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The mathematical analysis and the numerical simulation of reaction-diffusion phenomena in porous media have been discussed extensively in the literature. The fundamental equation governing diffusion in porous media is the equation of mass conservation, which is of parabolic type. It is established assuming that the dispersive mass flux is given by the Fick´s law where the dispersion tensor is assumed to be independent of the concentration and its gradient. It is well-known that this equation gives rise to an infinite speed of propagation. Small-scale and large-scale heterogeneities in porous matrix and/or fluid properties are the main sources of deviations of the so-called Fickian dispersion behavior. In order to overcome this deviation, a certain memory effect should be included in the flux modeling.
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