Science Direct Meoh Mtbe Equilibrium

Damkohler Thiele

0 unstable node -----d,Wl"cil ^uilibTlum

Fig. 5.16. Residue curve maps for heterogeneously catalyzed MTBE synthesis at operating pressure p = 0.8 MPa for different Damkohler numbers ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)

0 unstable node -----d,Wl"cil ^uilibTlum

Fig. 5.16. Residue curve maps for heterogeneously catalyzed MTBE synthesis at operating pressure p = 0.8 MPa for different Damkohler numbers ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)

pure MTBE to a point that has the composition x = (0.035, 0.2), while the unstable node has moved out of the physically relevant composition space.

Further enhancement of Damkohler number to Da = 2 X 10~4 (Fig. 5.16c) leads to the situation in which the lower stable node coincides with the saddle point so that they extinguish each other. Hence the trajectories run into pure MeOH. At Da = 1 (Fig. 5.16d) the reaction vector is dominant in relation to the separation vector. Thus every residue curve is dominated by the stiochiometric restriction when moving towards the curve of chemical equilibrium. Because of the dominance of chemical reaction, the trajectories do not pass this line, but remain on it until they reach the pure MeOH vertex.

saddle branch

® kinetic tangent pinch

- stable node branch

Fig. 5.17. Singular point curve starting from the MTBE vertex (left) and related Damkohler numbers (right) at p = 0.8 MPa ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)

The results of the simulation shown in Fig. 5.16 can be summarized as follows. At a given operating pressure, p, it is possible to pass the distillation boundary by determining an adequately high Damkohler number Da. Hence, one stable point in the region of MTBE vertex disappears and every trajectory ends at pure MeOH. The second effect of raising Da is that the collecting line, which is also a separatrix, approaches the curve of chemical equilibrium. These findings were reported by Thiel et al. [8] for heterogeneously catalyzed MTBE synthesis, and, with some quantitative differences, also by Venimadhavan et al. [9] for the homogeneously catalyzed case.

To study the behavior of the singular points in the vicinity of the MTBE vertex, Thiel et al. [8] used a continuation method with the Damkohler number as continuation parameter. The results computed at p = 0.8 MPa are shown in Fig. 5.17. It can be observed that a stable node branch beginning from pure MTBE in the absence of chemical reaction moves away from MTBE vertex with rising Da. As the Damkohler number Da = 1.49 X 10~4 is reached, the stable node branch turns into a saddle branch. This point is called the kinetic tangent pinch [9]. The saddle branch arrives at Da = 0.0 in the binary azeotropic point between MeOH and MTBE.

5.3.3.2 Synthesis ofTAME

TAME is produced by liquid-phase synthesis from methanol and isoamylenes. Among the three isoamylenes only 2-methyl-1-butene (2MB1) and 2-methyl-2-bu-tene (2MB2) are reactive in etherification; 3-methyl-1-butene (3MB1) is non-reactive. Besides the two synthesis reactions, the isomerization of the reactive isoamy-lenes takes place simultaneously [10]

2MB1 ^ 2MB2

To calculate residue curve maps for the synthesis of TAME one has to proceed in the same manner as the MTBE example and calculate phase equilibria between liquid and vapor phases, chemical equilibrium constants in the liquid phase, and kinetics of the chemical reactions.

Because there are three reactions taking place, three coupled chemical equilibria have to be considered. Rihko et al. [11] proposed the following expressions, which are based on their experiments (T in K)

TAME synthesis from 2MB1 K1 — 1.057X10~4exp(4273.5/T) (5.39a)

TAME synthesis from 2MB2 K2 — 1.629X10~4exp(3374.4/T) (5.39b)

Isomerization reaction K3 — K1/K2 (5.39c)

Oost and Hoffmann [10] have developed a kinetic expression for the TAME synthesis of the lumped C5-reactants 2MB1 and 2MB2 in terms of liquid-phase activities where the reaction rate constant for the lumped TAME synthesis k12 obeys the Arrhenius equation. For the isomerization reaction, the following rate expression was proposed [10]

For the sake of a simplified illustration, the mixture of isomers 2MB1 and 2MB2 is treated as one pseudo-component isoamylene (IA) so that its mole fraction is xIA =

Fig. 5.18 shows residue curve maps of pure distillation of the non-reactive mixture IA/MeOH/TAME. Corresponding to the mixture in the MTBE synthesis, two binary azeotropic points exist: an unstable node between the olefin IA and the alcohol MeOH, and a saddle point between the ether TAME and the alcohol. These two points are linked by a distillation boundary line, which separates the whole composition space into two distillation areas. In the lower one pure TAME is the stable node; in the upper area pure MeOH is the stable node. By increasing the operating pressure p, the two azeotropic points move towards pure MeOH.

0 unstable node separalrix

Fig. 5.18. Residue curve maps for distillation without reaction (Da = 0) of the mixture IA/ MeOH/TAME at two operating pressures ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)

0 unstable node separalrix

Fig. 5.18. Residue curve maps for distillation without reaction (Da = 0) of the mixture IA/ MeOH/TAME at two operating pressures ([8], reprinted from Chem. Eng. Sci., Vol 52, Thiel, Sundmacher and Hoffmann, Pages 993-1005, Copyright 1997, with permission from Elsevier Science)

In Fig. 5.19 the residue curve maps of RD for TAME synthesis are displayed. For these results the operating pressure was changed (0.1 MPa, 1.0 MPa) as the second parameter besides the Damkohler number (10~4, 10~3, 1.0). The results calculated with the lower pressure show basically the same characteristics as discussed for the synthesis of MTBE. At a low Damkohler number, Fig. 5.19a, the separation effect is still dominating over the reaction effect so that two stable nodes in MeOH and nearby TAME are developed. A slight enhancement of Da leads to Fig. 5.19c, which is qualitatively similar to Fig. 5.19a except that the slower stable point has discharged from the TAME vertex. If Da is increased to Da = 1, there is a strong influence of the chemical reactions and one stable node disappears and every trajectory runs into the collecting trajectory, which is the only remaining separatrix in the composition space. This separatrix is in the vicinity of the chemical equilibrium line and ends in the MeOH vertex, Fig. 5.19e.

By raising the operating pressure p a new behavior of the system can be studied. A new saddle point appears and at Da = 10~4 and p = 1.0 MPa three stable points exist (Fig. 5.19b). In addition to the stable node in the MeOH vertex and in the region between chemical equilibrium and TAME vertex a third stable point is built in the isoamylene (IA) vertex. This is remarkable since IA is the light-boiling pure component of the system. In addition, a second saddle point appears.

As in the MTBE system, by use of a continuation method the location of singular points in the TAME residue curve map can be tracked against the Damkohler number Da. The calculated results at various operating pressures are given in Fig. 5.20.

0.1 10 jIMPt

T.i,Ei 0 2 O.J 16 D.B """ r^FitdfortfPMcljntlMintftarçi,

0 1 1.0 jwJilPa

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