Non-equilibrium stage modeling and non-linear dynamic effects in the synthesis of TAME by reactive distillation Amit M. Katariya, Ravindra S. Kamath, Kannan M. Moudgalya, Sanjay M. Mahajani Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India Abstract Tertiary-amyl methyl ether (TAME) is a potential gasoline additive that can be advantageously synthesized using the reactive distillation (RD) technology. This work emphasizes on non-linear effects in dynamic simulations of reactive distillation column. For certain configurations, dynamic simulation with equilibrium stage (EQ) model leads to sustained oscillations (limit cycles) which have been reported in our earlier work [Katariya, A. M., Moudgalya, K. M., & Mahajani, S. M. (2006). Nonlinear dynamic effects in reactive distillation for synthesis of TAME. Industrial and Engineering Chemistry Research, 45 (12), 4233–4242]. Feed condition and Damkohler number are the important parameters that influence the existence of these effects. To confirm the authenticity of the observed non-linear behaviors, a more realistic and rigorous dynamic NEQ model for a packed column is developed which uses a consistent hardware design. The steady state behavior of the NEQ model is examined by varying the number of segments and the column height. The dynamic simulation and the bifurcation study with stability analysis indicate that the parameter space, in which oscillations may be observed, is shifted in the case of NEQ model. Keywords: Reactive distillation; Dynamic simulation; Continuation analysis; Non-equilibrium model; Hopf bifurcation; Oscillations 1. Introduction Computer-aided design and simulation of multi-component multistage separation processes such as distillation, gas absorp- tion and reactive distillation are important aspects of modern chemical engineering. Currently, such simulations are based on the well-known equilibrium stage model. The EQ model assumes that the vapor and liquid leaving a stage are in equi- librium. Equilibrium stage simulations are frequently termed rigorous, but this appellation is not entirely justified because in actual operation, columns rarely, if ever, operate at equilibrium. The degree of separation is, in fact, determined as much by mass and energy transfer between the phases being contacted on a tray or within sections of a packed column, as it is by thermodynamic equilibrium considerations. The usual way of Abbreviations: RD, reactive distillation; EQ, equilibrium stage modeling; NEQ, non-equilibrium stage modeling; MeOH, methanol; 2M1B, 2-methyl 1- butene; 2M2B, 2-methyl 2-butene; TAME, tertiary-amyl methyl ether; i-PENT, iso-pentane; Da, Damkohler number; DAE, differential algebraic equation. dealing with departures from equilibrium in multistage towers is through the use of stage and/or overall efficiencies or use of height equivalent to a theoretical plate (HETP) in case of packed towers. Though, this may be a useful approach for simulating an existing column for which there is a good deal of data avail- able, it may not be possible to predict safely how the column will perform under quite different operating conditions (Baur, Higler, Taylor, & Krishna, 2000). Furthermore, it is difficult to use this approach to simulate new processes in the design stage for which no plant data exists. It is advantageous to use NEQ model over the EQ model due to some of the following reasons. It eliminates the need for effi- ciencies and HETPs. The operating strategies for the influence of chemical reactions on separations can be accounted in a bet- ter way. The over-design or under-design can also be avoided as the tray and packed columns are modeled with greater accu- racy thereby reducing the capital and operating costs. Also, as mentioned before the NEQ model is more realistic as compared to the EQ model and represents a more accurate modeling of reactive systems. The non-equilibrium (NEQ) model assumes that the vapor–liquid equilibrium is established only at the interface