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Constraints on the Validity of Equilibrium and First‐Order Kinetic Transport Models in Structured Soils
Author(s) -
Parker J. C.,
Valocchi A. J.
Publication year - 1986
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr022i003p00399
Subject(s) - mathematics , diffusion , equating , dispersion (optics) , flux (metallurgy) , soil water , thermodynamics , aggregate (composite) , kinetic energy , mathematical analysis , statistics , chemistry , mechanics , physics , soil science , materials science , geology , classical mechanics , organic chemistry , optics , rasch model , composite material
Solutions are presented for solute transport in a system of spherical aggregates for flux concentrations C f 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 C f 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 D e 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 Δμ 3 LE between third moments of C f versus a temporal variable normalized by the mean residence time. The expression for Δμ 3 LE 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 Δμ 3 LE = 0.01 generally yields close correspondence between SD and LE models when appropriate D e 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 Δμ 3 FO 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.