Output Multiplicity due to Azeotropes

Azeotropes in mixtures of three or more components can result in a completely different type of distillation multiplicity. In this case, the multiplicity will be observable in any type of unit (i.e. molar, volumetric, mass, duty, etc.) and can be detected with a rigorous model or with a CMO model. Bekiaris and Morari (1993) were the first to elucidate the link between azeotropes and multiplicity in non-reactive distillation and were able to develop a geometrical tool to detect multiplicities without a bifurcation diagram. The tool, <»/co analysis, allows the product composition to be predicted from the feed composition and a product rate specification, assuming the column fractionation is sufficiently close to the ideal case (i.e. infinite stages and infinite reflux ratio, hence oo/oo).

The oo/oo approach is an excellent tool but it still has several shortcomings: the fractionation characteristics (i.e. the number of stages, etc.) required for the predictions to be accurate is uncertain so that the analysis is not always applicable for finite columns; to be applied, the system must be representable as a pseudo-ternary mixture; only single-feed, dual-product columns can be analysed; and, no predictions can be made for internal specifications (e.g. the reflux rate or ratio, or the reboiler duty). However, oo/oo analysis can be applied to reactive columns if transformed composition co-ordinates are used (Guttinger and Morari, 1997). The transformations required are the same as those proposed by Ung and Doherty (1995) and others, and were described in Chapter 5 (Section 5.1.3).

The principal result which is obtained from co/oo analysis is the region in composition space which will produce multiple steady states. The analysis is independent of the column configuration and only requires basic VLE data on the components and the azeotropes. Thus, an analysis that has been completed for the MTBE system is adequate for all MTBE columns. Such an analysis has been completed previously (Guttinger and Morari, 1997) and suggests that a feed which consists of 25% isobutene, 35% methanol and 40% n-butenes (40% stoichiometric excess of methanol) will produce multiple steady states. According to the oo/oo technique, this type of multiplicity can be detected more easily in the transformed composition co-ordinates.

The effectiveness of the oo/oo analysis was evaluated here for two different hybrid MTBE columns. Figure 8.7 was constructed using a bifurcation analysis of the column configuration indicated in Table 8.2 with the given feed composition and a constant reflux to feed ratio of 3.5. Figure 8.8 considers the same combination of feed composition and reflux ratio in a 10 stage column with two rectifying stages (including a total condenser), one reactive stage and seven stripping stages (including a partial reboiler). The feed to this column is split between the stage immediately above the reactive stage and the stage uppermost stripping stage. The transformed flow and composition are defined as follows:

The oo/oo analysis correctly predicts the multiplicity in the 17 stage column but does not recognise that the multiplicity disappears in a shorter column. The analysis of the 10 stage column is a stringent test for the oo/oo technique as there are several factors which contradict the oo/oo assumptions: the column contains both reactive and non-reactive sections; there are two feed points; and the column is relatively short (only 10 stages). It is, therefore, not surprising that the oo/oo predictions are incorrect in this case.

Azeotropes
Feed Composition Predicted to Produce Multiple Steady States by an qo/qo Analysis

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Figure 8 8 - Bifurcation Results for a 10 Stage MTBE Reactive Distillation Column with a Feed Composition Predicted to Produce Multiple Steady States by an qo/qo Analysis

Since there is uncertainty regarding the predictions for finite columns, perhaps the best application of the oo/oo technique is for screening reactive distillation systems and feed compositions for the possible existence of multiple steady states. For example, the reactive residue curve diagram for ETBE, in transformed variables, shows no azeotropes. Although an azeotrope exists between ETBE and ethanol, it is not independent of the reaction. Therefore, azeoiropic multiple steady states will not be present in ETBE reactive distillation for any feed composition in any column configuration. However, this does not preclude the possibility of another type of multiplicity occurring!

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