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Averaging over the catalyst particle

The first reduction of the two-scale model that we consider is already included in the equations from Table 3.1 and refers to the reaction-diffusion problem inside catalytic particles. The treatment of this question based on the effectiveness factor concept (rf) is widely generalized in the literature, after the seminal works of Damkohler [77], Thiele [78], and Zeldovitch [79]. It may be defined for a reaction j with respect to the conditions prevailing at the pellet surface by Ref. [80]  [Pg.61]

Equation 3.39 expresses an averaged reaction rate evaluated with the actual concentration and temperature profiles that are observed inside the pellet, in the presence of reaction superposed with the eventual presence of significant limitations from diffusion through the catalyst pores. If transport to the catalyst surface is also limited, conditions on the interface may differ significantly from those in the bulk fluid. In this case, it maybe more useful to refer the observed average rate of reactant consumption to the conditions in the interparticular bulk fluid, defining a global effectiveness factor fj, which is related to (3.39) by [Pg.61]

The relevance of interphase gradients distinguishes between two different classes of problems, and this is reflected on the type of boundary condition at the pellet s surface. It is known that specifying the value of the concentration (or temperature) at the surfece (Dirichlet boundary condition) may not be realistic, and thus finite external transfer effects have to be considered (in a Robin-type boundary condition) [72]. Apart from these, a large number of additional effects have also been considered. Some examples include the nonuniformity of the porous pellet structure (distribution of pore sizes [102], bidisperse particles [103], etc.), nonuniformity of catalytic activity [104], deactivation by poisoning [105], presence of multiple reactions [106], and incorporation of additional transport mechanisms such as Soret diffusion [107] or intraparticular convection [108]. [Pg.62]

As an illustration of the application of approximate analytical techniques, we derive the asymptotic forms of the efiectiveness factor and average solid concentration/temperature for a non-isothermal reaction in a catalyst particle with external heat/mass gradients. Adopting the normalization in Equations 3.16-3.20 for a solid porous particle ( o = 0) with characteristic dimension in the direction of diffusion Rp, the mass and heat balances become [Pg.62]

These reference conditions may be the ones at the reactor s inlet conditions, and therefore, Cr = 0, Ac = C , and fref = AT = fin in Equation 3.16. There is symmetry at = 0 (3cy3 = 0 and 3T /3 = 0) and flux continuity at the surface expressed by [Pg.62]


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