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WASTE_FORM_GENERAL¶
The Waste Form Process Model is formally documented here.
Specifies the waste form process model.
Under the SIMULATION block this process model is included by adding
the WASTE_FORM block:
SIMULATION SIMULATION_TYPE SUBSURFACE PROCESS_MODELS WASTE_FORM <name_string> TYPE GENERAL / SUBSURFACE_FLOW flow MODE GENERAL / SUBSURFACE_TRANSPORT transport MODE GIRT / / END
where <name_string> gives a user-defined name for the process model.
Required Cards:¶
- WASTE_FORM_GENERAL
Opens the WASTE_FORM_GENERAL block. Must have a matching END_WASTE_FORM_GENERAL.
MECHANISM <type_string>
The mechanism block specifies a waste form mechanism. The mechanism includes the details of the radionuclide species, the waste form bulk material details, and the canister that contains the waste form. Several different custom mechanisms can be defined, or chosen from pre-defined options. Each mechanism is given a unique name, and later associated with specific listed waste forms. The following types are currently supported: GLASS, DSNF, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR, WIPP, ANALYTICAL, and CUSTOM.
MECHANISM GLASS /Within the MECHANISM block, the following sub-blocks and cards must be included for any MECHANISM type:
NAME <name_string> (required for all mechanism types)
Specifies a name for the mechanism. This name should be unique.
NAME glass02
SPECIES sub-block (required for all mechanism types)
Specifies a list of waste form species, their formula weights (in units of g-species/mol-species), decay constant (in units of 1/sec), initial mass fraction within the waste form matrix (g-species/g-bulk), instant release fraction (a number between 0 and 1), and the name of the species daughter (if it exists). The species listed here must also be listed in the CHEMISTRY block under Primary Species. Isotopes decay and ingrowth occurs following a 3-generation analytical solution derived for multiple parents and grandparents and non-zero initial daughter concentrations, or by an implicit solution of the Bateman equation.
SPECIES I-129 128.90d0 1.29d-15 2.18d-4 0.7d0 Am-241 241.06d0 5.08d-11 8.70d-4 0.0d0 Np-237 Np-237 237.05d0 1.03d-14 8.59d-4 0.7d0 U-233 U-233 233.04d0 1.38d-13 9.70d-9 0.0d0 Th-229 Th-229 229.03d0 2.78d-12 4.43d-12 0.0d0 ... ... ... ... ... ... /MATRIX_DENSITY <double> <unit_string> (required for all mechanism types)
Specifies the density of the waste form bulk (or matrix).
MATRIX_DENSITY 2.0d3 kg/m^3The following sub-block cards are now separated by MECHANISM type:
MECHANISM GLASS sub-block cards:
SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the specific surface area of the waste form bulk (or matrix).
SPECIFIC_SURFACE_AREA 2.78d-3 cm^2/g
KIENZLER_DISSOLUTION (optional for type GLASS only)
If chosen, this option will implement the Kienzler (2012) glass dissolution equation. No other dissolution parameters are needed (i.e., no other sub-block cards other than SPECIFIC_SURFACE_AREA).
KIENZLER_DISSOLUTIONK0 <double> <unit_string> (optional for GLASS only)
Specifies the intrinsic dissolution rate. If no units are provided, default units are kg/m^2-sec. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
K0 580.d0 kg/m^2-day
K_LONG <double> <unit_string> (optional for GLASS only)
Specifies the constant dissolution rate over the long term when the pore fluid solution is at saturation with respect to SiO2. If no units are provided, default units are kg/m^2-sec. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
K_LONG 46.d0 g/m^2-day
NU <double> (optional for GLASS only)
Specifies the pH dependence parameter. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
NU 3.44d0
EA <double> <unit_string> (optional for GLASS only)
Specifies the effective activation energy. If no units are provided, default units are J/mol. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
EA 5.83d4 J/mol
Q <double or string> (optional for GLASS only)
Specifies the ion activity product of H4SiO4. If a constant value is desired, it should be entered following the Q keyword. Alternatively, Q can be calculated within the simulation by specifying the string AS_CALCULATED following the Q keyword. If you specify AS_CALCULATED, then SiO2(aq) must be included as a primary or secondary species in the CHEMISTRY block, and USE_FULL_GEOCHEMISTRY should also be specified if full geochemistry is otherwise not being calculated. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
Q 3.4d-8 Q AS_CALCULATED
K <double> (optional for GLASS only)
Specifies the equilibrium constant for the rate limiting step, which is the activity of H4SiO4 at saturation with the glass. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
V <double> (optional for GLASS only)
Specifies the exponent in the affinity term, as in [1-(Q/K)**(1/V)]. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
PH <double or string> (optional for GLASS only)
Specifies the pH value at the glass surface. If a constant value is desired, it should be entered following the PH keyword. Alternatively, pH can be calculated within the simulation by specifying the string AS_CALCULATED following the PH keyword. If you specify AS_CALCULATED, then H+ must be included as a primary or secondary species in the CHEMISTRY block, and USE_FULL_GEOCHEMISTRY should also be specified if full geochemistry is otherwise not being calculated. If KIENZLER_DISSOLUTION is chosen, this card should not be given.
