Case Description

This validation problem is taken from Holland and Jalbert (1986) and was part of the validation suite of TMAP4 Longhurst et al. (1992) and TMAP7 Ambrosek and Longhurst (2008). It has been updated and extended in Simon et al. (2025). Whenever tritium is released into a fusion reactor test cell, it is crucial to clean it up to prevent exposure. This case models an experiment conducted at Los Alamos National Laboratory at the tritium systems test assembly (TSTA) to study the behavior of tritium once released in a test cell and the efficacy of the emergency tritium cleanup system (ETCS).

The experimental set up, described in greater detail in Holland and Jalbert (1986), can be summarized as such: the inner walls of an enclosure of volume are covered with an aluminum foil and then covered in paint with an average thickness , which is then in contact with the enclosure air. A given amount, T, of tritium, T, is injected in the enclosure, which initially contained ambient air, representing tritium release. A flow rate through the enclosure represents the air replacement time expected for large test cells. The purge gas is ambient air with 20% relative humidity. A fraction of that amount is diverted through the measurement system to determine the concentrations of chemical species within the enclosure.

Several phenomena are taking place and need to be captured in the model to determine the concentrations of elemental tritium (i.e., T and HT), tritiated water (i.e., HTO), and water (i.e., HO). First, The following chemical reactions occur inside the enclosure: (1) (2) mostly as a consequence of the tritium reactivity. The reaction rates of these reactions are and , respectively, where (3) and (4) Here, represents the concentration of species , and is a constant.

Second, the different species will permeate in the paint. The elemental tritium species, T and HT, have a given solubility and diffusivity , while the tritiated water, HTO, and water, HO, have a solubility and diffusivity . It is expected that the species will initially permeate into the paint and later get released as the purge gas cleans up the enclosure air.

The objectives of this case are to determine the time evolution of T and HTO concentrations in the enclosure, match the experimental data published in Holland and Jalbert (1986), and display this comparison with the appropriate error checking (see Figure 1 and Figure 2).

Model Description

To model the case described above, TMAP8 simulates a one-dimensional domain with one block to represent the air in the enclosure, and another block to represent the paint. In each block, the simulation tracks the local concentration of T, HT, HTO, and HO. Note that this case can easily be extended to a two- or three-dimensional case, but consistent with previous analyses, we will maintain the one-dimensional configuration here.

In the enclosure, to capture the purge gas and the chemical reactions, the concentrations evolve as (5) (6) (7) and (8) where is the concentration of HO in the incoming purge gas.

In the paint, TMAP8 captures species diffusion through (9) (10) (11) and (12)

At the interface between the enclosure air and the paint, sorption is captured in TMAP8 with Henry's law thanks to the ADInterfaceSorption / InterfaceSorption object: (13) where and are the concentrations of species in the enclosure and in the paint, respectively, and is the solubility (either or ). The boundary conditions are set to "no flux" since no permeation happens at the interface between the paint and the aluminum foil and the only flux leaving the enclosure is already captured by the purge gas (Holland and Jalbert, 1986).

One of the assumptions made in the original paper and TMAP4 V&V case is that the tritium is immediately added to the enclosure (Holland and Jalbert, 1986; Longhurst et al., 1992). However, this leads to an early HTO peak concentration, which does not exactly match the experimental data. In Ambrosek and Longhurst (2008), TMAP7 introduces a new enclosure to account for a slower injection of tritium. Here, we model this case with two different approaches. The first approach, like (Holland and Jalbert, 1986; Longhurst et al., 1992), assumes that the entire tritium inventory is immediately injected in the enclosure at the beginning of the experiment. The second approach assumes that the tritium inventory is being injected into the enclosure at a linear rate during a period of time until the entire tritium inventory is injected. The results of these two approaches are presented and discussed below.

Case and Model Parameters

The case and model parameters used in both approaches in TMAP8 are listed in Table 1. Some of the parameters are directly leveraged from Holland and Jalbert (1986), Longhurst et al. (1992), and Ambrosek and Longhurst (2008), but others were adapted to better match the experimental data.

Results and discussion

Figure 1 and Figure 2 show the comparison of the TMAP8 calculations (both with immediately injected and delayed injected T) against the experimental data for T and HTO concentration in the enclosure over time. There is reasonable agreement between the TMAP8 predictions and the experimental data. In the case of immediate T injection, the root mean square percentage errors are equal to RMSPE = 58.98 % for T and RMSPE = 139.10 % for HTO, respectively. When accounting for a delay in T injection, the TMAP8 predictions best match the experimental data, in particular the position of the peak HTO concentration. The RMSPE values decrease to RMSPE = 58.05 % for T and RMSPE = 74.77 % for HTO, respectively. Note that the model parameters listed in Table 1 are somewhat different from Holland and Jalbert (1986), Longhurst et al. (1992), and Ambrosek and Longhurst (2008) to better match the experimental data. In particular, Longhurst et al. (1992) and Ambrosek and Longhurst (2008) did not validate the TMAP predictions against T concentration, which we do here in Figure 1. This affects some of the model parameters.

The agreement between modeling predictions and experimental data could be further improved by adjusting the model parameters. It is also possible to perform this optimization with MOOSE's stochastic tools module.

Figure 1: Comparison of TMAP8 calculations against the experimental data for T concentration in the enclosure over time. TMAP8 matches the experimental data well, with an improvement when T is injected over a given period rather than immediately.

Figure 2: Comparison of TMAP8 calculations against the experimental data for HTO concentration in the enclosure over time. TMAP8 matches the experimental data well, with an improvement when T is injected over a given period rather than immediately.

Input files

References