Asymptotic analysis of nonlinear equilibrium solute transport in porous media

We discuss the asymptotic behavior of a solute plume undergoing reversible sorption governed by a Freundlich isotherm after single-pulse injection. Our analysis predicts that the concentration at a fixed position decays asymptotically like a power law with an exponent alpha = 1/(1 - n) where n is the Freundlich exponent. Correspondingly, the shape of tail is time invariant. The results are checked by comparison with numerical solutions for one-dimensional transport in a homogeneous medium. Some further asymptotic results for this case are derived. The power law behavior provides an alternative way to derive the Freundlich n parameter from breakthrough curves in comparison to the use of inverse estimation methods. This is especially the case when evaluating breakthrough curves obtained in mio;or three-dimensional flow domains, for which indirect estimation of parameters becomes very difficult.