FESTIM and HTM: leading open-source hydrogen transport modelling

Remi Delaporte-Mathurin, MIT, USA

James Dark, CEA, France

Thomas Fuerst, INL, USA

FESTIM & HTM contributors

AMPMI 2024, Helsinki, Finland

H transport in materials (oversimplified)

\frac{\partial c_\mathrm{m}}{\partial t} = \nabla \cdot (D \nabla c_\mathrm{m}) - \sum \frac{\partial c_{\mathrm{t}, i}}{\partial t}

\frac{\partial c_{\mathrm{t}, i}}{\partial t} = k \ c_\mathrm{m} \ (n - c_{\mathrm{t}, i}) - p \ c_{\mathrm{t}, i}

Example: McNabb & Foster model

H transport in materials (oversimplified)

\frac{\partial c_\mathrm{m}}{\partial t} = \nabla \cdot (\textcolor{f3d7ac}{D} \nabla c_\mathrm{m}) - \sum \frac{\partial c_{\mathrm{t}, i}}{\partial t}

\frac{\partial c_{\mathrm{t}, i}}{\partial t} = \textcolor{f3d7ac}{k} \ c_\mathrm{m} \ (n - c_{\mathrm{t}, i}) - \textcolor{f3d7ac}{p} \ c_{\mathrm{t}, i}

X = X_0 \ \exp{\left(\frac{-E_X}{k_B \ T}\right)}

We need to solve this

We need to know this

Arrhenius law

Survey time! 🙋

Do you use open-source software for your research?

Two examples: HTM and FESTIM

The issues of

closed-source software

Lack of transparency

Duplication of work

Slow development

Reproducibility

Solution: open-source

Difficult to share

Example 1

HTM: a database for hydrogen transport properties

Motivation: literature reviews of H transport properties are unreliable

From

2020

review

Original paper

Review #1

Review #2

(citing #1)

13.1

11.7

Motivation

Even trusted organisations like ITER can make mistakes

Motivation

Making mistakes in review:

very easy

Catching them during peer-review: almost impossible

HTM is the solution to these pitfalls

Conversion errors

Automated unit conversion

Wrong references

Bibtex integration

Error propagation from other reviews

Only data from original papers

Fitting errors

Automated fitting

Open-source

Permanent errors in paper

Obsolete reviews

Lack of transparency

Easy access to 400+ properties

import h_transport_materials as htm

# filter only tungsten and H
diffusivities = htm.diffusivities.filter(
  material="tungsten", isotope="h")

htm.plotting.plot(diffusivities)

import matplotlib.pyplot as plt

plt.yscale("log")
plt.title("Tungsten diffusivity")

Filter by:

author
year
material
isotope
temp. range
...

Properties

diffusivity
solubility
permeability
recombination coeff.
dissociation coeff.

HTM is growing

45+ materials

160 references

438 properties

Current version v0.16

HTM is transparent

import h_transport_materials as htm
from h_transport_materials import Diffusivity, Solubility

u = htm.ureg

causey_diffusivity = Diffusivity(
    D_0=0.93e-4 * u.m**2 * u.s**-1,
    E_D=2.8 * u.eV * u.particle**-1,
    range=(900 * u.K, 1473 * u.K),
    source="causey_interaction_1989",
    isotope="H",
)

atsumi_diffusivity = Diffusivity(
    D_0=1.69 * u.cm**2 * u.s**-1,
    E_D=251 * u.kJ * u.mol**-1,
    range=(500 * u.degC, 900 * u.degC),
    isotope="D",
    source="atsumi_absorption_1988",
    note="Equation 5 of Atsumi's paper",
)

atsumi_solubility = Solubility(
    S_0=1.9e-1 * u.mol * u.m**-3 * u.Pa**-0.5,
    E_S=-19.2 * u.kJ * u.mol**-1,
  	range=(850 * u.degC, 1050 * u.degC),
    source="atsumi_absorption_1988",
    isotope="H",
)

properties = [causey_diffusivity, atsumi_diffusivity, atsumi_solubility]

for prop in properties:
    prop.material = htm.CARBON

htm.database += properties

Integration with BibTex for easy reference
Automatic unit conversion with Pint under the hood
Additional notes

github.com/remdelaportemathurin/h-transport-materials

Example HTM source file

HTM simplifies writing papers

import h_transport_materials as htm

htm.diffusivities
	.filter(material="tungsten")
  	.to_latex_table()

Use HTM to generate LaTeX tables

Allergic to code? We have a Web app

https://htm-dashboard-uan5l4xr6a-od.a.run.app/

Don't want to/can't use python?

