val-2c
Test Cell Release Experiment
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, originally by hand (see Table 1) and then using a rigorous calibration study (see Table 2), to better match the experimental data.
Table 1: Case and model parameters values used in both immediate and delayed injection approaches in TMAP8 with , the gas constant, and , Avogadro's number, as defined in PhysicalConstants. When values are the same for both approaches, they are noted as identical. Model parameters that have been adapted from Longhurst et al. (1992) show a corrective factor in bold. Units are converted in the input file.
| Parameter | Immediate injection approach | Delayed injection approach | Unit | Reference |
|---|---|---|---|---|
| 0.96 | Identical | m | Holland and Jalbert (1986) | |
| 0.16 (between 0.1 and 0.2) | Identical | mm | Holland and Jalbert (1986) | |
| T | 10 | Identical | Ci/m | Holland and Jalbert (1986) |
| 714 | Identical | Pa | Longhurst et al. (1992) | |
| 0.54 | Identical | m/hr | Holland and Jalbert (1986) | |
| 303 | Identical | K | Holland and Jalbert (1986) | |
| Total time | 180000 | Identical | s | Holland and Jalbert (1986) |
| m/Ci/s | Adapted from Longhurst et al. (1992) | |||
| 4.0 | Identical | m/s | Holland and Jalbert (1986) | |
| 1.0 | Identical | m/s | Holland and Jalbert (1986) | |
| 1/m/Pa | Adapted from Longhurst et al. (1992) | |||
| 1/m/Pa | Adapted from Longhurst et al. (1992) | |||
| N/A | 3 | hr |
The calibration study was performed using MOOSE's stochastic tools module, and in particular the Parallel Subset Simulation (PSS) approach. The inputs and methodology provided here do not correspond to the full PSS study, but a scaled down version of it to minimize the computational costs. For this PSS study, we used 5 subsets with a subset probability of 0.1 (default) and 1000 samples per subset for a total of 5000 simulations, which were performed in parallel on 5 processors. For a full PSS study, it is common to use 10 subsets with 10000 samples per subset.
To calibrate the model against both the T and HTO concentrations in the enclosure over time, we performed a multi-objective optimization study. The penalties for the difference between the experimental data and the modeling prediction is given by
(14)
for HTO, and
(15)
for T. The metric to be optimized is then defined as the time integral of
(16)
Notably, the integral difference is defined in logarithmic space to give equal weight to all data points in the logarithmic scale during the optimization process. The complexity of the optimization metric is due to the large difference in scale for each species, as well as the discrete nature of the T measurements compared to the almost continuous nature of the HTO measurements. These differences make it challenging to optimize the fits of both species.
The comparison between the original and calibrated values of selected model parameters is summarized in Table 2.
Table 2: Calibrated model parameters values for the delayed injection case in val-2c..
| Parameter | Non-calibrated values (see Table 1) | Calibrated values using Parallel Subset Simulation | Unit |
|---|---|---|---|
| 2.833 | m/Ci/s | ||
| 4.0 | 3.864 | m/s | |
| 1.0 | 1.737 | m/s | |
| 2.514 | 1/m/Pa | ||
| 9.862 | 1/m/Pa | ||
| 10800 | 9536 | s |
Results and Discussion
commentnote:Update from Simon et al. (2025)
The results presented here are updated results from those presented in Simon et al. (2025). First, the initial time step was reduced from dt=60 s in Simon et al. (2025) to dt=1 s in the current case. This slightly affects the results for both the immediate and delayed injection cases. However, the results are qualitatively unchanged and conclusions remain valid. Second, the calibration approach was updated since Simon et al. (2025) with an updated multi-objective function, and new results. This improves the previous calibration results from Simon et al. (2025).
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 (RMSPE) are equal to RMSPE = 58.68% for T and RMSPE = 146.23% 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 = 89.50% for T and RMSPE = 75.66% 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 and in Simon et al. (2025). This affects some of the model parameters.
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. Calibration of the delayed injection model delivers further improvements.
Figure 2: Comparison of TMAP8 calculations against the experimental data for HTO concentration in the enclosure over time. Calibration of the delayed injection model delivers further improvements, with more accurate simulation results when T is injected over a given period rather than immediately.
As shown in the red curve in Figure 1 and Figure 2, using MOOSE's stochastic tools module notably increased the agreement between the modeling predictions and experimental data for both the T and HTO concentrations. The RMSPE for T decreases from 89.50% to 30.18% and the RMSPE for HTO decreases from 75.66% to 67.07%. Note that although the calibration approach is similar to the one presented in Simon et al. (2025), the results presented here include more simulations and the quality of the calibration is increased here (RMSPE values are further decreased here).
Figure 3 and Figure 4 show the evolution of the model parameter values and of the optimization metric (time integral of defined in Eq. (16)) as a function of the number of simulation. The calibrated model corresponds to the highest value.
Figure 3: Evolution of the model parameter values as a function of the number of simulations.
Figure 4: Evolution of the optimization metric (time integral of defined in Eq. (16)) as a function of the number of simulations. The calibrated model corresponds to the highest value.
Figure 5 and Figure 6 show the value of the calibrated parameters and the range of the data that was explored in the Parallel Subset Simulation study. Figure 5 shows the parameters that followed a normal distribution, and Figure 6 shows those that followed a uniform distribution in log scale. In both cases, the calibrated parameters are not on the extremes of the distribution, suggesting that the ranges were properly defined.
Figure 5: Calibrated parameter values compared to the normalized normal distribution used in the Parallel Subset Simulation study. None of the parameters are at the extremes of the distribution.
Figure 6: Calibrated parameter values compared to the normal distribution in the log scale used in the Parallel Subset Simulation study. None of the parameters are at the extremes of the distributions.
Input files
The input files for this case can be found at (test/tests/val-2c/val-2c_immediate_injection.i) and (test/tests/val-2c/val-2c_delay.i). Note that both input files utilize a common base file (test/tests/val-2c/val-2c_base.i) with the line !include val-2c_base.i. The base input file contains all the features and TMAP8 objects common to both cases, reducing duplication, and this allows the immediate injection and delayed injection inputs to focus on what is specific to each case. Note that both input files are also used as TMAP8 tests, outlined at (test/tests/val-2c/tests).
For the calibration study, additional input files are provided.
(test/tests/val-2c/val-2c_base_pss.i) provides key functions and postprocessor blocks necessary for the PSS study, including calculations of the multi-objective optimization metric (i.e., the time integral of defined in Eq. (16)).
(test/tests/val-2c/val-2c_delay_pss.i) includes both (test/tests/val-2c/val-2c_base_pss.i) and (test/tests/val-2c/val-2c_delay.i) to generate the needed full input file for the simulation.
(test/tests/val-2c/val-2c_pss_main.i) is the main input file for the PSS study. It defines what model parameters to vary and how, defines what approach to use, and initiates simulations using (test/tests/val-2c/val-2c_delay_pss.i).
