# Integral Fuel Burnable Absorber Helium Production

Computes the Helium gas production as a result of an IFBA layer applied to the surface of a fuel rod

## Description

IFBAHeProduction computes the Helium gas production as a result of an IFBA layer applied to the surface of a fuel rod.

An integral fuel burnable absorber (IFBA) is used for optimizing fuel assembly reactivity and power distribution in a core. The IFBA is usually applied as a thin layer of ZrB over some length of a fuel rod. The boron-10 isotope in the IFBA material absorbs a neutron and results in a lithium and helium atom according to the following reaction: (1)

In addition, the IFBA layer is depleted very quickly and is typically used up in the first 3 percent of burnup or 18 months of exposure.

## Helium Production

Since the IFBA layer is normally on the order of a few microns thick, the helium atoms generated are assumed to be released immediately into the plenum.

Two models for the helium gas production (i.e., boron-10 depletion) have been implemented in Bison. The first model uses an equation based on burnup (Lee et al., 2012) and the second is the model used in FRAPCON (K. J. Geelhood et al., 2015).

### Burnup Based Model

This burnup based equation for boron-10 depletion was generated using a DeCART depletion calculation (Lee et al., 2012) for boron in an IFBA rod. The effects of boron concentration and U-235 enrichment were studied. In addition, an improved approximation for the time dependency of U-235 number density decrease and fissile plutonium production resulted in the following relationship for the number density of boron-10: (2) where is the boron-10 number density at time , is the initial boron-10 number density, is the U-235 enrichment, and is the burnup. The values of the parameters are given in Table 1.

Table 1: Parameters for the Evolution of Boron-10 Density with Burnup, Eq. 2 (Lee et al., 2012)

ParameterValue
1.59389
-0.00773
0.01051

### FRAPCON Model

In FRAPCON the helium production rate is derived using an MCNP calculation for boron depletion. The empirical fit to this calculation is (3) where is the helium production rate (number of atoms/cm-s), is the percent of IFBA rods in a reactor core (this value is limited to the range of 10 percent to 50 percent), and is the Boron-10 enrichment (percent) (restricted to 0 to 90 percent). The values of the parameters are given in Table 2.

Table 2: Parameters for the Empirical Fit to the MCNP Calculation for He Production Rate, Eq. 3 (K. J. Geelhood et al., 2015)

ParameterValue

The implementation of this empirical relationship in the FRAPCON code (K. J. Geelhood et al., 2015) uses the following form to calculate the helium production rate (4) where is the linear power in kW/ft, is the density of ZrB (g/cm), and the coefficients are given in Table 2.

Table 3: Parameters for the Numerical Implementation of the He Production Rate, Eq. 4 (K. J. Geelhood et al., 2015)

ParameterValue

Then the boron depletion rate is a function of , given as (5)

## Input Parameter Conventions

The parameters listed in Table 4 are used to calculate the initial number density of boron-10 atoms and therefore the limiting value for the moles of He gas generated by the IFBA material. Note that the units used by Bison differ from the units generally used in industry; the user must convert the input arguments to the appropriate Bison units.

Table 4: Input Parameters for IFBA Postprocessor

ParameterTypical UnitsBison Units
IFBA Lengthcmm
B-10 Enrichment%fraction
ZrB Density% TDkg/m
or
ZrB Thicknessmm

The model specific parameters for the two equations are listed in Table 5.

Table 5: Model Specific Input Parameters for IFBA

ModelParameterTypical UnitsBison Units
Burnup Based Model (Eq. 2)U-235 Enrichment%(fraction)
FRAPCON Model (Eq. 3)IFBA Rod %%(fraction)

In addition, the burnup model Eq. 2 requires a postprocessor to provide the average burnup in the fuel and the FRAPCON model Eq. 3 requires a postprocessor to provide the rod average linear power.

## Example Input Syntax


[./he_prod]
type = IFBAHeProduction
ifba_len = 1.0e-2
b10_enrich = 0.50
zrb2_rel_dens = 0.7
model = burnup
u235_enrich = 0.045
burnup = average_burnup
[../]
(test/tests/ifba_he_production/fill_gas_xenon_w_ifba.i)

Because this input file is using the burnup model Eq. 2, the average burnup in the fuel post processor is also required. Note that the name of the average burnup postprocessor is used as the argument to the burnup input parameter in the IFBAHeProduction post processor.


[./average_burnup]
type = ElementAverageValue
block = '3'
variable = burnup
[../]
(test/tests/ifba_he_production/fill_gas_xenon_w_ifba.i)

## Input Parameters

• ifba_lenAxial length of IFBA layer on pellets (m)

C++ Type:double

Description:Axial length of IFBA layer on pellets (m)

• b10_enrichB-10 enrichment (fraction)

C++ Type:double

Description:B-10 enrichment (fraction)

### Required Parameters

• u235_enrich-1Initial U-235 enrichment (fraction)

Default:-1

C++ Type:double

Description:Initial U-235 enrichment (fraction)

• rod_ave_lin_powThe power function

C++ Type:FunctionName

Description:The power function

• zrb2_thick-1Thickness of ZrB2 layer on pellets (m)

Default:-1

C++ Type:double

Description:Thickness of ZrB2 layer on pellets (m)

Default:-1

C++ Type:double

Default:-1

C++ Type:double

• ifba_rod_pct-1Percentage of fuel rods containing IFBA liners (fraction)

Default:-1

C++ Type:double

Description:Percentage of fuel rods containing IFBA liners (fraction)

• zrb2_rel_dens-1Relative density of ZrB2 material (fraction)

Default:-1

C++ Type:double

Description:Relative density of ZrB2 material (fraction)

Default:-1

C++ Type:double

Description:Fuel pellet outer radius (m)

• debug0Debugging output flag: 0 = no output (default), 1 = debugging output to console

Default:0

C++ Type:int

Description:Debugging output flag: 0 = no output (default), 1 = debugging output to console

• execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

Default:TIMESTEP_END

C++ Type:ExecFlagEnum

Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

• modelburnupHe generation model: Choices are burnup or frapcon. Default is burnup.

Default:burnup

C++ Type:MooseEnum

Description:He generation model: Choices are burnup or frapcon. Default is burnup.

• burnupThe name of the postprocessor containing the rod average burnup

C++ Type:PostprocessorName

Description:The name of the postprocessor containing the rod average burnup

### 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.

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

C++ Type:std::vector

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

• 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.

• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

Default:False

C++ Type:bool

Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

• force_preauxFalseForces the GeneralUserObject to be executed in PREAUX

Default:False

C++ Type:bool

Description:Forces the GeneralUserObject to be executed in PREAUX