External-diffusion regime regimes

Variation of catalyst area. The catalytic rate is proportional to the total surface area, A, external and internal, for reactions controlled by surface kinetics. In the case of internal or pore diffusion control, the rate is proportional to A1,2 and is also a function of the catalyst shape and size [49, 53]. Under an external diffusion regime, the catalytic rate is proportional to the external surface area of the catalyst, Aex. 

A more complete discussion of the heat regime in the external diffusion region which takes into account the fact that a and D values are not exactly equal can be found in the literature (9). Our presentation aimed to graphically demonstrate the main features of the phenomenon. 

Both in laboratory and power plant conditions the SCR reactor works under combined intraparticlc and external diffusion control, due to the high reaction rate and the laminar flow regime in the monolith channels. 

Pore diffusion regime - Diffusion in the pores is the slowest step in this type of catalysis. Reaction takes place mainly on the external surface of the catalysts,... 

Non-catalytic reactions involving two phases are common in the mineral industry. Reactions such as the roasting of ores or the oxidation of solids are carried out on a massive scale but the rates of these processes are often controlled by physical, not chemical, effects. Reactant or product diffusion is the main rate controlling factor in many cases. As a result, mechanisms of reaction become models of reaction with consideration of factors such as external diffusion film control or the shrinking core yielding the various models. Matters are further complicated by considerations regarding particle shape and external fluid flow regimes. 

Table 16-2 illustrates the functional dependence of ]criticai on the intrapellet Damkohler number, A. Notice that the numerical results for ]criticai = /(A) are identical for spheres and cylinders when A > 15. For all catalyst shapes, licriticai 1 in the diffusion-limited regime when A oo, and the mass transfer boundary layer thickness measured inward from the external surface of the catalyst becomes infinitesimally small. If equation (16-25), which defines / critical, is solved for A instead of ]criticab then ... 

Hence, it is not possible to redefine the characteristic length such that the critical value of the intrapellet Damkohler number is the same for all catalyst geometries when the kinetics can be described by a zeroth-order rate law. However, if the characteristic length scale is chosen to be V cataiyst/ extemai, then the effectiveness factor is approximately A for any catalyst shape and rate law in the diffusion-limited regime (A oo). This claim is based on the fact that reactants don t penetrate very deeply into the catalytic pores at large intrapellet Damkohler numbers and the mass transfer/chemical reaction problem is well described by a boundary layer solution in a very thin region near the external surface. Curvature is not important when reactants exist only in a thin shell near T] = I, and consequently, a locally flat description of the problem is appropriate for any geometry. These comments apply equally well to other types of kinetic rate laws. 

Estimate the maximum temperature at the center of a catalytic pellet at large intrapellet Damkohler numbers in the diffusion-limited regime when the thermal energy generation parameter P = 2 (i.e., exothermic chemical reaction), the temperature on the external surface of the pellet is surface = 300 K, and the average pore size is greater than 1 tim. 

Chapter 7 Catalysis by Solids, 2 The Catalyst and Its Microenvironment, 171 Modeling of Solid Catalyzed Reactions, 171 Role of Diffusion in Pellets Catalyst Effectiveness, 183 Effect of External Mass and Heat Transfer, 201 Combined Effects of Internal and External Diffusion, 204 Relative Roles of Mass and Heat Transfer in Internal and External Diffusion, 205 Regimes of Control, 206... 

Besides the apparent activation energy, the effective reaction order changes during the transition from the kinetic to the diffusion controlled regime. A first order reaction will be observed under external mass transfer control. The effective reaction order observed approaches w pp = n + l)/2 for severe influence of intraparticle diffusion. 

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. 

Simple experiments performed both in a continuous-fed tubular reactor or a batch reactor can discriminate between external or internal regimes. For external diffusion, runs are made in a tubular reactor in order to evaluate the conversion (X) of the reagent at different ratios between the weight of the catalyst (W, kg) and the amount of feed (F, kg/h or L/h). If two runs at the same temperature give the same value of X at the same value of W/F, but with two different amounts of catalyst (i.e., Wi and W2), then external diffusion is absent. In fact, to have the same value of W/F with two different weights W, it is necessary to change F and... 

The parameter t represents the reaction rate of a catalytic particle divided by the reaction rate if all of the particle surfaces (external and internal) are contacted with the reagent at the same concentration as in the surface. If t] = 1, the entire surface is accessible, i.e., there is no internal diffusion regime control. Figure 8 shows the dependence of t on three different reaction orders. Some plots are calculated for particles with a shape different from a sphere. Tb... 

Figure 4.5.25 Arrhenius plot of effective rate constant for the three regimes of control by reaction, interplay of reaction and pore diffusion, and control by external diffusion.

In the kinetic control regime (where the overall effectiveness factor t = 1), the rate is directly proportional to the concentration of active sites, L, which is incorporated into the rate constant. In the regime of internal (pore) diffusion control, the rate becomes proportional to and when external diffusion controls the rate there is no influence of L, i.e., there is a zero-order dependence on L. This can be seen by examining equations 4.47 and 4.68. This observation led to the proposal by Koros and Nowak to test for mass transfer limitations by varying L [62]. This concept was subsequently developed further by Madon and Boudart to provide a test that could verify the absence of any heat and mass transfer effects as well as the absence of other complications such as poisoning, channeling and bypassing [63]. 

Diffusion-limited regime When the diffusion of the macromolecule due to thermal motion dominates over the drift arising from any externally imposed flow fields and the barrier contributions, the steady-state flux is given by the law,... 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

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