Impact of Flow Constraint on the Performance of Square Thermal Diffusion Cascades for 82Kr Isotope Separation

This study investigates the separation of the intermediate isotope 82Kr to a purity exceeding 95% using optimized square cascades of thermal diffusion columns. While previous optimization studies have largely ignored equipment related flow constraints, a key practical challenge is that industrial processes are limited by minimum measurable flow rates of components such as control valves, flow meters, orifices, etc. The main contribution of this work is to systematically evaluate the impact of such flow constraints on cascade feasibility and to identify the minimum separation factor required for practical design. To address this, two operating modes are evaluated: (i) unconstrained flow, where all flow variables adjust freely, and (ii) constrained flow enforcing a minimum flow threshold (Fi  Fmin) to reflect real equipment limitations. Fifteen strategies, combining constant separation factors (1.02 to 1.20) across three cascade lengths (26, 48, and 68 stages), are optimized using Particle Swarm Optimization (PSO). Results show that applying flow constraints reduces the number of acceptable strategies-meeting criteria of steps ≤ 6, total recovery  50%, final purity  95%, and production  80 gr/year-from seven to four. Strategies with a separation factor of 1.07 become infeasible, while those with α0  1.10 remain viable, underscoring the need for high-efficiency columns in practical designs. These findings confirm that the key contribution of this study is to demonstrate that theoretical optimization without considering operational constraints may yield impractical solutions, thereby highlighting the importance of integrating engineering limitations from the outset.