Statistical and continuum models of fluid-solid reactions in porous media

In this review, we discuss past theoretical works on fluid-solid reactions in a porous medium. Such reactions are often accompanied by a continuous alteration of the pore structure of the medium, and at high conversions they exhibit percolation-type behavior, i.e. the solid matrix of the medium and/or the fluid phase lose their macroscopic connectivity. These phenomena are, therefore, characterized by a percolation threshold which is the volume or area fraction of a phase (solid or fluid) below which that phase exists only in isolated clusters or islands. Important classes of such processes are acid dissolution of a porous medium and gas—solid reactions with pore volume growth, e.g. coal gasification, and with pore closure, e.g. lime sulfation, and catalyst deactivation. These processes are characterized by continuous changes in the pore space as a result of a chemical reaction. We also consider here other processes such as the flow of fines, stable emulsions and solid particles in a porous medium which also alter the structure of the pore space, but by physical interaction of the particles and the solid surface of the pores. In this review we compare two different modelling approaches to reactions accompanied by structural changes. First we review the continuum approach, which is based on the classical equations of transport and reaction supplemented with constitutive equations describing the effect of structural changes on reaction and transport parameters. We then outline the relevant concepts, ideas and techniques of percolation theory and the statistical physics of disordered media, and review their application to the phenomena mentioned above. In particular, we emphasize the fundamental role of connectivity of the porous medium in such phenomena. Since in both approaches one needs to estimate the effective transport properties of the porous medium that is undergoing continuous change, we also review continuum and statistical methods of estimating the effective transport properties of disordered porous media.

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