Rates per unit mass of catalyst

The effectiveness factor for a single pore is identical with that for the particle as a whole. Thus the reaction rate per unit mass of catalyst can be written as... 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

The units on the rate constants reported by DeMaria et al. indicate that they are based on pseudo homogeneous rate expressions (i.e., the product of a catalyst bulk density and a reaction rate per unit mass of catalyst). It may be assumed that these relations pertain to the intrinsic reaction kinetics in the absence of any heat or mass transfer limitations. 

Now let Ry k be the rate (per unit mass of catalyst) of the k-th reaction. A mass balance on the i-th component then provides ... 

The selective oxidation reaction is carried out in excess air so that it can be considered pseudo-first-order with respect to naphthalene. Analysis of available data indicates that the reaction rate per unit mass of catalyst is represented by ... 

In Eq. (7-1) is the usual mass-transfer coefficient based on a unit of transfer surface, i.e., a unit of external area of the catalyst particle. In order to express the rate per unit mass of catalyst, we multiply k by the external area per unit mass, a. In Eq. (7-2) k is the reaction-rate constant per unit surface. Since a positive concentration difference between bulk gas and solid surface is necessary to transport A to the catalyst, the surface concentration Cj will be less than the bulk-gas concentration Q. Hence Eq. (7-2) shows that the rate is less than it would be for = Q. Here the effect of the mass-transfer resistance is to reduce the rate. Figure 7-1 shows schematically how the concentration varies between bulk gas and catalyst surface. 

Instead of rate per unit mass of catalyst, Eqs. (7-1) and (7-2) could be expressed as rates per unit external surface, in which case a would not be needed in Eq. (7-1). Alternately, a rate per particle could be used. We shall generally use the rate per unit mass. 

The equation for the local rate (per unit mass of catalyst) as developed in Chap. 9 may be expressed functionally as r = /(C,T), where C represents, symbolically, the concentrations of all the involved components. Then Eq. (11-41) gives for... 

Xp = global rate per unit mass of catalyst pp = density of catalyst in the bed u = superficial velocity in the axial direction... 

A recycle reactor containing 101 g of catalyst is used in an experimental study. The catalyst is packed into a segment of the reactor having a volume of 125 cm. The recycle lines and pump have an additional volume of 150 cm. The particle density of the catalyst is 1.12 g cm , its internal void fraction is 0.505, and its surface area is 400 m g . A gas mixture is fed to the system at 150 cm s . The inlet concentration of reactant A is 1.6 mol m . The outlet concentration of reactant A is 0.4 mol m . Determine the intrinsic pseudohomogeneous reaction rate, the rate per unit mass of catalyst, and the rate per unit surface area of catalyst. The reaction isA- - Psov.4 = —1. 

Ways in which rates of reaction may be expressed have been considered in Section 5.2.3. In the present context they are usually given in specific or areal terms, or as turnover frequencies, i.e. rate per (presumed) active centre. Where standard catalysts such as EUROPT-1 have been used, the rate per unit mass of catalyst or metal is sufficient, because this can readily be translated into areal units if comparison with other catalysts is desired. 

Figure P6.8-2 is a plot of the reaction rate per unit mass of catalyst versus the product The data correspond to reaction at 130°C at a catalyst loading of 0.5 g. The data in the figure represent two types of experiments the diamonds correspond to data at a fixed acid concentration (0.4 M) and variable hydrogen pressure.

The above discussion indicates an approach that may be used in deriving an expression for the reaction rate in terms of the physical and chemical parameters of the system. However, for most practical catalyst systems, it will not be possible to arrive at closed-form expressions for the reaction rate per unit mass of catalyst. Consequently, this approach is of extremely limited utility for reactor design purposes. The most common approach to the analysis of external mass transfer limitations in heterogeneous catalytic reactors is usually couched in terms of calculations of the difference in reactant concentrations between the bulk fluid and the exterior surface. Illustration 12.5 indicates the manner in which one can calculate such differences. 

Particle size effects. So far, we have shown the effect of the precursor used and the pretreatment (oxidation vs. reduction) in determining the resulting activity. Another important variable, controlled by the preparation and pretreatment, is the crystallite size. Changing the crystallite size was done by selection of the precursor and the pretreatment during its decomposition, as shown for the samples listed in Table 17.3. The activity of the reduced catalysts, with dispersions ranging from 0.29 to 0.76 (samples 6-9), was measured in the 10-port reactor. The catalysts were pretreated prior to reaction in two ways (a) oxidized at 200°C in air for 3 h, or (b) reduced in a 50% Hj-He mixture for 3 h at 200°C. After pretreatment, the CO conversion was determined from ambient to 200°C using a slow linear ramp of 0.5°C/min. Table 17.3 shows the rate per unit mass of catalysts at 100 and 130°C. Figure 17.11 (A-B) shows the TOE, or rate per surface Pt atom, at each temperature. 

Equation. (9-43) shows that the rate per unit mass of catalyst will depend on k, if the second term in the denominator of Eqn. (9-43) is significant compared to 1. In this case, —r will depend on the velocity of the fluid relative to the catalyst particle, since kc depends on this velocity. 

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