Nuclide and Element Atom Density Calculations

1. Given Atom Density for Each Nuclide

• Element Atom Density:

  $$\text{"Element" atom density} = \sum (\text{Nuclide densities})$$

• Element Mole Percent:

  $$\text{"Element" mole percent} = \frac{\text{"Element" atom density}}{\sum \text{All "Ele." atom density in timestep}}$$

• Surrogate Percentages:

  $$\text{"Nuclide" atom density} = \text{given value preserved} $$

  $$\text{"Nuclide" Contribution Perc.} = \frac{\text{"Nuclide" atom density}}{\text{"Element" atom density}} $$

2. Using Element Densities and Mole Percents

• Surrogate Atom Density:

  $$\text{"Surrogate" atom density} = \sum (\text{"Element" atom densities of correlated salt}) $$

• Surrogate Mole Percent:

  $$\text{"Surrogate" mole percent} = \frac{\text{"Element" atom density}}{\text{"Surrogate" atom density}} $$

• Element Contribution Percent:

  $$\text{"Element" contribution perc.} = \frac{\text{"Element" atom density}}{\text{"Surrogate" atom den.}} $$

3. Thermochemical Inputs

Thermochemical inputs are taken as the "Surrogate" mole percents.

4. Thermochemical Data Processing

Thermochemical data are condensed and processed into:

• Salt elements
• Gas elements
• Deposit elements

For each phase, the following will be reported:

• Phase Surrogate Mole Percent:

  $$= \frac{\text{Moles Pres of Sur. in Phase}}{\text{Moles of Phase}} $$

• Phase Mole Percent:

  $$= \frac{\text{Moles Phase}}{\text{Total Moles All Phases}} $$

• Total Moles All Phases

5. Post-Processing and Back Calculation

In Post Processor pt 2, back calculations will be done to verify calculations with nuclides. This is iterative and may require multiple passes.

5b. Getting Nuclide Atom Densities from Outputs

• Surrogate Sum:

  $$= \sum (\text{Phase surrogate mole perc.}) \times (\text{Phase mole perc.}) $$

• Total Moles Surrogate:

  $$= (\text{Surrogate sum}) \times (\text{Total Moles All Phases}) $$

• Surrogate Phase Percent:

  $$= \frac{\text{Moles of Phase} \times \text{Phase Surrogate mole perc.}}{\text{Total Moles Surrogate}} $$

• Element Mole Percent in Phase:

  $$= (\text{Surrogate Phase Perc.}) \times (\text{"Element" contribution perc.}) $$

• Element Atom Density in Phase:

  $$= (\text{"Surrogate" atom density}) \times (\text{Phase mole perc.}) \times (\text{"Element" contribution perc.}) $$

• Nuclide Atom Density in Phase:

  $$= (\text{"Ele." atom density in phase}) \times (\text{"Nuclide" Contribution Perc.}) $$