Semi-analytical and approximate solutions for contaminant transport from an injection well in a two-zone confined aquifer system

This study develops a mathematical model for contaminant transport due to well injection in a radial two-zone confined aquifer system, which is composed of a wellbore skin zone and a formation zone. The model contains two transient equations describing the contaminant concentration distributions; one is for contaminant transport in the skin zone while the other is for transport in the formation zone. The contaminants are injected into the well with given dispersive and advective fluxes; therefore, the well boundary is treated as a third-type (Robin) condition. The solution of the model derived by the method of Laplace transforms can reduce to a single-zone solution in the absence of the skin zone. In addition, an approximate solution in the time domain is also developed by neglecting dispersion for the case that the contaminants move away from the injection well. Analysis of the semi-analytical solution showed that the influence of the skin zone on the concentration distribution decreases as time elapses. The distribution will be over-estimated near the wellbore if the constant concentration (Dirichlet) condition is adopted at the well boundary. The approximate solution has advantages of easy computing and yield reasonable predictions for Peclet numbers larger than 50, and thus is a practical extension to existing methods for designing aquifer remediation systems or performing risk assessments.