Constraints on the Validity of Equilibrium and First‐Order Kinetic Transport Models in Structured Soils

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Abstract
Solutions are presented for solute transport in a system of spherical aggregates for flux concentrations Cf and for resident concentrations in mobile and immobile zones and in the bulk porous medium subject to continuous injection or pulse injection of infinitesimal or finite duration. By equating second moments of Cf versus time for the bicontinuum spherical diffusion model (SD) with those of a monocontinuum model which assumes local equilibrium (LE), an expression for the apparent dispersion coefficient De in the LE model is obtained in terms of physically meaningful SD model parameters, i.e., aggregate size, diffusion coefficient, etc. Constraints on the validity of the LE model are derived by evaluating differences Δμ3LE between third moments of Cf versus a temporal variable normalized by the mean residence time. The expression for Δμ3LE indicates the manner in which SD‐LE model deviation decreases with diminishing aggregate size and immobile zone retardation factor and with increasing mobile zone retardation, mobile pore fraction, and distance from source. For continuous injection Δμ3LE = 0.01 generally yields close correspondence between SD and LE models when appropriate De values are used in the latter. For pulse injection of diminising duration, criteria for the degeneration of the SD model to the LE model become more stringent. The SD model is also compared to a first‐order kinetic (FO) model to evaluate constraints on the latter in structured soils. Equating second moments of SD and FO models yields an expression for the apparent first‐order rate coefficient in terms of SD model parameters. Comparison of third moments yields a criterion Δμ3FO for SD‐FO model equivalence. A comparison of the error criteria for SD‐FO and SD‐LE equivalence indicates that the FO model always represents the diffusional kinetics more accurately than the LE model when near‐equilibrium conditions prevail. Surprisingly, for severe nonequilibrium conditions, the LE model may in some instances approximate the SD model results more accurately than the FO model.