Transport, reaction, and fragmentation in evolving porous media

Two models of reaction and consumption of porous media, such as coal and catalyst particles, are investigated. The first model is appropriate only for the kinetic regime (KR) in which the rate of reactant transport plays no role, and the consumption of the solid matrix of the medium depends only on the kinetics of the reaction. The second model incorporates the effect of the diffusion of the reactants into the pore space and, by changing the normalized reactivity of the medium, the model is capable of simulating the entire range of possible kinetic behavior, from the diffusion-limited regime (DLR) to the KR. The solid matrix of the medium is represented by a percolation cluster. In both the KR and the DLR, one observes fragmentation of the medium. However, while in the KR one can initially obtain large fragments, the fragments in the DLR are small and are mostly the result of the surface roughness of the medium (perimeter fragmentation). Moreover, in all cases the fragments obey a dynamic scaling ${\mathit{n}}_{\mathit{s}}$(t)∼${\mathit{t}}^{\mathit{w}}$ ${\mathit{s}}^{\mathrm{-}\mathrm{\tau }}$f(s/${\mathit{t}}^{\mathit{z}}$) where ${\mathit{n}}_{\mathit{s}}$ is the number of fragments of size s at time t, and w, τ, and z are dynamic exponents. The exponent w is positive before the maximum number of fragments has been obtained, and negative beyond that. The extension of the model for calculating other quantities of interest, e.g., the distribution of the mineral particle sizes that result from the complete consumption of the system, is also discussed. Possible similarities with other fragmentation phenomena are also discussed.