A dynamic mechanistic model of a multi-phase heterogeneous batch reactor processing a non-catalytic fluid-solid reaction is developed and numerically solved. The model takes into account both intra-particular convection and diffusion phenomena, as well as chemical reaction between the fluid and the solid. By addressing the until now ignored case of convection originated by the continuous increase of the particle porosity, this work enables a more realistic modeling of many non-catalytic fluid-solid reaction systems. The dependency of the convective term on the chemical reaction rates gives rise to a space and time dependency of the intra-particle velocity thus increasing the mathematical complexity of the problem. The model is characterized by a set of PDEs coupled with adequate boundary conditions that are solved by the method of lines. An example of application of great importance to the chemical pulping of wood is used, emphasizing the differences with the typical situation where only diffusion is considered.