Ash layer control

B = 0.80, t, which is a measure of the size of reactor, is about 1.7 min for ash-layer control, 9.5 min for reaction control, and 14.5 min for gas-film control. The relatively favorable behavior for ash-layer diffusion control in this example reflects primarily the low value of (1.67 min versus 6.67 min for the other two cases) imposed. 

If the results cited above are put another way, from the point of view of determining fB for a given f (or reactor size), a mean residence time of 1.7 min gives fB = 0.80 for ash-layer control, as noted, but only 0.37 for reaction control, and only 0.23 for gas-film control. 

These relations show that when the particle size R increases, the reaction rate of ash layer diffusion-controlled decreases faster than that of reaction-controlled. Therefore, if reaction is the control-step for given R, it is possible to find a corresponding point of the ash layer control for particle with large size. Therefore, it is unsafe when the reaction control is extrapolated to larger particles, while it is safe for small particles. In contrast, it is safe when ash layer is extrapolated to larger particles, and it is unsafe to smaller particles. 

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... 

Equations 9.1-28 and -29 both give rise to special cases in which either one term (i.e., one rate process) dominates or two terms dominate. For example, if De is small compared with either kAg or kj, this means that ash-layer diffusion is the rate-determining or controlling step. The value of f or q is then determined entirely by the second term in each equation. Furthermore, since each term in each equation refers only to one rate process, we may write, for the overall case, the additive relation ... 

For the reaction and assumptions in Example 22-1, except that reaction-rate control replaces ash-layer-diffusion control, suppose the feed contains 25% of particles of size R for which t = 1.5 h, 35% of particles of size 2R, and 40% of particles of size 3R. What residence time of solid particles, fB, is required for /B = 0.80 ... 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

For gas-film mass transfer control, we use equation 22.2-16a for reaction control, we use equation 22.2-18 and for ash-layer diffusion control, we integrate equation 22.2-13 numerically in conjunction with 22.2-19, as described in Example 22-3(c). The results generated by the E-Z Solve software (file ex22-4.msp) are shown in Figure 22.4. 

The cases considered thus far have all been based upon the premise that one process, ash-layer diffusion, surface reaction, or gas-film mass transfer, is rate controlling. However, in some cases, more than one process affects the overall kinetics for the conversion of the solid. This has two implications ... 

Repeat problem 22-8(a), if the rate is controlled by ash-layer diffusion... 

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

Figure 25.7 illustrates concentration gradients within a particle when chemical reaction controls. Since the progress of the reaction is unaffected by the presence of any ash layer, the rate is proportional to the available surface of unreacted core. Thus, based on unit surface of unreacted core, the rate of reaction for the stoichiometry of Eqs. 1, 2, and 3 is... 

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. 

Particles of constant size Gas film diffusion controls, Eq. 11 Chemical reaction controls, Eq. 23 Ash layer diffusion controls, Eq. 18 Shrinking particles Stokes regime, Eq. 30 Large, turbulent regime, Eq. 31 Reaction controls, Eq. 23... 

The shell progressive mechanism can be applied to some ion-exchenge processes. Any of the threa subsequant steps, that is. film diffusion, ash-layer diffusion, and chemical reaction control, can be rate determining, depending on the prevailing conditions. The following relationships have been obtained for the indicated conditions. 

The second-phase reaction is heterogeneous and occurs at the surface of the particle. The reaction causes the reacting surface to shrink and to leave an ash layer as the particle moves through the reactor. Unlike the first-phase reaction, which is only slightly affected by temperature, the second-phase reaction is quite sensitive to variations in temperature for tests conducted in a semiflow system (10). Since a high gas flow rate was maintained in semiflow tests, gas diffusion probably does not affect the rate. At temperatures below 1700°F., the first-phase reaction rate is an order or two larger than the second-phase reaction rate, but as the temperature approaches 2000°F., the two rates become comparable. This is, of course, true only when the reaction is controlled by the chemical step. 

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... 

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... 

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