Egan’s theory of fuel management for in-core fuel cycles covers both integer and noninteger strategies, where exact integer fractions imply changing, for example, one-third of the core at a time. Various typical problems can be identified that focus on the dynamics of such in-core fuel cycles. In the first problem, one can specify the initial enrichment and hence initial reactivity of the reload fuel and the fraction (integer or noninteger) to be changed in the reload strategy. Starting from an allclean core, there is a sequence of cycle times, measured in, say, megawatt days per kilogram. For both integer and noninteger strategies, this sequence converges to an equilibrium cycle time that repeats unchanged; the convergence is quite rapid. On the other hand, the fuel manager may prefer to maintain the strategy at each reload, changing the same fraction of fuel assemblies but varying the initial reactivity (via enrichment variation) to secure constant equilibrium burnup or cycle time from the start. Egan showed, by numerical examples, that integer strategies do not converge but oscillate through the sequences of initial reactivities. Although this behavior is true for all integer strategies, it turns out that noninteger strategies do converge, albeit very slowly. Finally, what about varying the fraction of standard fuel assemblies reloaded in each cycle while keeping the burnup time constant? It appears that the sequence of such fractional reloadings is also convergent, for integer and noninteger cases, a fact that can be proved with the aid of the proof for the initial problem of varying cycle times. So the fuel manager would be advised to consider this third option, varying the fractional reload, rather than the second option, varying the initial reactivity or enrichment to achieve an equilibrium cycle. The present work is done in the context of a simple lumped model using a linear variation of reactivity with burnup. Future extensions could be made to allow perhaps for coast down and energy distribution coefficients. Nevertheless, the present analysis provides a simple theory to underpin conventional and more complicated computer studies of distributed systems.
