Effects of pore diffusion

In the preceding example we assumed that reaction occurred on the external surface so we did not have to be concerned with diffusion within the catalyst pellet. Now we consider the effect of pore diffusion on the overall rate. We have to do considerable mathematical manipulation to find the proper expressions to handle this, and before we begin, it is worthwhile to consider where we are going. As before, we want the rate as a function of bulk concentration Ca >i and we need to know the rate coefficient for various approximations (Figure 7-1 1). 

An effect of pore diffusion in residuum demetallation is illustrated in Figure 9, which shows nickel and vanadium concentration profiles measured through a catalyst pill after residuum desulfurizing service. The catalyst originally contained neither of these metals. These profiles confirm that the rate of reaction of the metal-containing molecules in the feed (particularly the vanadium compounds) is high compared with their rate of diffusion. 

Although the effect of pore diffusion on catalyst activity is usually undesirable, its effect on selectivity can sometimes be used to advantage, as reported by Weisz and others at the Mobil Research Laboratories (27). 

The effect of pore diffusion is described through the term, 5, which represents a ratio of the kinetic rate to the diffusion rate in the electrode. In general increasing the value of, v, i.e., decreasing the diffusion rate relative to the kinetic rate, has the effect of causing a significant reduction in the local current densities and that more of the electrochemical activity of the electrode is focused closer to the membrane. This is a consequence of the reduced concentration of reactant away from the membrane due to, for example, a slower diffusion rate (lower diffusion coefficient). 

Next, consider the effect of pore diffusion on the reaction rate. The gasification reaction occurs principally within the particle. Except at very high temperatures, reactants must diffuse into the pore to the reacting surface. The average reaction rate within the particle may be related to the rate based on the surface concentration in terms of an effectiveness factor rj defined as... 

It is obvious from this discussion that control of pore size and distribution is important in developing the optimum catalyst for a specific process. The most common perception of the pores in a catalyst particle is that they are essentially holes of various diameters drilled into the particle at various angles or, perhaps, they resemble various sized tunnels randomly oriented throughout the particle. While such representations may be helplul in discussing the effects of pore diffusion and similar catalytic factors, it does not provide any basis for the development of methods that can produce supports or supported catalysts having specifrc pore characteristics. 

Effect of Pore Diffusion on Deactivation in Resid Hydrodesuifurization Y,-W, Chen. M,-C. Tsai and Y.-C, Kuo... 

EFFECT OF PORE DIFFUSION ON DEACTIVATION IN RESID HYDRODESULFURIZATION... 

Determination of the effects of pore diffusion, where the catalyst is being poisoned, have been discussed by Wheeler Complex kinetics involving parallel or consecutive reactions have also been studied by Wheeler a 3,184 more recently... 

The above approach was used to examine electrode kinetics at thin porous Pt electrodes (48a and to evaluate the effect of pore diffusion on selectivity (61). It permitted also analysis of gas diffusion electrodes at the limiting current, when a change of the utilized surface area occurred at tow reactant partial pressures due to the zero-order kinetics of the reactions (407). 

Effect of Pore Diffusion on Deactivalion in Resid Hydrodesulfurization... 

The concentration profile given by Eq. (4.22) and the effectiveness factor of Eq. (4.31) are applicable, but the rate constant in the Thiele modulus is k, not ki. For = I, k = 2ki and the effect of pore diffusion is significantly greater than if only the forward reaction is considered. 

With these average partial pressures, the actual reaction rate can be predicted and compared with the ideal rate based on P, P, Pq, andP, to get a new value for r]. If this differs significantly from the calculated rate can be divided by to get new estimates of 0 and and the procedure is repeated until convergence is obtained. Example (4.4) illustrates the procedure for a case where the major effect of pore diffusion comes from the buildup of product in the particle combined with strong product inhibition. 

A gas-phase hydrogenation reaction was studied using a catalyst fine enough to avoid any effect of pore diffusion. The rate equation is ... 

Nitta, Y., and Imanaka, T. (1988) Effect of pore diffusion in liquid-phase enantioselective hydrogenation with Ni-silica catalysts. Bull Chem. Soc. Jpn., 61, 295 - 297. 

Example 3.5.a-l Effect of Pore Diffusion in the Cracking of Alkanes on Zeolites... 

Table 7.5 Effect of pore diffusion on selectivities and yields in the more common classes of complex organic reactions... 

Carry out runs at different particle sizes. The rate will increase with decrease in particle size, reaching a constant value that indicates absence of pore diffusional effect. On an Arrhenius plot, the effect of pore diffusion for a given particle size will be as shown in Figure 7.13. This can be divided into two asymptotic regions, one corresponding to chemical control and the other to diffusion control. We are concerned only with the chemical control line. 

The model of Santacesaria et is an extension of the linear driving force model, with fluid side resistance, for a nonlinear multicomponent Langmuir system. It includes axial dispersion, and the combined effects of pore diffusion and external fluid film resistance are accounted for throu an overall rate coefficient. Intracrystalline diffusional resistance is neglected and equilibrium between the fluid in the macfopores and in the zeolite crystals is... 

Table 6.5 (continued) Effect of Pore Diffusion on Selectivities/Yields in the More Common Classes of Reactions... 

Mass transfer resistances lead to a lower effective rate compared to the intrinsic chemical reaction, but may also significantly change the selectivity of parallel and consecutive reactions. In the following, this is discussed for two first-order reactions occurring in series or parallel, for simplification, the influence of external mass transfer is only discussed for a non-porous catalyst (to exclude pore diffusion), and the effect of pore diffusion is examined for a negligible influence of external mass transfer. Other more complicated cases are treated elsewhere (Baerns et al, 2006 Levenspiel, 1999 froment and Bischoff, 1990). 

For a linear isotherm system, Eq.(5-59) is applicable since no distinction between the effect of pore diffusion and that of surface diffusion is possible in the case of a linear isotherm. For dimensionless time t Eq. (5-27) must be employed. 

The importance of pore diffusion can be assessed by plotting catalytic activity against catalyst particle size, at a given pressure and temperature. Catalytic activity will increase as particle size decreases, until a constant activity is reached. At this maximum activity the effects of pore diffusion are no longer significant. 

An external transport resistance will affect the apparent selectivity of a multiple-reaction system, in the same manner as an internal resistance. The effect of pore diffusion on selectivity is discussed in Section 9.3.8, and the effect of external transport can be understood qualitatively from that discussion. 

---