Award Date


Degree Type


Degree Name

Doctor of Philosophy in Mechanical Engineering


Mechanical Engineering

First Committee Member

Robert Boehm, Chair

Second Committee Member

Denis Beller

Third Committee Member

Charlotta Sanders

Fourth Committee Member

Gary Cerefice

Fifth Committee Member

Mark Williams

Graduate Faculty Representative

Julie Staggers

Number of Pages



The Monte Carlo method provides powerful geometric modeling capabilities for large problem domains in 3-D; therefore, the Monte Carlo method is becoming popular for 3-D fuel depletion analyses to compute quantities of interest in spent nuclear fuel including isotopic compositions. The Monte Carlo approach has not been fully embraced due to unresolved issues concerning the effect of Monte Carlo uncertainties on the predicted results.

Use of the Monte Carlo method to solve the neutron transport equation introduces stochastic uncertainty in the computed fluxes. These fluxes are used to collapse cross sections, estimate power distributions, and deplete the fuel within depletion calculations; therefore, the predicted number densities contain random uncertainties from the Monte Carlo solution. These uncertainties can be compounded in time because of the extrapolative nature of depletion and decay calculations.

The objective of this research was to quantify the stochastic uncertainty propagation of the flux uncertainty, introduced by the Monte Carlo method, to the number densities for the different isotopes in spent nuclear fuel due to multiple depletion time steps. The research derived a formula that calculates the standard deviation in the nuclide number densities based on propagating the statistical uncertainty introduced when using coupled Monte Carlo depletion computer codes. The research was developed with the use of the TRITON/KENO sequence of the SCALE computer code.

The linear uncertainty nuclide group approximation (LUNGA) method developed in this research approximated the variance of ψN term, which is the variance in the flux shape due to uncertainty in the calculated nuclide number densities.

Three different example problems were used in this research to calculate of the standard deviation in the nuclide number densities using the LUNGA method. The example problems showed that the LUNGA method is capable of calculating the standard deviation of the nuclide number densities and k inf . Example 2 and Example 3 demonstrated a percent difference of much less than 1 percent between the LUNGA and the exact methods for calculating the standard deviation in the nuclide number densities.

The LUNGA method was capable of calculating the variance of the ψ N term in Example 2, but unfortunately not in Example 3. However, both Example 2 and 3 showed the contribution from the ψN term to the variance in the number densities is minute compared to the contribution from the ψS term and the variance and covariances of the number densities themselves. This research concluded with validation and verification of the LUNGA method.

The research demonstrated that the LUNGA method and the statistics of 100 different Monte Carlo simulations agreed with 99 percent confidence in calculating the standard deviation in the number densities and kinf based on propagating the statistical uncertainty in the flux introduced by using the Monte Carlo method in coupled Monte Carlo depletion calculations.


Error analysis (Mathematics); Error propagation; Monte Carlo method; Nuclide number densities; Spent nuclear fuel; Spent reactor fuels; Uncertainty propagation


Electro-Mechanical Systems | Nuclear Engineering | Numerical Analysis and Scientific Computing | Theory and Algorithms