Unsteady State Performance and Stabilization Time in Square Cascades for Stable Krypton Isotope Separation

The inherently low single stage separation factor of stable krypton isotopes makes their enrichment through multistage cascades a challenging task, requiring precise optimization of cascade parameters and a thorough understanding of transient behavior. In this work, we numerically investigate the unsteady state performance of a square cascade for krypton isotope separation, using a multicomponent mass balance model discretized by the Crank–Nicolson scheme and solved iteratively via a q method. The study focuses on how two key design variables—the cascade cut (θ) and the unit separation factor (α)—affect the stabilization time of individual isotopes and of the entire system. Simulations are conducted for θ = ۰.۱۴۲ (targeting light isotopes in the product) and θ = ۰.۸۲۷ (targeting heavy isotopes in the waste), at α = ۱.۲ and ۱.۴. Results reveal that the isotope governing the overall transient response is not fixed: at low cut, intermediate isotope Kr ۸۲ controls the stabilization (≈۱۸۴ min), whereas at high cut, the heaviest isotope Kr ۸۶ becomes the rate limiting component (≈۱۵۰–۸۸۴ min depending on α). Increasing α from ۱.۲ to ۱.۴ substantially prolongs the global steady state attainment—from ~۱۹۰ to ~۴۸۱ min at θ = ۰.۱۴۲, and from ~۱۵۶ to ~۹۴۱ min at θ = ۰.۸۲۷—due to sharper concentration gradients and stronger interstage coupling. These findings demonstrate that steady state analysis alone is insufficient for cascade design; transient simulation is essential to correctly identify the bottleneck isotope and to optimize start up strategies.

کلیدواژه ها:

Krypton isotope separation ، square cascade ، transient behavior ، cascade stability ، Numerical modeling