APPROXIMATION OF ASYMPTOTIC DISPERSIVITY OF CONSERVATIVE SOLUTE IN UNSATURATED HETEROGENEOUS MEDIA WITH STEADY-STATE FLOW

The relation between the heterogeneity of hydraulic properties and eff ective asymptotic transport is studied for microscopically heterogeneo us but macroscopically homogeneous unsaturated media with steady flow. Heterogeneity is described by the scaling of the hydraulic functions theta(psi(m)) and K(theta). The study is based on an analytical approx imation of asymptotic dispersivity under the assumption that matric po tential is spatially constant. For the special case of a water-saturat ed medium the result of the stochastic continuum theory is recovered. When applied to several published numerical simulations, the approxima ted asymptotic dispersivities are found to agree well with the numeric al values. By exploring the heterogeneous media for various hydraulic states, the approximation resolves some apparent inconsistencies found in the simulations. The cases considered span the entire range from p erfect to zero correlation between scaling factors of matric potential and hydraulic conductivity. It is demonstrated that this correlation is crucial for the behavior of asymptotic dispersivity with changing f low rate. Since weak to moderate correlations are often found in soils , this result has significant implications for solute transport throug h heterogeneous soils.