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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
      GLOBAL_IMPLICIT
    /
  /
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, WIPP, 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^3

The 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; 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_DISSOLUTION
    

    K0 <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:

    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; 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
    
  • 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, 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, or WIPP)

    Specifies the fractional dissolution rate for the waste form bulk (or matrix), in units of fractional volume per time. The unit string should resemble 1/time.

    FRACTIONAL_DISSOLUTION_RATE 3.4d-8 1/day
    

    SPECIFIC_SURFACE_AREA <double> <unit_string> (required for types GLASS, FMDM; 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 sub-block for ALL 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  237.05d0  1.03d-14  8.59d-4   0.2d0  Am-241
    U-233   233.04d0  1.38d-13  9.70d-9   0.0d0  Np-237
    Th-229  229.03d0  2.78d-12  4.43d-12  0.0d0  U-233
  /
  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   236.05d0  9.20d-16  4.33d-3  0.0d0  Pu-240
    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   236.05d0  9.20d-16  4.33d-3  0.0d0  Pu-240
    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 #MWd/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
    /
  /

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.
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
/

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.

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 #MWd/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   236.05d0  9.20d-16  4.33d-3  0.0d0  Pu-240
      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