The database is compiled to JSON at each release

github.com/RemDelaporteMathurin/h-transport-materials/releases/download/v0.16.1/database.json

HTM

MOOSE

COMSOL

Experimental analysis

FESTIM

HTM can be easily integrated

Material properties

Example 2

FESTIM: a powerful and accessible H transport code

github.com/festim-dev/FESTIM

User inputs

Material properties
Trap properties
Geometry
Boundary conditions
Initial conditions
...

Heat transfer model

Hydrogen transport model

McNabb & Foster
Multi-level trapping
Multi-isotopes
...

FESTIM

Outputs

H concentration fields \(c(x,t)\)
Temperature field \(T(x,t)\)

surface fluxes
inventories
average concentration
...

User inputs

Material properties
Trap properties
Geometry
Boundary conditions
Initial conditions
...

Heat transfer model

Hydrogen transport model

McNabb & Foster
Multi-level trapping
Multi-isotopes
...

FESTIM

Outputs

H concentration fields \(c(x,t)\)
Temperature field \(T(x,t)\)

surface fluxes
inventories
average concentration
...

FEniCS

Available H transport models in FESTIM

\frac{\partial c_\mathrm{m}}{\partial t} = \nabla \cdot (D \nabla c_\mathrm{m}) - \frac{\partial c_{\mathrm{t}, i}}{\partial t}

\frac{\partial c_{\mathrm{t}, i}}{\partial t} = k \ c_\mathrm{m} \ (n - c_{\mathrm{t}, i}) - p \ c_{\mathrm{t}, i}

McNabb & Foster

Multi-occupancy trapping

Multi-isotope transport

Pick & Sonnenberg

\dfrac{d c_{\mathrm{s}}}{dt} = J_{\mathrm{bs}} - J_{\mathrm{sb}} + J_{\mathrm{vs}}

-D \nabla c_\mathrm{m} \cdot \mathbf{n} = -\lambda_{\mathrm{IS}} \dfrac{\partial c_{\mathrm{m}}}{\partial t} - J_{\mathrm{bs}} + J_{\mathrm{sb}}

\frac{\partial c_\mathrm{H}}{\partial t} = \nabla \cdot (D_\mathrm{H} \nabla c_\mathrm{H}) + ...

\frac{\partial c_\mathrm{D}}{\partial t} = \nabla \cdot (D_\mathrm{D} \nabla c_\mathrm{D}) + ...

\mathrm{H} + [\ \ \ \ ]_\mathrm{trap} \ \substack{p_1 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_1} \ [\mathrm{H}_1]_\mathrm{trap}

\mathrm{H} + [\mathrm{H}_1]_\mathrm{trap} \ \substack{p_2 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_2} \ [\mathrm{H}_2]_\mathrm{trap}

\mathrm{H} + [\mathrm{H}_2]_\mathrm{trap} \ \substack{p_3 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_3} \ [\mathrm{H}_3]_\mathrm{trap}

History of FESTIM

2022

2019

Start of development

Open-source

Oct 2023

v1.0 release

2024

Check it out on Github

github.com/festim-dev/FESTIM

FESTIM is user-friendly

python-based
very easy to learn
plenty of libraries: numpy, scipy, matplotlib, HTM...
intuitive interface

conda install -c conda-forge fenics
pip install festim

Easy install

import festim as F
import numpy as np

my_model = F.Simulation()

my_model.mesh = F.MeshFromVertices(
    vertices=np.linspace(0, 1e-6, num=1001)
)

my_model.materials = F.Material(id=1, D_0=1.9e-7, E_D=0.2)

my_model.T = 500  # K

my_model.boundary_conditions = [
    F.DirichletBC(
        surfaces=[1, 2],
        value=1e15,  # H/m3/s
        field=0
        )
]

my_model.settings = F.Settings(
    absolute_tolerance=1e10,
    relative_tolerance=1e-10,
    final_time=100  # s
    )


my_model.dt = F.Stepsize(0.1)  # s

my_model.initialise()

my_model.run()

FESTIM is verified & validated

Validated against TDS, permeation experiments...
Verified against analytical solutions in many different problems
New V&V online book
festim-vv-report.readthedocs.io

