Ash layer resistance

Combination of Resistances. The above conversion-time expressions assume that a single resistance controls throughout reaction of the particle. However, the relative importance of the gas film, ash layer, and reaction steps will vary as particle conversion progresses. For example, for a constant size particle the gas film resistance remains unchanged, the resistance to reaction increases as the surface of unreacted core decreases, while the ash layer resistance is nonexistent at the start because no ash is present, but becomes progressively more and more important as the ash layer builds up. In general, then, it may not be reasonable to consider that just one step controls throughout reaction. 

Rate of transfer of A (r by diffusion through the ash layer resistance Rj from the surface of the particle to the surface of the unreacted core... 

Note that the time for complete conversion x is proportional to R when ash layer resistance controls the overall rate. Combining Equations 4.30 and 4.29, we have... 

The mechanism of reaction-control can transform into ash layer-control, but the reverse does not occur during the conversion. This is because there is no ash layer and therefore no ash layer resistance at the begiiming of reaction. Generally, if the ash layer diffusion exists when the conversion is low, it means that the reaction... 

Diffusion through a product layer can be treated like a film resistance. The surface concentration is measured inside the ash layer at the unbumed surface of the particle. If the ash thickness is constant and as 0, then the rate has the form of Equation (11.48). The ash thickness will probably increase with time, and this will cause the rate constant applicable to a single particle to gradually decline with time. 

Figure 9.2(a) or (b) shows the essence of the SCM, as discussed in outline in Section 9.1.2.1, for a partially reacted particle. There is a sharp boundary (the reaction surface) between the nonporous unreacted core of solid B and the porous outer shell of solid product (sometimes referred to as the ash layer, even though the ash is desired product). Outside the particle, there is a gas film reflecting the resistance to mass transfer of A from the bulk gas to the exterior surface of the particle. As time increases, the reaction surface moves progressively toward the center of the particle that is, the unreacted core of B shrinks (hence the name). The SCM is an idealized model, since the boundary between reacted and unreacted zones would tend to be blurred, which could be revealed by slicing the particle and examining the cross-section. If this... 

Referring to the concentration profiles for A in Figure 9.2, we realize that if there is no resistance to the transport of A in either the gas film or the ash layer, cA remains constant from the bulk gas to the surface of the unreacted core. That is,... 

An important difference between a shrinking particle reacting to form only gaseous product(s) and a constant-size particle reacting so that a product layer surrounds a shrinking core is that, in the former case, there is no product or ash layer, and hence no ash-layer diffusion resistance for A. Thus, only two rate processes, gas-film mass transfer of A, and reaction of A and B, need to be taken into account. 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

Figure 25.6 Representation of a reacting particle when diffusion through the ash layer is the controlling resistance.

Step 3. Diffusion of reaction products from the surface of the solid through the gas film back into the main body of gas. Note that the ash layer is absent and does not contribute any resistance. 

Assuming that reaction proceeds by the shrinking-core model calculate the time needed for complete conversion of a particle and the relative resistance of ash layer diffusion during this operation. 

Note that film resistance can safely be neglected as long as a growing ash layer is present. 

It may be noted from this plot that the fractional conversion of solid Xg is the least when the gas film resistance controls the overall rate. This is because the gas film resistance limits the amount of A that would be available at the reaction site in the solid particle for conversion of B. The plots of Xg versus 0/x for the ash layer diffusion controlling mechanism and the chemical reaction rate-controlling mechanism intersect with each other at (9/x = 0.5) and Xg = (7/8). Conversion is higher when the ash layer diffusion controls the... 

Data CasFSm Resistance Ash Layer Diffusion Reaction Rate fc. 

Since the carbon particle is porous and also char particle in a stagnant environment will leave a residual ash uninterrupted, the diffusion coefficient involves the resistance to flow of oxygen and combustion products through the ash layer and through the porous carbon itself. The rate of reaction of the carbon with oxygen at the reaction front can be expressed in terms of the oxygen partial pressure at the surface and the surface reaction rate constant as... 

In general, the resistances that affect conversion are more than one, and therefore, three equations of film, ash layer and reaction should be combined, and by eliminating the intermediate concentration Cas and Cao the instantaneous reaction rate can be obtained ... 

Here, t is time considering overall resistance, and tflim>tash,treaction are the time needed when conversion reaches Xb for the gas film, ash layer and reaction controlled, respectively. When the particle is transformed completely Xb = 1), the... 

In the three mechanisms mentioned above, the resistance of diffusion of ash layer is usually greater than that of the diffusion of gas film, and thus, the diffusion... 

When the chemical reaction at the interface presents a negligible resistance to the progress of reaction compared with diffusion through the ash layer, the overall rate is controlled by the latter. In order to obtain the rate of diffusion (hence the overall rate), we make the pseudosteady state approximation [7,8] as far as diffusion is concerned the reaction interface may be considered stationary at any time due to the high density of a solid compared to that of a gas.t... 

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