Nonisothermal catalysts

ILLUSTRATION 12.4 EFFECTIVENESS FACTOR DETERMINATION FOR A NONISOTHERMAL CATALYST PELLET-EXOTHERMIC REACTION... 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

There are several factors that may be invoked to explain the discrepancy between predicted and measured results, but the discrepancy highlights the necessity for good pilot plant scale data to properly design these types of reactors. Obviously, the reaction does not involve simple first-order kinetics or equimolal counterdiffusion. The fact that the catalyst activity varies significantly with time on-stream and some carbon deposition is observed indicates that perhaps the coke residues within the catalyst may have effects like those to be discussed in Section 12.3.3. Consult the original article for further discussion of the nonisothermal catalyst pellet problem. 

For the most adroit scaling we shall need the best estimates of the variables that we can get, and in any case, it is important get as much a priori information as possible.14 Some bounds are physically obvious, as when we have a system in which a substance is disappearing by an irreversible reaction and its concentration cannot exceed the value at the inlet. A nice illustration of a less trivial estimate is provided by the nonisothermal catalyst pellet, the equations of which are here transcribed from (Eqs. 112-114 and 123-125) for u(x), the concentration of the reactant,... 

For the nonisothermal catalyst pellet with negligible external mass and heat transfer resistances, i.e., with Sh —> 00 and Nu —> 00 and for a first-order reaction, the dimensionless concentration and temperature are governed by the following couple of boundary value differential equations... 

Assuming a steady state, for first-order reaction-diffusion system A -> B under nonisothermal catalyst pellet conditions, the mass and energy balances are... 

Hie Aris numbers Anx and An0 can be applied to nonisothermal catalyst pellets. Three items will be discussed ... 

Nonisothermal Catalyst Pellets and First-order Reactions... 

Effectiveness factors for a first-order reaction in a spherical, nonisothermal catalysts pellet. (Reprinted from R B. Weisz and J. S. Hicks, The Behavior of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chem. Eng. Sci., 17 (1962) 265, copyright 1962, with permission from Elsevier Science.)... 

Mass transfer in combination with even quite "normal" reaction kinetics can produce a wealth of phenomena including multiple steady states, instabilities, and oscillations. An example is the behavior of nonisothermal catalyst particles outlined in Section 9.5.2. Such phenomena are covered in detail in standard texts on reaction engineering, to which the reader is referred. The examination in this section will remain restricted to effects produced by vagaries of multistep or multiple simultaneous reactions. 

Single-Bed, Nonisothermal Catalysts. In an attempt to circumvent the undesirable formation of hydrogen sulfide in the presence of water vapor, a nonisothermal reactor was constructed by placing 536 g of Jamaican red mud catalyst in a 2-cm diameter 96%-silica tube. The catalyst-filled tube was inserted into the bottom half of the furnace. This resulted in a 15-cm uniform temperature hot zone and a 25-cm zone with temperatures gradually decreasing to about 100 °C at the lower reactor exit. The inlet gas consisted of 17% water vapor, 5.8% carbon monoxide, and 3.0% sulfur dioxide, and 74.2% helium. Figure 5 shows the dependence of the exhaust gas analysis on the hot-zone temperature of the Jamaican red mud catalyst. No sulfur dioxide was removed at hot-zone temperatures lower than 240 °C. At 250 °C, some sulfur dioxide was removed, and small quantities of hydrogen sulfide were formed. Above 300°C, more than 80% of the sulfur dioxide and virtually all of the carbon monoxide... 

Double-Bed Catalysts. Because the temperature of the colder section in the nonisothermal catalyst bed could not be readily controlled, an apparatus was constructed that contained two separate furnaces, each containing 20 g of Surinam red mud. The temperature of the first bed was varied to determine the optimum operating conditions with an inlet gas of 0.57% sulfur dioxide, 0.89% carbon monoxide, and 3% water vapor in helium. The exhaust gas analyses from the first furnace are shown in Figure 6. These results indicate that the hydrogen sulfide and sulfur dioxide removal efficiency increases with temperature up to about 400 °C. Beyond this temperature there is little improvement. 

Figure 3.7.a-I Effectiveness factor with first-order reaction in a spherical nonisothermal catalyst pellet from Weisz and Hicks [112]). 

ILLUSTRATION 12.4 Effectiveness Factor Determination for a Nonisothermal Catalyst Pellet Employed to Effect an Exothermic Reaction... 

B under nonisothermal catalyst pellet conditions, the mass and energy... 

Heat conduction through an adsorbent particle or through an assemblage of adsobent particles is generally much faster than heat transfer at the external surface so it is usually a good approximation to consider the particle as essentially isothermal with all heat transfer resistance concentrated in the external film. This is essentially the same situation as in a nonisothermal catalyst particle. ... 

The exciting issue of steady-state multiplicity has attracted the attention of many researchers. First the focus was on exothermic reactions in continuous stirred tanks, and later on catalyst pellets and dispersed flow reactors as well as on multiplicity originating from complex isothermal kinetics. Nonisothermal catalyst pellets can exhibit steady-state multiplicity for exothermic reactions, as was demonstrated by P.B. Weitz and J.S. Hicks in a classical paper in the Chemical Engineering Science in 1962. The topic of multiplicity and oscillations has been put forward by many researchers such as D. Luss, V. Balakotaiah, V. Hlavacek, M. Marek, M. Kubicek, and R. Schmitz. Bifurcation theory has proved to be very useful in the search for parametric domains where multiple steady states might appear. Moreover, steady-state multiplicity has been confirmed experimentally, one of the classical papers being that of A. Vejtassa and R.A. Schmitz in the AIChE Journal in 1970, where the multiple steady states of a CSTR with an exothermic reaction were elegantly illustrated. 

In this paper we will first review some basic concepts and apply them to the design of isothermal reactors working in the diffusional regime.Then we will concentrate our attention on the problem of intraparticle convection in large pore catalysts.Several aspects of this question will be dealt with - effectiveness factors for iso -thermal and nonisothermal catalysts, measurement of effective diffu-sivities and the implication of intraparticle convection effects on the design and operation of fixed bed catalytic reactors. 

INTRAPARTICLE CONVECTION,DIFFUSION AND REACTION IN NONISOTHERMAL CATALYSTS. 

Let us now extend the analysis to the case of a nonisothermal catalyst following our pi evious work (Ferreira et al. l5l)JThe model equations for a volume element of a slab catalyst in the case of a first order irreversible reaction are ... 

Figure 10a - Concentration profiles inside nonisothermal catalysts (y=20,6=0.1,X =0,X =25)...

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