PH 6.8d0 PH AS_CALCULATED
MECHANISM DSNF sub-block cards:
No additional sub-block cards are required.
MECHANISM FMDM sub-block cards:
For additional inputs required for this mechanism see FMDM Mechanism.
If the FMDM mechanism is used, follow these instructions on how to link the external FMDM: Running PFLOTRAN linked to FMDM.
SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the specific surface area of the waste form bulk (or matrix).
SPECIFIC_SURFACE_AREA 2.78d-3 cm^2/g
BURNUP <double> (required for types FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the burnup of the waste form bulk (or matrix).
BURNUP 6.0d1 ! GWd/MTHM
MECHANISM FMDM_SURROGATE sub-block cards:
For additional inputs required for this mechanism see FMDM Surrogate Mechanism.
SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the specific surface area of the waste form bulk (or matrix).
SPECIFIC_SURFACE_AREA 2.78d-3 cm^2/g
BURNUP <double> (required for types FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the burnup of the waste form bulk (or matrix).
BURNUP 6.0d1 ! GWd/MTHM
DECAY_TIME <double> <unit_string> (required for types FMDM_SURROGATE and FMDM_SURROGATE_KNNR; do not include for types CUSTOM, DSNF, FMDM, and WIPP)
Specifies the offset for the age of the fuel relative to the beginning of simulation time.
DECAY_TIME 1.0d2 year
MECHANISM FMDM_SURROGATE_KNNR sub-block cards:
For additional inputs required for this mechanism see FMDM Surrogate Mechanism.
SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the specific surface area of the waste form bulk (or matrix).
SPECIFIC_SURFACE_AREA 2.78d-3 cm^2/g
BURNUP <double> (required for types FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the burnup of the waste form bulk (or matrix).
BURNUP 6.0d1 ! GWd/MTHM
DECAY_TIME <double> <unit_string> (required for types FMDM_SURROGATE and FMDM_SURROGATE_KNNR; do not include for types CUSTOM, DSNF, FMDM, and WIPP)
Specifies the offset for the age of the fuel relative to the beginning of simulation time.
DECAY_TIME 1.0d2 year
MECHANISM WIPP sub-block cards:
No additional sub-block cards are required. If the WIPP mechanism is used, the UFD_DECAY process model must also be used or the solubility limit functionality will not work properly. Please read the formal documentation here.
MECHANISM CUSTOM sub-block cards:
DISSOLUTION_RATE <double> <unit_string> (semi-optional for type CUSTOM; do not include for type GLASS, DSNF, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR or WIPP)
Specifies the dissolution rate for the waste form bulk (or matrix), in units of mass per surface area per time. If dissolution rate is given for the CUSTOM mechanism type, the SPECIFIC_SURFACE_AREA must also be specified (see below).
DISSOLUTION_RATE 7.8d-8 kg/m^2-day
FRACTIONAL_DISSOLUTION_RATE <double> <unit_string> (semi-optional for type CUSTOM; do not include for types GLASS, DSNF, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR or WIPP)
Specifies the fractional dissolution rate for the waste form bulk (or matrix), in units of fractional volume per time of the remaining volume. The unit string should resemble 1/time.
FRACTIONAL_DISSOLUTION_RATE 3.4d-8 1/day
FRACTIONAL_DISSOLUTION_RATE_VI <double> <unit_string> (semi-optional for type CUSTOM; do not include for types GLASS, DSNF, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR or WIPP)
Specifies the fractional dissolution rate for the waste form bulk (or matrix), in units of fraction of the initial volume per time. The unit string should resemble 1/time.
FRACTIONAL_DISSOLUTION_RATE_VI 9.1d-5 1/day
SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM, FMDM_SURROGATE, FMDM_SURROGATE_KNNR; semi-optional for type CUSTOM; do not include for types DSNF and WIPP)
Specifies the specific surface area of the waste form bulk (or matrix). If specific surface area is given for the CUSTOM mechanism type, the DISSOLUTION_RATE keyword must also be specified (see above).
