The safety of Deep Geological Repositories (DGR) for spent nuclear fuel is a highly important issue, and should be assessed using the Best Available Technology (BAT). With this motivation in mind, Amphos 21 has recently developed a numerical tool, denoted as iDP (interface between DarcyTools and PFLOTRAN; Molinero et al., 2016), which provides aJuqueen unique High Performance Computing(HPC)-based framework for the simulation of multicomponent reactive transport problems in fractured crystalline media. iDP combines two powerful state-of-the-art software: DarcyTools (Svensson and Ferry, 2014), which is used to compute groundwater flow in sparsely fractured rocks using a stochastic continuum approach, and the massively parallel reactive transport code PFLOTRAN (Hammond and Lichtner, 2010). iDP has been tested during the JUQUEEN Extreme Scaling Workshop 2016 (Brömmel et al., 2016) showing excellent scalability up to 131,072 processes (8 racks).

<figure className="image">
  <StrapiImage  src="/uploads/HPC_Blog_Post_1_c4a1155a9d.png" alt=""/>
  <figcaption> </figcaption>
</figure>

<div className="grid grid-cols-5 gap-4">
  <div className="col-span-2">
    <StrapiImage  className="" src="/uploads/HPC_Blog_Post_2_9212e50e5d.jpg"/>
</div>

  <div className="col-span-3">
In cooperation with the Forschungszentrum Jülich and the Swedish Nuclear Fuel and Waste Management Company (SKB), Amphos 21 has used iDP to carry out two challenging reactive transport simulations. The first set of calculations has focused on evaluating the potential ingress of oxygenated glacial-meltwater into initially anoxic fractured media. This is an issue of concern for the safety of deep geological Pocos de Caldasrepositories for spent nuclear fuel as oxidizing conditions would increase the solubility and mobility of many radionuclides and O2-rich waters would corrode canister materials containing the nuclear waste.
</div>
</div>

<div className="grid grid-cols-7 gap-4">

  <div className="col-span-5">
The reactive transport models have pointed out the strong buffering capacity of a typical crystalline medium (e.g. Forsmark in Sweden), with the infiltration of oxygen being limited to few highly transmissive deformation zones. These findings are in agreement with data from the natural analogue site of Poços de Caldas (Brazil) (Nordstrom et al., 1992). For more details about these reactive transport simulations, the reader is referred to a paper recently published in Journal of Contaminant Hydrology (Trinchero et al, 2017a).
</div>
  <div className="col-span-2">
    <StrapiImage  className="" src="/uploads/HPC_Blog_Post_4_7e2c2e6e88.jpg"/>
</div>
</div>



Another important issue for the safety of a DGR is related to the potential of the host rock to retain those radionuclides that are released due to a possible failure of the engineered barriers.Total CS This potential, in turn, depends on two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces of the available reactive minerals. A typical modelling assumption is to use an equivalent (homogeneous) description of sorption sites. This assumption is here assessed using a very detailed micro-scale model of the rock matrix, which is built upon a numerical grid consisting of more than 50 million elements. The results of the calculations, in which the distribution of sorption sites is described at the grain scale, show that mineralogical heterogeneity has a significant impact on the retention of radionuclides, namely cesium. Not considering that sorption sites are sparse and unevenly distributed results in an important overestimation of the rock retention capacity. Further details can be found in a paper recently published in Transport in Porous Media (Trinchero et al., 2017b).

<figure className="image">
  <StrapiImage  src="/uploads/HPC_Blog_Post_5_7a7da1df76.png" alt=""/>
  <figcaption> </figcaption>
</figure>


Acknowledgement
==============
This work has been funded by the Swedish Nuclear Fuel and Waste Management Company (SKB). The authors gratefully acknowledge the computing time granted by the JARA-HPC Vergabegremium and provided on the JARA-HPC Partition part of the supercomputer JUQUEEN at Forschungszentrum Jülich. The authors also thank Ignasi Puigdomenech, Björn Gylling, Guido Deissmann, Urban Svensson, Glenn Hammond, Peter Lichtner and the PFLOTRAN development group for their help and valuable suggestions during the project.

