(359c) Avoid Instability in Distillation Using Control Based on the Second Law of Thermodynamics

The distillation column is one of the primary unit operations for separations in the chemical and petroleum industries. Because of their significance, the literature for theory and practice of distillation columns is vast and mature. Most of the literature focuses on the instabilities that may arise when using certain controllers. Despite the identification of the many causes for instability, however, a general stability analysis of the multi-component distillation column has yet to be made.

In this talk we show, for the first time, a rigorous stability analysis that reveals the asymptotically stable operation of the multi-component distillation column. The stability analysis utilizes the thermodynamics availability function, first employed by Alonso and Ydstie [1], to show asymptotic stability of the distillation column using pressure, temperature, and level controllers on the reboiler and condenser. For this analysis, we model the multi-component distillation column as a stack of independent mass exchange units which isolates each phase in each tray of the column. The mass exchange unit is a modeling tool used to isolate the differential equations that describe the dynamics of the vapor and liquid in each tray. A Lyapunov function is then developed for each mass exchange unit. We then stack these mass exchange units to model a distillation column, eventually allowing us to construct the overall Lyapunov function for the distributed system. Ultimately, the overall Lyapunov function is used to show that if the hydrodynamics of the column are well controlled, the thermodynamics will drive the system to asymptotic stability.

References

[1] A. Alonso, B. E. Ydstie, “Stabilization of distributed systems using irreversible thermodynamics” Automatica, 2001, 37, 1739 - 1755