A generalization of the virtual components concept for numerical simulation of multi-component isotope separation in cascades

The total flow of the optimal isotope separation cascade should be kept at a minimum to ensure economic viability. The concept of virtual components has proven useful in optimizing and designing cascades for multi-component isotope separation, but is only used in cases with an available analytical solution. Practical situations are complicated and resort to numerical simulations because there are no analytical solutions. Therefore, a generalization for numerical methods is required. A major difficulty in generalization is that mass conservation requires the concentration of a virtual component to be zero, which causes numerical problems. This paper proposes an approach to overcome this difficulty and develops a numerical method accordingly. The matched-R cascade is used as an example for numerical experiments to show that a cascade is solely determined by the choice of the two virtual components, and to demonstrate how the numerical method is applied to find the optimal cascade.