References
=========
*Brömmel, D., Wylie, B. J., Frings, W.*, 2016.** JUQUEEN extreme scaling workshop 2016. **Tech. Rep. FZJ-JSC-IB-2016-01, Jülich Supercomputing Centre.

*Hammond, G. E., Lichtner, P. C.*, 2010. **Field-scale model for the natural attenuation of uranium at the Hanford 300 area using high-performance computing. **Water Resources Research 46 (9), W09527, 131.

*Molinero, J., Trinchero, P., Ebrahimi, H., de Vries, L., Luna, M., Svensson, U., Lichtner, P. *2016. **The BRIDGE project: development, testing and application of a High Performance Computing framework for reactive transport modelling in crystalline roks (iDP)**. R-15-17, Svensk Kärnbränslehantering AB, Stockholm, Sweden.

*Nordstrom, D., McNutt, R., Puigdomènech, I., Smellie, J. A., Wolf, M. *1992. **Ground water chemistry and geochemical modeling of water-rock interactions at the Osamu Utsumi mine and the Morro do Ferro analogue study sites,** Poços de Caldas, Minas Gerais, Brazil. Journal of Geochemical Exploration 45 (1-3), 249-287

*Svensson, U., Ferry, M., *2014. **Darcytools: A computer code for hydrogeological analysis of nuclear waste repositories in fractured rock. **Journal of Applied Mathematics and Physics 2 (06), 365.

*Trinchero, P., Molinero, J., Deissmann, G., Svensson, U., Gylling, B., Ebrahimi, H., Hammond, G., Bosbach, D., Puigdomenech, I.*, 2017b.** Implications of grain-scale mineralogical heterogeneity for radionuclide transport in fractured media.** Transport in Porous Media 116: 73. doi:10.1007/s11242-016-0765-0

*Trinchero, P., Puigdomenech, I., Molinero, J., Ebrahimi, H., Gylling, B., Svensson, U., Bosbach, D., Deissmann, G.*, 2017a. **Continuum-based DFN-consistent numerical framework for the simulation of oxygen infiltration into fractured crystalline rocks. **Journal of Contaminant Hydrology DOI: 10.1016/j.jconhyd.2017.04.001

large_HPC_BlogPost_1.png

medium_HPC_BlogPost_1.png

small_HPC_BlogPost_1.png

thumbnail_HPC_BlogPost_1.png

HPC_BlogPost_1.png

The safety of Deep Geological Repositories (DGR) for spent nuclear fuel is a highly important issue, and should be assessed using the Best Available Technology (BAT)

High Performance Computing as a prognostic tool for Deep Geological Repositories for spent nuclear fuel

Introduction
==========
PFLOTRAN is an open source subsurface flow and reactive transport code. It is capable of simulating many of the processes the affect flow and transport in porous media.

MARFA, on the other hand, is a code that simulates radionuclide transport in porous media. It uses a Monte Carlo algorithm to represent several processes, such as decay, longitudinal dispersion, diffusion into a rock matrix or equilibrium sorption. These processes are applied to particles, which represent packets of radionuclide mass. In the MARFA Static Path (MARFA-SP) version, transport is simulated in a fixed set of trajectories, with known parameters.

It is easy to see that some models can be computed in both PFLOTRAN and MARFA. While PFLOTRAN is more flexible, MARFA’s Monte Carlo algorithm is very efficient, due to it using solutions that have been precomputed and stored in lookup tables. Therefore, it would be interesting to compare the two codes. In this article, a model is run in both PFLOTRAN and MARFA, and its results and execution time are studied.

Model setup
=========
The model is a simple straight fracture, with groundwater flow and a limited rock matrix on top. The size and parameters of this model are taken from (Iraola et al., 2019).
The rock matrix could be modeled explicitly in PFLOTRAN by dividing the model in two sections. The bottom section would be the fracture and the top section would be the matrix. However, the performance is much better if we use PFLOTRAN’s multiple continuum capability. The multiple continuum method takes advantage of the fact that equations in the matrix are 1-dimensional to introduce several powerful optimizations.


