Bateman Equation

[tolstoy]

Wondering if anyone has the Bateman equation in Excel, C++, or VB format? Thanks.

[Rennhack]

http://sti.srs.gov/fulltext/tr2004293/tr2004293.pdf

Appendix A.

Public Function Vegetable_Ingestion(Plant_to_Soil_RadMassConc_Rat io As Double, _
RadVolConc_Waste As Double, _
Soil_Mixing_Dilution_Factor As Double, _
Annual_ConsumedMass_Vegetable s As Double, _
DCF_Ingestion As Double, _
BulkDensity_Soil As Double) As Double
'Vegetable Ingestion Pathway
'Returns annual EDE (rem/yr) from vegetable ingestion for given inputs
' Plant_to_Soil_RadMassConc_Rat io - plant-to-soil concentration ratio for radionuclide
(uCi/kg vegetable per uCi/kg dry soil)
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Soil_Mixing_Dilution_Factor - dilution factor for mixing of exhumed waste with garden soil
' Annual_ConsumedMass_Vegetable s - annual consumption of vegetables (kg/yr)
' DCF_Ingestion - DCF for ingestion of radionuclide (rem/uCi)
' BulkDensity_Soil - bulk density of soil (kg/m3)
Vegetable_Ingestion = Plant_to_Soil_RadMassConc_Rat io * _
RadVolConc_Waste * Soil_Mixing_Dilution_Factor * _
Annual_ConsumedMass_Vegetable s * _
DCF_Ingestion / BulkDensity_Soil
End Function

Public Function Soil_Ingestion(RadVolConc_Waste As Double, _
Soil_Mixing_Dilution_Factor As Double, _
Annual_ConsumedMass_Soil As Double, _
DCF_Ingestion As Double, _
BulkDensity_Soil As Double) As Double
'Soil Ingestion Pathway
'Returns annual EDE (rem/yr) from soil ingestion for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Soil_Mixing_Dilution_Factor - dilution factor for mixing of exhumed waste with garden soil
' Annual_ConsumedMass_Soil - annual consumption of soil (kg/yr)
' DCF_Ingestion - DCF for ingestion of radionuclide (rem/uCi)
' BulkDensity_Soil - bulk density of soil (kg/m3)
Soil_Ingestion = RadVolConc_Waste * Soil_Mixing_Dilution_Factor * _
Annual_ConsumedMass_Soil * DCF_Ingestion / BulkDensity_Soil
End Function

Public Function Garden_Exposure(RadVolConc_Waste As Double, _
Soil_Mixing_Dilution_Factor As Double, _
Year_Fraction_Garden_Exposure As Double, _
DCF_15cmSoil As Double) As Double
'External Exposure to Soil Working in Garden
'Returns annual EDE (rem/yr) from exposure working in garden for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Soil_Mixing_Dilution_Factor - dilution factor for mixing of exhumed waste with garden soil
' Year_Fraction_Garden_Exposure - fraction of year that exposure in garden occurs
' DCF_15cmSoil - DCF for uniform distribution in 15 cm of surface soil (rem/yr per uCi/m3)
Garden_Exposure = RadVolConc_Waste * Soil_Mixing_Dilution_Factor * _
Year_Fraction_Garden_Exposure * DCF_15cmSoil
End Function

Public Function Home_AG_Exposure(RadVolConc_Waste As Double, _
Year_Fraction_Home_Exposure As Double, _
DCF_InfSoil_NoShield As Double, _
Shielding_Factor_Home As Double) As Double
'External Exposure Residing in Home for Agriculture
'Returns annual EDE (rem/yr) from exposure residing in home for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Year_Fraction_Home_Exposure - fraction of year that exposure in home occurs
' DCF_InfSoil_NoShield - DCF for uniform distribution in infinite soil with no shielding
(rem/yr per uCi/m3)
' Shielding_Factor_Home - shielding factor for home (uniform for all radionuclides)
Home_AG_Exposure = RadVolConc_Waste * Year_Fraction_Home_Exposure * _
DCF_InfSoil_NoShield * Shielding_Factor_Home
End Function

