Use of temporal moment analysis to study reactive solute transport in aggregated porous media

The paper presents an overview of the use of temporal moment analysis as a useful alternative to more complete analytical or numerical solutions of mathematical models describing adsorbing solute transport in aggregated, saturated porous media. The goal of temporal moment analysis is to derive analytical formulas for the lower-order time moments of the solute breakthrough curve, thereby yielding significant physical insight into the behavior of solute transport models. Only the bi-continuum conceptual model and one-dimensional systems are emphasized in this paper. The transfer function approach for calculating temporal moments is described and illustrated with several examples involving diffusion into spherical aggregates, first-order mass transfer, and kinetically controlled intra-aggregate adsorption. The use of moment analysis for model comparison and sensitivity analysis is discussed; in particular, the paper shows how simplified empirical first-order mass transfer models can be utilized to approximate more complex models involving diffusion into nonuniformly sized spherical aggregates.