To run the PSS study in the terminal, users can perform:
cd ~/projects/TMAP8/test/tests/val-2c/
mpirun -np 5 ~/projects/TMAP8/tmap8-opt -i val-2c_pss_main.i
Note that this study is time consuming since a large number of simulations are being run. Modifying the PSS parameters can reduce the computational cost.
Although a very short PSS study is simulated as a test in (test/tests/val-2c/tests) to ensure these files run properly, the full calibration study is not performed regularly in tests to limit computational costs within the TMAP8 testing suite. The gold files (test/tests/val-2c/gold/val-2c_pss_results/val-2c_pss_main_out.json) and (test/tests/val-2c/gold/calibrated_parameter_values.txt) are, therefore, not continuously tested, and the calibrated model parameters used in (test/tests/val-2c/tests) are not continuously updated.
References
- James Ambrosek and GR Longhurst.
Verification and Validation of TMAP7.
Technical Report INEEL/EXT-04-01657, Idaho National Engineering and Environmental Laboratory, December 2008.[BibTeX]
@techreport{ambrosek2008verification, author = "Ambrosek, James and Longhurst, GR", title = "{Verification and Validation of TMAP7}", year = "2008", number = "INEEL/EXT-04-01657", month = "December", institution = "Idaho National Engineering and Environmental Laboratory" } - D F Holland and R A Jalbert.
A model for tritium concentration following tritium release into a test cell and subsequent operation of an atmospheric cleanup system.
In Eleventh Symposium on Fusion Engineering. IEEE Cat. No. CH2251-7, Vol 1. pp. 638-643, 11 1986.[BibTeX]
@inproceedings{Holland1986, author = "Holland, D F and Jalbert, R A", city = "Austin, TX", booktitle = "Eleventh Symposium on Fusion Engineering", month = "11", publisher = "IEEE Cat. No. CH2251-7, Vol 1. pp. 638-643", title = "A model for tritium concentration following tritium release into a test cell and subsequent operation of an atmospheric cleanup system", year = "1986" } - GR Longhurst, SL Harms, ES Marwil, and BG Miller.
Verification and Validation of TMAP4.
Technical Report EGG-FSP-10347, Idaho National Engineering Laboratory, Idaho Falls, ID (United States), 1992.[BibTeX]
@techreport{longhurst1992verification, author = "Longhurst, GR and Harms, SL and Marwil, ES and Miller, BG", title = "{Verification and Validation of TMAP4}", year = "1992", institution = "Idaho National Engineering Laboratory, Idaho Falls, ID (United States)", number = "EGG-FSP-10347" } - Pierre-Clément A. Simon, Casey T. Icenhour, Gyanender Singh, Alexander D Lindsay, Chaitanya Vivek Bhave, Lin Yang, Adriaan Anthony Riet, Yifeng Che, Paul Humrickhouse, Masashi Shimada, and Pattrick Calderoni.
MOOSE-based tritium migration analysis program, version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling.
Fusion Engineering and Design, 214:114874, May 2025.
doi:10.1016/j.fusengdes.2025.114874.[BibTeX]
@article{Simon2025, author = "Simon, Pierre-Clément A. and Icenhour, Casey T. and Singh, Gyanender and Lindsay, Alexander D and Bhave, Chaitanya Vivek and Yang, Lin and Riet, Adriaan Anthony and Che, Yifeng and Humrickhouse, Paul and Shimada, Masashi and Calderoni, Pattrick", title = "{MOOSE}-based Tritium Migration Analysis Program, Version 8 ({TMAP8}) for Advanced Open-Source Tritium Transport and Fuel Cycle Modeling", journal = "Fusion Engineering and Design", publisher = "Elsevier", volume = "214", pages = "114874", year = "2025", month = "May", issn = "0920-3796", doi = "10.1016/j.fusengdes.2025.114874" }
(test/tests/val-2c/val-2c_immediate_injection.i)
# This input file utilizes val_2c_base and adds specific parameter values and capabilities to inject T2 immediately
# Physical Constants (from PhysicalConstant.h)
kb = '${units 1.380649e-23 J/K}' # Boltzmann constant based on number used in include/utils/PhysicalConstants.h
NA = '${units 6.02214076e23 at/mol}' # Avogadro's number based on number used in include/utils/PhysicalConstants.h
## Geometry
paint_thickness = '${units 0.16 mm -> mum}'
mesh_num_nodes_paint = 12 # impose by manual mesh
mesh_node_size_paint = '${fparse paint_thickness/mesh_num_nodes_paint}'
length_domain = '${fparse paint_thickness + 2*mesh_node_size_paint}'
volume_enclosure = '${units 0.96 m^3 -> mum^3}'
## Conditions
temperature = '${units 303 K}'
## Conversion
Curie = '${units 3.7e10 1/s}' # desintegrations/s - activity of one Curie
decay_rate_tritium = '${units 1.78199e-9 1/s/at}' # desintegrations/s/atoms
conversion_Ci_atom = '${units ${fparse decay_rate_tritium / Curie} 1/at}' # 1 tritium at = ~4.82e-20 Ci
concentration_to_pressure_conversion_factor = '${units ${fparse kb * temperature} Pa*m^3 -> Pa*mum^3}' # J = Pa*m^3
## Material properties
diffusivity_elemental_tritium = '${units 4.0e-12 m^2/s -> mum^2/s}'
diffusivity_tritiated_water = '${units 1.0e-14 m^2/s -> mum^2/s}'
diffusivity_artificial_enclosure = '${fparse diffusivity_elemental_tritium*1e3}'
reaction_rate = '${units ${fparse 1.5 * 2.0e-10*conversion_Ci_atom} m^3/at/s -> mum^3/at/s}' # ~ 1.5* 9.62e-30 m^3/at/s, close to the 1.0e-29 m3/atoms/s in TMAP4
solubility_elemental_tritium = '${units ${fparse 5e-2 * 4.0e19} 1/m^3/Pa -> 1/mum^3/Pa}' # molecules/microns^3/Pa = molecules*s^2/m^2/kg
solubility_tritiated_water = '${units ${fparse 3.5e-4 * 6.0e24} 1/m^3/Pa -> 1/mum^3/Pa}' # molecules/microns^3/Pa = molecules*s^2/m^2/kg
## Initial conditions
# The units below are actually in molecules, not atoms
initial_T2_inventory = '${units ${fparse 10 / 2 / conversion_Ci_atom} at}' # (equivalent to 10 Ci) - the 1/2 is to account for 2 tritium atoms per molecules, both contributing to activity
initial_T2_concentration = '${units ${fparse initial_T2_inventory / volume_enclosure} at/mum^3}'
initial_H2O_pressure = '${units 714 Pa}' # Found in TMAP4 input file, which corresponds to ambient air with 20% relative humidity.
initial_H2O_concentration = '${units ${fparse initial_H2O_pressure / concentration_to_pressure_conversion_factor} at/mum^3}'
## Numerical parameters
time_step = '${units 1 s}'
time_end = '${units 180000 s}'
dtmax = '${units 1e3 s}'
dtmin = '${units 1 s}'
lower_value_threshold = '${units -1e-20 at/mum^3}' # lower limit for concentration
## Inflow and outflow
inflow = '${units 0.54 m^3/h -> mum^3/s}' # inflow of normally moist (20% relative humidity) air at the same temperature as the enclosure
inflow_concentration = '${fparse initial_H2O_concentration * inflow / volume_enclosure}'
outflow = '${units 0.54 m^3/h -> mum^3/s}' # outflow of enclosure air # even if only 0.06 m^3/h is used to do measurements, all that air is purged out.
