Predicting multiple steady states in equilibrium reactive distillation. 2. Analysis of hybrid systems

Guttinger and Morari (Ind. Eng. Chem. Res. 1998, 38, 1633-1648) developed graphical methods for the prediction of output multiplicities caused by the reactive vapor-liquid equilibrium in reactive distillation. These methods rest upon the limiting case of reactive columns of infinite length operated at infinite internal flows (infinity/infinity analysis) and are directly applicable to systems where the reactions take place in the entire column ("nonhybrid" columns). In this work, the reactive infinity/infinity analysis is extended to columns with a reactive core ("hybrid" columns) by introduction of two new procedures. First, necessary and sufficient feasibility conditions for hybrid column profiles are derived under the assumption that each of the reactive and nonreactive column sections has infinite length. Using these conditions, an "exact" method is formulated where all possible products of such an infinity/infinity hybrid column can be located in the composition space (by a continuation of solutions). The existence of multiple steady states and the feed region leading to output multiplicities can be predicted. Second, an "approximate" procedure is proposed to obtain an estimate of the product locations of a hybrid column with finite nonreactive sections. The exact method was applied to an "ideal" reactive system, and a new type of multiplicity, which is purely caused by the hybrid nature of the system, is shown. Moreover, the methyl tert-butyl ether (MTBE) reactive distillation process is analyzed using both methods, and the physical causes of the MTBE multiplicities are studied in detail. All analytical results are verified by simulation.