Theory of anomalous dispersion in porous media

A theory of anomalous dispersion in porous media is developed by taking the high Peclet number limit of the equations describing cross-diffusion in concentrated suspensions. This leads to a modified advection-dispersion equation containing a reflection coefficient in the advection term. The reflection coefficient accounts for the effect of matrix heterogeneity, velocity fluctuations and pore-scale eddies on solute transport, and can be determined as a function of the relative tracer concentration from a single measured breakthrough curve. Once the reflection coefficient is known the model predicts anomalous breakthrough curves at various positions and flowrates within the porous medium. In addition the model uses the actual fluid velocity, in contrast to the classical advection-dispersion model in which the velocity is treated as an adjustable parameter.