Shrinking-core model system

The shrinking core models described by Levenspiel cater for both reaction- and diffusion-controlled systems. Referring to the literature, how do these systems differ and which of these models do skeletal catalysts fit during their preparation by leaching ... 

Despite these complications Wen (1968) and Ishida et al. (1971), on the basis of studies of numerous systems, conclude that the shrinking core model is the best simple representation for the majority of reacting gas-solid systems. 

Shrinking core model The shrinking core model has been derived for noncatalytic solid-fluid reactions (Levenspiel, 1972). However, it has been successfully used for specific ion-exchange systems—those using synthetic ion exchangers, mainly chelating resins (Cortina et al, 1998 Juang, 1999). 

All three models have been used as bases for integrating rate equations. Choice of the most appropriate one depends on the initial form of the solid reactant and the changes that occur with reaction. However, in the remainder of this chapter the shrinking-core model will be used. It is amenable to quantitative treatment and represents many real systems rather well. 

Ruether (29) examined the case of oxydesulfurization for completely backmixed stirred tanks in series assuming the diffusion-controlled mechanism. The reaction in the particles was described by the shrinking core model. The results obtained on the conversion as a function of residence time were shown for various number of reactors in series. The procedure to calculate the conversion for a system having a distributed particle size... 

With these we enlist the two fundamental approaches to the noncatalytic gas-solid reaction systems The shrinking core model and volume reaction model. In the volnme reaction model, the solid is porous, the fluid easily diffuses in or ont of the solid, such that the reaction can take place homogeneously everywhere in the solid. On the other hand, with the shrinking core model (SCM), also called the sharp interface model (SIM), there is a sharp interface between the unreacted core and reacted shell of the particles. 

The reader had previously been introduced to the concepts that must be applied in modeling the progress of a gas-solid reaction. They involve separating the system into a core, which reacts and continuously shrinks in size, and an external layer, which grows with time but is assumed to be at a quasisteady state. This configuration is referred to as the shrinking core model and has associated with it the assumption of a quasi- or pseudo-steady state. 

Figure 2.3 Left, reduction models. In the shrinking core or contracting sphere model the rate of reduction is initially fast and decreases progressively due to diffusion limitations. The nucleation model applies when the initial reaction of the oxide with molecular hydrogen is difficult. Once metal nuclei are available for the dissociation of hydrogen, reduction proceeds at a higher rate until the system comes into the shrinking core regime. Right the reduction rate depends on the concentration of unreduced sample (1-a) as f(a) see Expressions (2-5) and (2-6).

We can model the FCC catalyst system as a combination of a shrinking core of sites not yet deactivated by coke and a progressing shell of large hydrocarbon molecules and metal contaminants, penetrating into the catalyst particle.The relative velocities of these fronts will be of great importance and will be strongly determined by the accessibility of the various functional sites of the catalyst [40]. 

The reaction system studied includes reactions R1 and R2 only. Gaseous reduction of a single iron ore particle proceeds following the shrink unreacted core model. Gas film resistance on mass transfer around the particle could be ignored since ore fines are under bubbling state. The shrink unreacted core model is used for expressing the reaction rates of R1 and R2 and they are expressed as Eqs.( 3-4). 

The most common models are derived isothermally and are associated with the shrinking core of a globular particle, which maintains a sharp reaction boundary [3,413,414]. Using a simple geometrical representation, the reacting system can be classified as a set of spheres where each reaction interface is... 

Since many solid reactants have some initial porosity and the simple shrinking unreacted-core model is often inapplicable to such systems, there have been recent efforts to find valid models for these reaction systems. A review of these will be presented. 

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