Wl. Chen et Rj. Wagenet, SOLUTE TRANSPORT IN POROUS-MEDIA WITH SORPTION-SITE HETEROGENEITY, Environmental science & technology, 29(11), 1995, pp. 2725-2734
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.