# Modified Forsberg-Massih Model

Outdated model. It's recommended to use Sifgrs instead

## Description

warning

The ForMas model is maintained but not actively developed. The Sifgrs model is recommended.

As an additional option, fission gas release (FGR) can be computed based on the traditional Forsberg-Massih model, ForMas, (Forsberg and Massih, 1985). This model considers FGR only, hence the fission gas swelling must be calculated separately by means of an empirical model (see section on Fission Product Swelling).

ForMas incorporates a two-stage approach to predict gas release. The first stage computes diffusion of fission gas atoms from within the fuel grains to the grain boundaries, by solving numerically the relevant diffusion equation in spherical co-ordinates. An effective diffusion coefficient is employed, which accounts for gas atom resolution from and trapping into intra-granular bubbles. A formulation based on Turnbull et al. (1987) and Denis and Piotrkowski (1996) is used to calculate the single gas atom diffusion coefficient, and correction for the effects of intra-granular bubbles is modeled based on the correlations reported in White and Tucker (1983). The second stage of the model utilizes time-dependent boundary conditions to determine grain boundary gas accumulation as inter- granular lenticular bubbles, resolution, saturation, and release. FGR from the grain boundaries is controlled using a grain boundary saturation criterion that involves a threshold concentration of gas at the grain boundaries.

For the current implementation, the fuel grains are assumed to be constant in diameter, thus grain growth and grain-boundary sweeping effects are not considered. Further, the model describes a smooth continuous release process, and is thus not applicable to sudden releases or bursts. These are significant limitations, which must be alleviated to provide more realistic FGR predictions. Accordingly, a more mechanistic model is currently being implemented in Bison which considers the structure of both the fuel (fuel grains and pores) and grain boundaries, and includes the effects of grain growth and grain boundary sweeping. This model will be directly coupled to the volumetric swelling calculation, thus replacing the empirical model described at the bottom of VSwellingUO2.

Following Wallin (2012), the ForMas model implemented in Bison includes some modifications compared to the original Forsberg and Massih (1985) model, namely:

• The following three-term formulation, based on Turnbull et al. (1987) and Denis and Piotrkowski (1996), is used to calculate the single gas atom diffusion coefficient (1) where (K) is the temperature and (ms) is the fission rate.

• The rate of gas atom resolution from the grain boundaries back into the grains is scaled by fission rate, in line with White and Tucker (1983).

• Instead of assuming release of the total gas inventory at the grain boundaries upon saturation (Forsberg and Massih, 1985), only the gas above the saturation level is considered to be released.

The modified Forsberg-Massih model implemented in Bison was tested using a single LWR fuel pellet, assuming uniform constant power. Typical input parameters for UO fuel, as shown in Table 1, were assumed. Calculations were compared to the well known Vitanza or Halden threshold Vitanza et al. (1979), which correlates a large set of FGR data in terms of fuel centerline temperature versus burnup at roughly one percent gas release; this threshold is often used to evaluate and calibrate FGR models. A typical comparison is shown in Figure 1, which considers the effect of hydrostatic pressure on the computed gas release (the Vitanza et al. (1979) threshold is included for comparison). Symbols in the figure indicate individual simulations at various axial power levels. As has been reported earlier (Uffelen, 2002), an increase in hydrostatic pressure significantly shifts the onset of gas release to higher burnups.

Table 1: Input parameters for the modified Forsberg-Massih fission gas release model

Input parameterValue
Fuel grain radius (m)
Frac. yield of fission gas atoms per fission
Reference resolution rate of intergranular gas (s)
Resolution layer depth (m)
Grain boundary bubble radius (m)
Nonspherical bubble shape factor (-)
Bubble surface tension (J/m)
Grain boundary frac. coverage at saturation (-)

Figure 1: Effect of hydrostatic pressure on centerline temperature versus burnup for 1 percent average fission gas release. The Vitanza threshold is included for comparison.

