Surface reaction, shrinking core model

Single pellet reduction. The reduction occurs at high temperatures and a shrinking core model is appropriate as confirmed experimentally(5). Removal of oxygen occurs at the advancing interface while the water gas shift reaction occurs in the outer layer of reduced iron. The mechanism of the water gas shift reaction is thought to be (10,11) between adsorbed oxygen and CO on the active surface of the product iron, i.e ... 

In the second case, as shown in Fig. 2, the entire surface of the reactant particle is covered with a thin layer of the solid product very soon after contacting the reactant gas and the reaction boundary advances inward as reaction proceeds. This model has been known as the shrinking core model [2, 3] and has been used by many investigators. Since the functional dependence of S on t behaves well in this model, provided that the assumption of smooth advancement of the reaction boundary without changing its shape is valid, consideration of a variety of forms of r can conveniently be included and the kinetics can be described up to the completion of reaction. Moreover, even in the first case, in which the... 

As with the shrinking core model, boundary layer mass and heat transfer fluxes are applicable as well as the surface reaction flux. The fluxes are combined in a way similar to that of the shrinking core model to give the results in Table 5.3 for a. shrinking sphere model. When this model is applicable, the partide morphology dianges drastically during reaction from particles to flakes of partides. 

Where conditions eliminate diffusion resistance to reaction (12.1) [25], the rate is proportional to the surface area of the undecomposed CaCOj, consistent with the interface advance or shrinking core model. Calcite breakdown with greater than 90% efficiency is achieved in 2.5 s at 1270 K and the surface area of the product CaO is a maximum (about 100 m g ) after reaction at 1270 K. 

The number of active sites per unit surface of B will presumably be constant, and the rate proportional to the total number of sites. Hence the rate should be proportional to the surface area of the unreacted core. A feature of the shrinking-core model is that this area is known and is equal to 47rr - for a spherical core. This may not be a realistic area for reaction in real situations, but it is the characteristic of the model that permits mathematical analysis of the process. 

Concentrating now on the phenomena inside a particle, an easily visualized situation is that of a gas reacting with a solid of low porosity to yield a porous reacted layer, often called ash layer. The reaction then takes place in a narrow zone that moves progressively from the outer surface to the center of the particle. Such a situation is described by the so-called heterogeneous shrinking-core model heterogeneous because there are two distinct layers inside the particle, with clearly... 

Roman et al. developed a model for the leaching of copper oxide ores using the shrinking-core model. They found that the surface reaction is fast so that only the diffusicm term need be considered. The consumption of acid. A, is related to the copper recoveiy by the expression... 

The reaction would occur only on the outer surface of the solid particle if the solid is non-porous and A carmot penetrate into the solid. A model called shrinking core model (SCM) proposed for non-porous solid particles is widely used for the design of gas-solid reactors. The SCM is discussed in detail in the following section. 

For the quantitative description of G/S reactions, chfferent models have been developed to derive equations that are not too comphcated to describe the conversion of a solid reactant. These equations are based on simphfications. An example is the shrinking core model, which assumes that the reaction starts at the outer surface and that a sharp reaction zone moves into the particle. Subsequently, several cases are discussed based on the fohowing assumptions ... 

If the transport of the gaseous reactant through the product layer of the cylindrical particle is the rate-determining step (fast chemical reaction, no mass transfer resistance by external diffusion), the concentration at the surface of the shrinking core almost reaches zero. Thus the reaction is confined to a front. In contrast to the shrinking core model with the influence of reaction (combined model. Section 4.6.3.3), the reactant concentration is zero at the reaction front, and no reaction occurs within the core. Equation (4.6.56) simplifies as we can assume a negligibly small value of the term and we obtain ... 

The type of process where a solid is converted to a product with a smaller volume (a) by the action of a gas (eq. (6.14)) lends itself best to a general analysis. There is the well known "shrinking core" model, that describes the conversion of a massive solid reactant into a porous product by the action of a gaseous reactant. (Yagi and Kunii, 1952, Levenspiel, 1980). As the reaction process, the massive unreacted core will shrink and a layer of porous reaction product ("ash") will cover the core. Reactants have to dif fuse through the porous "ash" to reach the surface of the massive core, where the reaction takes place. In principle, the rate of the process is determined by diffusion through the porous layer, that becomes thicker on conversion, and reaction at the core si ace, that becomes smaller. 

Experiments with a coarser sample of B show that time for total conversion is roughly proportional to the mean particle size. It follows from a comparison with eq. (6.20) that a shrinking core model is likely to be applicable, and that the surface reaction rate at the core is rate determining. The shell and core structure is confirmed by microscopic pictures taken of product particles that are cut with a microtome. 

It is assumed that the reaetion of PET in nitric acid is a reaction occurring just at the surfaee of the PET partieles [18], Nitric acid does not swell the particles and eaves and pores are not formed, though the attaek of deeper partiele layers is excluded. Further, the solution of PET is negligible due to the long time partieles resist in the solution. In order to deal with the deposition of TPA on the partiele surface a modified shrinking core model for PET powder was developed (Figure 3). 

B = 0.67. This reaction order corresponds to the shrink core reaction model. The reaction is under diffusion control, and the oxidizing agent reacts only on the surface because it has no time to diffuse internally, so the particle size becomes smaller as the conversion degree increases. In this case, the apparent kinetic constant will depend on the particle size and parameters derived fiem internal diffusion, in addition to the parameters mentioned before. 

Figure 15.7a shows reaction at the interface between a solid reactant (B) and a product (5) after the fluid has diffused through an inwardly advancing shell of the product (ash). There is no reaction in either the ash layer or in the body of the reactant B (the core), but only at the surface of B. This is the shrinking core or sharp interface model and represents perhaps the most common mechanism of gas-solid reactions for nonporous solids. The overall reaction can be controlled... 

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