SPECIFIC_SURFACE_AREA 2.78d-3 cm^2/g
Optional keywords for ALL MECHANISM types:
SEED <integer>
Specifies a seed number (must be an integer) which seeds the random number generator that selects waste package degradation rates from the truncated normal distribution. If this keyword is omitted, the default seed value is 1.
Optional sub-block for ALL MECHANISM types:
CANISTER_DEGRADATION_MODEL sub-block (optional for all mechanism types)
If this optional block is included, the canister degradation model will be turned on. Currently, this model will keep track of canister vitality, a parameter which controls the time of waste form breach. At the beginning of the simulation, vitality = 1. Waste form breach occurs when the canister vitality falls to zero. The reference vitality degradation rate (Rv0) is either (a) chosen at the beginning of the simulation, for each waste form, based on a normal distribution of degradation rates, (b) specified for each waste form by the user, or (c) ignored if the user specifies a canister breach time for each waste form instead of a rate. The effective vitality degradation rate (Rv) is calculated as an Arrhenius function of temperature, canister material constant (C), and the reference vitality degradation rate:
log10(Rv) = log10(Rv0) + C * (1/333.15[K] - 1/T[K])
If option “a” is desired, the normal distribution for the reference rate is formed by providing the following block keywords (all required):
VITALITY_LOG10_MEAN
Specifies the Log(base10) mean vitality degradation rate (in units of log10-1/yr). If this distribution parameter is omitted, then CANISTER_VITALITY_RATE must be included for all waste forms associated with this mechanism.
VITALITY_LOG10_STDEV
Specifies the Log(base10) standard deviation of the vitality degradation rate (in units of log10-1/yr). If this distribution parameter is omitted, then CANISTER_VITALITY_RATE must be included for all waste forms associated with this mechanism.
VITALITY_UPPER_TRUNCATION
Specifies the Log(base10) upper truncation of the mean vitality degradation rate (in units of log10-1/yr). If this distribution parameter is omitted, then CANISTER_VITALITY_RATE must be included for all waste forms associated with this mechanism.
CANISTER_MATERIAL_CONSTANT
Specifies the canister material constant (ex: 1500 for 316L stainless steel).
CANISTER_DEGRADATION_MODEL VITALITY_LOG10_MEAN -4.5 VITALITY_LOG10_STDEV 0.5 VITALITY_UPPER_TRUNCATION -3.0 CANISTER_MATERIAL_CONSTANT 1500 /
Full examples of the MECHANISM sub-block (note some values may be unrealistic, these are just examples for form, not parameter values):
MECHANISM GLASS
NAME glass02
SPECIFIC_SURFACE_AREA 2.78d-3 m^2/kg
MATRIX_DENSITY 2.0d3 kg/m^3
KIENZLER_DISSOLUTION
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
I-129 128.90d0 1.29d-15 2.18d-4 0.2d0
Am-241 241.06d0 5.08d-11 8.70d-4 0.0d0 Np-237
Np-237 237.05d0 1.03d-14 8.59d-4 0.2d0 U-233
U-233 233.04d0 1.38d-13 9.70d-9 0.0d0 Th-229
Th-229 229.03d0 2.78d-12 4.43d-12 0.0d0
/
CANISTER_DEGRADATION_MODEL
VITALITY_LOG10_MEAN -3.5
VITALITY_LOG10_STDEV 1.5
VITALITY_UPPER_TRUNCATION -2.75
CANISTER_MATERIAL_CONSTANT 1500.0
/
/
MECHANISM GLASS
NAME glass05
SPECIFIC_SURFACE_AREA 2.78d-3 m^2/kg
MATRIX_DENSITY 2.46d3 kg/m^3
K0 560.d0 kg/m^2-day #
K_LONG 400.d0 kg/m^2-day #
NU 5.d-2 #
EA 60211.58 J/mol #
Q 1.d0 # Dissolution model parameters
K 1.d0 #
V 1.d0 #
PH AS_CALCULATED #
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac, daughter
I-129 128.90d0 1.29d-15 2.18d-4 0.2d0
Am-241 241.06d0 5.08d-11 8.70d-4 0.0d0 Np-237
Np-237 237.05d0 1.03d-14 8.59d-4 0.2d0 U-233
U-233 233.04d0 1.38d-13 9.70d-9 0.0d0 Th-229
Th-229 229.03d0 2.78d-12 4.43d-12 0.0d0
/
