Water x x ene
Fig. 5.23. Bifurcation behavior of stable node and saddle point for the cyclohexanol reaction system with respect to the Damkohler number : a) pseudohomogeneous liquid system, b) heterogeneous liquid system (, reprinted from Chem. Eng. Sci., Vol 57, Qi, Kolah and Sundmacher, Pages 163-178, Copyright 2002, with permission from Elsevier Science)
The kinetic RCMs for the pseudohomogeneous system and for the heterogeneous system at different Damköhler numbers are shown in Fig. 5.22. For the pseudohomogeneous RCMs, with increasing Damköhler number the saddle point on the water-cyclohexanol edge and the stable node (pure cyclohexanol) move into the composition triangle (Fig. 5.22). There they meet and extinguish each other at the critical Damköhler number Da = 0.165. Meanwhile, the saddle point (pure cyclohexene) in the non-reactive RCM also moves into the triangle, shifts towards the PCE and leaves the pure cyclohexene vertex as a stable node (Fig. 5.22b). Fig. 5.22c shows the pseudohomogeneous equilibrium RCM (Da = 500). The reactive azeotropes in the two systems are identical because they are located outside the L-L phase splitting region.
For the heterogeneous liquid system, the reaction was assumed to take place in both liquid phases. When we compare the RCMs at the same Da for the pseudo-homogeneous and heterogeneous systems, again we can find that the properties (including the reactive azeotrope) of the RCMs outside the L-L region are identical. But they are distinct inside the L-L region because of their different chemical equilibrium curves (compare Fig. 5.21).
Moreover, the bifurcation behavior for the pseudohomogeneous and heterogeneous kinetic RCMs is different, as shown in Figs.5.23. For the heterogeneous case (Fig. 5.23b), the saddle point branch starting from the water-cyclohexanol edge and the stable point branch starting from the pure cyclohexanol vertex meet on the L-L envelope (extract side) at the critical Da = 0.109. This point represents the kinetic tangent pinch point of the system. For the pseudohomogeneous system (Fig. 5.23a), bifurcation occurs at the critical Damköhler number Da = 0.165.
Recently, Steyer et al.  presented an extended analysis of cyclohexanol synthesis and splitting, supposing that the chemical reaction will proceed in the two liquid phases at different rates, that is with different Damköhler numbers. Based on their results, these authors proposed a flow-sheet of two coupled RD columns for the separation of cyclohexene/cyclohexane mixtures.
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