Output Multiplicity due to the Influence of the Energy Balance

This cause of multiplicity was also originally described by Jacobsen and Skogestad (1991) with respect to an ideal, binary, non-reactive distillation column. In certain cases, multiple steady states were not observed when the energy balances around each distillation stage were neglected (i.e. the constant molar overflow, CMO, solution was considered). Although they only considered non-reactive distillation, this concept is equally valid in other areas, including reactive distillation and hybrid columns.

Essentially, multiple steady states arise where the energy balances produce a change in the product compositions that has an opposite and more substantial effect on the product flows than the direct effect of the change in the internal liquid (or vapour) flow. This is summansed by inequalities (8.6) and (8.7) which are necessary and sufficient conditions for multiple steady states (Jacobsen and Skogestad, 1991). Under these conditions, an increase in the reflux rate has an inverse effect on the bottoms product draw rate or, similarly, an increase in the boilup rate decreases the distillate draw rate. Thus, multiple values of the product rate (and, therefore, product composition) can exist for a single value of the reflux or boilup rate.

The heat of reaction has been postulated as a possible cause for multiple steady states in reactive distillation (Jacobs and Krishna, 1993). In light of the above explanation of the effect of the energy balances in the distillation model (or, conversely, the effect of ignoring the energy balances), the basis for the postulation becomes clearer: the heat of reaction introduces another term to the energy balances which will create a difference between the molar How rate entering and leaving a stage. This effect may be directionally different from the normal effect of the internal flow rate. For example, increasing the reflux rate may have

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