CANISTER_DEGRADATION_MODEL
CANISTER_MATERIAL_CONSTANT 1500
/
/
MECHANISM DSNF
NAME dsnf01
MATRIX_DENSITY 3.56d3 kg/m^3
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Am-243 243.06d0 2.98d-12 1.12d-5 0.0d0
Th-230 230.03d0 2.75d-13 2.45d-8 0.0d0
/
CANISTER_DEGRADATION_MODEL
VITALITY_LOG10_MEAN -3.2
VITALITY_LOG10_STDEV 0.75
VITALITY_UPPER_TRUNCATION -2.0
CANISTER_MATERIAL_CONSTANT 1200.0
/
/
MECHANISM WIPP
NAME wipp3
MATRIX_DENSITY 1.d0 g/m^3
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
tracer 100.d0 2.d-15 1.12d0 0.0d0
tracer2 200.d0 2.d-15 1.12d0 0.0d0
/
/
MECHANISM CUSTOM
NAME custom05
FRACTIONAL_DISSOLUTION_RATE 2.0d-9 1/day
MATRIX_DENSITY 2.44d3 kg/m^3
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Pu-240 240.05d0 3.34d-12 2.84d-3 0.2d0 U-236
U-236 236.05d0 9.20d-16 4.33d-3 0.0d0
Tc-99 98.91d0 1.04d-13 8.87d-4 0.0d0
/
CANISTER_DEGRADATION_MODEL
CANISTER_MATERIAL_CONSTANT 1500.0
/
/
MECHANISM CUSTOM
NAME custom03
DISSOLUTION_RATE 4.1d-8 kg/m^2-day
SPECIFIC_SURFACE_AREA 2.11d-3 m^2/kg
MATRIX_DENSITY 2.44d3 kg/m^3
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Pu-240 240.05d0 3.34d-12 2.84d-3 0.2d0 U-236
U-236 236.05d0 9.20d-16 4.33d-3 0.0d0
Tc-99 98.91d0 1.04d-13 8.87d-4 0.0d0
/
CANISTER_DEGRADATION_MODEL
VITALITY_LOG10_MEAN -3.5
VITALITY_LOG10_STDEV 0.5
VITALITY_UPPER_TRUNCATION -2.75
CANISTER_MATERIAL_CONSTANT 1500.0
/
/
MECHANISM FMDM
NAME fmdm02
MATRIX_DENSITY 10.97d3 kg/m^3
BURNUP 60 #GWd/MTHM
SPECIFIC_SURFACE_AREA 0.001 m^2/g
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Uranium 238.02d0 1.00d-90 0.50d0 0.0d0
/
CANISTER_DEGRADATION_MODEL
CANISTER_MATERIAL_CONSTANT 1500.0
/
/
MECHANISM FMDM_SURROGATE
NAME fmdm_surrogate01
MATRIX_DENSITY 10.97d3 kg/m^3
BURNUP 60 #GWd/MTHM
SPECIFIC_SURFACE_AREA 0.001 m^2/g
DECAY_TIME 100 year
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Uranium 238.02d0 1.00d-90 0.50d0 0.0d0
/
CANISTER_DEGRADATION_MODEL
CANISTER_MATERIAL_CONSTANT 1400.0
/
/
WASTE_FORM sub-block
Specifies the details of each waste form. This block should be repeated for each waste form, and can include the following cards:
COORDINATE <double> <double> <double> -or- REGION <string>
If COORDINATE, <double> <double> <double> gives the location of each waste form in x, y, z. Waste forms can be co-located (i.e., there can be multiple waste forms located at the same coordinate point. If REGION, <string> gives the name of a defined region that the waste form occupies. The source term will be released over the cells of the REGION, or the single cell of the COORDINATE. Note that REGION and COORDINATE can’t be given, only one is allowed.
EXPOSURE_FACTOR <double> (optional)
Gives the exposure factor of each waste form, which is a multiplier to the waste form dissolution rate. If this keyword is not specified, the default value is 1.
VOLUME <double> <unit_string>
Gives the volume of each waste form.
MECHANISM_NAME <string>
Specifies the name of the mechanism associated with the waste form. The mechanism name given here must match one of the mechanisms defined in the MECHANISM sub-block(s).
CANISTER_VITALITY_RATE <double> <unit_string> (optional)
Specifies the waste form canister’s vitality degradation rate in units of 1/time. If this parameter is specified, the mechanism associated to this waste form must include the CANISTER_DEGRADATION_BLOCK, but without the distribution parameters (e.g. VITALITY_LOG10_MEAN, VITALITY_LOG10_STDEV, and VITALITY_UPPER_TRUNCATION). This option cannot be combined with CANISTER_BREACH_TIME for a single waste form, but both CANISTER_BREACH_TIME and CANISTER_VITALITY_RATE can be combined for different waste forms under the same mechanism which omits the distribution parameters.
