Definition and Description

The concept of pseudo-multiplicity is proposed here to describe the difference between output multiplicity that is physically realisable and that which is not. Essentially, pseudo-multiplicity arises where multiple steady states are observed for a system which is described in molar units (which have no practical significance as a molar flow controller cannot be implemented in practice) but not in mass or volumetric units.

Several examples of pseudo-multiplicity in reactive distillation have been reported in the literature although they have not been described as such (e.g. Hauan et al., 1995; Schrans et al., 1996). Importantly, these examples have been reported as output multiplicities and the fact that they are not physically realisable has been overlooked. This creates a false sense of the significance of these results and has, perhaps, contributed to the delay in providing experimental verification for multiplicity in hybrid reactive distillation.

Figure 8.14 shows pseudo-multiplicity in the 10 stage ETBE column which was introduced in Chapter 3 (Section 3.4). Some values of the reflux rate correspond to multiple steady state solutions with the same value of the molar boilup rate but only one steady state was observed for every reflux rate where a reboiler duty specification was applied (see Figure 4.3).

The 17 stage MTBE column described in Table 8.2 also exhibits pseudo-multiplicity. Figure 8.15 was constructed from simulation results with a molar bottoms rate of 674 kmol/hr (both parts of the curve satisfy this condition). Three steady states are seen for reflux rates above 900 m3/hr. However, if the bottoms rate is fixed with a mass or volumetric specification, only one steady state is observed for all values of the reflux rate (see Figure 8.2).

Reflux Rate (Urn in)

Figure 8.14 - Pseudo-Multiplicity in the 10 Stage ETBE Column

Reflux Rate (Urn in)

Figure 8.14 - Pseudo-Multiplicity in the 10 Stage ETBE Column

Column Tray Design Definition
Figure 8.15 - Pseudo-Multiplicity in the 17 Stage MTBE Column
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