In single-pellet studies, it is assumed that no concentration or temperature gradients are present in the fluid phase surrounding the pellet. A reactor with external or internal recycle is one of the experimental realizations of the single-pellet concept. However, in a fixed-bed reactor, the fluid-phase composition and temperature vary with position. For this reason, the optimization problem becomes more complex. Thus, it is not surprising that relatively few reactor studies have appeared in the literature as compared with those for single pellets. In this chapter, we first discuss theoretical studies of single and multiple reactions under isothermal and nonisothermal conditions, and then present experimental work which supports the theoretical developments.

A Single Reaction

Isothermal Conditions

One of the earliest works in this area considered CO oxidation in excess oxygen over platinum catalyst, in monolith reactors for automobile converters (Becker and Wei, 1977a). Recall that this reaction exhibits a maximum in the rate as a function of CO concentration. The CO conversion to CO2 as a function of the Thiele modulus (or equivalently, the catalyst temperature) for a fixed inlet CO concentration is shown in Figure 3.1 for four monoliths with different catalyst distributions (cf. Figure 2.1). The conversion of CO below 650°F was significantly higher in the inner catalyst, while above 650°F the middle catalyst performed better and attained 100% conversion. The uniform and outer catalysts also showed 100% conversion at progressively higher temperatures.

The optimization of the isothermal fixed-bed reactor, where a bimolecular Langmuir–Hinshelwood reaction occurs, was performed analytically by Morbidelli et al. (1986a,b).