Diffusion combined with external mass transfer

External Mass Transfer and Intraparticle Diffusion Control With a linear isotherm, the solution for combined external mass transfer and pore diffusion control with an infinite fluid volume is (Crank, Mathematics of Diffusion, 2d ed., Clarendon Press, 1975) ... 

Table 6.8 presents the details of calculations for spherical particles with an equivalent diameter of 2.4mm. It may be observed that the pore diffusion considerably affects the process rate, particularly at higher temperatures. The external mass transfer plays a minor role. Their combination leads to a global effectiveness that drops from 75% to 35% when the temperature varies from 160 to 220°C. Based on the above elements the apparent reaction constant may be expressed by the following Arrhenius law ... 

The curves calculated in this way at constant for different combinations of Pe and S [i.e., for different combinations of axial dispersion and mass transfer resistance but the same linear combination 1/Pe + 5(1 + 5/0/15] show close agreement with each other and with the curve calculated from the simple linearized rate model using an overall lumped coefficient to account for the combined effects of axial dispersion, diffusion, and external mass transfer resistance. 

The study of the intra-phase mass transfer in SCR reactors has been addressed by combining the equations for the external field with the differential equations for diffusion and reaction of NO and N H 3 in the intra-porous region and by adopting the Wakao-Smith random pore model to describe the diffusion of NO and NH3 inside the pores [30, 44]. The solution of the model equations confirmed that steep reactant concentration gradients are present near the external catalyst surface under typical industrial conditions so that the internal catalyst effectiveness factor is low [27]. 

Once adequate airflow rate, temperature, and moisture are defined to intensify the external exchange processes, drying operation usually becomes completely dependent on internal mass transfer rate. To calculate the effective diffusivity, Aff. one has to combine experimental results with Fick-type model. However, diffusion phenomenon has to be studied out the starting drying time (1 0). Hence, a starting accessibility is defined as the difference between the initial moistme content Wj and the value Wq calculated by extrapolating the diffusion model till f = 0. 

Inter- and Intraphase Mass Transfer Limitations in the DeNOx Reaction. It is well established that in both laboratory and power plant conditions, extruded monolithic SCR catalysts work under combined intraparticle and external diffusion control because of the high reaction rate and of the laminar flow regime prevailing in the channels of the monolith catalysts. As an example. Figure 12 points out that, for the same reaction conditions, different extents of NO reduction are observed over SCR honeycomb catalysts with identical composition but different channel openings. 

If the transport of the gaseous reactant through the product layer of the cylindrical particle is the rate-determining step (fast chemical reaction, no mass transfer resistance by external diffusion), the concentration at the surface of the shrinking core almost reaches zero. Thus the reaction is confined to a front. In contrast to the shrinking core model with the influence of reaction (combined model. Section 4.6.3.3), the reactant concentration is zero at the reaction front, and no reaction occurs within the core. Equation (4.6.56) simplifies as we can assume a negligibly small value of the term and we obtain ... 

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