Optimal active zone configurations

Numerical Experiments in Computing Optimal Active Zone Configurations... 

In this chapter, the problem of optimization of multizone configurations will be dealt with. When talking about a zone, we consider a thin active zone in which perfect mixing is assumed. Typically, thin catalyst zones are used in temporal analysis of products (TAP) studies, but other types of experiments involving thin active zones are also conceivable. 

Based on Eq. (8.15), it is easy to show that the optimal configuration of a cascade of imaginary CSTRs is one with equal distances between these CSTRs, independent of whether k is small or large. This is very different from the case analyzed previously, in which a unitary reactor consists of an active zone and a diffusion zone. 

For Nz = 2, Li stops being zero and detaches when Da becomes equal to one. For Da > 1, the optimal configuration, therefore, consists of the first active zone always at the reactor inlet and the second zone at some distance Li from the reactor inlet (with L > 0). As the value of Da tends to oo, Li tends from 0 to L/2 and L2 tends from L to L/2, which is the limit value of the optimal configuration. At all values of Da, L < L. ... 

For Nz = 3, the theoretical analysis is also confirmed. In this case, the configuration with all zones as close as possible to the reactor inlet is optimal for Da< 1/2. At Da=1/2, La detaches and up to Da=3/2 the optimal configuration has two active zones as close as possible to the reactor inlet and the third at a distance L2 from the inlet. When Da=3/2, Li detaches and for all values Da >3/2 the optimal configuration consists of three separate active zones the first zone at the reactor inlet, the second at a distance Li, and the third at a distance L2 from the first zone. As Da —> 00, the three distances tend to L/3 and in the limit the optimal zone configuration again is one with equal distances between the zones. Again, at all values of Da, L < Z/2 < Z/3. 

In the case of four active zones, Nz = 4, L3, L2, and Li successively detach as Da increases (see Fig. 8.2C). Remarkably, Li detaches exactly at the point where L2 and L3 become equal. Furthermore, the equality of L2 and L3 is preserved for all values of Da larger than two. This means that at Da > 2, the optimal configuration consists of four separate active zones the first zone is always at the inlet of the reactor, the distance Li between the first and second zone is smallest, the distances and L3 between, respectively, the second and third zone and the third and fourth zone are equal and larger than Li, and the distance L4 between the fourth zone and the reactor outlet is largest Li < L2 = 7-3 < 7/4- Again, when Da 00, all L, tend to the same value, in this case L/4. 

The above flowsheet can be simplified tremendously by catalytic distillation. Figure 7.32 depicts a conceptual configuration. The RD column consists of a reactive zone at the top, and a distillation section at the bottom. The reaction mixture is sent to a purification column, from which ethylbenzene is obtained as top distillate. A side-stream containing PEB is sent to transalkylation for EB recovery. Obviously, the feasibility of this process depends largely on the availability of an active and selective catalyst. For zeolites the optimal operating conditions are about pressure around 3 MPa, temperature less than 200 °C, and reaction rate capable to give a space-time of 5 h" for almost complete ethylene conversion. 

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