Effect of reactivity loss on apparent reaction order of burning char particles

Considerable debate still exists in the char combustion community over the expected and observed reaction orders of carbon reacting with oxygen. In particular, very low values of the reaction order (approaching zero) are commonly observed in char combustion experiments. These observations appear to conflict with porous catalyst theory as first expressed by Thiele, which suggests that the apparent reaction order must be greater than 0.5. In this work, we propose that this conflict may be resolved by considering the decrease in char reactivity with burnout due to ash effects, thermal annealing, or other phenomena. Specifically, the influence of ash dilution of the available surface area on the apparent reaction order is explored. Equations describing the ash dilution effect are combined with a model for particle burnout based on single-film nth-order Arrhenius char combustion and yield an analytical expression for the effective reaction order. When this expression is applied for experimental conditions reflecting combustion of individual pulverized coal particles in an entrained flow reactor, the apparent reaction order is shown to be lower than the inherent char matrix reaction order, even for negligible extents of char conversion. As char conversion proceeds and approaches completion, the apparent reaction order drops precipitously past zero to negative values. Conversely, the inclusion of the ash dilution model has little effect on the char conversion profile or char particle temperature until significant burnout has occurred. Taken together, these results suggest that the common experimental observation of low apparent reaction orders during char combustion is a consequence of the lack of explicit modeling of the decrease in char reactivity with burnout.