Convective-Dispersive Stream Tube Model for Field-Scale Solute Transport: II. Examples and Calibration

Abstract

The use of the stream tube model developed in the first part of this study is illustrated for several examples with a stochastic pore-water velocity, v, and distribution coefficient, Kd. The model allows quantification of the concentration variance in the horizontal plane to evaluate models for transport in heterogeneous fields. Increased vertical solute spreading due to stochastic local-scale parameters is accompanied by increased horizontal variations of the field-scale mean concentration. Solute application at the surface is modeled as a boundary value problem (BVP) and an initial value problem (IVP). The field-averaged concentration vs. depth exhibits more spreading for the BVP than the IVP since a variable solute mass is applied to each stream tube in the latter case. Flow is also modeled by a lognormal probability density function for the saturated conductivity, Ks, and the unit gradient assumption instead of v. The use of a random v instead of Ks is preferable for small variations in water content. Results of the stream tube model are compared with those of a one-dimensional macroscopic convection-dispersion equation (CDE) with effective parameters (i.e., depth-dependent constants). When these constants are determined from time moments of the field-scale flux-averaged concentration, ĉf, for the BVP, the stream tube model and the macroscopic CDE will give different results if the effective parameters are used to model other transport scenarios. Finally, the stream tube model was fitted to the concentrations obtained from a detailed numerical simulation of flow and transport in a (hypothetical) heterogeneous field. The (simple) stream tube model appears to provide a sensible description of the field-averaged concentration and variance.