 ## Overview and model setup

This benchmark is focused on the simulation of the migration of $U(VI)$ in a porous media. An important chemical process happening is the surface sorption, which favors the retardation of radionuclide migration. Therefore, it is necessary to quantify its overall impact on the transport. We use a Surface Complexation approach as a mechanistic model to describe the chemical reactions happening at the solid surface. The surface reactions considered in this benchmark were added to the PSI/NAGRA chemical thermodynamic database version 12/07 (Thoenen et al., 2014) for the speciation calculations. A schematic representation of the 1D model with relevant parameters is shown in Fig. 1. A permeability = $1.019368 \times 10^{-11}~m^2$, porosity = $0.2$, molecular diffusion coefficient = $1.0 \times 10^{-9}~m^2/s$, longitudinal/ horizontal/ vertical dispersivities = $0.2~m$, tortuosity = $1$, density = $1000~kg/m^3$ and viscosity = $1\times 10^{-3}~kg~m^{-1} s^{-1}$ are the input parameters of the porous medium.

The benchmark uses the ComponentTransport process in OGS-6 (see HC-Process.pdf) coupled with the IPhreeqc interface (Parkhurst et al, 2013) for the chemical speciation calculations. The porewater initial composition and injected for the first 10 000 s is shown in Table 1. The porewater solution is equilibrated with Calcite.

Parameter Unit Initial solution Inlet solution
$Na^+$ mol/L $1.0 \times 10^{-3}$ $1.0 \times 10^{-3}$
$Cl^-$ mol/L $60.0 \times 10^{-3}$ $60.0 \times 10^{-3}$
$Ca^{2+}$ mol/L $25.02 \times 10^{-3}$ $25.02 \times 10^{-3}$
$DIC$ mol/L $1.0 \times 10^{-3}$ $1.0 \times 10^{-3}$
$U(VI)$ mol/L 0 $1 \times 10^{-8}$

Table 1: Porewater solution compositions.

## Results

Sorption of U(VI) in porous media has been previously modeled in a German research project on safety of nuclear waste repositories (Noseck et al., 2018). In there, simulations are done by using a chemical thermodynamic database (consulted 08-DEC-2020). Since this database (we refer to it as ESTRAL database) is available via personal contact only, in this benchmark, we compare the results obtained with the ESTRAL database and open-access data.

To approximate the results obtained with the ESTRAL database, we use data from the RES³T - Rossendorf Expert System for Surface and Sorption Thermodynamics (https://www.hzdr.de/db/RES3T.queryData) for the available mineral phases (see Table 2) to update the PSI/NAGRA chemical thermodynamic database (version 12/07) for the surface complexation model. In addition, we use the surface characterization provided in Noseck et al., 2018. Note that the mineral groups of the ESTRAL database contains a larger number of individual phases. Because the composition of each mineral group is not provided for the surface characterization of Table 2, we choose only one representative phase at a time for each mineral group in our simulations. Further, to keep the chemical system simple, the chosen chemical reactions and log K values for the surface complexation model are only those of mineral-OH sites, with the exception of gibbsite, where only Aluminol sites are available for $U(VI)$. In total, 19 chemical reactions are considered in the surface complexation model. All log K values are reported for 298.15 K and normalized to 2.31 sites/nm$^2$.

Mineral group/phase Representative phases Reference binding sites (sites/nm$^2$) Specific surface area (m$^2$/g) Solid mass ($g/kgw$)
Quartz - 2.31 0.007 9010
Feldspars albite, orthoclase 2.31 0.21 1060
Mica muscovite 2.31 1.72 53
Fe(III)-oxids/-hydroxids goethite, hematite 2.31 0.26 53
Al-hydroxids gibbsite 2.31 0.11 53
2-layer-clay minerals kaolinite 2.31 0.07 159

Table 2: Surface parameters and characterization used in the simulations.

Four different combinations can be simulated taking the albite and orthoclase phases of the Feldspars group and the goethite and hematite phases for the Fe(III)-oxids/-hydroxids group. Mineral combinations from 1 to 4 (see Fig. 2) are as follows: 1) albite-goethite, 2) albite-hematite, 3) orthoclase-goethite and 4) orthoclase-hematite. From the concentration profiles in Fig. 2, it is clear that the combination 2 approximates better the profile obtained with the ESTRAL database. We choose this combination for the next part of our simulations. Furthermore, this combination is written in the RadionuclideSorption.prj file of this benchmark.

The temporal evolution of the concentration profiles of the chosen mineral combination (albite-hematite) compared to the ESTRAL database is shown in Fig. 3. In addition, a simulation of the reactive transport treating $U(VI)$ as a non-sorbing radionuclide is presented. Recall that the contaminated solution with $U(VI)$ is injected only for the first 10 000 s of simulation. On the one hand, we note the difference between the profile with the augmented PSI/Nagra database and with the ESTRAL database. This is expected, since different reactions and significant differences in log K values are considered for each simulation. However, we note that the trend is similar enough to capture the relevant sorption process happening at the surface.