Nonlinear model reduction and control of multiple-time-scale chemical processes: Chemical reaction systems and reactive distillation columns

The dynamics of chemical processes are inherently nonlinear and may occur over widely varying time scales. Dynamic models of such multiple time scale processes are inherently stiff, and thus, difficult and costly to simulate. This motivates the need to obtain reduced order models capturing the dynamics only in the time scale of interest, while approximating the dynamics in other (faster) time scales in a systematic fashion. The majority of existing research to this end has focused on two time scale systems, with an explicit separation of fast and slow variables. However, many processes exhibit dynamics in more than two time scales, with their variables not associated with a distinct time scale. Motivated by this, the objectives of this thesis are two-fold: (i) the development of a model reduction methodology for nonlinear multiple time scale systems, and (ii) the application of the developed methodology to representative multiple time scale chemical processes, along with a comprehensive dynamics and control study of such processes.; Specifically, we consider a broad class of multiple time scale systems with non-explicit time scale separation that arises in rate-based models of chemical processes. For such systems, we develop a methodology for the systematic decomposition of their dynamics into dynamics in individual time scales. Then we focus on systems of chemical reactions occurring in different time scales, and develop a methodology for deriving reduced order models of their dynamics in the time scale of interest. This model reduction methodology is applied to an ozone decomposition, a carboxylic acid esterification and a hydrogen oxidation reaction system. We also study the occurrence of time scale multiplicity in reactive distillation, a process that combines reaction and separation in a single unit. We present a modeling framework that structurally identifies different physical phenomena (potentially) responsible for time scale multiplicity and address the systematic derivation of reduced order models of the slow dynamics of this process. Finally, we perform a detailed dynamics and control study for an ethyl acetate reactive distillation column.