A model for describing solute nonequilibrium transport influenced by sorption-site heterogeneity in porous media was proposed and analyzed in terms of its time moments. The sorption-site heterogeneity was conceptualized as variable sorbing fractions/compartments that are grouped into classes according to a probability density function (pdf) for both equilibrium (linear partitioning, K D ) and rate (first-order sorption time, T s ) parameters. Two typical pdfs, a simple two-site (TS) and a general y site (GS), were employed for comparison. The correlation 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 ∼log K D ) holds or completely independent. As the LFER holds, the impact of sorption rate statistics presents on all moments (except the zeroth) of a solute breakthrough curve (btc), resulting in simultaneous 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 to the rate sorption statistics, rendering a substantial deviation between 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 achieved up to the second. It is indicative in either case, therefore, that 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 become more stringent as the time scale increases.