Input/output transfer models of binary distillation columns derived from convection-diffusion partial differential equations

Purity control in distillation columns often relies on linear models whose parameters (gains, delays, time constants) may be hard to fit satisfyingly. In this paper, we linearize a convection-diffusion model inspired from wave-models, in the case of vanishing diffusion. We obtain a linear transfer model which is explicitly parameterized with the usual column´s operating parameters. This model consists in gains and pure delays only. It is derived from an unusual asymptotic expansion (Laurent series with exponentially precise terms) versus the diffusion coefficient. We validate such linear transfer models in simulation and also on real plants data for cryogenic air separation units. Similar transfer models can be constructed for other cases of binary distillation.