One-dimensional solute transport in porous media with partial well-to-well recirculation: Application to field experiments

Abstract

A solute transport model incorporating well-to-well recirculation was developed to facilitate the interpretation of pilot-scale field experiments conducted for the evaluation of a test zone chosen for in situ restoration studies of contaminated aquifers, where flow was induced by recirculation of the extracted fluid. A semianalytical and an approximate analytical solution were derived to the one-dimensional advection-dispersion equation for a semi-infinite medium under local equilibrium conditions, with a flux-type inlet boundary condition accounting for solute recirculation between the extraction-injection well pair. Solutions were obtained by taking Laplace transforms to the equations with respect to time and space. The semianalytical solution is presented in Laplace domain and requires numerical inversion, while the approximate analytical solution is given in terms of a series of simple nested convolution integrals which are easily determined by numerical integration techniques. The applicability of the well-to-well recirculation model is limited to field situations where the actual flow field is one dimensional or where an induced flow field is obtained such that the streamlines in the neighborhood of the monitoring wells are nearly parallel. However, the model is fully applicable to studies of solute transport through packed columns with recirculation under controlled laboratory conditions.