Growth of the dispersion coefficient with the mean travelled distance in porous media

A general formulation of the transport equation of solutes in porous media is developed theoretically for a slug injection, with the assumption that the distribution of the velocities in the medium is gaussian, and that molecular diffusion is negligible. The equivalent of the dispersion coefficient in the equation is then shown to be a function of time. Tracer experiments performed both in situ and in the lab seem to be in accordance with this hypothesis; as an example, this model is shown to give an excellent fit for the data published by Coats & al. in 1964, and for which these authors had developed the “dead end pore” model.