On the Initial Rate of Fluid–Solid Reactions

It is argued in this paper that the initial rate should not be used for the measurement or analysis the kinetics of a fluid–solid reaction, especially for a reaction in which the effect of pore diffusion starts appearing even moderately as the reaction proceeds. Even in the absence of external mass transfer effects, it is shown in this work by rigorous mathematical analysis that the range of conditions where the initial rate represents the intrinsic kinetics is very narrow. For an initially non-porous solid in the absence of external mass transfer effects, the very initial rate should mathematically be the intrinsic rate even when pore diffusion becomes important as the reaction proceeds. However, even in this case, the range of conditions for this statement is very limited. For the reaction of an initially porous solid, the rate at time zero is already affected by pore diffusion unless its effect is negligible over the entire range of conversion. Furthermore, the initial reaction rates of porous solids reacting under large values of k/D _e ratio (chemical reactivity is much greater than the capacity for pore diffusion) have an apparent rate constant of \( \sqrt {k \cdot D_{\text{e}} } \) and thus pore diffusion alone does not control the initial rate no matter how large the effect of pore diffusion is overall.