!include val-2c_base.i
[Variables]
# T2 concentration in the enclosure in molecules/microns^3
[t2_enclosure_concentration]
initial_condition = ${initial_T2_concentration}
[]
[]
(test/tests/val-2c/val-2c_delay.i)
# This input file utilizes val_2c_base and adds specific parameter values and capabilities to inject T2 with a delay
!include val-2c_delay.params
!include val-2c_base.i
[Functions]
[injection_window]
type = ParsedFunction
expression = 'if(t<${time_injection_T2_start}, 0., if(t<${time_injection_T2_end}, ${injection_rate_T2}, 0.))'
[]
[]
[Kernels]
[t2_inflow]
type = MaskedBodyForce
variable = t2_enclosure_concentration
value = '1'
function = 'injection_window'
mask = '1'
block = 1
[]
[]
(test/tests/val-2c/val-2c_base.i)
# Validation problem #2c from TMAP4/TMAP7 V&V document
# Test Cell Release Experiment based on
# D. F. Holland and R. A. Jalbert, "A Model for Tritium Concentration Following Tritium
# Release into a Test Cell and Subsequent Operation of an Atmospheric Cleanup Systen,"
# Proceedings, Eleventh Symposium of Fusion Engineering, November 18-22, 1985,. Austin,
# TX, Vol I, pp. 638-43, IEEE Cat. No. CH2251-7.
# Note that the approach to model this validation case is different in TMAP4 and TMAP7.
[Mesh]
[base_mesh]
type = GeneratedMeshGenerator
dim = 1
nx = '${fparse mesh_num_nodes_paint + 2}'
xmax = ${length_domain}
[]
[subdomain_id]
input = base_mesh
type = SubdomainPerElementGenerator
subdomain_ids = '0 0 0 0 0 0 0 0 0 0 0 0 1 1'
[]
[interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomain_id
primary_block = '0' # paint
paired_block = '1' # enclosure
new_boundary = 'interface'
[]
[interface_other_side]
type = SideSetsBetweenSubdomainsGenerator
input = interface
primary_block = '1' # enclosure
paired_block = '0' # paint
new_boundary = 'interface_other'
[]
[]
[Variables]
# T2 concentration in the enclosure in molecules/microns^3
[t2_enclosure_concentration]
block = 1
[]
# HT concentration in the enclosure in molecules/microns^3
[ht_enclosure_concentration]
block = 1
[]
# HTO concentration in the enclosure in molecules/microns^3
[hto_enclosure_concentration]
block = 1
[]
# H2O concentration in the enclosure in molecules/microns^3
[h2o_enclosure_concentration]
block = 1
initial_condition = ${initial_H2O_concentration}
[]
# concentration of T2 in the paint in molecules/microns^3
[t2_paint_concentration]
block = 0
[]
# concentration of HT in the paint in molecules/microns^3
[ht_paint_concentration]
block = 0
[]
# concentration of HTO in the paint in molecules/microns^3
[hto_paint_concentration]
block = 0
[]
# concentration of H2O in the paint in molecules/microns^3
[h2o_paint_concentration]
block = 0
[]
[]
[AuxVariables]
# Used to prevent negative concentrations
[bounds_dummy_t2_paint_concentration]
order = FIRST
family = LAGRANGE
[]
[bounds_dummy_t2_enclosure_concentration]
order = FIRST
family = LAGRANGE
[]
[bounds_dummy_hto_paint_concentration]
order = FIRST
family = LAGRANGE
[]
[bounds_dummy_hto_enclosure_concentration]
order = FIRST
family = LAGRANGE
[]
[bounds_dummy_h2o_paint_concentration]
order = FIRST
family = LAGRANGE
[]
[bounds_dummy_h2o_enclosure_concentration]
order = FIRST
family = LAGRANGE
[]
[]
[Bounds]
# To prevent negative concentrations
[t2_paint_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_t2_paint_concentration
bounded_variable = t2_paint_concentration
bound_type = lower
bound_value = ${lower_value_threshold}
[]
[t2_enclosure_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_t2_enclosure_concentration
bounded_variable = t2_enclosure_concentration
bound_type = lower
bound_value = ${lower_value_threshold}
[]
[hto_paint_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_hto_paint_concentration
bounded_variable = hto_paint_concentration
bound_type = lower
bound_value = ${lower_value_threshold}
[]
[hto_enclosure_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_hto_enclosure_concentration
bounded_variable = hto_enclosure_concentration
bound_type = lower
bound_value = ${lower_value_threshold}
[]
[h2o_paint_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_h2o_paint_concentration
bounded_variable = h2o_paint_concentration
bound_type = lower
bound_value = -1e-4
[]
[h2o_enclosure_concentration_lower_bound]
type = ConstantBounds
variable = bounds_dummy_h2o_enclosure_concentration
bounded_variable = h2o_enclosure_concentration
bound_type = lower
bound_value = -1e-4
[]
[]
[Kernels]
# In the enclosure
[t2_time_derivative]
type = TimeDerivative
variable = t2_enclosure_concentration
block = 1
[]
[t2_outflow]
type = MaskedBodyForce
variable = t2_enclosure_concentration
value = '-1'
mask = t2_enclosure_concentration_outflow
block = 1
[]
[t2_diffusion]
type = MatDiffusion
variable = t2_enclosure_concentration
block = 1
diffusivity = ${diffusivity_artificial_enclosure}
[]
[ht_time_derivative]
type = TimeDerivative
variable = ht_enclosure_concentration
block = 1
[]
[ht_outflow]
type = MaskedBodyForce
variable = ht_enclosure_concentration
value = '-1'
mask = ht_enclosure_concentration_outflow
block = 1
[]
[ht_diffusion]
type = MatDiffusion
variable = ht_enclosure_concentration
block = 1
diffusivity = ${diffusivity_artificial_enclosure}
[]
[hto_time_derivative]
type = TimeDerivative
variable = hto_enclosure_concentration
block = 1
[]
[hto_outflow]
type = MaskedBodyForce
variable = hto_enclosure_concentration
value = '-1'
mask = hto_enclosure_concentration_outflow
block = 1
[]
[hto_diffusion]
type = MatDiffusion
variable = hto_enclosure_concentration
block = 1
diffusivity = ${diffusivity_artificial_enclosure}
[]
[h2o_time_derivative]
type = TimeDerivative
variable = h2o_enclosure_concentration
block = 1
[]
[h2o_inflow]
type = MaskedBodyForce
variable = h2o_enclosure_concentration
mask = ${inflow_concentration}
block = 1
[]
[h2o_outflow]
type = MaskedBodyForce
variable = h2o_enclosure_concentration
value = '-1'
mask = h2o_enclosure_concentration_outflow
block = 1