CANISTER_BREACH_TIME <double> <unit_string> (optional)
Specifies the waste form canister’s breach time in units of time. The canister will breach during the next timestep where time > CANISTER_BREACH_TIME. If this parameter is specified, the mechanism associated to this waste form must include the CANISTER_DEGRADATION_BLOCK, but without the distribution parameters (e.g. VITALITY_LOG10_MEAN, VITALITY_LOG10_STDEV, and VITALITY_UPPER_TRUNCATION). This option cannot be combined with CANISTER_VITALITY_RATE for a single waste form, but both CANISTER_BREACH_TIME and CANISTER_VITALITY_RATE can be combined for different waste forms under the same mechanism which omits the distribution parameters.
DECAY_START_TIME <double> <unit_string> (optional)
Specifies the time that the waste within the waste form will begin to decay. If this card is not specified, the default decay start time is 0 seconds (e.g. at the first time step of the simulation). This card is useful if you have an inventory that is specific to a certain time in the simulation, and you don’t want to back-calculate what the inventory should have been at the beginning of the simulation.
CRITICALITY_MECHANISM_NAME <string> (optional)
Specifies the name of the associated criticality mechanism defining the criticality event in the waste form. The criticality mechanism name given here must match one of the mechanisms defined in the CRITICALITY_MECH sub-block(s).
SPACER_MECHANISM_NAME <string> (optional)
Specifies the name of the associated spacer grid degradation mechanism in the waste form. The spacer grid degradation mechanism name given here must match one of the mechanisms defined in the SPACER_DEGRADATION_MECHANISM sub-block(s).
WASTE_FORM COORDINATE 0.5d0 4.5d0 0.5d0 EXPOSURE_FACTOR 4.d0 VOLUME 1.14d0 m^3 MECHANISM_NAME glass02 / WASTE_FORM REGION WF-a1 VOLUME 2.1d0 m^3 CANISTER_BREACH_TIME 250 yr MECHANISM_NAME custom01 CRITICALITY_MECHANISM_NAME crit_01 SPACER_MECHANISM_NAME spc_01 / WASTE_FORM REGION WF-3b VOLUME 0.55d0 m^3 CANISTER_VITALITY_RATE 1.0d-7 1/yr MECHANISM_NAME custom01 /
Optional Cards:¶
PRINT_MASS_BALANCE
If this option is included, output will be generated at each timestep that the waste form process model is called. The output includes the cumulative mass and instantaneous mass rate for each species in each waste form, the volume, dissolution rate, and the canister vitality of each waste form.
IMPLICIT_SOLUTION
Including this card will solve the decay and ingrowth of the radionuclide inventory within the waste form using an implicit approach based on solving the Bateman equation using Newton’s method. This option should be used if the 3-generation analytical solution is not appropriate.
SPACER_DEGRADATION_MECHANISM
If this optional block is included, a time- and temperature-dependent spacer grid corrosion model will be evaluated as a means of terminating criticality events associated with the waste form. The model becomes active after the canister is breached. When the spacer grids have degraded below 1% of the original total mass, they are assumed to fail, which implies a loss of critical configuration.
The spacer grid vitality \(V_{s}\) is determined using the corrosion rate \(R\) and initial spacer thickness \(\tortuosity\) over time steps \(t_{i}\) to \(t_{i+1}\), where \(V_{s,0}=1\) until the canister breach time:
\(V_{s,i+1}=V_{s,i}-\frac{2R_{i+1}\cdot(t_{i+1}-t_{i})}{\tortuosity}\)
The areal weight gain \(W\) of the oxide layer is governed by a scaling constant \(\mathcal{C}\) and an Arrhenius term with the average temperature of the waste form \(\bar{T}\), the activation energy \(Q\), and the ideal gas constant \(\mathcal{R}\):
\(W_{i+1}=\mathcal{C}\exp{\left(-\frac{Q}{\mathcal{R}\bar{T}_{i+1}}\right)}\)
The total corrosion rate \(R\) is found by including the metal loss ratio \(\alpha\), an irradiation factor \(\beta\), and a saturation-dependent term \(f_{S}(S_{l})\):
\(R_{i+1}=f_{S}(S_{l,i+1})\cdot \alpha\cdot\beta\cdot W_{i+1}\)
The extent of original metal consumed in the oxide layer formation \(\Delta\tortuosity|_{lab}\) and the areal weight gain of oxide layer \(\Delta W|_{lab}\), as observed in the laboratory, are used to determine the metal loss ratio \(\alpha\), which is considered constant. The factor \(\beta\) is used to adjust the rate based on the effects of prior irradiation.
