Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review


  • M. Sardin,

  • D. Schweich,

  • F. J. Leij,

  • M. Th. van Genuchten


The transport of linearly interacting solutes in porous media is investigated with the help of residence time distributions, transfer functions, methods of system dynamics, and time-moment analyses. The classical one-dimensional convection-dispersion equation is extended to two-region (mobile-immobile water) transport by including diffusional mass transfer limitations characteristic of aggregated soils. The two-region model is further revised by incorporating the effects of multiple retention sites (in parallel or in series), multiple porosity levels, and arbitrary but steady flow fields. It is shown that different physical situations can be represented by a relatively small number of transfer functions containing only two types of parameters: distribution coefficients to account for equilibrium properties and characteristic times reflecting kinetic processes. Relevant kinetic processes include convective transport, hydrodynamic dispersion, adsorption-desorption, and physical or chemical mass transfer limitations. In most situations, theoretical breakthrough curves are found to be relatively insensitive to the mathematical structure of the transfer function, irrespective of the physical interpretation of the distribution coefficients and the characteristic times in the model. This means that alternative physical and chemical interpretations of model parameters can lead to nearly identical breakthrough curves. Certain transfer time distributions can lead to quite unusual shapes in the breakthrough curves; these curves strongly depend on the characteristic times and a few operational variables. Results of this study show that the transfer time distribution is an extremely useful tool for explaining some unexpected experimental results in the solute transport literature.