Nonlinear wave modeling and dynamic analysis of internal thermally coupled distillation columns

Internal thermally coupled distillation column (ITCDIC) is a frontier in the energy saving distillation research. It is well known for the complex dynamics, which challenge the establishment of an excellent reduced model for further control strategy design greatly. In this article, a physical approach of the ITCDIC process based on nonlinear wave theory is explored, where it is first discovered that traditional wave theory in conventional distillation columns (CDIC) could not be directly applied in ITCDIC, due to: First, the internal thermal coupling results in mole flow rates varying evidently over each stage, which not only makes the wave modeling of the wave phenomenon in ITCDIC more difficult but also makes wave dynamics greatly different between ITCDIC and CDIC; Second, an interesting wave phenomenon of ITCDIC is discovered that waves located in the rectifying section and stripping section travel under opposite tendencies when the steady state is disturbed by the step change of thermal condition q, one sharpens and the other is likely to spread synchronously, it means the movement of wave profiles in ITCDIC could not be simply described by shock wave velocity, which is usually used in wave modeling of CDIC; more seriously, shapes of the self‐sharpening wave profiles in ITCDIC change obviously during the traveling processes, which further reveals that shape influence on wave velocity has to be considered in the wave modeling of ITCDIC. A rigorous wave velocity and a natural wave velocity are derived, respectively, based on which, the detailed analyses of traveling wave characteristics are carried out. A novel wave velocity, based on the profile trial function which has been well developed by Marquardt, is further derived to consider the obvious change of profile shape. And a completed nonlinear wave model of ITCDIC is thereby established by combining the proposed wave velocity with thermal coupling relations and material balance relations. The benzene‐toluene system is illustrated as an example, where component concentration prediction and distinct dynamic characteristics are carried out in detail based on the proposed nonlinear wave models. The research results reveal the accuracy and validity of the proposed nonlinear wave model of ITCDIC. © 2011 American Institute of Chemical Engineers AIChE J, 2012