\(\alpha=\frac{\Delta\tortuosity|_{lab}}{\Delta W|_{lab}}\)
The saturation-dependent term modifies the corrosion rate depending on an exposure level \(S_{l}^{exp}\), which is the saturation for which the spacer grids are considered fully-inundated with water. When the saturation of the waste form is at or above this limit, the corrosion rate is unaffected. Otherwise, the rate is reduced proportionally based on the saturation.
\(f_{S}(S_{l})=\left\{{\begin{array}{cc} \frac{S_{l}}{S_{l}^{exp}} & S_{l}<S_{l}^{exp} \\ 1 & S_{l}\geq S_{l}^{exp} \\ \end{array} }\right.\)
NAME <name_string>
Specifies a unique name for the spacer grid degradation model.
METAL_LOSS_RATIO <double> <unit_string>
The ratio of the extent [m] of original metal that is consumed by corrosion to the areal weight gain \(\left[\frac{kg}{m^2}\right]\) of the oxide layer, \(\alpha\,\left[\frac{m^{3}}{kg}\right]\).
THICKNESS <double> <unit_string>
Initial thickness of the spacer grid metallic separators, \(\tortuosity\) [m] .
EXPOSURE_LEVEL <double> (optional)
Threshold saturation \(S_{l}^{exp}\) for spacer grids to be considered fully-inundated with water. Saturation-dependence can be turned off by setting \(S_{l}^{exp}=0\) or by not including this entry.
C <double> <unit_string>
Empirical coefficient of the Arrhenius term governing corrosion, \(\mathcal{C}\,\,\left[\frac{kg}{m^{2}s}\right]\).
Q <double> <unit_string>
Activation energy operating on the reciprocal of temperature within the Arrhenius term governing corrosion, \(Q\) [J/mol].
RAD_FACTOR <double>
Factor by which to increase the corrosion rate based on the effect of prior irradiation, \(\beta\). This should be set to 1.0 for non-irradiated Zircaloy or a higher value (around 2.0) for spacer grids that have been irradiated. \(\beta\) cannot be less than or equal to zero.
CRITICALITY_MECH
Including this card will define a criticality mechanism that can specified for a waste form containing fissile material.
NAME <name_string>
Specifies a unique name for the criticality mechanism.
CRIT_START <double> <unit_string>
The start time of the criticality event.
CRIT_END <double> <unit_string>
The end time of the criticality event.
CRITICAL_WATER_SATURATION <double>
This is the liquid saturation below which the criticality event cannot be sustained. There is no heat emission from criticality until the waste form saturation is at or above this level. This is meant to be used for canisters in unsaturated systems and is not a permanent criticality termination mechanism.
CRITICAL_WATER_DENSITY <double> <unit_string>
This the liquid density below which the criticality event cannot be sustained. There is no heat emission from criticality until the waste form liquid density is at or above this level. This is meant to be used for canisters in saturated systems where moderator voiding is a key reactivity feedback mechanism, and it is not a permanent criticality termination mechanism.
HEAT_OF_CRITICALITY
This sub-block defines the heat source term from criticality either as a constant (CONSTANT_POWER) or as a value that can obtained from a temperature-based lookup table (DATASET). The average temperature of the waste form and CRIT_START are used for interpolation of the lookup table to provide the power output from the waste form for the duration of the criticality event.
CONSTANT_POWER <double> <unit_string>
DATASET <file_string>
Please refer to the example “crit_heat.txt” provided for the regression test “glass_general.in” for formatting. The data file specified by <file_string> contains the following input segments:
NUM_START_TIMES <integer>
The number of criticality start times provided in START_TIME (see below).
NUM_VALUES_PER_START_TIME <integer>
The number of data values per given criticality start time.
TIME_UNITS <unit_string> (optional)
The units of time provided for the START_TIME values (see below).
POWER_UNITS <unit_string> (optional)
The units of power provided for the POWER values (see below).
START_TIME
The start times of the criticality events relative to the beginning of the PFLOTRAN simulation, which are provided after the keyword as a list of reals. This affects the power output as the quantity of fissile nuclides, precursors, and neutron absorbers forming the source term for sustained chain reactions are affected by the decay period.
TEMPERATURE
The average waste form temperatures determining power output for a given start time, which are provided after the keyword as a list of reals. The temperature affects the power output via reactivity feedback from Doppler broadening, thermal expansion, and moderator voiding. Such phenomena are factored into the original neutronics calculations forming the basis of this surrogate model.