[]
[h2o_diffusion]
type = MatDiffusion
variable = h2o_enclosure_concentration
block = 1
diffusivity = ${diffusivity_artificial_enclosure}
[]
# reaction T2+H2O->HTO+HT
[reaction_1_t2]
type = ADMatReactionFlexible
variable = t2_enclosure_concentration
block = 1
coeff = -1
reaction_rate_name = reaction_rate_t2
[]
[reaction_1_h2o]
type = ADMatReactionFlexible
variable = h2o_enclosure_concentration
block = 1
coeff = -1
reaction_rate_name = reaction_rate_t2
[]
[reaction_1_hto]
type = ADMatReactionFlexible
variable = hto_enclosure_concentration
block = 1
coeff = 1
reaction_rate_name = reaction_rate_t2
[]
[reaction_1_ht]
type = ADMatReactionFlexible
variable = ht_enclosure_concentration
block = 1
coeff = 1
reaction_rate_name = reaction_rate_t2
[]
# reaction HT+H2O->HTO+H2
[reaction_2_HT]
type = ADMatReactionFlexible
variable = ht_enclosure_concentration
block = 1
coeff = -1
reaction_rate_name = reaction_rate_ht
[]
[reaction_2_h2o]
type = ADMatReactionFlexible
variable = h2o_enclosure_concentration
block = 1
coeff = -1
reaction_rate_name = reaction_rate_ht
[]
[reaction_2_hto]
type = ADMatReactionFlexible
variable = hto_enclosure_concentration
block = 1
coeff = 1
reaction_rate_name = reaction_rate_ht
[]
# In the paint
[t2_paint_time]
type = TimeDerivative
variable = t2_paint_concentration
block = 0
[]
[t2_paint_diffusion]
type = MatDiffusion
variable = t2_paint_concentration
block = 0
diffusivity = '${diffusivity_elemental_tritium}'
[]
[ht_paint_time]
type = TimeDerivative
variable = ht_paint_concentration
block = 0
[]
[ht_paint_diffusion]
type = MatDiffusion
variable = ht_paint_concentration
block = 0
diffusivity = '${diffusivity_elemental_tritium}'
[]
[hto_paint_time]
type = TimeDerivative
variable = hto_paint_concentration
block = 0
[]
[hto_paint_diffusion]
type = MatDiffusion
variable = hto_paint_concentration
block = 0
diffusivity = '${diffusivity_tritiated_water}'
[]
[h2o_paint_time]
type = TimeDerivative
variable = h2o_paint_concentration
block = 0
[]
[h2o_paint_diffusion]
type = MatDiffusion
variable = h2o_paint_concentration
block = 0
diffusivity = '${diffusivity_tritiated_water}'
[]
[]
[InterfaceKernels]
# solubility at the surface of the paint
[t2_solubility]
type = ADInterfaceSorption
variable = t2_paint_concentration
neighbor_var = t2_enclosure_concentration # molecules/microns^3
unit_scale_neighbor = '${fparse 1e18/NA}' # to convert neighbor concentration to mol/m^3
K0 = ${solubility_elemental_tritium}
Ea = 0
n_sorption = 1 # Henry's law
temperature = ${temperature}
diffusivity = diffusivity_elemental_tritium
boundary = 'interface'
[]
[ht_solubility]
type = ADInterfaceSorption
variable = ht_paint_concentration
neighbor_var = ht_enclosure_concentration # molecules/microns^3
unit_scale_neighbor = '${fparse 1e18/NA}' # to convert neighbor concentration to mol/m^3
K0 = ${solubility_elemental_tritium}
Ea = 0
n_sorption = 1 # Henry's law
temperature = ${temperature}
diffusivity = diffusivity_elemental_tritium
boundary = 'interface'
[]
[hto_solubility]
type = ADInterfaceSorption
variable = hto_paint_concentration
neighbor_var = hto_enclosure_concentration # molecules/microns^3
unit_scale_neighbor = '${fparse 1e18/NA}' # to convert neighbor concentration to mol/m^3
K0 = ${solubility_tritiated_water}
Ea = 0
n_sorption = 1 # Henry's law
temperature = ${temperature}
diffusivity = diffusivity_tritiated_water
boundary = 'interface'
[]
[h2o_solubility]
type = ADInterfaceSorption
variable = h2o_paint_concentration
neighbor_var = h2o_enclosure_concentration # molecules/microns^3
unit_scale_neighbor = '${fparse 1e18/NA}' # to convert neighbor concentration to mol/m^3
K0 = ${solubility_tritiated_water}
Ea = 0
n_sorption = 1 # Henry's law
temperature = ${temperature}
diffusivity = diffusivity_tritiated_water
boundary = 'interface'
[]
[]
[Materials]
[reaction_rate_t2]
type = ADDerivativeParsedMaterial
coupled_variables = 't2_enclosure_concentration ht_enclosure_concentration hto_enclosure_concentration'
expression = '${reaction_rate} * 2 * t2_enclosure_concentration * (2*t2_enclosure_concentration + ht_enclosure_concentration + hto_enclosure_concentration)'
property_name = reaction_rate_t2
block = 1
[]
[reaction_rate_ht]
type = ADDerivativeParsedMaterial
coupled_variables = 't2_enclosure_concentration ht_enclosure_concentration hto_enclosure_concentration'
expression = '${reaction_rate} * ht_enclosure_concentration * (2*t2_enclosure_concentration + ht_enclosure_concentration + hto_enclosure_concentration)'
property_name = reaction_rate_ht
block = 1
[]
[diffusivity_elemental_tritium_paint]
type = ADConstantMaterial
value = ${diffusivity_elemental_tritium}
property_name = 'diffusivity_elemental_tritium'
block = 0
[]
[diffusivity_elemental_tritium_enclosure]
type = ADConstantMaterial
value = ${diffusivity_artificial_enclosure}
property_name = 'diffusivity_elemental_tritium'
block = 1
[]
[diffusivity_tritiated_water_paint]
type = ADConstantMaterial
value = ${diffusivity_tritiated_water}
property_name = 'diffusivity_tritiated_water'
block = 0
[]
[diffusivity_tritiated_water_enclosure]
type = ADConstantMaterial
value = ${diffusivity_artificial_enclosure}
property_name = 'diffusivity_tritiated_water'
block = 1
[]
[t2_enclosure_concentration_outflow]
type = DerivativeParsedMaterial
coupled_variables = 't2_enclosure_concentration'
expression = 't2_enclosure_concentration * ${outflow} / ${volume_enclosure}'
property_name = 't2_enclosure_concentration_outflow'
block = 1
[]
[ht_enclosure_concentration_outflow]
type = DerivativeParsedMaterial
coupled_variables = 'ht_enclosure_concentration'
expression = 'ht_enclosure_concentration * ${outflow} / ${volume_enclosure}'
property_name = 'ht_enclosure_concentration_outflow'
block = 1
[]
[hto_enclosure_concentration_outflow]
type = DerivativeParsedMaterial
coupled_variables = 'hto_enclosure_concentration'
expression = 'hto_enclosure_concentration * ${outflow} / ${volume_enclosure}'
