Optimization of flexible square cascade for high separation of stable isotopes using enhanced PSO algorithm

The optimal parameters of a flexible square cascade for the separation of multicomponent isotopes have been calculated in this paper. In this regard, a new code called “MCSQCA-PSO” has been developed, which uses the particle swarm algorithm with mutation operator to find the optimal solution. Maximizing the amount of product recovery in a square cascade with the certain number of centrifuges machines and considering the concentration of the desired isotope in specific values, as well as increasing the D function as an objective function have been evaluated and studied. Cascade feed flow rate, machine feed flow rate, cascade cut, feed entrance point, and stages cut have been defined as optimization variables in the code. Optimization calculations are performed as an example for separation of Te-123, which has the most challenging separation between the eight stable isotopes of tellurium. In this paper, all possible arrangements of a square cascade assuming 200 centrifuges for two different separation factors have been investigated, and the enrichment of Te-123 has been increased from 0.89 % in natural feed to 65 %. The results show that the recovery coefficient increases nonlinearly with increasing the number of stages from 10 to 100, so that it is not significantly different for cascades in 40, 50, and 100 stages. In contrast, the amount of product in the cascade with 50 stages is the highest in comparison with the other cascades. Finally, the recovery coefficients of Te-123 in the cascade with 50 stages for two different separation factors have obtained 99.46 % and 92.38 %, respectively. The amount of product after two steps of separation and assuming one year of operation have been obtained 4.6 kg and 4.1, respectively. Furthermore, the ability of MCSQCA-PSO is evaluated with other optimization algorithms. Suitable alignment of the results indicates that the use of the PSO for this problem guarantees the calculation of the optimal parameters. [Display omitted] •Optimization of square cascade for the separation of stable isotopes in several steps have been done.•Enhanced PSO is used for optimization of the parameters in the square cascades.•Optimization calculation is done for two separation factor.•An objective function with a new approach has been introduced.•It is possible to increase the enrichment of each isotope at any concentration.