Advanced Reactors

and Fuel Cycles

Simulation of Multiple Physics

at Disparate Scales


Kathryn (Katy) Huff

THW Software Carpentry book NCSA Logo cyclus pyrk pyne Moltres ARFC Logo

Insights at Disparate Scales

synergistic insights
science is people
Fission.
Chain reaction

\[\phi(E,\vec{r},\hat{\Omega},T)\]

\[\phi(E, x, y, z, \theta, \omega, T)\]

Fission.

\[\sigma(x, i, E, T)\]

Fission yield

\[\gamma(f, i)\]

Nucleus Stability

\[i\]

Resonances

\[E\]

Nucleus Stability

nuclear structure

Evaluated Nuclear Data Sets

Nuclear Resonance Theory and Evaluation

\[\sigma(x, i, E, T)=\] nuclear structure + experiments

Experiments

Schematic of a DANCE-like detector

Experiments

The DANCE detector at Los Alamos

Nuclear Data is for Simulations

PBFHR

Simulation Methods

  • Monte Carlo Methods
  • Deterministic Methods
  • Hybrid Methods
  • Other keywords...
    • lattice codes
    • ray tracing algorithms
    • acceleration schemes
    • adjoint methods
    • ...

Application Specific Data Processing

  • Energy discretization
    • multigroup
    • pointwise
    • piecewise linear continuous
  • Angular quadratures
  • Resonance integration
  • ...

Molten Salt Reactor Designs

MSR

MSBR Full Core Simulation

MSBR

(Robertson, 1979)

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

Reactor Kinetics

Fission.

\[\sigma(E,\vec{r},\hat{\Omega},T,x,i)\]

Chain reaction

\[k=1\]

Reactivity

\[ \begin{align} k &= \mbox{"neutron multiplication factor"}\\ &= \frac{\mbox{neutrons causing fission}}{\mbox{neutrons produced by fission}}\\ \rho &= \frac{k-1}{k}\\ \rho &= \mbox{reactivity}\\ \end{align} \]
Feedback
Delayed Neutrons

\[\beta_i, \lambda_{d,i}\]

Point Reactor Kinetics

\[ \begin{align} p &= \mbox{ reactor power }\\ \rho(t,&T_{fuel},T_{cool},T_{mod}, T_{refl}) = \mbox{ reactivity}\\ \beta &= \mbox{ fraction of neutrons that are delayed}\\ \beta_j &= \mbox{ fraction of delayed neutrons from precursor group j}\\ \zeta_j &= \mbox{ concentration of precursors of group j}\\ \lambda_{d,j} &= \mbox{ decay constant of precursor group j}\\ \Lambda &= \mbox{ mean generation time }\\ \omega_k &= \mbox{ decay heat from FP group k}\\ \kappa_k &= \mbox{ heat per fission for decay FP group k}\\ \lambda_{FP,k} &= \mbox{ decay constant for decay FP group k}\\ T_i &= \mbox{ temperature of component i} \end{align} \]
\[ \frac{d}{dt}\left[ \begin{array}{c} p\\ \zeta_1\\ .\\ \zeta_j\\ .\\ \zeta_J\\ \omega_1\\ .\\ \omega_k\\ .\\ \omega_K\\ T_{i}\\ .\\ T_{I}\\ \end{array} \right] = \left[ \begin{array}{ c } \frac{\rho(t,T_{i},\cdots)-\beta}{\Lambda}p + \displaystyle\sum^{j=J}_{j=1}\lambda_{d,j}\zeta_j\\ \frac{\beta_1}{\Lambda} p - \lambda_{d,1}\zeta_1\\ .\\ \frac{\beta_j}{\Lambda}p-\lambda_{d,j}\zeta_j\\ .\\ \frac{\beta_J}{\Lambda}p-\lambda_{d,J}\zeta_J\\ \kappa_1p - \lambda_{FP,1}\omega_1\\ .\\ \kappa_kp - \lambda_{FP,k}\omega_k\\ .\\ \kappa_{k p} - \lambda_{FP,k}\omega_{k}\\ f_{i}(p, C_{p,i}, T_{i}, \cdots)\\ .\\ f_{I}(p, C_{p,I}, T_{I}, \cdots)\\ \end{array} \right] \]
MOOSE

Coupled Multi-Physics Analysis


Using the MOOSE framework and its Jacobian-Free Newton Krylov solver, severe accident neutronics and thermal hydraulics can be simulated beautifully for simple geometries and well studied materials. (below, INL BISON work.)

from INL, Rich Williamson

Moltres: Dr. Alexander Lindsay

Moltres

Moltres Current Capabilities

  • Navier Stokes + Multi-Group Neutron Diffusion + Kinetics
  • arbitrary number of neutron energy groups
  • arbitrary number of delayed neutron precursor groups
  • neutron power coupled to salt temperature and flow
  • Precursor capability requires discontinuous galerkin upwind scheme.
  • Few group constants can be generated with SCALE-NEWT or Serpent

