Illustrative example

Remediation of a contaminated aquifer

An aquifer is contaminated with small amounts of phenantrene. By estimating the equilibrium partition coefficient you can estimate how much water must be flushed through the aquifer to reduce the phenantrene concentration below the acceptable threshold value. However, this calculation assumes instantaneous sorption/desorption equilibrium. How realistic is this assumption?

Assume that the aquifer contains grain size fractions up to 1 mm. In the pores between these grains the water is moving and exchanged depending on the flushing conditions. Transport of phenantrene in and out of the grains however can happen only by diffusion (either as diffusion within organic matter or as retarded diffusion in the intraparticle pore space).
Let us assume that the maximal diffusion path length is half of the grain diameter and let us neglect the tortuosity (although in practice this is not negligible, Rügner et al. 1999  Journal link  Download paper). A typical diffusion coefficient for phenantrene in such an aquifer material is D of 10^-10 cm²/sec (Rügner et al., 1999).
The time needed to diffuse over a distance of 0.5 mm is:
t = x² /2 D => (0.05 cm)² / (2 · 10^-10 cm²/sec) = 1.25 · 10⁷ sec = 145 d

Thus we can conclude that the success of any remediation effort by flushing this aquifer will be controlled by very long diffusion times (see Rügner et al. 1999; ter Laak et al. 2007 Journal link  Download paper). The rate of flushing will hardly have any effect on the remediation success. Such situations have indeed often been experienced in practice.