Instant vs constant injections
----------------------------------
In MARFA, (permanent) constant injection is not possible. The reason is that the code simulates particles until they reach the end of the model. If new particles were always released, there would never be a “final time”. Therefore, instant injection will be used. In other words, the source function will be a Dirac delta function centered at t=0.

$$
\dot{m}_{in}\left(t\right)=m_{0}\delta(t)
$$

Where $\dot{m}_{in}$ is the mass rate at the inlet and $m_0$ is the total mass that is injected in the model. For simplicity, we will set $m_0=1\ mol$.

The same Dirac delta function could be applied to the PFLOTRAN model. However, PFLOTRAN shows high numerical dispersion for source functions with high discontinuities, such as the Dirac delta injection. Therefore, constant injection will be used for PFLOTRAN.

Although it may seem that this prevents comparison to the MARFA model, we can use the fact that the instantaneous mass breakthrough when using constant injection is proportional to the cumulative mass breakthrough when using Dirac delta injection. One way to see this is by using the solution from (Sudicky and Frind, 1982) for a fracture model with retention in finite matrix. In Laplace space, if we use a Dirac delta injection:

$$
\bar{\dot{m}}_{Dirac}\left(s\right)=\bar{{\dot{m}}_{in}}\left(s\right)\bar{f_{ret}}\left(s\right)=m_0\bar{f_{ret}}\left(s\right)
$$

Where $\bar{f_{ret}} \left(s\right)$ is the retention time function, 
$\bar{\dot{m}}_{Dirac}\left(s\right)$ is the breakthrough mass rate and $s$ is the Laplace variable. If we look at the cumulative breakthrough:

$$
m\left(t\right)=\int_{0}^{t}{\dot{m}\left(\widetilde{t}\right)}d\widetilde{t}
$$

An integral in Laplace space becomes a division by $s$, so:

$$
{\bar{m}}_{Dirac}\left(t\right)=\frac{\bar{{\dot{m}}_{in}}\left(s\right)}{s}=\frac{m_0}{s}\bar{f_{ret}}\left(s\right)
$$

While, if we instead used a constant injection ${\dot{m}}_{in}\left(t\right)={\dot{m}}_0H(t)$, where $H(t)$ is the Heaviside step function and {\dot{m}}_0 the mass rate at the inlet, the instantaneous breakthrough is:

$$
{\bar{\dot{m}}}_{const}\left(s\right)=\bar{{\dot{m}}_{in}}\left(s\right)\cdot\bar{f_{ret}}\left(s\right)=\frac{{\dot{m}}_0}{s}\bar{f_{ret}}\left(s\right)
$$

By comparing the two previous equations, we conclude that $m_{Dirac}$ and ${\dot{m}}_{const}$ are proportional to one another.

Low vs high velocity
------------------------
In the model from (Iraola et al., 2019), groundwater velocity is set to $7.6\cdot{10}^{-7}\frac{m}{s}$. Due to the relatively high velocity and the rest of parameters used in the model, matrix retention is relatively small. Therefore, another model will be run as well, using a velocity value of $7.6\cdot{10}^{-8}\frac{m}{s}$, which is 10 times lower.
The high velocity PFLOTRAN model was run up to 20 days in the paper. However, this is not sufficient for the low velocity case. In that case, the model was run up to 500 days. The timestep size was increased, in order to minimize the execution time.

Results
======
Execution time
------------------
Both codes were run in an Ubuntu version 20.04 virtual machine.

MARFA is not a parallel code; in other words, it always uses a single CPU. In order to compare the execution time, PFLOTRAN was run with only one CPU as well, so that the same amount of computational power is used in both codes.

PFLOTRAN took approximately 5 minutes and 15 seconds to compute the high velocity model, while 6 minutes and 19 seconds were required for the low velocity model. This contrasts with MARFA, which only took 22 seconds for the high velocity model and 8 seconds to run the low velocity model (run with 1 million particles). Therefore, MARFA computed the model about 14 times faster in the first case, and about 47 times faster in the second case! It might be possible to decrease the PFLOTRAN computation time by using less strict tolerances or timesteps, but the solution would be more numerically dispersive then.

