Reactors packed tubular, stability

A great savings in enzyme consumption can be achieved by immobilizing the enzyme in the reactor (Fig. 12). In addition to the smaller amount of enzyme required, immobilization often increases the stability of the enzyme. Several designs of immobiliz-ed-enzyme reactors (lERs) have been reported, with open-tubular and packed-bed being the most popular. Open-tubular reactors offer low dispersion but have a relatively small surface area for enzyme attachment. Packed-bed reactors provide extremely high surface areas and improved mass transport at the cost of more dispersion. 

Of the various methods of weighted residuals, the collocation method and, in particular, the orthogonal collocation technique have proved to be quite effective in the solution of complex, nonlinear problems of the type typically encountered in chemical reactors. The basic procedure was used by Stewart and Villadsen (1969) for the prediction of multiple steady states in catalyst particles, by Ferguson and Finlayson (1970) for the study of the transient heat and mass transfer in a catalyst pellet, and by McGowin and Perlmutter (1971) for local stability analysis of a nonadiabatic tubular reactor with axial mixing. Finlayson (1971, 1972, 1974) showed the importance of the orthogonal collocation technique for packed bed reactors. 

In critical cases it may well be worthwhile to make a complete analysis of stability. In many cases, however, enough can be learned by studying what Bilous and Amundson (B7) called parametric sensitivity. These authors derived formulas for calculating the amplification or attenuation of disturbances imposed on an unpacked tubular reactor originally in a steady state, with the idea that if the disturbances grow unduly the performance of the reactor is too sensitive to the conditions imposed on it, that is, to the parameters of the system. The effect of feedback from a control system was not considered. As pointed out by the authors, it would be a much more complicated task to apply their procedure to a packed reactor, but it still would entail far less computation than a study of the transient response. 

The averaging technique characteristic of the second approach may apply to the case of a tubular reactor where the ratio of the characteristic catalyst particle size to the diameter of a single tube is close to unity, but it is invalid, as will be shown, in the general case of fixed-bed reactors. This approach keeps out of a researcher s field of vision the problem of the reactor stability to local perturbations. At the same time, the technologist is often faced with hot spots in the catalyst bed of a fixed-bed reactor, which make its operation imperfect and even lead to an emergency situation in a number of cases, Until recently, nonuniformity of the fields of external parameters (e.g., nonuniform packing of the catalyst bed or nonuniformity of reactant stream velocity ) was considered the only cause of these phenomena. The question naturally arises whether the provision for uniformity of external conditions guarantees the uniformity of temperature and concentration profiles at the reactor cross-section. The present paper seeks to answer this question, which, as a matter of fact, has not yet been posed in such a form in the theory of chemical reactors. 

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