property_name = 'hto_enclosure_concentration_outflow'
block = 1
[]
[h2o_enclosure_concentration_outflow]
type = DerivativeParsedMaterial
coupled_variables = 'h2o_enclosure_concentration'
expression = 'h2o_enclosure_concentration * ${outflow} / ${volume_enclosure}'
property_name = 'h2o_enclosure_concentration_outflow'
block = 1
[]
[]
[Postprocessors]
# Pressures in enclosure
[t2_enclosure_edge_concentration] # (molecules/microns^3)
type = PointValue
point = '${length_domain} 0 0' # on the far side of the enclosure
variable = t2_enclosure_concentration
execute_on = 'initial timestep_end'
[]
[ht_enclosure_edge_concentration] # (molecules/microns^3)
type = PointValue
point = '${length_domain} 0 0' # on the far side of the enclosure
variable = ht_enclosure_concentration
execute_on = 'initial timestep_end'
[]
[hto_enclosure_edge_concentration] # (molecules/microns^3)
type = PointValue
point = '${length_domain} 0 0' # on the far side of the enclosure
variable = hto_enclosure_concentration
execute_on = 'initial timestep_end'
[]
[h2o_enclosure_edge_concentration] # (molecules/microns^3)
type = PointValue
point = '${length_domain} 0 0' # on the far side of the enclosure
variable = h2o_enclosure_concentration
execute_on = 'initial timestep_end'
[]
# Inventory in enclosure
[t2_enclosure_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = t2_enclosure_concentration
execute_on = 'initial timestep_end'
block = 1
[]
[ht_enclosure_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = ht_enclosure_concentration
execute_on = 'initial timestep_end'
block = 1
[]
[hto_enclosure_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = hto_enclosure_concentration
execute_on = 'initial timestep_end'
block = 1
[]
[h2o_enclosure_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = h2o_enclosure_concentration
execute_on = 'initial timestep_end'
block = 1
[]
# Inventory in paint
[t2_paint_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = t2_paint_concentration
execute_on = 'initial timestep_end'
block = 0
[]
[ht_paint_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = ht_paint_concentration
execute_on = 'initial timestep_end'
block = 0
[]
[hto_paint_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = hto_paint_concentration
execute_on = 'initial timestep_end'
block = 0
[]
[h2o_paint_inventory] # (molecules/microns^2)
type = ElementIntegralVariablePostprocessor
variable = h2o_paint_concentration
execute_on = 'initial timestep_end'
block = 0
[]
[tritium_total_inventory]
type = LinearCombinationPostprocessor
pp_names = 't2_enclosure_inventory ht_enclosure_inventory hto_enclosure_inventory t2_paint_inventory ht_paint_inventory hto_paint_inventory'
pp_coefs = '2 1 1 2 1 1'
execute_on = 'initial timestep_end'
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
scheme = 'bdf2'
petsc_options_iname = '-pc_type -sub_pc_type -snes_type'
petsc_options_value = 'asm lu vinewtonrsls' # This petsc option helps prevent negative concentrations with bounds'
nl_rel_tol = 1.e-10
automatic_scaling = true
compute_scaling_once = false
end_time = ${time_end}
dtmax = ${dtmax}
dtmin = ${dtmin}
nl_max_its = 16
[TimeStepper]
type = IterationAdaptiveDT
dt = ${time_step}
optimal_iterations = 12
iteration_window = 1
growth_factor = 1.1
cutback_factor = 0.7
[]
[]
[Outputs]
perf_graph = true
[csv]
type = CSV
execute_on = 'initial timestep_end'
[]
[]
(test/tests/val-2c/tests)
[Tests]
design = 'val-2c.md'
validation = 'val-2c.md'
issues = '#12 #98'
[val-2c_immediate_injection_csv]
type = CSVDiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_immediate_injection_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_immediate_injection_exodus]
type = Exodiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_immediate_injection_csv
should_execute = false # this test relies on the output files from val-2c_immediate_injection_csv, so it shouldn't be run twice
exodiff = val-2c_immediate_injection_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_csv]
type = CSVDiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_delay_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 3e-5
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_exodus]
type = Exodiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_delay_csv
should_execute = false # this test relies on the output files from val-2c_delay_csv, so it shouldn't be run twice
exodiff = val-2c_delay_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_calibrated_csv]
type = CSVDiff
input = 'val-2c_delay.i'
# the parameter values below are from gold/calibrated_parameter_values.txt
cli_args = 'reaction_rate=2.8331901331213944e-11
diffusivity_elemental_tritium=3.8640662435310973
diffusivity_tritiated_water=0.017373835349450507
log_solubility_elemental_tritium=-3.683352919815223
log_solubility_tritiated_water=6.8938628913078555
time_injection_T2_end=9536.239653312441
Outputs/file_base=val-2c_delay_calibrated_out'
csvdiff = val-2c_delay_calibrated_out.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection using calibrated model parameters.'
abs_zero = 1e-8
rel_err = 2e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_pss_study_csv]
type = JSONDiff
input = val-2c_pss_main.i
cli_args = 'num_samplessub=2
num_subsets=1
Samplers/sample/num_parallel_chains=1
subset_probability=0.5
Samplers/sample/seed=1518
file_base_output=val-2c_pss_results_short/val-2c_pss_main_short_out'
jsondiff = val-2c_pss_results_short/val-2c_pss_main_short_out.json
requirement = 'The system shall be able to perform a Parallel Subset Simulation study using a model of the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 1e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_comparison]
type = RunCommand
command = 'python3 comparison_val-2c.py'
requirement = 'The system shall be able to generate comparison plots between simulated solutions and experimental data of validation cases val-2c, modeling a Test Cell Release Experiment.'
