u* a.i ■■ j u :■■ l' 1 i>d il; ùf m'j iîi

u* a.i ■■ j u :■■ l' 1 i>d il; ùf m'j iîi

tion. The branches of fixed points were calculated using the pseudo-arclength continuation method in Auto [8].

For the IPOAc system, the fixed point branches are shown in bifurcation diagrams for the rectifying and stripping cascades in Fig. 6.10. The left edge of the diagrams (D = 0) represents the limit of no reaction. Here, there is a minimum boiling ternary azeotrope containing isopropanol, isopropyl acetate, and water, which is an unstable node; six intermediate boiling fixed points (all saddles); acetic acid is the heaviest species (stable node). Starting from these initial conditions, fixed point branches are tracked for both the rectifying and stripping cascades.

The branches of interest are the unstable nodes in the rectifying bifurcation diagram and the stable nodes in the stripping cascade bifurcation diagram. These node branches are shown separately in a feasibility diagram, Fig. 6.11.

The feasibility diagram provides a global view of the feasible products to expect from a continuous distillation at any rate of reaction (D). For any feed composition and for D in the range, 0 < D < 0.395, it is possible to obtain acetic acid as bot-

Chemical Equilibrium
Fig. 6.11 Feasibility diagram showing the feasible distillates (unstable nodes) and feasible bottom products (stable nodes) from the rectifying and stripping cascade bifurcation diagrams, respectively

toms from a continuous RD. However, for 0.395 < D < 1 we can obtain either iso-propanol or acetic acid as the bottoms product depending on the feed composition. The potential distillates are all quaternary mixtures, with compositions that depend on D. Thus, different splits are feasible for different ranges of the Damkohler number. Conversely, any given split may or may not be feasible as the reaction rate or residence time is changed, so that the feasibility of a given separation may depend on production rates, catalyst levels, and liquid holdup. The results mean that IPOAc cannot be obtained as a pure product from a single-feed fully reactive column, no matter what rate of reaction the column is operated at.

Thus, we propose the following rule.

Rule for Feasible Products: Unstable node branches in the feasibility diagram represent potential distillates while the stable node branches represent the potential bottoms from a continuous RD column.

Chadda et al. [5] have compared the predictions made by this approach with detailed column simulations at values of D = 0.25 and D = 0.75 using the methods described in Huss et al. [27], and find the predictions to be in good agreement with the simulations.

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