One-stage column

Due to the simplicity of the model, the phenomena causing multiplicity can easily be verified. The multiplicity is caused by the relations between the heat of vaporization and the boiling points of the educts, which are Tfl MeOH < f s.PA and AH MeOH > ffvFA- Such relations have also been identified by Jacobsen and Sko-gestad [48] to cause multiplicity in a separation of non-reacting binary mixtures in a one-stage column. Hence, multiplicity is not caused by the reaction but is just the result of the separation only in methyl formate synthesis. Similar results have also been foimd for the esterification of ethanol with acetic acid [25, 50]. 

Rg. 10.3 Singularity set with organizing center for the methyl formate one stage column (left). Bifurcation diagram for the methyl formate one-stage column for a fixed reflux ratio, cross section A-A (right)... 

As in the case of the esterification process presented before, we study first a one-stage column by singularity analysis to gain some physical insight and then continue with a numerical bifurcation study of an industrial size RD column. 

The findings from singularity analysis of the one-stage column will be checked for their relevance for the nonlinear behavior of an industrial size RD column by means of numerical bifurcation analysis using DIVA [53, 63]. The model used is of moderate complexity. The major assumptions are constant liquid holdup on every tray negligible vapor holdup, constant heat capacities and heats of vaporization of all the species, ideal gas phase, almost ideal liquid phase, perfect mixing on... 

Fig. 10.8 Bifurcation diagrams for ethylene glycol synthesis one-stage column (bottom) and ten-stage distillation column (top)...

In the one-stage process (Fig. 2), ethylene, oxygen, and recycle gas are directed to a vertical reactor for contact with the catalyst solution under slight pressure. The water evaporated during the reaction absorbs the heat evolved, and make-up water is fed as necessary to maintain the desired catalyst concentration. The gases are water-scmbbed and the resulting acetaldehyde solution is fed to a distUlation column. The tad-gas from the scmbber is recycled to the reactor. Inert materials are eliminated from the recycle gas in a bleed-stream which flows to an auxdiary reactor for additional ethylene conversion. 

Bubble columns in series have been used to establish the same effective mix of plug-flow and back-mixing behavior required for Hquid-phase oxidation of cyclohexane, as obtained with staged reactors in series. WeU-mixed behavior has been established with both Hquid and air recycle. The choice of one bubble column reactor was motivated by the need to minimize sticky by-products that accumulated on the walls (93). Here, high air rate also increased conversion by eliminating reaction water from the reactor, thus illustrating that the choice of a reactor system need not always be based on compromise, and solutions to production and maintenance problems are complementary. Unlike the Hquid in most bubble columns, Hquid in this reactor was intentionally weU mixed. 

Estimate base pressure, assume column efficiency of 60 per alent to one stage. 

A simple model for side-rectifiers suitable for shortcut calculation is shown in Figure 11.12. The side-rectifier can be modeled as two columns in the thermally coupled direct sequence. The first column is a conventional column with a condenser and partial reboiler. The second column is modeled as a sidestream column, with a vapor sidestream one stage below the feed stage4. The liquid entering the reboiler and vapor leaving can be calculated from vapor-liquid equilibrium (see Chapter 4). The vapor and liquid streams at the bottom of the first column can then be matched with the feed and sidestream of the second column to allow the calculations for the second column to be carried out. 

As the name implies, stage-by-stage calculations are useful for calculating from a composition and set of flows in one stage to the composition and flows in an adjoining stage. By successive repetition of the procedure it is possible to calculate from one end of a column of stages to the other end. 

Uncondensed vapors are removed at the top of the column with a one-stage steam jet ejector equipped with a barometric condenser. 

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