required_python_packages = 'matplotlib numpy pandas scipy os json'
[]
[]
(test/tests/val-2c/val-2c_base_pss.i)
# This input file adds key blocks to the val-2c_base.i input files for the PSS study
## Conversion
lengthscale = 1e18 # ${units 1 m^3 -> mum^3}
times_measurement_HTO_start = 2440.415722 # s
times_measurement_HTO_end = 174765.6056 # s
times_measurement_T2_1 = 32003.54498 # s
times_measurement_T2_2 = 49281.50916 # s
times_measurement_T2_3 = 57804.64646 # s
times_measurement_T2_4 = 71561.68891 # s
time_measurement_T2 = 600 # s - assuming it takes 10 minutes to take the measurement
default_diff_value = 3 # value to be used as difference between modeling prediction and experimental data when experimental data is not available
[Functions]
[experimental_data_hto] # time (s), concentrations (Ci/m^3)
type = PiecewiseLinear
data_file = gold/Experimental_data_HTO_concentration.csv
scale_factor = 1
format = columns
[]
[experimental_data_t2] # time (s), concentrations (Ci/m^3)
type = PiecewiseLinear
data_file = gold/Experimental_data_T2_concentration.csv
scale_factor = 1
format = columns
[]
[]
[Postprocessors]
[time]
type = TimePostprocessor
execution_order_group = -3
[]
[concentration_hto_interp]
type = FunctionValuePostprocessor
function = experimental_data_hto
time = time
execution_order_group = -2
execute_on = 'INITIAL TIMESTEP_END'
[]
[concentration_hto]
type = ParsedPostprocessor
pp_names = 'hto_enclosure_edge_concentration'
expression = 'hto_enclosure_edge_concentration * ${fparse decay_rate_tritium / Curie * lengthscale}'
execute_on = 'TIMESTEP_END'
[]
[concentration_t2_interp]
type = FunctionValuePostprocessor
function = experimental_data_t2
time = time
execution_order_group = -2
execute_on = 'INITIAL TIMESTEP_END'
[]
[concentration_t2]
type = ParsedPostprocessor
pp_names = 't2_enclosure_edge_concentration'
expression = 't2_enclosure_edge_concentration * 2 * ${fparse decay_rate_tritium / Curie * lengthscale}'
execute_on = 'TIMESTEP_END'
[]
[diff_concentration_hto]
type = ParsedPostprocessor
pp_names = 'time concentration_hto_interp concentration_hto'
expression = 'if((${times_measurement_HTO_start} <= time & time <= ${times_measurement_HTO_end}),
(log(concentration_hto_interp) - log(max(concentration_hto,1e-42)))^2*concentration_hto_interp*1e5, ${default_diff_value})' # the 1e-42 is to avoid the Inf at the first timesteps, which would make csvdiff fail
execution_order_group = -1
execute_on = 'TIMESTEP_END'
[]
[diff_concentration_t2]
type = ParsedPostprocessor
pp_names = 'time concentration_t2_interp concentration_t2'
expression = 'if((${fparse times_measurement_T2_1-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_1+time_measurement_T2/2})
| (${fparse times_measurement_T2_2-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_2+time_measurement_T2/2})
| (${fparse times_measurement_T2_3-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_3+time_measurement_T2/2})
| (${fparse times_measurement_T2_4-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_4+time_measurement_T2/2}),
(log(concentration_t2_interp) - log(max(concentration_t2,1e-42)))^2, ${default_diff_value})' # the 1e-42 is to avoid the Inf at the first timesteps, which would make csvdiff fail
execution_order_group = -1
execute_on = 'TIMESTEP_END'
[]
[objective1]
type = ParsedPostprocessor
pp_names = 'diff_concentration_hto diff_concentration_t2'
expression = '(diff_concentration_hto^2+8000)/(30*diff_concentration_hto^4+400*diff_concentration_hto^2+1) + (diff_concentration_t2^2+45000)/(0.1*diff_concentration_t2^4+50*diff_concentration_t2^2+1)'
[]
[objective]
type = TimeIntegratedPostprocessor
value = objective1
[]
[]
[Executioner]
error_on_dtmin = false
[]
[Outputs]
sync_times = '${fparse times_measurement_T2_1-time_measurement_T2/2} ${times_measurement_T2_1} ${fparse times_measurement_T2_1+time_measurement_T2/2}
${fparse times_measurement_T2_2-time_measurement_T2/2} ${times_measurement_T2_2} ${fparse times_measurement_T2_2+time_measurement_T2/2}
${fparse times_measurement_T2_3-time_measurement_T2/2} ${times_measurement_T2_3} ${fparse times_measurement_T2_3+time_measurement_T2/2}
${fparse times_measurement_T2_4-time_measurement_T2/2} ${times_measurement_T2_4} ${fparse times_measurement_T2_4+time_measurement_T2/2}'
[]
(test/tests/val-2c/val-2c_delay_pss.i)
# This input file utilizes val_2c_delay and adds specific blocks to perform the PSS study
!include val-2c_delay.i
!include val-2c_base_pss.i
(test/tests/val-2c/val-2c_base_pss.i)
# This input file adds key blocks to the val-2c_base.i input files for the PSS study
## Conversion
lengthscale = 1e18 # ${units 1 m^3 -> mum^3}
times_measurement_HTO_start = 2440.415722 # s
times_measurement_HTO_end = 174765.6056 # s
times_measurement_T2_1 = 32003.54498 # s
times_measurement_T2_2 = 49281.50916 # s
times_measurement_T2_3 = 57804.64646 # s
times_measurement_T2_4 = 71561.68891 # s
time_measurement_T2 = 600 # s - assuming it takes 10 minutes to take the measurement
default_diff_value = 3 # value to be used as difference between modeling prediction and experimental data when experimental data is not available
[Functions]
[experimental_data_hto] # time (s), concentrations (Ci/m^3)
type = PiecewiseLinear
data_file = gold/Experimental_data_HTO_concentration.csv
scale_factor = 1
format = columns
[]
[experimental_data_t2] # time (s), concentrations (Ci/m^3)
type = PiecewiseLinear
data_file = gold/Experimental_data_T2_concentration.csv
scale_factor = 1
format = columns
[]
[]
[Postprocessors]
[time]
type = TimePostprocessor
execution_order_group = -3
[]
[concentration_hto_interp]
type = FunctionValuePostprocessor
function = experimental_data_hto
time = time
execution_order_group = -2
execute_on = 'INITIAL TIMESTEP_END'
[]
[concentration_hto]
type = ParsedPostprocessor
pp_names = 'hto_enclosure_edge_concentration'