POWER
The waste form power outputs from the criticality event per given average temperature and start time, which are provided after the keyword as a list of reals.
DECAY_HEAT <type_string>
This sub-block defines the heat source term from radioactive decay, which is obtained from a time-dependent lookup table. The types of decay heat treatment include TOTAL, ADDITIONAL, and CYCLIC. By default, when a criticality event is active, the criticality source term is assumed to account for decay heat and this data is ignored.
DATASET <file_string>
INVENTORY
This sub-block defines the fractional (g/g) nuclide inventory during criticality, which is obtained from a time-dependent lookup table and overrides the implicit calculation with the Bateman equations. The number of data entries in this table must equal the number of species specified in the waste form process model.
DATASET <file_string>
This option allows for the specification of simple lookup table specified by <file_string> where each row has the time of evaluation followed by mass fractions for each nuclide in the waste form listed in the order provided within SPECIES in MECHANISM. The table is linearly interpolated during the simulation and is assumed to correspond to the criticality conditions implied in the CRITICALITY_MECHANISM sub-block. The data table is preceded by the following keywords in the file:
TIME_UNITS <unit_string> (optional)
The units of time.
DATA_UNITS <unit_string> (optional)
The units for the nuclide inventory.
EXPANDED_DATASET <file_string>
This option allows for the specification of an expanded inventory lookup table that can be interpolated in three dimensions for a given criticality start time (CRIT_START), criticality power output (HEAT_OF_CRITICALITY), and a given time during the simulation. These values are used to interpolate a data matrix where the start time and power are pivot variables and the simulation time is the independent variable. Please refer to the example data tables provided for the regression test “glass_criticality_inventory.in” for guidance on formatting. The data file specified by <file_string> contains the following input segments:
MODE <string> (optional)
- POLYNOMIAL (default)
The lookup table will be interpolated with Lagrange polynomials.
- LINEAR
The lookup table will be interpolated using the trilinear method.
NUM_START_TIMES <integer> (optional)
Checks the number of criticality start times expected in the START_TIME list.
NUM_POWERS <integer> (optional)
Checks the number of powers expected in the POWER list.
TOTAL_POINTS <integer> (optional)
Checks the total number of inventory evaluation times expected in the REAL_TIME list. This keyword can be used if the real time arrays for each dataset are of different lengths and cannot be described completely by NUM_REAL_TIMES.
NUM_REAL_TIMES <integer> (optional)
Checks the maximum length of an individual real time array expected in the REAL_TIME list. This keyword can be used without TOTAL_POINTS if the real time arrays for each dataset are the same length.
NUM_SPECIES <integer> (optional)
TIME_UNITS <unit_string> (optional)
The units of time for the values in START_TIME and REAL_TIME (used for conversion to internal units).
POWER_UNITS <unit_string> (optional)
The units of power for the values in POWERS (used for conversion to internal units).
DATA_UNITS <unit_string> (optional)
The units of inventory for the values in each INVENTORY block (used for conversion to internal units).
START_TIME
The start times of the criticality events relative to the beginning of the PFLOTRAN simulation, which are provided after the keyword as a list of reals. This is the first pivot variable used to construct the data matrix.
POWER
The power outputs of the criticality events, which are provided after the keyword as a list of reals. This is the second pivot variable used to construct the data matrix so the list is not duplicated per START_TIME. Per combination of START_TIME and POWER, there must be a dataset (i.e. no sparse data matrix).
REAL_TIME
The arrays of evaluation times for the radionuclide inventory, which are provided after the keyword as a list of reals. These values serve as the independent variables for the data matrix and the arrays have a multiplicity based on START_TIME and POWER. If TOTAL_POINTS is specified, the times must increase monotonically as a means of separating arrays.
INVENTORY <name_string>
For each radionuclide in the waste form using this lookup table, an INVENTORY block provides the mass fractions per given value in the REAL_TIME list. The name of the radionuclide is provided as <name_string> and must follow the spellings of SPECIES in the waste form MECHANISM. However, the INVENTORY blocks do not have to follow the same order as SPECIES. The mass fractions are listed as real numbers after the keyword line.
OPTION (optional)
This sub-block allows for the specification of options for the INVENTORY block.
USE_LOOKUP_AND_IMPLICIT (optional)
If EXPANDED_DATASET is being used, this option allows for the PFLOTRAN implicit solution to be employed (i.e., radionuclide decay with no external sources) if the simulation time exceeds the maximum REAL_TIME in the relevant portion of the lookup table.