Quality of the solution
---------------------------
In both tests, MARFA and PFLOTRAN solutions are compared to the semianalytical solution by (Sudicky and Frind, 1982).

**Figure 1** shows the MARFA and PFLOTRAN results in the high velocity case. Both codes agree very well with Sudicky’s solution.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Imagen1_7d65318ad6.png" alt=""/>
  <figcaption>
<b>Figure 1</b>. 
Results for the high velocity case.
</figcaption>
</figure>

Results for the low velocity model are shown in **Figure 2**. There is now some early arrival in the PFLOTRAN solution, which is likely due to numerical dispersion. However, the quality of the solution is still very good in both codes.
 
<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/marfa_results_image_2_330df2b016.png" alt=""/>
  <figcaption>
<b>Figure 2</b>. 
Results for the low velocity case.
</figcaption>
</figure>

In conclusion, both codes can be used to accurately simulate a simple fracture-matrix model, although MARFA-SP can compute the solution in significantly less time. On the other hand, note that the two codes are used quite differently: MARFA requires a set of trajectories with known advective time and transport resistance, while PFLOTRAN is applied to 3d models, with specified material properties and a velocity field.

References
==========
*Iraola, A., Trinchero, P., Karra, S., Molinero, J.,* 2019.** Assessing dual continuum method for multicomponent reactive transport**. Computers & Geosciences 130, 11–19. https://doi.org/10.1016/j.cageo.2019.05.007

*Sudicky, E.A., Frind, E.O*., 1982. **Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures***. Water Resources Research 18, 1634–1642. https://doi.org/10.1029/WR018i006p01634



medium_marfa_results_image_1.png

small_marfa_results_image_1.png

thumbnail_marfa_results_image_1.png

marfa_results_image_1.png

Discover how MARFA compares with PFLOTRAN 

How does MARFA compare to PFLOTRAN?

Since 2000, Amphos 21 has been deeply involved in the development and maintenance of ThermoChimie, the database managed by Andra (France), Nuclear Waste Services (UK) and Ondraf/Niras (Belgium).

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/thermochimie_11_1_088c1c1dd8.png" alt=""/>
</figure>
The ThermoChimie database is under constant revision and development. After its public release in 2014 and further updates in 2015, 2018 and 2021, <b> a new database version (11a) </b> is now <b><a href="http://www.thermochimie-tdb.com"> available on-line</a></b>  .

ThermoChimie version 11 contains significant updates on <b> U, Np, Pu, Am/Cm, and Tc</b>  following the NEA-TDB update (Grenthe et al. 2020) and beyond. In addition, an exhaustive and accurate review of Fe thermodynamic properties has been carried out, using the NEA-TDB reviews (Lemire et al. 2013, 2020) and additional literature publications. Furthermore, <b> PFlotran</b>  extraction has been newly added to the list of geochemical compatible codes.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/thermochimie_11_2_11c25fd05a.png" alt=""/>
</figure>
A new <b> XCheck</b>  tool to consult, filter, retrieve and export the information available in the latest database version is also now available for the user’s at <a href="https://register.thermochimie-ctool.com">https://register.thermochimie-ctool.com</a>.

Please stay tuned to the website  http://www.thermochimie-tdb.com/ or contact consortium-tc3-tech@thermochimie-tdb.com for additional information.



large_thermochimie_11_1.png

medium_thermochimie_11_1.png

small_thermochimie_11_1.png

thumbnail_thermochimie_11_1.png

thermochimie_11_1.png

After its public release in 2014 and further updates in 2015, 2018 and 2021, a new database version (11a) is now available on-line.

Pflotran

High Performance Computing as a prognostic tool for Deep Geological Repositories for spent nuclear fuel

How does MARFA compare to PFLOTRAN?

ThermoChimie database version 11a released!