Nonisothermal reactions in packed beds

Correlations for E are not widely available. The more accurate model given in Section 9.1 is preferred for nonisothermal reactions in packed-beds. However, as discussed previously, this model degenerates to piston flow for an adiabatic reaction. The nonisothermal axial dispersion model is a conservative design methodology available for adiabatic reactions in packed beds and for nonisothermal reactions in turbulent pipeline flows. The fact that E >D provides some basis for estimating E. Recognize that the axial dispersion model is a correction to what would otherwise be treated as piston flow. Thus, even setting E=D should improve the accuracy of the predictions. 

What models should be used, either for scaleup or to correlate pilot-plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though... 

What models should be used either for scaleup or to correlate pilot plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though they use empirical parameters D, hr, and Kr to account for the packing and the complexity of the flow field. For laminar flow in open tubes, use the methods in Chapter 8. For highly turbulent flows in open tubes (with reasonably large L/dt ratios) use the axial dispersion model in both the isothermal and nonisothermal cases. The assumption D = E will usually be safe, but do calculate how a PFR would perform. If there is a substantial difference between the PFR model and the axial dispersion model, understand the reason. For transitional flows, it is usually conservative to use the methods of Chapter 8 to calculate yields and selectivities but to assume turbulence for pressure drop calculations. 

There may be radial temperature gradients in the reactor that arise from the interaction between the energy released by reaction, heat transfer through the walls of the tube, and convective transport of energy. This factor is the greatest potential source of disparities between the predictions of the model and what is observed for real systems. The deviations are most significant in nonisothermal packed bed reactors. 

Chen et al. [70] suggested that temperature gradients may have been responsible for the more than 90 % selectivity of the formation of acetylene from methane in a microwave heated activated carbon bed. The authors believed that the highly nonisothermal nature of the packed bed might allow reaction intermediates formed on the surface to desorb into a relatively cool gas stream where they are transformed via a different reaction pathway than in a conventional isothermal reactor. The results indicated that temperature gradients were approximately 20 K. The nonisothermal nature of this packed bed resulted in an apparent rate enhancement and altered the activation energy and pre-exponential factor [94]. Formation of hot spots was modeled by calculation and, in the case of solid materials, studied by several authors [105-108],... 

Tubular reactors are normally used in the chemical industry for extremely large-scale processes. When filled with solid catalyst particles, such reactors are referred to as fixed-bed or packed-bed reactors. In this section we treat general design relationships for tubular reactors in which isothermal homogeneous reactions take place. Nonisothermal tubular reactors are treated in Section 10.4 and packed-bed reactors in Section 12.7. 

For a nonisothermal catalytic packed bed, the energy balance Equation 5.158 is coupled to the mass balances and the system therefore consists ofN + I (number of components -F 1) of ordinary differential equations (ODEs), which are solved applying the same numerical methods that were used in the solution of the homogeneous plug flow model (Chapter 2). If the key components are utilized in the calculations, the system can be reduced to S -F 1 (number of reactions + 1) differential equations—provided that the number of reactions (S) is smaller than the number of components (N). 

To illustrate the above points in a simple manner, let us consider a nonisothermal adiabatic fixed-bed reactor packed with nonporous catalyst pellets for a simple exothermic reaction... 

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