Convective-Dispersive Stream Tube Model for Field-Scale Solute Transport: I. Moment Analysis

Abstract

Field-scale solute transport is typically difficult to model due to the complexity and heterogeneity of flow and transport in natural soils. The stream tube model attempts to stochastically describe transport across the field for relatively short travel distances by viewing the field as a series of independent vertical soil columns. This study investigates the stream tube model with the chemical equilibrium and nonequilibrium convection-dispersion equation (CDE) for local-scale transport. A bivariate (joint) lognormal probability density function was used for three pairs of random transport parameters: (i) the dispersion coefficient, D, and the pore-water velocity, v; (ii) the distribution coefficient for linear adsorption, &, and v; and (iii) the firstorder rate coefficent for nonequilibrium adsorption, a, and v. Expressions for travel time moments as a rsult of a Dirac input were derived to characterize field-scale transport according to the stream tube model. The mean breakthrough time for the field-scale flux-averaged concentration, 21, was found to be identical to that for the deterministic CDE. Variability in D has generally a minor effect on solute spreading compared with variability in v. Spreading of reactive solutes increased for negatively correlated v and Kd, even if the variability in K,, was relatively small, while nonequilibrium adsorption further increased spreading. If a was variable, a negative correlation between v and a enhanced the skewness of the breakthrough curve for&while spreading was independent of the correlation between (I and v.