Reversibility with catalyst decay

A second way of ensuring that the reaction does not become artificially switched off by the complete disappearance of the autocatalyst is to recognize the reversibility of the two reactions. Thus the extent of reaction can never proceed beyond the equilibrium state, which itself has a non-zero concentration for B. We will again neglect the uncatalysed step but include in our discussion those systems which may be fed not just by an inflow of A and B, but also by an inflow of C. The latter allows the reaction to proceed backwards , if the inflow composition has a product concentration exceeding its equilibrium value. 

Parameter values exemplifying the 14 stationary-state responses for the reversible autocatalator model with Xo = -05 corresponding to Fig. 6.22 

and Scott, S. K. (1988). Modelling cubic autocatalysis by successive bimolecular steps. Chem. Eng. Sci., 43, 207-11. 

Balakotaiah, V. (1987). On the steady-state behaviour of the autocatalator model A + 2B 3B, B in a continuous-flow stirred-tank reactor Proc. R. Soc., A411, 193-206. 

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The optimal temperature policy in a batch reactor, for a first order irreversible reaction was formulated by Szepe and Levenspiel (1968). The optimal situation was found to be either operating at the maximum allowable temperature, or with a rising temperature policy, Chou el al. (1967) have discussed the problem of simple optimal control policies of isothermal tubular reactors with catalyst decay. They found that the optimal policy is to maintain a constant conversion assuming that the decay is dependent on temperature. Ogunye and Ray (1968) found that, for both reversible and irreversible reactions, the simple optimal policies for the maximization of a total yield of a reactor over a period of catalyst decay were not always optimal. The optimal policy can be mixed containing both constrained and unconstrained parts as well as being purely constrained. 

Additional Factors Influencing Decay. Numerous other factors may influence the observed change in activity of catalyst. These include pore mouth blocking by deposited solid, equilibrium, or reversible poisoning where some activity always remains, and the action of regeneration (this often leaves catalyst with an active exterior but inactive core). 

Decay and poisoning. In all situations studied to this point, the external pathway was that of a reversible reaction fast enough to become quasi-stationary. Of course, the reaction may also be irreversible. If so, catalyst material that has left the cycle does not return and is permanently lost, and the reaction eventually comes to a stand-still unless the catalyst is replenished. If the loss of catalyst material is fast, the system obviously is of no practical interest. In contrast, slow irreversible loss is a problem the practical engineer often has to contend with. 

The second relevant phenomenon is the decrease of the overall rate or the increase of the decay rate which is often observed when the alkyl concentration increases beyond certain limits. According to some authors 88 11this may be due to the adsorption of the Al-alkyl on catalytic sites in competition with the monomer. Still others 92,95 107) attribute it to an overreduction of titanium. This seems plausible when considering the results obtained by Kashiwa78) who showed that Ti2+ is less active than Ti3+ or Ti4+ in ethylene polymerization and completely inactive in the polymerization of propylene. Keii98), in turn, based on the results of Fig. 32, hypothesizes that the decay rate is due to a bimolecular disproportionation of the Ti—R bonds, favored by Al-alkyl reversibly adsorbed on the catalyst surface. 

Overall, it can be seen to be an ABC system involving three species the closed form A, the open form B, and the set of degradation products [DA 4- DB] = C (DA from the degradation of the closed form and DB from that of the open form). The consequences of the photodegradation will be seen as a continuous decay in the photostationary state, with an increase in the rate constant fcBA with increase in the duration of irradiation. This change in rate indicates that the photolysis products of [Da + Db] act as catalysts of the thermal reverse reaction. 

Because of the type of the enzyme-support binding, reversibly immobilized enzymes can be detached from the support under gende conditions. The use of reversible methods for enzyme immobilization is highly attractive, mostly for economic reasons because when the enzymatic activity decays, the support can be regenerated and reloaded with fresh enzyme. Indeed, the cost of the support is often a primary factor in the overall cost of immobilized catalyst. The reversible immobilization of enzymes is particularly important for immobilizing labile enzymes and for applications in bioanalytical systems. 

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