Two-block decomposition of nuclide concentration vector for depletion calculation

Abstract

The accurate prediction of the time dependent nuclide concentration in fuel is necessary to evaluate many issues, for example, the neutron multiplication factor in criticality safety, decay heat sources for thermal analysis, neutron and gamma-ray sources for radiation shielding and dose rate analysis, and radionuclide concentrations and toxicities for assessment of long-term environmental waste management concepts. This calculation is done by depletion codes e.g., ORIGEN2.2. The main function of the codes is to solve the Bateman equation for nuclide concentrations. ORIGEN2.2, one of the widely used depletion code uses alternative techniques for short-lived nuclides calculation. Because of that, it performs depletion calculation very efficiently giving accurate results for nuclides that are important in reactor physics. However, it gives inaccurate results for the nuclides that are important in source term analysis in reactor safety studies, since their reactions are related with short-lived nuclides. Recently a Krylov subspace method was suggested. It gives good accuracy if a sufficient Krylov subspace dimension is used. However it needs considerable computing time if very large norm of burnup matrix like in the ORIGEN code is related since very large Krylov subspace dimension is required. In this thesis, a new method decomposing nuclide concentration vector into two blocks (short-lived nuclides block and long-lived nuclides block) is introduced. For short-lived nuclides block calculation, since matrix norm of that is too big to calculate matrix exponential, general Bateman solution of each nuclide is used. However since considering all parents of short-lived nuclides in Bateman solution calculation requires big computation burden, importance concept is introduced for selecting important parent nuclides which produce short-lived nuclides. The importance depends on nuclear data (cross sections, decay data, fission yields, and neutron flux). Therefore importa...