows
Cycle length and batches are also non- physical, can use any combination to solve 2nd equation
Estimated core mass of tHM (incl. external loops) is 2X active core mass of tHM, so cycle length x batches must equal 200 to solve 2nd equation
Parameters
SFR
MSR
Core Power, GWt
1.000
1.528
Thermal Efficiency
40%
Capacity Factor
0.9
Cycle Length, CY
1.1560 1
Batches 4
200
Burnup, GWt-d/tHM
60.7
987
Core Mass, tHM
25.0
101.8
Annual Refueling Rate, tHM/y
5.4
0.51
Parameters
SFR
MSR
Core Power, GWt
1.000
1.528
Thermal Efficiency
40%
Capacity Factor
0.9
Cycle Length, CY
1.1560 ?
Batches 4
Burnup, GWt-d/tHM
60.7
Core Mass, tHM
25.0
101.8
Annual Refueling Rate, tHM/y
5.4
0.51

10. MSR BUrnup How is this defined for MSRs?
For continuously refueled MSRs, as time approaches infinity, the burnup is equal to 987 MWd/kg (100% FIMA)
After 60 years of operation (54 EFPY), the physical burnup for the example fast chloride MSR is 370 MWd/kg
However, only the non-physical (or infinite burnup) of 987 MWd/kg is used in the DYMOND input based on the mass flow equations

11. Transition simulations with DYMOND
Scenario Assumptions
Constant energy demand (no growth)
Existing 100 GWe of US LWRs retires at rate of 5 GWe/y from , are replaced by fast MSRs started on 15% enr. LEU with only NU feed
U/TRU is continuously recycled within each MSR while FPs are removed

12. ExamPLE Results (slide 1 of 2)
Note: based on very specific assumptions about technologies
Annual fuel loading
MSRs SFRs (7y recycle time)
For MSR transition, first 100 GWe are started up on LEU, second wave of 100 GWe (after 60y lifetime) are started up on recovered U/TRU from retired cores (core spawning)
For SFR transition, centralized reprocessing facility assumed (7y recycle time). Driver fuel is made of LEU until there is sufficient U/TRU recycled to replace it

13. ExamPLE Results (slide 2 of 2)
Note: based on very specific assumptions about technologies
Enrichment Requirements
MSRs SFRs (7y recycle time)
MSR transition requires 33% more cumulative SWU requirements (503 vs million kgSWU) and 40% more cumulative U mined (390,000 vs. 552,000 tU)
This is completely due to assumptions regarding total core HM mass (2X active core load may be too high), power density (30 W/gHM vs ~170 W/gHM), etc.

14. Verification of DYMOND results
External spreadsheet calculations were performed to verify cumulative results
Slight differences due to difficulty of using spreadsheet to model time delays (and changing time step sizes) in the fuel cycle mass flows
Running many parametric calculations with DYMOND and spreadsheets helped identify the key technology characteristics among MSRs and SFRs that determine fuel cycle transition performance (foreshadowing Ed’s talk!)

15. Summary
Reviewed approach for how MSRs can be modeled using system dynamics (fleet-based) codes such as DYMOND
Continuous refueling of MSRs is inherently represented by these codes
However, approximations required for various inputs (burnup, cycle length, batches)
Used calculated equilibrium FP concentration in external reactor physics codes (MCODE) to provide required enrichment (first core fuel recipe)
For the transition scenarios modeled, fuel isotopic evolution within the core did not need to be captured within DYMOND, but it may be important if surplus U/TRU or U/Pu were diverted to startup new MSRs
Acknowledgement: Funding for this activity was provided by the U.S. Department of Energy Office of Nuclear Energy’s Fuel Cycle Options Campaign

16. Thank you for your attention!

17. DYMOND INPUTS and OUTPUTS
Main Inputs
Initial fleet and retirement profile
Energy demand vs. time
10 Reactor types, 4 Fuel types per reactor
Charge/discharge compositions (U,Pu,MA,FP)
Fuel cycle facility properties
Reactor/facility deployment strategy
Time delays, process losses, etc.
Main Outputs
Time-dependent mass flows (mining, enrichment, fabrication, separations, etc.)
Energy generated
Deployed reactor and facility profiles
Reactor and facility throughputs
Inventories (DU/RU, Pu, UNF in storage, HLW…)
User can decide (just add a column in EXCEL)

18. MSR Fuel Evolution