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Show -7- where k is the thermal conductivity of the wall. We artificially accelerate this diffusion process by decreasing the value of c by several orders of magni- Pw tude. With such an accelerated diffusion, a steady-state solution with wall-heat transfer can be achieved in approximately the same problem time as would be required with adiabatic wall conditions. For transient studies, one would start from the steady-state solution and use the real value of c Pw Equation (17) is subject to the boundary condition at the outer wall (41) -TT <T - T > , (18) vdr'ew k e w w where the subscript e refers to the external environment, and H is the heat transfer coefficient on the environment side. C. Devolatilization, Cracking, and Char Oxidation Coal devolatilization is the evolution of volatile species as the result of the heating of coal particles, with the particle residue becoming progressively richer in carbon as devolatilization proceeds. Despite many investigations of devolatilization, the detailed kinetics and mechanism of the process remain unclear, with orders of magnitude variation in kinetic rates. Solomon and Hamblen [7] indicate that these discrepancies can be attributed in large part to variations in experimental procedures, and they show that when different coals are pyrolyzed under identical procedures there is surprising similarity in the behavior of most species. The amounts of each species evolved varies from coal to coal, but when yields are normalized by the maximum yield, then the temperature and time dependence of the evolution are relatively insensitive to coal rank (excluding anthracite). They propose kinetic rate coefficients for the most important species, CO , CO, H O , HCN, NH , CH (aliphatic compounds), CH , H, and tar, with the yields of some of these species best described by a combination of two or three kinetic rates. Unfortunately, it would be costly to include kinetic reactions for all of these species in a numerical model. Nevertheless, the need to include a multi-step devolatilization process to account for the temperature dependence of species evolution has led us to adapt a two-step competing reaction process, as described in References 8-10, ^a. Volatile 1 + (1 - a, ) Char Residue ^\yS 1 1 Coal <^ , (19) <? «? Volatile 2 + (1 - a ) Char Residue |