expression = 'hto_enclosure_edge_concentration * ${fparse decay_rate_tritium / Curie * lengthscale}'
execute_on = 'TIMESTEP_END'
[]
[concentration_t2_interp]
type = FunctionValuePostprocessor
function = experimental_data_t2
time = time
execution_order_group = -2
execute_on = 'INITIAL TIMESTEP_END'
[]
[concentration_t2]
type = ParsedPostprocessor
pp_names = 't2_enclosure_edge_concentration'
expression = 't2_enclosure_edge_concentration * 2 * ${fparse decay_rate_tritium / Curie * lengthscale}'
execute_on = 'TIMESTEP_END'
[]
[diff_concentration_hto]
type = ParsedPostprocessor
pp_names = 'time concentration_hto_interp concentration_hto'
expression = 'if((${times_measurement_HTO_start} <= time & time <= ${times_measurement_HTO_end}),
(log(concentration_hto_interp) - log(max(concentration_hto,1e-42)))^2*concentration_hto_interp*1e5, ${default_diff_value})' # the 1e-42 is to avoid the Inf at the first timesteps, which would make csvdiff fail
execution_order_group = -1
execute_on = 'TIMESTEP_END'
[]
[diff_concentration_t2]
type = ParsedPostprocessor
pp_names = 'time concentration_t2_interp concentration_t2'
expression = 'if((${fparse times_measurement_T2_1-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_1+time_measurement_T2/2})
| (${fparse times_measurement_T2_2-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_2+time_measurement_T2/2})
| (${fparse times_measurement_T2_3-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_3+time_measurement_T2/2})
| (${fparse times_measurement_T2_4-time_measurement_T2/2} <= time & time <= ${fparse times_measurement_T2_4+time_measurement_T2/2}),
(log(concentration_t2_interp) - log(max(concentration_t2,1e-42)))^2, ${default_diff_value})' # the 1e-42 is to avoid the Inf at the first timesteps, which would make csvdiff fail
execution_order_group = -1
execute_on = 'TIMESTEP_END'
[]
[objective1]
type = ParsedPostprocessor
pp_names = 'diff_concentration_hto diff_concentration_t2'
expression = '(diff_concentration_hto^2+8000)/(30*diff_concentration_hto^4+400*diff_concentration_hto^2+1) + (diff_concentration_t2^2+45000)/(0.1*diff_concentration_t2^4+50*diff_concentration_t2^2+1)'
[]
[objective]
type = TimeIntegratedPostprocessor
value = objective1
[]
[]
[Executioner]
error_on_dtmin = false
[]
[Outputs]
sync_times = '${fparse times_measurement_T2_1-time_measurement_T2/2} ${times_measurement_T2_1} ${fparse times_measurement_T2_1+time_measurement_T2/2}
${fparse times_measurement_T2_2-time_measurement_T2/2} ${times_measurement_T2_2} ${fparse times_measurement_T2_2+time_measurement_T2/2}
${fparse times_measurement_T2_3-time_measurement_T2/2} ${times_measurement_T2_3} ${fparse times_measurement_T2_3+time_measurement_T2/2}
${fparse times_measurement_T2_4-time_measurement_T2/2} ${times_measurement_T2_4} ${fparse times_measurement_T2_4+time_measurement_T2/2}'
[]
(test/tests/val-2c/val-2c_delay.i)
# This input file utilizes val_2c_base and adds specific parameter values and capabilities to inject T2 with a delay
!include val-2c_delay.params
!include val-2c_base.i
[Functions]
[injection_window]
type = ParsedFunction
expression = 'if(t<${time_injection_T2_start}, 0., if(t<${time_injection_T2_end}, ${injection_rate_T2}, 0.))'
[]
[]
[Kernels]
[t2_inflow]
type = MaskedBodyForce
variable = t2_enclosure_concentration
value = '1'
function = 'injection_window'
mask = '1'
block = 1
[]
[]
(test/tests/val-2c/val-2c_pss_main.i)
# This is the parallel subset simulation file for val-2c
## Conversion
Curie = '${units 3.7e10 1/s}' # disintegrations/s - activity of one Curie
decay_rate_tritium = '${units 1.78199e-9 1/s/at}' # disintegrations/s/atoms
conversion_Ci_atom = '${units ${fparse decay_rate_tritium / Curie} 1/at}' # 1 tritium at = ~4.82e-20 Ci
## Material properties
diffusivity_elemental_tritium = '${units ${fparse 4.0e-12 * (1.0-0.1)} m^2/s -> mum^2/s}'
diffusivity_tritiated_water = '${units ${fparse 1.0e-14 * (1.0+0.4)} m^2/s -> mum^2/s}'
reaction_rate = '${units ${fparse 2.8 * 2.0e-10*conversion_Ci_atom} m^3/at/s -> mum^3/at/s}' # ~ 1.5* 9.62e-30 m^3/at/s, close to the 1.0e-29 m3/atoms/s in TMAP4
solubility_elemental_tritium = '${units 4.0e19 1/m^3/Pa -> 1/mum^3/Pa}' # molecules/microns^3/Pa = molecules*s^2/m^2/kg
solubility_tritiated_water = '${units 6.0e24 1/m^3/Pa -> 1/mum^3/Pa}' # molecules/microns^3/Pa = molecules*s^2/m^2/kg
## Numerical parameters
time_injection_T2_end = '${units 3 h -> s}'
## PSS parameters
num_samplessub = 1000 # should be higher for a full PSS study (~6000-10000)
num_subsets = 5 # should be higher for a full PSS study (~10)
subset_probability = 0.2 # should be closer to 0.1 for a full PSS study
## Outputs
file_base_output = val-2c_pss_results/val-2c_pss_main_out
sub_app_input = "val-2c_delay_pss.i"
[StochasticTools]
[]
[Distributions]
[reaction_rate] # K^0
type = Normal
mean = ${reaction_rate}
standard_deviation = '${fparse 5/100 * reaction_rate}' # 5% of mean
[]
[diffusivity_elemental_tritium] # D^e
type = Normal
mean = ${diffusivity_elemental_tritium}
standard_deviation = '${fparse 10/100 * diffusivity_elemental_tritium}' # 10% of mean
[]
[diffusivity_tritiated_water] # D^w
type = Normal
mean = ${diffusivity_tritiated_water}
standard_deviation = '${fparse 20/100 * diffusivity_tritiated_water}' # 20% of mean
[]
[log_solubility_elemental_tritium] # KS^e
type = Uniform
lower_bound = '${fparse log(1e-4 * solubility_elemental_tritium)}'
upper_bound = '${fparse log(1e-3 * solubility_elemental_tritium)}' # a preliminary study has shown that the calibrated value is much lower than the original value.
[]
[log_solubility_tritiated_water] # KS^w
type = Uniform
lower_bound = '${fparse log(1e-4 * solubility_tritiated_water)}'
upper_bound = '${fparse log(1e-3 * solubility_tritiated_water)}' # a preliminary study has shown that the calibrated value is much lower than the original value.