## Example Input Syntax


[./Fission_Gas_Release]
type = ForMas
block = 1
#   resolution_rate = 1.55e-5
resolution_rate = 0.
calibration_factor = 0
temp = T
fission_rate = fission_rate
[../]
(test/tests/fission_gas_release_formas/formas_second_stage_1.i)

## Input Parameters

• release_fraction0fraction of boundary and resolved gas released at saturation

Default:0

C++ Type:double

Description:fraction of boundary and resolved gas released at saturation

• resolution_rate1e-07resolution rate from intergranular bubbles (1/s)

Default:1e-07

C++ Type:double

Description:resolution rate from intergranular bubbles (1/s)

• bubbles_per_fragment24number of intragranular bubbles nucleated per fission fragment

Default:24

C++ Type:double

Description:number of intragranular bubbles nucleated per fission fragment

• fractional_coverage0.5fractional coverage of grain boundary at saturation

Default:0.5

C++ Type:double

Description:fractional coverage of grain boundary at saturation

• calibration_factor1calibration factor multiplied by gas saturation density

Default:1

C++ Type:double

Description:calibration factor multiplied by gas saturation density

• resolution_depth1e-08resolution layer depth (m)

Default:1e-08

C++ Type:double

Description:resolution layer depth (m)

• surface_tension0.626bubble surface tension (J/m**2)

Default:0.626

C++ Type:double

Description:bubble surface tension (J/m**2)

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• external_pressure_functionThe name of the external pressure function.

C++ Type:FunctionName

Description:The name of the external pressure function.

• fractional_yield0.3017fraction yield of fission gas atoms per fission

Default:0.3017

C++ Type:double

Description:fraction yield of fission gas atoms per fission

• hydrostatic_stressCoupled Hydrostatic Stress

C++ Type:std::vector

Description:Coupled Hydrostatic Stress

• fragment_influence1e-09fission fragment range of influence (m)

Default:1e-09

C++ Type:double

Description:fission fragment range of influence (m)

• fragment_range6e-06fission fragment travel distance before coming to rest (m)

Default:6e-06

C++ Type:double

Description:fission fragment travel distance before coming to rest (m)

• external_pressure1e+07external hydrostatic pressure (Pa)

Default:1e+07

C++ Type:double

Description:external hydrostatic pressure (Pa)

Default:1e-05

C++ Type:double

Description:fuel grain radius (m)

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• bubble_shape_factor0.287non-spherical bubble shape factor

Default:0.287

C++ Type:double

Description:non-spherical bubble shape factor

• fission_rateCoupled Fission Rate

C++ Type:std::vector

Description:Coupled Fission Rate

• tempCoupled Temp

C++ Type:std::vector

Description:Coupled Temp

Default:5e-07

C++ Type:double

Description:grain boundary bubble radius (m)

• plenum_pressureThe name of the plenum_pressure postprocessor value.

C++ Type:PostprocessorName

Description:The name of the plenum_pressure postprocessor value.

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• testing_outputFalseWhether or not to output information for debugging purposes

Default:False

C++ Type:bool

Description:Whether or not to output information for debugging purposes

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

## References

1. Alicia Denis and Rosa Piotrkowski. Simulation of isothermal fission gas release. Journal of Nuclear Materials, 229:149â€“154, 1996.[BibTeX]
2. K. Forsberg and A. R. Massih. Diffusion theory of fission gas migration in irradiated nuclear fuel UO$_2$. Journal of Nuclear Materials, 135(2-3):140â€“148, 1985.[BibTeX]
3. J. A. Turnbull, R. White, and C. Wise. The diffusion coefficient for fission gas atoms in UO$_2$. Technical Report IAEA-TC-659/3.5, International Atomic Energy Agency, 1987.[BibTeX]
4. Paul van Uffelen. Modelling isothermal fission gas release. In Technical and economic limits to fuel burnup extension, number IAEA-TECDOC-1299, 17–30. International Atomic Energy Agency, 2002.[BibTeX]
5. C. Vitanza, E. Kolstad, and U. Graziani. Fission gas release from UO$_2$ pellet fuel at high burnup. In Proceedings of the American Nuclear Society Meeting on Light Water Reactor Fuel Performance, 361. Portland, Oregon, Apr 29 to May 3, 1979.[BibTeX]
6. H. Wallin. Forsberg-Massih fission gas model in BISON: calibration using the RisÃ¶3 fuel test AN2. Technical Report Anatech, San Diego, CA, 2012.[BibTeX]
7. R.J. White and M.O. Tucker. A new fission-gas release model. Journal of Nuclear Materials, 118:1â€“38, 1983.[BibTeX]