An analytic model for a C13 isotope separation process by cryogenic distillation

In this paper we present a structured approach to the modeling of an isotope separation plant that makes use of distillation principles for C13 isotope separation. In the first part of the paper, after a brief review of isotope separation processes with an accent on isotope separation by distillation, we define our initial-boundary-value problem, which is a partial differential equation. By applying the Laplace transform to the partial differential equation that governs the evolution of the desired isotope with respect to height and time, we obtain a linear homogeneous ordinary differential equation. After solving the obtained ordinary differential equation, we use Heaviside's expansion theorem to find the inverse Laplace transform, and thus, the analytic model of the isotope separation process follows. Using the analytic model it is possible to determine the concentration of the desired isotope at any height, at any moment of time, with respect to plant parameters and thus, expensive experiments can be avoided. In the second part of the paper we use the analytic model to simulate the isotope separation process, followed by the assessment of the results against experimental data.