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FIGURE 5-8. Relationship between temperature and reaction rate. Cg, concentration of oxygen in the bulk gas; S, boundary layer thickness; n, effectiveness factor; Ea, apparent activation energy; E, true activation energy. (Source: Walker et al., 1967.)

a chemical reaction controls the rate, P is the partial pressure of oxygen at the surface (atm), E is the true activation energy (J/mol), and m is the true reaction order.

As the temperature is increased, the chemical reaction becomes sufficiently rapid for the diffusion of oxygen through the pores to exert a notable rate-limiting effect. Under these conditions (Regime II), the diameter and the density of the particle will both change. The apparent activation energy and apparent order of reaction (n) are approximated by

so that the apparent reaction rate does not change as rapidly with temperature.

A further increase in temperature eventually causes the chemical reactions to become so rapid that the oxygen is consumed as it reaches the outer surface of the particle. In this case (Regime III), the reaction is entirely controlled by the diffusion from the free stream to the particle, and only the diameter of the particle changes.

Field etal. [18] give an expression for the overall reaction rate coefficient k as:

1/kd + 1/kc where kd is the diffusional rate coefficient, and kc is the chemical rate coefficient defined in Equation (5-2); the diffusional rate coefficient can be defined as:

ir 240D

where $ is a mechanism factor that takes the value of 1 for reaction to CO2 and 2 for reaction to CO; D is the diffusion coefficient (cm2/sec) of oxygen through the boundary layer at temperature Tm given by:

where x is the particle diameter (cm); R is the universal gas constant; and Tm is the mean temperature (K) for the boundary layer taken as the average of the surface temperature of the particle and the bulk gas temperature.

For the char sizes, porosities, internal surface areas, and temperatures typical to pulverized coal-fired furnaces, the char combustion rate is influenced by the chemical reactivity of the char, the external diffusion rate of oxygen from the bulk stream, and the internal diffusion of oxygen into the porous char matrix. Char ignition is likely to occur in Regime I or II when a large proportion of the internal surface is available for reaction. The final burn out is likely to occur in Regimes II and III, when external diffusion may have a significant influence on the combustion rate of large particles. The time for the char to burn out is proportional to the square of the initial size of the char particles from the coarse end of the grind [15].

The processes controlling the rate of char combustion in fluidized-bed systems differ slightly from those for pulverized coal-fired systems. In fluidized-bed combustion, particle sizes are larger, the processes by which oxygen is brought to the coal surface differ because of the presence of the surrounding bed particles, and the heat-transfer processes also differ from those in a pulverized coal-fired furnace [15].

All three regimes illustrated in Figure 5-8 are important in fluidized-bed combustion: Regime I, during ignition and for the smaller particles burning in the bed and freeboard; Regime II, for medium-sized particles; and Regime III, for large particles in the bed. The surface reaction rate, q (mass of carbon oxidized per unit area of particle outer surface per second), for the region separating Regimes II and III, which are of special interest in coal combustion, is defined as:

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