Insights at Disparate Scales

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

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

$\sigma(x, i, E, T)$

$\gamma(f, i)$

$i$

$E$

nuclear structure

Evaluated Nuclear Data Sets

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

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
• ...

MSBR Full Core Simulation

(Robertson, 1979)

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

Reactor Kinetics

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

$k=1$

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}

$\beta_i, \lambda_{d,i}$

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}
$\frac{d}{dt}\left[ \begin{array}{c} p\\ \zeta_1\\ .\\ \zeta_j\\ .\\ \zeta_J\\ \omega_1\\ .\\ \omega_k\\ .\\ \omega_K\\ T_{i}\\ .\\ T_{I}\\ \end{array} \right] = \left[ \begin{array}{ c } \frac{\rho(t,T_{i},\cdots)-\beta}{\Lambda}p + \displaystyle\sum^{j=J}_{j=1}\lambda_{d,j}\zeta_j\\ \frac{\beta_1}{\Lambda} p - \lambda_{d,1}\zeta_1\\ .\\ \frac{\beta_j}{\Lambda}p-\lambda_{d,j}\zeta_j\\ .\\ \frac{\beta_J}{\Lambda}p-\lambda_{d,J}\zeta_J\\ \kappa_1p - \lambda_{FP,1}\omega_1\\ .\\ \kappa_kp - \lambda_{FP,k}\omega_k\\ .\\ \kappa_{k p} - \lambda_{FP,k}\omega_{k}\\ f_{i}(p, C_{p,i}, T_{i}, \cdots)\\ .\\ f_{I}(p, C_{p,I}, T_{I}, \cdots)\\ \end{array} \right]$

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.)

Moltres: Dr. Alexander Lindsay

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

The Nuclear Fuel Cycle

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

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.

...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.

Agent Based Systems Analysis

A facility might create material.

Agent Based Systems Analysis

It might request material.

Agent Based Systems Analysis

It might do both.

Agent Based Systems Analysis

Even simple fuel cycles have many independent agents.

Dynamic Resource Exchange

$N_i \subset N$

Dynamic Resource Exchange

$N_j \subset N$

Dynamic Resource Exchange

$N_i \cup N_j = N$

Feasibility vs. Optimization

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

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



mox
-    waste
+    spent_fuel
mox_fresh_fuel
mox_spent_fuel



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 generated by reactor type.

Transition Analysis

Capacity deployed each year, by reactor type.

THE END

Katy Huff

katyhuff.github.io/2017-02-02-cse

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.