Simultaneous diffusion and reaction

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

The previous discussion focused on simultaneous diffusion and reaction in isothermal catalyst pellets. Since A//, is significant for many industrially relevant reactions, it is necessary to address how heat transfer might affect solid-catalyzed... 

The route from reactant to product molecule in a monolith reactor comprises reactant transport from the bulk gas flow in a channel toward the channel wall, simultaneous diffusion and reaction inside the porous washcoat on the channel wall, and product transport from the wall back to the bulk flow of the gas phase. 

A circumstance in which this formulation has a very definite advantage is the simultaneous diffusion and reaction that takes place within a catalyst pellet. However, we shall not have occasion to advert to this. 

Metal deposition occurs with sharp gradients within a catalyst pellet, usually concentrated on the outside of catalyst pellets forming a U-shaped distribution. Sato et at [3] related this metal deposition with simultaneous diffusion and reaction, and suggested a value of 8 for the Thiele modulus in a slab geometry, Tamm [4] suggested that this distribution can be characterized by a theta factor defined in a ( Undricat geometry as... 

We now discuss some of the main features of LLPTC models developed for reaction under neutral conditions. Evans and Palmer (1981) were among the first to consider the effect of diffusion and mass transfer inPTC. They considered PTC in liquid-liquid systems by considering two well-mixed bulk phases of uniform composition separated by a uniform stagnant mass-transfer layer at the interface, and set up equations for bulk phase species balance and mass conservation equations for simultaneous diffusion and reaction in the film. Dynamics of the interaction between reaction and diffusion were studied under these assumptions for two special cases (a) reaction which is pseudo-first-order in the quaternary ion-pair (b) mass-transfer controlled instantaneous reaction. 

The heparin degradation rate at any radial position inside the catalyst particle is proportional to the bound heparinase concentration at that position. If the immobilized enzyme concentration is not uniform, the conventional analysis of simultaneous diffusion and reaction within a porous catalytic particle must be modified. The reaction rate within the catalyst particle will have an explicit radial dependence introduced via the enzyme concentration, as well as a dependence on the substrate concentration. 

The validity of both the immobilized Km and the model of simultaneous diffusion and reaction was examined by comparing the experimental data with predictions. At each substrate concentration, an effectiveness factor, 7], using the experimentally observed reaction rate and the Km was calculated from... 

When the reaction rate depends on the concentrations of several species, or when more than one reaction is involved, analytical solutions of the pore diffusion equations are impossible or too complicated to be useful. The equations for simultaneous diffusion and reaction of several species can be solved numerically if concentrations at the center are specified, but then many cases must be solved to match given external concentrations. For such cases, a simplified method can be used instead to show the approximate effect of gradients for each species. 

Diffusion of reactants to the external surface is the first step in a solid-catalyzed reaction, and this is followed by simultaneous diffusion and reaction in the pores, as discussed in Chapter 4. In developing the solutions for pore diffusion plus reaction, the surface concentrations of reactants and products are assumed to be known, and in many cases these concentrations are essentially the same as in the bulk fluid. However, for fast reactions, the concentration driving force for external mass transfer may become an appreciable fraction of the bulk concentration, and both external and internal diffusion must be allowed for. There may also be temperature differences to consider these will be discussed later. Typical concentration profiles near and in a catalyst particle are depicted in Figure 5.6. As a simplification, a linear concentration gradient is shown in the boundary layer, though the actual concentration profile is generally curved. 

When the reaction is fast enough so that diffusion of B toward the reaction zone is important, the penetration theory does not give the same results as the stagnant-film model. Numerical solutions of the equations for simultaneous diffusion and reaction of A and B based on the penetration theory have been reported [5] the enhancement factors are shown in Figure... 

The use of the volumetric coefficient k a for predicting reactor performance is appropriate if the reaction takes place almost entirely in the bulk liquid, and the equations for consecutive mass transfer and reaction apply [Eqs. (7.10) and (7.12)]. For simultaneous diffusion and reaction in the liquid film, the coefficient per unit area, ki, must be known to predict the enhancement factor. Unfortunately, the data for k show much more scatter than the data for kj a because of the difficulty in measuring a or calculating a from bubble size measurements. Also, has been shown to vary appreci-... 

The example above suggests that the simple mapping of experimental and real times can be obtained only in the simplest case of a uniform in space reaction. A concerted action of species diffusion and reaction makes the mapping problem much more difficult. The situation of simultaneous diffusion and reaction, however, is typical of ageing processes. One thing is obvious accelerated ageing experiments should always be preceded by a theoretical analysis. 

Figure 9 Spherical model for simultaneous diffusion and reaction R spherical catalyst pellet of radius, dr spherical shell of thickness, r. spherical shell of radius) (Charles and Thomas, 1963).

Simultaneous diffusion and reaction in two-phase systems 5.4.1. The general problem... 

We consider simultaneous diffusion and reaction of reactants A and in the reaction phase, which in a first simplification is thought to have unlimited dimensions. We choose a coordinate x perpendicular to the interface at the interface jc = 0. The concentration of A at the interface, and the concentration of B well away from the interface, are both given. In the simplest situation these concentrations are both constant in time, which means either diat both phases are practically unlimited, or that the reactants are continually supplied in a manner that does not interfere with the process of diffusion and reaction under consideration. We shall see later that in many situations these assumptions are in fact correct with good approximation. Consider the following reaction scheme ... 

Solution You should use diffusion coefficients to describe the simultaneous diffusion and reaction in the pores in the catalyst. You should not use mass transfer coefficients because you cannot easily include the effect of reaction (see Sections 16.1 and 17.1). 

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