Component balances catalyst pellet

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

The tubes are loaded with industrial catalyst pellets which usually are nickel catalysts. In the mass-balance equations, methane and carbon dioxide are the key components and their conversion and yield are defined respectively as... 

Equation (7.172) is the generalized equation for the flux of component i diffusing through the catalyst pellet, subject to the boundary condition Ni(0) = 0 at the center z = 0. The mass-balance equations and the dusty gas model equations provide necessary equations for predicting the diffusion through the catalyst pellet. The dusty gas model equations are... 

Further, make the same assumptions as in Appendix D of no viscous flow, no surface diffusion, an isothermal catalyst pellet and no external forces. According to the dusty gas model a force balance for component A then yields ... 

The catalyst is made by impregnating the beads with aqueous solutions of salts of some rare earth metals and of salts of the desired precious metals such as Pt, Pd and Rh these impregnated beads are then dried and calcined. The distribution of precious metals over the bead radius must be achieved with care, to balance the mass transfer requirements with the poison resistance requirements (Figs. 24-26). The distribution of the active component over the pellet radius can be measured by an Energy Dispersive X-ray (EDX) scan on an individual pellet. However, since in the application a relatively broad distribution in diameters occurs, special procedures have been developed to determine some kind of average distribution of the active components over the pellet radius. The most common procedure is the attrition test, in which a known mass of pellets of known diameter distribution is immersed in a liquid that neither dissolves the active components nor the carrier. The pellets are stirred for a defined time, and are separated from the attrited powder. The powder mass is determined, and its chemical composition analyzed by sensitive methods. 

The governing mass and heat balance equations were derived in section 5.1.9 which simulate the concentration and temperature gradient between the bulk fluid and the external surface of the catalyst pellet. The effectiveness factors which represent the ratios of the observed actual rates of reactions to the intrinsic reactions rates where there is no mass and heat transfer resistances are computed for different reactions and different components. 

A differential mass balance on the consumed /-th component in a catalyst pellet of slab geometry (Figure 5.59) gives the following equations ... 

Mass balance on component P adsorbed on the internal surface of a differential element of the catalyst pellet at radius z and thickness dz gives,... 

Rate equations will be discussed in Section 3.5, but in the mass balance equation (3.5), the reaction rate refers to the production of component A and one equation must formally be solved for each component. A typical feed may, however, contain more than 25 components and since the conversions of some of them are bounded by stoichiometry, it is more convenient to transform the mass balance equations so that only one equation must be solved for each independent reaction instead of one reaction for each component. Rj is the effective rate defined as the rate in mol/s/kg cat formed of a component with stoichiometric coefficient +1 and appearing in reaction j only. The reaction rate is based on mass of catalyst, whereas Equation (3.5) is per m bed. This is the reason for including the bulk catalyst density pbuik calculated from the void fraction s and the catalyst pellet density as ... 

Using the symbols in the schematic diagram of the catalyst pellet as shown in Figure 3.1, the mass balance for component A (for a case with negligible intraparticle mass and heat transfer resistances) is given by... 

As the considered particle is spherical in shape, it is symmetrical around the center. The concentration profile inside the catalyst pellet is shown in Figure 6.21. Molar balance on component A over the element Ar (here, r is the radial position from the center of the pellet [in cm]) gives... 

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