Influence of the spatial distribution of velocities in porous media on the form of solute transport

Solute transport in porous media is studied theoretically using the concept of movement of particles in a random velocity field. Under some assumptions, it is shown that the resulting transport equation is different for early times from the classical one, the dispersion tensor being time-dependent, both in direction and magnitude. Its components depend on the covariance matrix of the velocity of the particle, but should, in general, reach an asymptotic value after sufficient time, thus giving rise to the classical dispersion equation. Examples of similar behavior for stratified systems are also given, with some estimates of the orders of magnitude of the time needed for reaching asymptotic behavior, which can be very large. Field experiments are presented to support this theory, as well as new interpretations of the classical dead end pore model and the laboratory data presented by Coat and Smith in 1964