Sensitivity Analysis of Ideal Centrifuge Cascade for Producing Slightly Enriched Uranium

Characteristics of an ideal cascade are analyzed by two differential equations representing the conservation of UF₆ and ²³⁵UF₆ flow. The controlling variables are identified as the cut and the separation factor of centrifuges and of stages as well as feed flow rate. The controlled variables are flow rate and enrichment of stages, especially of the product and waste. The sensitivity of the controlled variables to the controlling variables are analyzed by linearizing the conservation equations, and analytic expressions are obtained. The change in the separative work of the cascade is a sum of changes in the separative work of the constituent centrifuges. When the flow rate is chosen to optimize the separative work of a single centrifuge, the plant separative work is maximum and stationary at the rated feed flow. It has been demonstrated in a few examples that these simple relations for the ideal cascade are useful for the planning, design, and operation of cascade plants.