Convective and pore scale dispersive solute transport in unsaturated heterogeneous fields

Abstract

Transport of an inert solute in unsaturated horizontally heterogeneous field soils, which differs from that in laboratory conditions, is investigated. Four solute transport factors and their variabilities have been examined: (1) convection by vertical velocity V, which changes in plane because of variability in soil properties, (2) recharge R, applied on the surface, constant in time but varying in plane, (3) pore scale dispersivity λ, variable in the field, and (4) average dispersivity λ, with field condition value. The variables V, R, λ, and solute concentration C are regarded as random. Closed form equations (requiring a numerical quadrature at most) for the probability distribution of C are derived by using several simplifying assumptions concerning the water flow regime. The mathematical solutions are capable of determining detailed statistical information about solute distribution in the field. Two soils are examined: (1) Panoche soil (150 hectares in area) with low average saturated conductivity and relatively large variance and (2) Bet Dagan soil (0.8 hectare in area) with larger average conductivity and a smaller variance. It is found that for both soils the variability of λ has very little influence and that adopting the value of λ for the entire field is sufficient. The variability of R when it is moderate has a modest effect. The three major factors are the variability in soil hydraulic conductivity, average values of rate of recharge R, and pore scale dispersion λ. It is concluded that (1) average concentration profile in the heterogeneous field cannot be modeled as the solution of convective‐diffusion equation with constant coefficients and (2) if λ is taken at its laboratory‐measured value, its effect upon solute distribution is negligible compared with that of soil variability, but if the large field value is adopted, it has an impact upon solute distribution. The dominant spreading mechanism in Panoche soil is heterogeneity combined with convection. Accounting for both mechanisms is warranted in most cases.