Public Function Garden_Inhalation(RadVolConc_Waste As Double, _
Soil_Mixing_Dilution_Factor As Double, _
AtmMassLoading_Soil_Garden As Double, _
Year_Fraction_Garden_Exposure As Double, _
Annual_AirVolIntake_Garden As Double, _
DCF_Inhalation As Double, _
BulkDensity_Soil As Double) As Double
'Inhalation of Particles Working in Garden
'Returns annual EDE (rem/yr) from soil inhalation in garden for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Soil_Mixing_Dilution_Factor - dilution factor for mixing of exhumed waste with garden soil
' AtmMassLoading_Soil_Garden - atmospheric mass loading of surface soil for garden (kg/m3)
' Year_Fraction_Garden_Exposure - fraction of year during which inhalation exposure in garden occurs
' Annual_AirVolIntake_Garden - annual air intake in garden (m3/yr)
' DCF_Inhalation - DCF for inhalation of radionuclide (rem/uCi)
' BulkDensity_Soil - bulk density of soil (kg/m3)
Garden_Inhalation = RadVolConc_Waste * Soil_Mixing_Dilution_Factor * _
AtmMassLoading_Soil_Garden * _
Year_Fraction_Garden_Exposure * _
Annual_AirVolIntake_Garden * _
DCF_Inhalation / BulkDensity_Soil
End Function

Public Function Home_Inhalation(RadVolConc_Waste As Double, _
AtmMassLoading_Soil_Home As Double, _
Year_Fraction_Home_Exposure As Double, _
Annual_AirVolIntake_Home As Double, _
DCF_Inhalation As Double, _
BulkDensity_Soil As Double) As Double
'Inhalation of Particles Residing in Home
'Returns annual EDE (rem/yr) from soil inhalation in home for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' AtmMassLoading_Soil_Home - atmospheric mass loading of surface soil for home (kg/m3)
' Year_Fraction_Home_Exposure - fraction of year during which inhalation exposure in home occurs
' Annual_AirVolIntake_Home - annual air intake in home (m3/yr)
' DCF_Inhalation - DCF for inhalation of radionuclide (rem/uCi)
' BulkDensity_Soil - bulk density of soil (kg/m3)
Home_Inhalation = RadVolConc_Waste * _
AtmMassLoading_Soil_Home * _
Year_Fraction_Home_Exposure * _
Annual_AirVolIntake_Home * _
DCF_Inhalation / BulkDensity_Soil
End Function

Public Function Home_Res_Exposure(RadVolConc_Waste As Double, _
Year_Fraction_Home_Exposure As Double, _
DCF_InfSoil_100cmShield As Double, _
Shielding_Factor_Home As Double) As Double
'External Exposure Residing in Home for Resident
'Returns annual EDE (rem/yr) from exposure residing in home for given inputs
' RadVolConc_Waste - concentration of radionuclide in exhumed waste (uCi/m3)
' Year_Fraction_Home_Exposure - fraction of year that exposure in home occurs
' DCF_InfSoil_100cmShield - DCF for uniform distribution in infinite soil with 100 cm shielding
(rem/yr per uCi/m3)
' Shielding_Factor_Home - shielding factor for home (uniform for all radionuclides)
Home_Res_Exposure = RadVolConc_Waste * Year_Fraction_Home_Exposure * _
DCF_InfSoil_100cmShield * Shielding_Factor_Home
End Function

Public Function RadDose(Inventory As Double, _
WasteVolume As Double, _
SDCF As Double, _
GeometryFactor As Double, _
RadFractionRemaining As Double)
'Returns dose for given nuclide in rem/yr for given inputs
' Inventory - rad waste inventory in uCi
' WasteVolume - volume of waste in disposal unit (m3)
' SDCF - scenario dose conversion factor for nuclide (rem/yr per uCi/m3)
' This is scenario EDE that is calculated for concentration of 1 uCi/m3
' GeometryFactor - geometrical correction factor
' RadFractionRemaining - fraction of initial inventory remaining for rad
RadDose = (Inventory / WasteVolume) * SDCF * GeometryFactor * RadFractionRemaining
End Function

That should get you started.