Carbon burning rate, equation

Even when the reaction rate at the surface is effectively infinite, chemical kinetics in the gas can influence the carbon-burning rate. Equation (28) requires that residence times in the gas are short enough to prevent chemical depletion of O2 from occurring before oxygen reaches the solid surface. At sufficiently high temperatures—for example, above about 3500K—a substantial amount of dissociation of O2 may occur [39] O atoms are appreciably more reactive than O2 molecules on carbon surfaces... 

In either event, the products are ZnCl 2, CO, and A12O 3 The zinc oxide cools and whitens the smoke by consuming atomic carbon in an endothermic reaction that occurs spontaneously above 1000°C (equation 8.6). The reaction with aluminum (equation 8.4 or 8.8) is quite exothermic, and this heat evolution controls the burning rate of the smoke mixture. A minimum amount of aluminum metal will yield the best white smoke. Several "HC" smoke compositions are listed in Table 8.4. 

Accurate measurement of reaction rate of char particles is necessary to predict the rate-controlling mechanism in fluidized bed. Most researchers assume that carbon-oxygen reaction is first order with respect to oxygen, i.e., n = 1 in Equation 33. This leads to the simple mathematical expression of burning rate in fluidized beds. Recent studies indicate fractional order of reaction. This will lead to a more complicated equation of burning rate and may require numerical solution. Table 2 depicts reactivities of various fuels. 

The sulfate (Equation 6) and sulfite (Equation 5) can be reduced by numerous substances. Fluidized coke is particularly good for this application because it is relatively inexpensive and has a low ash content. Depending on the sulfate to carbonate ratio, about 1.5-2 lbs of coke are consumed per pound of sulfur reduced. This includes coke consumed in the reaction and coke burned to cover heat of reaction, heat required to increase salt temperature to reducing temperature, and heat losses from the system. The reaction rate increased by about 2 to 3 for each 50 °C temperature rise reduction times of 170, 30,15, and 4 min were observed at 700, 800, 875, and 950°C, respectively. Therefore, the reduction reaction is carried out at about 850°C or above. 

For the inner zone, in which both transport and reaction occurs, the differential equations are those of the first stage, but the boundary conditions arc dC Jdr = 0 at r = 0 and Eq. 4.2-11 at the boundary with the outer zone. This mt el corresponds to that set up by Ausman and Watson, to describe the rate of burning of carbon deposited inside a catalyst particle [8]. Analytical integration of this fairly general two-stage model is only possible for a zero-order, first-order or pseudo-first-order rate law, whereby Eq. 42-8 reduces to... 

Shrinkage of each coal particle occurs both by combustion and attrition. The attrition contribution to the shrinkage rate of a burning carbon particle may be obtained from Equation 18 as [22],... 

The overall shrinkage rate enters in the population balance equation to determine the size distribution and carbon concentration of burning carbon particles. 

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