Modelling Techniques

Two fundamentally different approaches to simulating distillation systems have been developed: the equilibrium stage model and the non-equilibrium, transfer rate model (Kister, 1992). Theoretically, both of these methods can be applied to reactive distillation with appropriate modifications and additions to reflect the reaction.

The steady state simulation of reactive distillation has been tackled frequently since the 1970s. Simandl and Svrcek (1991) provided an excellent review of the work in this area and alluded to the range of numerical methods that can be applied to solve the system of equations which describe the reactive column. Their survey indicated that only the equilibrium stage model had been used to that point.

Yuxiang and Xien (1992b) considered the rate-based approach and produced a steady state model of a reactive MTBE column. The primary advantage of this approach is that equipment dimensions and packing (or tray) characteristics can be accounted for within the model so that a more realistic view of the column is afforded. However, this is more than offset by the increased demand on empirical constants and the much larger number of equations that must be solved. To support their methodology, Yuxiang and Xien conducted experiments to determine mass transfer coefficients and some other properties. They were able to show that the rate-based approach yields almost identical results to the equilibrium stage model provided sufficient detail is included in the model but did not demonstrate any advantage with respect to model accuracy or efficiency.

Sundmacher and Hoffman (1996) also developed a rate-based model of a reactive distillation process but used correlations instead of experiments to find the necessary mass transfer parameters. They attempted to validate their model with experimental data but the agreement between the model and the experimental was weak and they provided insufficient data to fully assess the effectiveness of their model.

Grosser et al. (1987) proposed a simplified non-steady state model of reactive distillation for a nylon 6,6 column but their assumption of constant molar overflow in the vapour phase is considered unrealistic for most systems, including MTBE and ETBE processes. More recently, several rigorous dynamic models have been proposed for simulating transient events and investigating process dynamics of reactive distillation. Abufares and Douglas

(1995) proposed a model based on the equilibrium stage approach that included expressions to account for tray hydraulics and reaction kinetics. They successfully demonstrated the validity of this approach by comparing simulation results to previously published experimental results from a laboratory scale column. Ruiz et al. (1995), Schrans et al.

(1996) and Pilavachi et al. (1997) have subsequently produced dynamic models with a similar structure and have shown that these models can be used effectively for reactive MTBE columns although limited data has been provided for model validation.

Alejski and Duprat (1996) provided a comprehensive review on reactive distillation simulation and also proposed a rigorous dynamic model of their own which they subsequently applied to a reactive ethyl acetate column. The most important contribution of this work was to compare dynamic models of varying complexity to determine whether various simplifying assumptions were valid or invalid. They concluded that it was necessary to model the hold-up on each staye (e.g. using the Francis weir formula) where the hold-ups are large, but simpler models are acceptable where the hold-ups are smaller and the dynamics are much faster.

The application of ETBE reaction chemistry to reactive distillation appears not to have been considered previously. However, the modelling techniques used previously, particularly the equilibrium stage model, appear to be sound, and appropriate equilibrium and kinetic expressions for the ETBE reaction are available (Section 2.3). This approach is developed in Chapters 3 and 6 for steady state and dynamic problems, respectively. The experimental equipment described in Chapters 11 and 12 will also provide the basis for more detailed validation of the modelling techniques.

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