Catalytic reactor design with effectiveness factors

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. 

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

In this section we have presented and solved the BVPs associated with the diffusion and reaction that take place in the pores of a porous catalyst pellet. The results were expressed graphically in terms of the effectiveness factor rj versus the Thiele modulus d> for two cases One with negligible external mass and heat transfer resistances, i.e., when Sh and Nu —> oo, and another with finite Sh and Nu values. This problem is very important in the design of fixed-bed catalytic reactors. The sample results presented here have shown that for exothermal reactions multiple steady states may occur over a range of Thiele moduli d>. Efficient numerical techniques have been presented as MATLAB programs that solve singular two-point boundary value problems. 

As seen from Fig. 13, which gives a model unit of the laboratory cell reactor, this cell contains specially designed nets, to provide turbulence of the liquid flow. From the experimental result it was shown that the effectiveness factor was very high (up to 0.84) in experiments with plates with a very thin catalytic layer located close to the liquid side. In experiments with plates with a thick catalytic layer located in the middle of the plate, the effectiveness factor was very low (down to 0.02), and only a small part of the catalyst layer was utilized, since p-nitrobenzoic acid vanished in the plate after only 10% of the thickness of the catalytic layer had been passed in this particular run. 

Application of the theory in this case is quite simple, in fact, since we have been careful to define quantities such as the effectiveness factor or the enhancement factor in terms of the rate under observable conditions. Consider as an example a PFR catalytic reactor model in which we wish to include possible diffusion limitations on the catalyst activity. This becomes, de facto, a two phase model since the inclusion of an effectiveness factor means that we are considering the catalyst as a separate phase. We start with the design equation written in the following form... 

The mass balance with homogeneous one-dimensional diffusion and irreversible nth-order chemical reaction provides basic information for the spatial dependence of reactant molar density within a catalytic pellet. Since this problem is based on one isolated pellet, the molar density profile can be obtained for any type of chemical kinetics. Of course, analytical solutions are available only when the rate law conforms to simple zeroth- or first-order kinetics. Numerical techniques are required to solve the mass balance when the kinetics are more complex. The rationale for developing a correlation between the effectiveness factor and intrapellet Damkohler number is based on the fact that the reactor design engineer does not want to consider details of the interplay between diffusion and chemical reaction in each catalytic pellet when these pellets are packed in a large-scale reactor. The strategy is formulated as follows ... 

Immobilized enzyme reactors are increasingly popular due to their advantages over conventional catalysts. For efficient reactor design and performance prediction, quantitative knowledge of reaction kinetics and the factors affecting them is required. In this chapter, enzyme catalytic mechanisms are described and the kinetic models developed from these mechanisms are discussed. The chapter also discusses the kinetics of immobilized enzymes and their related mass transfer effects. Diffusion restrictions are described with a particular focus on packed bed reactors. The chapter concludes with a brief discussion of immobilized enzyme reactor design and scale-up. 

Xu and Chang (1996), have conducted kinetic measurements in a batch reactor for the esterification of dilute acetic acid with methanol in presence of Amberlyst 15 at 367 K. The internal mass transfer resistance was found to be insignificant. A kinetic equation was developed and used in the simulation and design of a catalytic distillation column for removing dilute acetic acid from wastewater. Xu and Chang (1997) have also presented a theoretical analysis to determine the effect of internal diffusion on second order reversible esterification. The results of the analysis showed that the catalyst effectiveness factors were above 0.94 for beads smaller than 0.6 mm diameter at a temperature lower than 353 K. However, the effectiveness factors were lower than 0.77 for the beads larger than 1.0 mm diameter at reaction temperature higher than 367 K. 

Various types of reactor configuration may be employed to effect non-catalytic gas—solid reactions. Events occurring during such reactions (see Sect. 5) are complex and industrial equipment for particular applications has evolved with operating experience rather than as a result of analytical design. Those factors which influence the course of the reaction are the reaction kinetics (as observed for a single particle), the size distribution of the solid reactant feed and the flow pattern of both solid and gas phases through the reactor. An excellent account of gas—solid reactions and... 

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