USE_LOOKUP_AND_EXTRAPOLATION (optional)
If EXPANDED_DATASET is being used, this option allows for the interpolation subroutine to also be used for extrapolation when the simulation time exceeds the maximum REAL_TIME in the relevant portion of the lookup table.
USE_LOOKUP_AFTER_CRITICALITY (optional)
If EXPANDED_DATASET is being used, this option allows for the lookup table to continue defining radionuclide inventories after the criticality event has ended (see CRIT_END). Otherwise, the implicit solution (decay-only) is employed when time exceeds CRIT_END.
LOG10_TIME_INTERPOLATION (optional)
If EXPANDED_DATASET is being used, this option allows for REAL_TIME interpolation of the lookup table to be based on the logarithm (base 10) of those values. For instances of \(t=0\,[s]\) in the lookup table, a substitute value of \(t=10^{-20}\,[s]\) is used, which may introduce bias depending on the choice of time steps in the simulation and the degree of time fidelity in the table. This option is recommended only if the simulation extends across multiple decades of time and if the time points in the table also extend logarithmically but are sparse.
WASTE_FORM REGION wf EXPOSURE_FACTOR 1.d0 VOLUME 1.5d0 m^3 MECHANISM_NAME csnf CANISTER_BREACH_TIME 2.50d+2 y CRITICALITY_MECHANISM_NAME crit_01 SPACER_MECHANISM_NAME spc_01 / CRITICALITY_MECH NAME crit_01 CRIT_START 3.00d+2 y CRIT_END 2.00d+3 y CRITICAL_WATER_SATURATION 0.700d+0 CRITICAL_WATER_DENSITY 9.200d+2 kg/m^3 HEAT_OF_CRITICALITY CONSTANT_POWER 4.0d+0 kW # DATASET criticality_heat.txt / DECAY_HEAT TOTAL DATASET ./decay_heat.txt / INVENTORY DATASET ./inventory_crit.txt / / SPACER_DEGRADATION_MECHANISM NAME spc_01 METAL_LOSS_RATIO 4.42953d-04 m^3/kg THICKNESS 5.00000d-04 m EXPOSURE_LEVEL 9.93317d-01 C 3.47000d+07 mg/day-dm^2 Q 2.27570d+04 cal/mol RAD_FACTOR 2.00000d+00 /
Full Example:¶
The following example specifies several waste forms, each associated with one of two particular mechanisms. Output will be generated for each waste form.
WASTE_FORM_GENERAL
PRINT_MASS_BALANCE
MECHANISM FMDM
NAME fmdm01
MATRIX_DENSITY 10.97d3 kg/m^3
BURNUP 60 #GWd/MTHM
SPECIFIC_SURFACE_AREA 0.001 m^2/g
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Uranium 238.02d0 1.00d-90 0.50d0 0.0d0
/
CANISTER_DEGRADATION_MODEL
VITALITY_LOG10_MEAN -3.2
VITALITY_LOG10_STDEV 0.75
VITALITY_UPPER_TRUNCATION -2.0
CANISTER_MATERIAL_CONSTANT 1200.0
/
/
MECHANISM CUSTOM
NAME custom05
FRACTIONAL_DISSOLUTION_RATE 2.0d-9 1/day
MATRIX_DENSITY 2.44d3 kg/m^3
SPECIES
#name, MW[g/mol],dcy[1/s], initMF, inst_rel_frac,daughter
Pu-240 240.05d0 3.34d-12 2.84d-3 0.2d0 U-236
U-236 236.05d0 9.20d-16 4.33d-3 0.0d0
Tc-99 98.91d0 1.04d-13 8.87d-4 0.0d0
/
CANISTER_DEGRADATION_MODEL
CANISTER_MATERIAL_CONSTANT 1500.0
/
/
WASTE_FORM
REGION WF-custom-1
EXPOSURE_FACTOR 3.d0
VOLUME 1.14d0 m^3
MECHANISM_NAME custom05
CANISTER_BREACH_TIME 375 yr
/
WASTE_FORM
REGION WF-custom-2
EXPOSURE_FACTOR 4.d0
VOLUME 1.14d0 m^3
MECHANISM_NAME custom05
CANISTER_VITALITY_RATE 3.d-6 1/day
/
WASTE_FORM
COORDINATE 12.5d0 55.5d0 0.5d0
VOLUME 1.55d0 m^3
MECHANISM_NAME fmdm01
/
WASTE_FORM
COORDINATE 5.5d0 4.5d0 0.5d0
VOLUME 1.55d0 m^3
MECHANISM_NAME fmdm01
/
END_WASTE_FORM_GENERAL
