Unidimensional solute transport incorporating equilibrium and rate‐limited isotherms with first‐order loss: 3. Approximate simulations of the front propagating after a step input

Sorptive processes which accompany unidimensional solute flow through a porous medium can be modeled in terms of rate‐limiting isotherms. Both the rate limitations and dispersive processes combine to degrade or distend an otherwise sharp solute front initially introduced to the “column” as a step. Whenever dispersion is the dominant distending mechanism, the model simulation can be well approximated by replacement of the isotherm with a local equilibrium assumption (LEA). Conversely, if kinetics dominate distension, the neglect of dispersion can provide an efficacious approximant. I develop and illustrate the double Laplace‐like approximation (DLA) as a useful approximant when neither of these extremes is realized. The development is for a simulation model of unidimensional dispersive and advective transport which, in its most general form, incorporates combined linear Freundlich and rate‐limited isotherms, and first‐order loss, as formulated in paper 1 of this series (Lassey, 1988a). The DLA is about as computationally onerous as the LEA and the nondispersive assumption (NDA). The DLA‐predicted gradients of solute and sorbed concentration at the front are related to the Péclet and Damköhler numbers (characteristic of dispersion and kinetics, respectively), and include as special cases those predicted by the LEA and NDA. A numerical survey of the three approximants indicates that, for a propagating solute front of relatively minor distension, the DLA is the superior approximant.