D.C. Dumitrache, B. De Schutter, A. Huesman, and E. Dulf, "Modeling, analysis, and simulation of a cryogenic distillation process for 13C isotope separation," Journal of Process Control, vol. 22, no. 4, pp. 798-808, Apr. 2012.
This paper presents a structured and insightful approach to modeling and simulation of an isotopic enrichment plant that uses distillation principles for 13C isotope separation. First, after a brief review of distillation and mass transfer-related topics, a full nonlinear model for the cryogenic distillation process for 13C isotope separation is derived from first-principles knowledge. In order to derive the mathematical description of the concerned isotope separation process, based on the two-film theory, we will derive the rate of transfer of the 13C isotope from the vapor phase to the liquid phase. Since the isotope separation by cryogenic distillation is usually carried out in a very long column with a small diameter, a good approximation arises by neglecting the radial diffusion. We continue with the determination of the system of the partial differential equations that governs the evolution of desired isotope during the separation process. Next, we solve the system of partial differential equations, resulting in the full nonlinear model. Due to the complexity of the full nonlinear model, we consider two additional alternative modeling approaches resulting in a quasi-linear model and, when the isotope concentration achieved is low, a linear approximation model. In the second part of the paper we use the finite-differences method for the numerical analysis and numerical simulation of the three models, followed by the assessment of the linear model for future tasks in modeling, optimization, and process control.