Finite element solution of the fluid–solid reaction equations with structural changes

The finite element solution for gas–solid reactions is developed to include fluid accumulation term in the solid pellet (liquid–solid reactions) accompanied with structural changes in the solid phase. In these reactions the fluid balance equation in the pellet is an unsteady state equation which is coupled with the solid phase equation. The fluid balance equation is analyzed numerically by the combination of Rayleigh–Ritz finite element method and finite difference approximation while the solid equation is solved by fourth order Runge–Kutta method simultaneously. This method shows flexible behavior in all reaction regimes even in the diffusion-limited regimes accompanied with significant structural changes. Equations of the modified grain model and random pore model are considered in this work. Finally results of this work are compared with some other existing solutions and experimental data successfully.