Unreacted core model

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

For the noncatalytic reaction of particles with surrounding fluid, we consider two simple idealized models, the progressive-conversion model and the shrinking unreacted-core model. 

Most of the gas-solid reactions that have been studied appear to proceed by the shrinking core reaction mode. In the simplest type of unreacted core model it is assumed that there is a non-porous unreacted solid with the reaction taking place in an infinitely thin zone separating the core from a completely reacted product as shown in Fig. 3.36 for a spherical particle. Considering a reaction between a gaseous reactant A and a solid B and assuming that a coherent porous solid product is formed, five consecutive steps may be distinguished in the overall process ... 

Fig. 3.36. Unreacted core model, impermeable solid, showing gas phase reactant...

Unreacted Core Model—Fast Chemical Reaction... 

It is shown that the mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure of the solid during the reaction. By the investigation of the pore structures of the limestone particles at different extents of calcination, it has been shown that the mechanism of this particular system can be successfully represented by a two stage zone reaction model below 1000 °C. It has also been observed that the mechanism changes from zone reaction to unreacted core model at higher temperatures. 

The mechanism of many of the noncatalytic fluid-solid reactions can be described by a model in between unreacted core and homogeneous reactions models. Ishida and Wen (9) formulated such a model using the zone reaction concept of Ausman and Watson (10). In this model the reaction is not restricted to the surface of the core as in the unreacted core model but occurs homogeneously within a retreating core of reactant. Wen and Ishida (11) combined the grain concept with the zone reaction model and analyzed the reaction of SO2 with CaO particles. In the study conducted by Mantri, Gokarn and Doraiswamy (12) the concept of finite reaction zone model was further developed. 

In Equation 8 the first two terms (x = 1 - E ) give the conversion for the unreacted core model. The remaining terms in this equation give the conversion in the inner core for the two stage model. The data at 1000 °C and 1040 °C showed that fractional conversions of the samples are approximately the same as the values predicted by the first two terms of Equation 8. This shows that at high temperatures unreacted core model becomes the controlling mechanism due to the increased concentration of CO2 in the pores and diffusion limitations. Experiments carried out at different temperatures also showed that the ratio of macropore... 

Particle diameter as a function of the conversion measured particle radius a homogeneous reaction model b shrinking unreacted core model c local volumetric rate model... 

A classic example of the use of the unreacted core model is that of Weisz and Goodwin who studied the regeneration of fluidized-bed cracking catalyst. Although the cracking catalyst was porous, at a reaction temperature of 700° C the global rate was... 

The unreacted core model, suitably modified for cylindrical geometry, was used to describe the behavior... 

A simple case of a batch reactor will be explained briefly. If the powder is mixed well in a container or pasted on a wall (case a), the reaction proceeds continuously throughout the solid particle. If most of the primary particles have similar diameter, the reaction proceeds at the same rate for all the particles. Under such conditions, the reaction rate analysis is rather simple, and two idealized models have been presented continuous reaction model and unreacted core model. For the former case. 

The two sequential processes that lead to the chemical degradation of a polymer due to oxidation are (1) oxygen diffusion and (2) chemical reaction [15], Researchers [16] have used the so-called unreacted core model to characterize and predict thermo-oxidative degradation in a composite laminate. According to this model, the composite weight loss due to oxidation, q can be expressed as a power law function of time ... 

Shrinking Unreacted Core Model (Rate Determined by Diffusion Through Product Layer)... 

These models are classified into two groups. The models listed in the first group do not consider pore diffusion resistence. First group models are extensions of the unreact core model and they are limited to small particle sizes in the order of magnitude of a few microns. Pore diffusion resistence becomes important especially at high temperatures and at the initial stages... 

The controlling differential equation for the unreacted core model with diffusion of SO2 through the product layer can be expressed as ... 

For the chemical reaction and product layer diffusion controlling regimes conversion-time relations for the unreacted core model simplifies Kinetics controlling ... 

Borgwardt and Bruce (1986) used the unreacted core model with product layer diftusion control and showed good aggrement with the experimental data obtained with 1 /im particles. Combining Eq.2.11 with Eq.2.10, and expressing the diffusion coefficient (DJ in the product layer in Arrhenius form (see Section 2.3) and writing the grain radius in terms of surface area as... 

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). 

Therefore, one should use the shrinking unreacted-core model with the utmost care, especially in extrapolating results beyond the range of parameters employed in obtaining experimental data. 

In Chapter 3 we discussed gas-solid reactions involving nonporous solids and showed how different reaction steps that are coupled in series interact with each other. In many gas-solid reactions the solid is porous, allowing diffusion and chemical reaction to occur simultaneously throughout the solid therefore, the reaction occurs in a diffuse zone rather than at a sharp boundary. The reaction of a porous solid with a gas has not been investigated as extensively as that of a nonporous solid due to the difficulties in analyzing the experimental data. Furthermore, even the analysis of the results of experiments on a porous solid has often been based on the shrinking unreacted-core model. 

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. 

Most of the studies on the nonisothermal effects in gas-solid reactions have been based on the shrinking unreacted-core model. Ishida et al. [64]... 

---