Effectiveness factor methane steam reforming

The profiles of the effectiveness factor g along the length of a steam reformer as well as a methanator can be computed in three different ways, namely by the dusty gas model, as well as by our simplified models (A) and (B). 

A fixed-bed reactor often suffers from a substantially small effectiveness factor (e.g., 10 to 10 for a fixed-bed steam reformer according to Soliman et al. [1988]) due to severe diffusional limitations unless very small particles are used. The associated high pressure drop with the use of small particles can be prohibitive. A feasible alternative is to employ a fluidized bed of catalyst powders. The effectiveness factor in the fluidized bed configuration approaches unity. The fluidization system also provides a thermally stable operation without localized hot spots. The large solid (catalyst) surface area for gas contact promotes effective catalytic reactions. For certain reactions such as ethylbenzene dehydrogenation, however, a fluidized bed operation may not be superior to a fixed bed operation. To further improve the efficiency and compactness of a fluidized-bed reactor, a permselective membrane has been introduced by Adris et al. [1991] for steam reforming of methane and Abdalla and Elnashaie [1995] for catalytic dehydrogenation of ethylbenzene to styrene. 

Elnashaie SSEH, Abashar MEE (1993) Steam reforming and methanation effectiveness factors using the dusty gas model under industrial conditions. Chem Eng Proc 32 177-189... 

Elnashaie, S.S.E.H. and Abashar, M.E., Steam Reforming and Methanation Effectiveness Factors Using the Dusty Gas Model Under Industrial Conditions. Chem. Eng. and Processing (in Press, 1993). 

All these factors are functions of the concentration of the chemical species, temperature and pressure of the system. At constant diffu-sionai resistance, the increase in the rate of chemical reaction decreases the effectiveness factor while al a constant intrinsic rate of reaction, the increase of the diffusional resistances decreases the effectiveness factor. Elnashaie et al. (1989a) showed that the effect of the diffusional resistances and the intrinsic rate of reactions are not sufficient to explain the behaviour of the effectiveness factor for reversible reactions and that the effect of the equilibrium constant should be introduced. They found that the effectiveness factor increases with the increase of the equilibrium constants and hence the behaviour of the effectiveness factor should be explained by the interaction of the effective diffusivities, intrinsic rates of reaction as well as the equilibrium constants. The equations of the dusty gas model for the steam reforming of methane in the porous catalyst pellet, are solved accurately using the global orthogonal collocation technique given in Appendix B. Kinetics and other physico-chemical parameters for the steam reforming case are summarized in Appendix A. 

FIGURE 5.60 Reactions and component effectiveness factors and rates of reactions versus bulk phase temperature for the steam reforming of methane, (a) ij s for reactions, (b) Rates of reactions, (c) j/ s for components, (d) Components rates. 

The effectiveness factors profiles along the length of the steam reformers as well as the methanators are computed by the dusty gas model and simplified models I and II. 

The effect of steam to methane ratios on the performance of reformer U was investigated by considering three different steam to methane ratios S/M- 2.5, 5/M= 5.0, 5/A/= 8.0). At the entrance of reformer II an increase of steam to methane ratio decreases the effectiveness factors of methane while in the rest of the reformer the increase in steam to methane ratios increase the effectiveness factor of methane as shown in Figure 6.33a. The increase of the steam to methane ratios have a slight effect on the effectiveness factors of carbon dioxide (Figure 6.33b), but near the exit of the reformer, the profiles fluctuate between positive and negative values. The differences between the effectiveness factors of methane obtained by the dusty gas model and simplified models I and II are large, while for the effectiveness factors of carbon dioxide the simplified models deviate from the dusty gas model in the second half of the catalyst tube. 

FIGURE S.6components effectiveness factors for the steam reforming of methane. A case of relatively high steam to methane latio (S/M = 5). 

The effectiveness factor is a global multiplier of the intrinsic reaction rate that accounts for the severe diffusion limitations encountered in industrial reformers. Effectiveness factors of industrial Ni-based catalysts for the methane-steam and shift reactions are of the order of 0.02 this means that the actual reaction rate experienced by the bulk fluid in the reformer is typically only about few percents of the reaction rate measured in the laboratory under the same conditions but writh very small catalyst particle sizes. 

A low effectiveness factor — see Figure 3.23 — implies that the effectiveness factor and thus the effective rate for the steam reforming of methane is inversely proportional to the Thiele modulus [199] and hence the equivalent particle diameter assuming that the particle is isotherm. For a first-order equilibrium rate expression, a general effectiveness factor can be evaluated as shown in [199] [389]. For a large equilibrium constant, this equation can be simplified to ... 

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