Mathematical Modeling and Its Applications for Mass Flow in a Nuclear Fuel Cycle

Abstract

A mathematical model for mass flow in a generic nuclear fuel cycle was developed. The model can describe various fuel cycle configurations (ranging from once-through to multiple recycling) and reactor types with several regions and batches. It can also be used as a submodel in a regional or global fuel cycle system. Recursive equations for the fuel composition at each point of the cycle were obtained. For specific simplified cases, nonrecursive and equilibrium equations were also derived for compositions, with which the waste reduction ratio was formulated as a function of the system parameters, to show usage of this model for theoretical understanding of the relationship between parameters and performances of the system. A numerical code for this mathematical model was developed. For a simplified equilibrium cycle, sensitivity and constrained optimization of the toxicity reduction ratio with respect to the system parameters were investigated by using the present model and code. It appears that the most important parameter to minimize waste toxicity is the separation efficiency at reprocessing. High fuel enrichment is beneficial because it expands the parametric space within the constraints. Also, depending on the constraints that apply, either the irradiation time or the fraction of core reprocessed at each cycle will be the second most important parameter.