Concentration profile spherical pellet

Use of the boundary condition at the external surface of the spherical pellet (r = R) leads to the following expression for the concentration profile in the spherical pellet. 

Figure 12.5 contains a series of curves representing the concentration profile in the spherical pellet for different values of the Thiele modulus s. For small values of 0S, (say less than 0.5) the concentration profile is relatively flat and the reactant concentration is reasonably uniform. For large values of (say greater than 5), the reaction is rapid relative to diffusion and the reactant concentration at the center of the catalyst pellet is less than 7% of that at the external surface. Notice that in all cases the concentration gradient approaches zero at the center of the pellet. 

The considered particle is spherical in shape and it is symmetrical around its center. The concentration profile inside the catalyst pellet is shown in Figure 5.18, as well as the molar balance over an element Ar. 

Figure 4. Temperature and concentration profiles for a partial oxidation reaction in a spherical catalyst pellet.

Figure 6.3.7 illustrates the effect of the Thiele modulus on the concentration profile within a spherical catalyst pellet. 

The concentration profile for a first-order reaction occurring in a spherical catalyst pellet is... 

We want to evaluate r in terms of Dg and k. The first step is to determine the concentration profile of A in the pellet. This is shown schematically in Fig. 11-6 for a spherical pellet (also shown is the profile from to CJ. The differential equation expressing vs r is obtained by writing a mass For example, for the reaction A + C, Eq. (9-32) indicates that f(C,T) would be... 

Fig. 14-3 Concentration profile in a spherical pellet shrinking-core model)...

The theory of nonisothermal effectiveness is sufficiently well advanced to allow estimates for rj. The analysis requires simultaneous solutions for the concentration and temperature profiles within a pellet. The solutions are necessarily numerical. Solutions are feasible for actual pellet shapes (such as cylinders) but are significantly easier for spherical pellets since this allows a one-dimensional form for the energy equation ... 

Consider the case of a nonisothermal reaction A B occurring in the interior of a spherical catalyst pellet of radius R (Figure 6.4). We wish to compute the effect of internal heat and mass transfer resistance upon the reaction rate and the concentration and temperature profiles within the pellet. If Z)a is the effective binary diffusivity of A within the pellet, and we have first-order kinetics, the concentration profile CA(f) is governed by the mole balance... 

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