[]
[time_injection_T2_end]
type = Normal
mean = ${time_injection_T2_end}
standard_deviation = '${fparse 10/100 * time_injection_T2_end}' # 10% of mean
[]
[]
[Samplers]
[sample]
type = ParallelSubsetSimulation
distributions = 'reaction_rate diffusivity_elemental_tritium diffusivity_tritiated_water log_solubility_elemental_tritium log_solubility_tritiated_water time_injection_T2_end'
execute_on = 'PRE_MULTIAPP_SETUP'
subset_probability = ${subset_probability}
num_samplessub = ${num_samplessub}
num_subsets = ${num_subsets}
# num_parallel_chains = 5 # using multiple parallel chains helps with convergence
inputs_reporter = 'adaptive_MC/inputs'
output_reporter = 'constant/reporter_transfer:objective:value'
seed = 1012
[]
[]
[MultiApps]
[sub]
type = SamplerFullSolveMultiApp
input_files = ${sub_app_input}
sampler = sample
ignore_solve_not_converge = true
[]
[]
[Transfers]
[reporter_transfer]
type = SamplerReporterTransfer
from_reporter = 'objective/value'
stochastic_reporter = 'constant'
from_multi_app = sub
sampler = sample
[]
[]
[Controls]
[cmdline]
type = MultiAppSamplerControl
multi_app = sub
sampler = sample
param_names = 'reaction_rate diffusivity_elemental_tritium diffusivity_tritiated_water log_solubility_elemental_tritium log_solubility_tritiated_water time_injection_T2_end'
[]
[]
[Reporters]
[constant]
type = StochasticReporter
[]
[adaptive_MC]
type = AdaptiveMonteCarloDecision
output_value = constant/reporter_transfer:objective:value
inputs = 'inputs'
sampler = sample
[]
[]
[Executioner]
type = Transient
[]
[Outputs]
file_base = ${file_base_output}
[out]
type = JSON
[]
[]
(test/tests/val-2c/val-2c_delay_pss.i)
# This input file utilizes val_2c_delay and adds specific blocks to perform the PSS study
!include val-2c_delay.i
!include val-2c_base_pss.i
(test/tests/val-2c/tests)
[Tests]
design = 'val-2c.md'
validation = 'val-2c.md'
issues = '#12 #98'
[val-2c_immediate_injection_csv]
type = CSVDiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_immediate_injection_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_immediate_injection_exodus]
type = Exodiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_immediate_injection_csv
should_execute = false # this test relies on the output files from val-2c_immediate_injection_csv, so it shouldn't be run twice
exodiff = val-2c_immediate_injection_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_csv]
type = CSVDiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_delay_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 3e-5
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_exodus]
type = Exodiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_delay_csv
should_execute = false # this test relies on the output files from val-2c_delay_csv, so it shouldn't be run twice
exodiff = val-2c_delay_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_calibrated_csv]
type = CSVDiff
input = 'val-2c_delay.i'
# the parameter values below are from gold/calibrated_parameter_values.txt
cli_args = 'reaction_rate=2.8331901331213944e-11
diffusivity_elemental_tritium=3.8640662435310973
diffusivity_tritiated_water=0.017373835349450507
log_solubility_elemental_tritium=-3.683352919815223
log_solubility_tritiated_water=6.8938628913078555
time_injection_T2_end=9536.239653312441
Outputs/file_base=val-2c_delay_calibrated_out'
csvdiff = val-2c_delay_calibrated_out.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection using calibrated model parameters.'
abs_zero = 1e-8
rel_err = 2e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_pss_study_csv]
type = JSONDiff
input = val-2c_pss_main.i
cli_args = 'num_samplessub=2
num_subsets=1
Samplers/sample/num_parallel_chains=1
subset_probability=0.5
Samplers/sample/seed=1518
file_base_output=val-2c_pss_results_short/val-2c_pss_main_short_out'
jsondiff = val-2c_pss_results_short/val-2c_pss_main_short_out.json
requirement = 'The system shall be able to perform a Parallel Subset Simulation study using a model of the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 1e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_comparison]
type = RunCommand
command = 'python3 comparison_val-2c.py'
requirement = 'The system shall be able to generate comparison plots between simulated solutions and experimental data of validation cases val-2c, modeling a Test Cell Release Experiment.'
required_python_packages = 'matplotlib numpy pandas scipy os json'
[]
[]
(test/tests/val-2c/gold/val-2c_pss_results/val-2c_pss_main_out.json)
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(test/tests/val-2c/gold/calibrated_parameter_values.txt)
reaction_rate = 2.8331901331213944e-11
diffusivity_elemental_tritium = 3.8640662435310973
diffusivity_tritiated_water = 0.017373835349450507
log_solubility_elemental_tritium = -3.683352919815223
log_solubility_tritiated_water = 6.8938628913078555
time_injection_T2_end = 9536.239653312441
(test/tests/val-2c/tests)
[Tests]
design = 'val-2c.md'
validation = 'val-2c.md'
issues = '#12 #98'
[val-2c_immediate_injection_csv]
type = CSVDiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_immediate_injection_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_immediate_injection_exodus]
type = Exodiff
input = val-2c_immediate_injection.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_immediate_injection_csv
should_execute = false # this test relies on the output files from val-2c_immediate_injection_csv, so it shouldn't be run twice
exodiff = val-2c_immediate_injection_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with immediate T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_csv]
type = CSVDiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
csvdiff = val-2c_delay_csv.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 3e-5
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_exodus]
type = Exodiff
input = val-2c_delay.i
cli_args = 'Outputs/exodus=true'
prereq = val-2c_delay_csv
should_execute = false # this test relies on the output files from val-2c_delay_csv, so it shouldn't be run twice
exodiff = val-2c_delay_out.e
custom_cmp = 'val-2c_exodus.exodiff'
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection and properly compute the exodus file.'
max_parallel = 1 # see #200
recover = false # see #196
[]
[val-2c_delay_calibrated_csv]
type = CSVDiff
input = 'val-2c_delay.i'
# the parameter values below are from gold/calibrated_parameter_values.txt
cli_args = 'reaction_rate=2.8331901331213944e-11
diffusivity_elemental_tritium=3.8640662435310973
diffusivity_tritiated_water=0.017373835349450507
log_solubility_elemental_tritium=-3.683352919815223
log_solubility_tritiated_water=6.8938628913078555
time_injection_T2_end=9536.239653312441
Outputs/file_base=val-2c_delay_calibrated_out'
csvdiff = val-2c_delay_calibrated_out.csv
requirement = 'The system shall be able to model the Test Cell Release Experiment (val-2c) with delayed T2 injection using calibrated model parameters.'
abs_zero = 1e-8
rel_err = 2e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_pss_study_csv]
type = JSONDiff
input = val-2c_pss_main.i
cli_args = 'num_samplessub=2
num_subsets=1
Samplers/sample/num_parallel_chains=1
subset_probability=0.5
Samplers/sample/seed=1518
file_base_output=val-2c_pss_results_short/val-2c_pss_main_short_out'
jsondiff = val-2c_pss_results_short/val-2c_pss_main_short_out.json
requirement = 'The system shall be able to perform a Parallel Subset Simulation study using a model of the Test Cell Release Experiment (val-2c) with delayed T2 injection.'
abs_zero = 1e-8
rel_err = 1e-5
max_parallel = 1 # see #200
recover = false # see #196
issues = '#266'
[]
[val-2c_delay_comparison]
type = RunCommand
command = 'python3 comparison_val-2c.py'
requirement = 'The system shall be able to generate comparison plots between simulated solutions and experimental data of validation cases val-2c, modeling a Test Cell Release Experiment.'
required_python_packages = 'matplotlib numpy pandas scipy os json'
[]
[]