Transport of reactive solute in spatially variable soil systems

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Abstract
Transport is studied for reactive solutes and one‐dimensional fluid flow with sorption described by the Freundlich equation (Q = kcn). For a physically and chemically homogeneous soil column and if the constant feed concentration is larger than the initial concentration, the transport occurs in a traveling wave–type displacement, with a constant shape of the solute concentration front and constant front propagation velocity, provided 0 < n < 1. For a negligible initial concentration it is shown that a shock front may be assumed if n is small enough. Field scale transport is described as an ensemble of shock fronts in parallel columns with different flow velocities ν, retardation factors r, and times of solute input, tc. These stochastic variables are characterized by probability density functions (PDF). If we assume lognormal distributions, a simple expression for the field‐averaged profile of dimensionless sorbed solute 〈Γ〉 at a particular time is derived. If tc is not a distributed variable, but equal to the total time τ the profile 〈Γ〉 coincides with the field‐averaged dimensionless concentration profile. It is shown how scaling theory, leading to the PDF of the fluid velocity, may be incorporated in the model. For reasonable parameter values and statistics of the stochastic variables the 〈Γ〉 profiles are calculated. Notably, the effect of a stochastic retardation factor, with statistics derived from the distributions of pH and oc (organic carbon content) found for 84 soils, appears to be profound. The field‐averaged displacement calculated is nonsigmoid for the PDFs of oc, pH, and tc chosen. This phenomenon is amplified if v and r are assumed negatively correlated. From the results it is clear that modeling of horizontally large soil systems with averaged properties will in general lead to an underestimation of the moment of first breakthrough at a particular reference level, such as the phreatic water level.