📈5 years of development

📑13+ publications

🗣️110+ citations

🧑‍💻16+ contributors

🏛️25+ institutions using the code

🧑‍💻30+ Slack members

⭐80+ stars on GitHub

3 workshops

FESTIM in numbers

Evolution of GitHub stars

Open source

SOFE workshop

New reference paper

FESTIM is used worldwide

8 private companies

10 universities

16 research organisations

Neutron-induced damage and tritium trapping

Dynamic evolution of trap densities including annealing
\(\dot{n} = \Phi \ K (1-\frac{n}{n_\mathrm{max}}) - A \ n \)
Parametrised on TDS data from IPP Garching

James Dark et al 2024 Nucl. Fusion 64 086026

Influence of ELMs on retention

1D ITER monoblock model
Coupled transient heat transfer
Varying surface heat flux

Kulagin, V., & Gasparyan, Y. Numerical Simulation of deuterium retention in tungsten under ELM-like conditions. J. Nucl. Mater. (under revision)

Retention studies

Delaporte-Mathurin et al 2024 International Journal of Hydrogen Energy 63 786–802
Delaporte-Mathurin et al 2024 Nucl. Fusion 64 026003

ITER plasma facing components
Transient estimation of tritium retention

Detritiation studies

Delaporte-Mathurin et al 2024 Nucl. Fusion 64 026003

Breeding Blanket modelling

DEMO WCLL
Complex 3D geometry
Coupled to fluid dynamics
Tritium generation in the LiPb volume (computed from OpenMC)

James Dark et al 2021 Nucl. Fusion 61 116076

Tritium extraction system

courtesy of K. Dunnell (MIT)

Permeation Against Vacuum
Complex 3D geometry
Coupled with fluid dynamics
Tritium extraction from permeable membranes

Tritium extraction system

courtesy of K. Dunnell (MIT)

BABY breeding experiment

Velocity

Temperature

Tritium concentration

Metal Foil Pumps for DIR

H is implanted in the first \( 10 \ \mathrm{nm} \)
Super-permeation regime is attained at high recombination energy (upstream surface)
Source code

Benedikt & Day, (2017) Fusion Engineering and Design

Isotope swapping

Multi-isotope, multi-level trapping

7 different species
6 reactions
\( c_H = 10^{20} \ \mathrm{m^{-3}} \) on the left
\( c_D = 10^{19} \ \mathrm{m^{-3}} \) on the right
Source code available here

Spherical cavity trapping

see Zibrov and Schmid, NME, 2024

for complete description

Implementation in FESTIM of the spherical cavity trapping model developed by Zibrov and Schmid
Custom trapping equations
Smooth implementation in FESTIM

Anisotropy

Anisotropic materials can be simulated with very few modifications

D = \begin{bmatrix} D_{xx} & 0\\ 0 & D_{yy} \end{bmatrix}

Other applications

PAV Tritium Extraction System

TDS

PFC

Breeding blankets

No barrier

Barrier

Permeation barriers

Surface kinetics analysis

Community & Collaboration

Why we should all go open-source

AMPMI website: "The meeting fosters global collaboration for fusion R&D in the public and private sectors"

Collaborative environment

External contributions:
- FESTIM: boundary conditions (PoliTo), post-processing (CEA), chemical reactions (Digilab), kinetic surface model (MEPhI), documentation and bug fixes...
- HTM: database contributions (INL), fixes (IAEA)...
Transparency
User support & community: Discourse forum, Slack workspace

Open-source improves collaboration

www.festim.discourse.group

Open-source improves collaboration

Cross-institution work

Removes barrier to access to software
Avoid work duplication

Accelerates Development and Innovation

Continuous distribution
Rapid growth
Reduced loss of technical knowledge

FESTIM community

Evolution of HTM properties

Anyone can make a copy of the repository and make changes there
Changes are reviewed by official maintainers via pull-requests
~500 tests are run automatically
Changes are only merged when all the tests pass ✅

fork

pull request

FESTIM

Jane

FESTIM

John

FESTIM

festim-dev

pull request

Open-source improves software quality

✅

❌

Open-source improves documentation

FESTIM (available at festim.readthedocs.io)

HTM (available at h-transport-materials.readthedocs.io)

Installation instructions
User guide
Contribution guide
Tutorials
Theory background
API reference

✅Open-source is:

a successful model for hydrogen transport modelling benefiting the whole community
Other relevant projects: OpenMC, TMAP8, Xolotl, Paramak, LAMMPS, QE...

Take-aways

github.com/festim-dev/FESTIM

github.com/remdelaportemathurin/h-transport-materials

❌Open-source is not:

only code: documentation, community, testing
a silver bullet: releasing the code isn't enough
unidirectional: needs to be a win-win

⭐What open-source needs for fusion:

Sustained support from institutions
Appropriate training and awareness
Recognition for contributors