Dt

eq rp

P'yt=rr*rP7

This system of equations (5.7-5.14) has one less degree of freedom than the corresponding set of equations for non-reactive residue curves (5.1-5.6) since the chemical equilibrium definition requires two new equations but only one new variable (K^,). The physical interpretation of this result is that the feed composition cannot be defined independently where chemical equilibrium is assumed. Although any combination of components can be introduced to a reactive still, the composition will change immediately if the mixture is not already in chemical equilibrium.

5.1.2.2 ETBE System

In a ternary system (i.e. ethanol, isobutene and ETBE only), there is only one possible reactive residue curve at any given pressure. In a quaternary system (e.g. with n-butene added to the reactive mixture), the initial amount of n-butene uniquely defines the residue trajectory. Note that this is slightly different to the initial concentration, as the reaction can change the concentration by altering the total number of moles in the system.

ETBE Mole Fraction

Figure 5.6 - Reactive Residue Curve Diagram for the ETBE System at 950 kPae

ETBE Mole Fraction

Figure 5.6 - Reactive Residue Curve Diagram for the ETBE System at 950 kPae

Figure 5.6 shows the residue trajectories for a family of reactive, quaternary mixtures with differing amounts of inert. The n-butene concentrations shown on the diagram indicate the approximate feed composition only. A positive slope (e.g. near the C4 node) indicates El BE formation while a negative slope (e.g. near the ethanol node) indicates ETBE decomposition. Although the highest concentration of ETBE is achieved with no inert present, the ETBE synthesis reaction continues with much higher ethanol concentrations when the system is diluted with n-butene.

5.1.2.3 MTBE System

Figure 5.7 indicates the reactive residue trajectories for the MTBE system at the same pressure. Interestingly, the effect of the C4 inerts is greatly diminished. The maximum MTBE concentration is higher than the maximum ETBE concentration (due to the more favourable reaction thermodynamics) but the synthesis reaction cannot be sustained at a methanol concentration above 25%, regardless of the initial inert concentration. The diagram also suggests that the cooling effect of additional C4 inerts is negligible for initial n-butene concentrations above 50%. Although all of the residue curves originate from the methanol-C4 azeotrope, the trajectories are severely curved near the pure C4 node that will act as a distillation pinch point.

MTBE Mole Fraction

Figure 5.7 - Reactive Residue Curve Diagram for the MTBE System at 950 kPag

MTBE Mole Fraction

Figure 5.7 - Reactive Residue Curve Diagram for the MTBE System at 950 kPag

5.1.2.4 Kinetically Controlled Reactions

An alternative representation of the reactive still uses a kinetic model of the reaction and requires the specification of a catalyst loading. Under these conditions, the heating rate is important in controlling the residue trajectory. A very slow heating rate combined with any quantity of catalyst will approximate chemical equilibrium while a faster heating rate will suppress the reaction. This effect is demonstrated by Figure 5.8, which compares three trajectories with very low catalyst loadings. The residue trajectories with moderate to high catalyst loadings align closely with the equilibrium curves, thereby confirming that the equilibrium model is appropriate for the ETBE system.

The upper curve in Figure 5.8 corresponds to the lowest catalyst loading. The trajectory is strongly influenced by the shape of the non-reactive residue curve (Figure 5.3), particularly near the C4 node where the reaction is slowest (due to the colder temperatures implied by the phase equilibrium requirement). As the reaction rate increases with the rising temperature and changing composition, the system approaches reaction equilibrium and the residue trajectory assumes a similar shape to the equilibrium reactive residue curves (Figure 5.6). A higher catalyst loading (e.g. the lower curve in Figure 5.8) results in a trajectory that approximates the reaction equilibrium model more closely.

Pure C40 o 0 -i 0 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

ETBE Mole Fraction

Figure 5.8 - ETBE Reactive Residue Curves (Limited bv Reaction Kinetics^

Pure C40 o 0 -i 0 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

ETBE Mole Fraction

Figure 5.8 - ETBE Reactive Residue Curves (Limited bv Reaction Kinetics^

5.1.2.5 Significance for Reactive Distillation Column Design

The reactive residue diagrams for both the ETBE and the MTBE system include no azeotropes, only one stable node (ethanol or methanol) and only one unstable node (pure C4 in the ETBE system or the C4-methanol azeotrope in the MTBE system). A pure ether product is not possible in either system. This defines the requirements for hybrid columns for both syntheses. While a stopping section is clearly required to obtain the pure ether product, there is no specific requirement for a rectifying section in either process since both the reactive and non-reactive residue curves converge to the same node. However, a non-reactive section can be seen to purify the distillate product more efficiently and is, therefore, recommended.

The reactive residue trajectories in both the ETBE and MTBE systems all reach a maximum value of the ether concentration before converging towards the ethanol or methanol node. At ethanol/methanol concentrations below the 'turning point' the reaction proceeds to the right (ether synthesis) while the reaction proceeds to the left (ether decomposition) at higher alcohol concentrations. In order to avoid the decomposition reaction, a hybrid column should be designed to produce a reactive section composition profile on the ether synthesis branch of the residue curve. Therefore, the reactive residue curve diagram can be used to provide a priori knowledge of the approximate feed compositions to the non-reactive sections, and to determine the approximate influence of the column feed composition on the operating conditions.

The initial concentration of inert C4 components clearly has a significant effect on the reactive residue trajectory in an ETBE system (Figure 5.6). Although a directionally similar effect is evident from the MTBE reactive residue curve diagram (Figure 5.7), there is a much lesser dependency on the inerts. This observation highlights a key difference between the two systems. A high concentration of inerts in the feed to an ETBE column will significantly increase the ethanol concentration in the stripping section and also increase the likelihood of crossing the non-reactive distillation boundary so that the stripping section would act to purify ethanol rather than ETBE. However, the residue curve diagram does not provide sufficient information to determine whether the additional inerts would have a favourable effect on the synthesis reaction. An MTBE column could be expected to operate similarly over a wide range of feed compositions.

Although both the ETBE and MTBE reactions are essentially limited by thermodynamics rather than kinetics, it is relevant to consider the effect that reaction kinetics have on reactive residue curves for cases when the installed catalyst is poisoned or loses substantial activity.

Figure 5.8 considers such a case and shows that higher ethanol concentrations should be expected in the reaction zone. This suggests that the reactive section is somewhat self-regulating, as the increased ethanol availability will increase the reaction zone temperature and, therefore, increase the reaction rate constant. Although lower isobutylene conversions might be expected as the reaction becomes thermodynamic ally less favourable, adequate reaction rates should be maintained.

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