10.2.2 Step 2 Overview: Internal Diffusion
Now consider that we are operating at a fluid velocity where external diffusion is no longer the rate-limiting step and that internal diffusion is the slowest step. In Step 2 the reactant A diffuses from the external pellet surface at a concentration CAs into the pellet interior, where the concentration is CA. As A diffuses into the interior of the pellet, it reacts with catalyst deposited on the sides of the pore walls.
For large pellets, it takes a long time for the reactant A to diffuse into the interior, compared to the time that it takes for the reaction to occur on the interior pore surface. Under these circumstances, the reactant is only consumed near the exterior surface of the pellet and the catalyst near the center of the pellet is wasted catalyst. On the other hand, for very small pellets it takes very little time to diffuse into and out of the pellet interior and, as a result, internal diffusion no longer limits the rate of reaction. The rate of reaction can be expressed as
Rate = kr CAs
where CAs is the concentration at the external pellet surface and kr is an overall rate constant, which is a function of particle size. The overall rate constant, kr, increases as the pellet diameter decreases. In DVD-ROM Chapter 12, we show that DVD-ROM Figure 12-5 can be combined with DVD-ROM Equation (12-34) to arrive at the plot of kr as a function of DP, shown in Figure 10-9(b).
Figure 10-9. Effect of particle size on the overall reaction rate constant. (a) Branching of a single pore with deposited metal; (b) Decrease in rate constant with increasing particle diameter. (See DVD-ROM Chapter 12.)
We see in Figure 10-9 that at small particle sizes internal diffusion is no longer the slow step and that the surface reaction sequence of adsorption, surface reaction, and desorption (Steps 3, 4, and 5 in Figure 10-5) limit the overall rate of reaction. Consider now one more point about internal diffusion and surface reaction. These steps (2 through 6) are not at all affected by flow conditions external to the pellet.
In the material that follows, we are going to choose our pellet size and external fluid velocity such that neither external diffusion nor internal diffusion is limiting. Instead, we assume that either Step 3 (adsorption), Step 4 (surface reaction), or Step 5 (desorption), or a combination of these steps, limits the overall rate of reaction.