Causes of Input Multiplicity Fundamental Explanation

The non-reactive distillation residue curve diagrams in Chapter 5 (Section 5.1.1) show that the ETBE and the MTBE system each comprise two distillation regions separated by a distillation boundary. The phase behaviour of each system is governed by the low boiling azeotrope, ETBE-ethanol or MTBE-methanol, and the distillation boundary extends from this azeotrope to the unstable node in each system (i.e. pure C4 or the low boiling azeotrope between C4 and methanol). The distillation boundary cannot be crossed unless the components react so that, in non-reactive distillation, the distillation products are constrained to the same distillation region as the feed.

Homogenous reactive distillation is subject to a similar set of constraints due to the reactive phase behaviour: reactive azeotropes create reactive distillation boundaries that cannot be crossed. It should be noted that the reactive residue curve diagrams for the ETBE and the MTBE system (Section 5.1.2) indicate that no such azeotropes exist so that there is only one reactive distillation region in each case. In both non-reactive distillation and homogenous reactive distillation, the trajectories of the residue curves are readily predicted and extend from the most volatile node to the least volatile node in the distillation region that contains the feed. This occurs if there are one, two or more distillation regions. In all cases, the temperature of the residue increases steadily along the trajectory from the unstable node to the stable node.

These considerations, although based on a batch distillation process, carry over to continuous distillation and approximately reflect the product compositions obtained by varying the bottoms yield from 100% to 0% of the feed. The residue curve diagrams predict a steady decrease in the concentration of the least volatile component and a steady increase in the temperature of the bottoms product.

Hybrid reactive distillation is unusual since the distillation boundary that exists for the non-reactive sections of the column can be traversed via the reaction which occurs in the reactive section of the column. The feasible product region is effectively unconstrained. The stable node that directs the residue trajectory can change from one distillation region to the other as the bottoms yield decreases, depending on the extent of the reaction and the path of the reactive section of the hybrid residue trajectory. Consequently, it is possible for the bottoms composition to change such that the temperature decreases rather than increases,

The reactive residue curves for the ETBE and the MTBE system terminate at the ethanol and the methanol node, respectively. This controls the direction of the hybrid residue trajectories such that the first drop of bottoms is always pure ethanol or methanol. Since the ether product is less volatile than the reactants and the ETBE and MTBE nodes are feasible product compositions due to the influence of the reaction, the maximum bottoms temperature exceeds the bottoms temperature at the stable node (i.e. the first drop of bottoms product). Note that this only occurs in a hybrid distillation system. The presence of a global maximum temperature (i.e. near the ETBE or MTBE node) higher than the local maximum (i.e. at the ethanol or methanol node) produces the possibility of bidirectionality, where the bottoms temperature can decrease as the distillate yield is increased. This is the basis for input multiplicity in this system. Mechanistic Explanation

Input multiplicity in hybrid reactive distillation can also be explained from a mechanistic perspective by considering the conditions required for high ether purity in the bottoms product. Reactive distillation is only feasible if the temperature and pressure required for the reaction and the separation coincide. If the conditions required for effective fractionation are such that temperatures are too high for effective reaction (e.g. the reaction is restricted by thermodynamics) or too low (e.g. the reaction is restricted by kinetics or the availability of reactants), reactive distillation cannot be utilised successfully. This premise implies that the column operating conditions must be optimised to concurrently achieve adequate reaction and separation and, therefore, the existence of a maximum ether production rate. Since the purity will decrease on either side of the optimum, there will always exist two input conditions for at least some values of any output conditions other than at the stationary point. This exactly describes the conditions for input multiplicity.

The important parameters for optimisation are the column pressure and the heat input (i.e. the reboiler duty) since these directly affect the stage-to-stage temperatures within the column. The effects of these parameters were discussed extensively in Chapter 4 and bidirectionality with respect to the reaction rate and the bottoms composition was demonstrated and explained for both the pressure and the reboiler duty. Essentially, two operating regions exist for the hybrid column: separation controlled (heat input below the optimum) and reaction controlled (heat input above the optimum). A given value of any output condition can usually be found for input conditions in both regions. For example, a reboiler temperature of 130°C can be produced with a low and a high reboiler duty (i.e. there is input multiplicity).

Typically, a low heat input will produce operating conditions which are favourable for the reaction (i.e. high conversion of reactants) but provide insufficient vapour-liquid traffic for good separation (i.e. low ether purities). The converse applies for a high heat input. A narrow range of heat inputs (or bottoms yields, etc.) will permit a high conversion and a high purity to be obtained simultaneously.

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