SOLUTE TRANSPORT IN POROUS-MEDIA WITH SORPTION-SITE HETEROGENEITY

A model for describing solute nonequilibrium transport influenced by s orption-site heterogeneity in porous media was proposed and analyzed i n terms of its time moments. The sorption-site heterogeneity was conce ptualized as variable sorbing fractions/compartments that are grouped into classes according to a probability density function (pdf) for bot h equilibrium (linear partitioning, K-D) and rate (first-order sarptio n time, T-s) parameters. Two typical pdfs, a simple two-site (TS) and a general gamma site (GS), were employed for comparison. The correlati on between K-D and T-s was considered in two extreme cases: perfectly correlated as the linear free-energy relationship (LFER, linear log T- s similar to log K-D) holds or cam pletely independent. As the LFER ho lds, the impact of sorption rate statistics presents on all moments (e xcept the zeroth) of a solute breakthrough curve (btc), resulting in s imultaneous enhanced peakedness and long time scale tailing on the btc . When K-D and T-s are uncorrelated, equivalency between the simple TS and the more general GS models can be established up to the third btc moment. However, higher moments immediately become highly sensitive t o the rate sorption statistics, rendering a substantial deviation betw een TS and GS in the description of the long time scale behavior. The model deviation can be enhanced in the existence of the LFER since the ultimate equivalence of the btc moments in this case can only be achi eved up to the second. It is indicative in either case, therefore, tha t when sorption heterogeneity exists, simple distributions such as TS is inherently not sufficient to represent a more generally distributed sorption process (e.g., GS), which can even became more stringent as the time scale increases.