MSR Neutronics and TH Coupling

Moltres Base Case Moltres Base Case Moltres Base Case

MSR Precursors

Moltres Base Case Moltres Base Case

Insights at Disparate Scales

synergistic insights
image generated by Anthony Scopatz, Paul P.H. Wilson, and Katy Huff

A Nuclear Fuel Cycle Simulation Framework

The Nuclear Fuel Cycle

Hundreds of discrete facilities mine, mill, convert, fabricate, transmute, recycle, and store nuclear material.

from Paul Lisowski

Fuel Cycle Metrics

  • Mass Flow
    • inventories, decay heat, radiotoxicity,
    • proliferation resistance and physical protection (PRPP) indices.
  • Cost
    • levelized cost of electricity,
    • facility life cycle costs.
  • Economics
    • power production, facility deployments,
    • dynamic pricing and feedback.
  • Disruptions
    • reliability, safety,
    • system robustness.

Current Simulators

  • CAFCA (MIT)
  • COSI (CEA)
  • DANESS (ANL)
  • DESAE (Rosatom)
  • Evolcode (CIEMAT)
  • FAMILY (IAEA)
  • GENIUSv1 (INL)
  • GENIUS v2 (UW)
  • NFCSim (LANL)
  • NFCSS (IAEA)
  • NUWASTE (NWTRB)
  • ORION (NNL)
  • MARKAL (BNL)
  • VISION (INL)

State of the Art

Performance

  • Speed interactive time scales
  • Fidelity: detail commensurate with existing challenges
  • Detail: discrete material and agent tracking
  • Regional Modeling: enabling international socio-economics

Beyond the State of the Art

Access

  • Openness: for collaboration, validation, and code sustainability.
  • Usability: for a wide range of user sophistication

Extensibility

  • Modularity: core infrastructure independent of proprietary or sensitive data and models
  • Flexibility with a focus on robustness for myriad potential developer extensions.

Extensibility

framework

Openness

private, export controlled, etc.

Growing Ecosystem


a growing number of scientists are adding modules to cyclus.

...Well Beyond

Algorithmic Sophistication

  • Efficient: memory-efficient isotope tracking
  • Customizable: constrained fuel supply
  • Dynamic: isotopic-quality-based resource routing
  • Physics-based: fuel fungibility

Agent Based Systems Analysis

An agent-based simulation is made up of actors and communications between those actors.

from Paul Lisowski

Agent Based Systems Analysis

A facility might create material.

source

Agent Based Systems Analysis

It might request material.

sink

Agent Based Systems Analysis

It might do both.

fac

Agent Based Systems Analysis

Even simple fuel cycles have many independent agents.

material flow

Dynamic Resource Exchange

abm \[N_i \subset N\]

Dynamic Resource Exchange

abm \[N_j \subset N\]

Dynamic Resource Exchange

abm \[N_i \cup N_j = N\]

Feasibility vs. Optimization

polynomial hardness

If a decision problem is in NP-C, then the corresponding optimization problem is NP-hard.

Multi-Commodity Transportation Formulation

multicommoditiy transportation problem formulation multicommoditiy transportation problem formulation

Multi-Commodity Transportation Formulation


\[ \begin{align} \min_{x} z &= \sum_{i\in I}\sum_{j\in J} c_{i,j}x_{i,j} & \\ s.t & \sum_{i\in I_s}\sum_{j\in J} a_{i,j}^k x_{i,j} \le b_s^k & \forall k\in K_s, \forall s\in S\\ & \sum_{J\in J_r}\sum_{i\in I} a_{i,j}^k x_{i,j} \le b_r^k & \forall k\in K_r, \forall r\in R\\ & x_{i,j} \in [0,x_j] & \forall i\in I, \forall j\in J \end{align} \]

Dynamic Resource Exchange

modified open

Dynamic Resource Exchange

closed

Dynamic Resource Exchange


   
     mox
-    waste
+    spent_fuel
     mox_fresh_fuel
     mox_spent_fuel

Dynamic Resource Exchange

Plutonium buildup

Transition Analysis

  • LWR to SFR
  • $T_0 = 2015$
  • $T_f <= 2215$
  • $C_0 = 100$ GWe LWR
  • Annual nuclear energy demand growth: 1%
  • Legacy LWRs have either 60-year lifetimes or 80-year lifetimes.
  • Spent LWR fuel reprocessed to fabricate FR fuel
  • Spent FR fuel reprocessed to fabricate FR fuel

Transition Analysis

power deployed by reactor type.

Power generated by reactor type.

Transition Analysis

polynomial hardness

Capacity deployed each year, by reactor type.

Detailed Metrics

possible metrics

Material Attractiveness

possible metrics

How Do We Know It's Right?

Dangerous ladies, Jezebel and Godiva

The Data Dilemma

Morgan C. White talk

Links

THE END

Katy Huff

katyhuff.github.io/2017-02-02-cse
Creative Commons License
Advanced Reactors and Fuel Cycles: Simulation of Multiple Physics at Disparate Scales by Kathryn Huff is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://katyhuff.github.io/2017-02-02-cse.