An analytical solution for contaminant extraction using well injection depth extraction technology

Well injection depth extraction (WIDE) is used to remediate contaminated fine-grained soil with low hydraulic conductivity. The flow path is short because the prefabricated vertical wells (PVW) are closely installed in the WIDE system. The current analytical solution that considers the infinite extraction boundary is not suitable to describe the close distance between the injection PVWs (IPVW) and the extraction PVWs (EPVW). A Neumann boundary is proposed as an extraction boundary that can reflect the characteristics of the WIDE system. A flux-type boundary is proposed as an injection boundary to meet the requirements for mass conservation. An analytical solution for a simplified planar two-dimensional model of the WIDE system is presented to take into account the proposed extraction and injection boundaries. Moreover, the initial concentration that is exponentially distributed along the depth is taken into account. The results are consistent with those obtained from the finite-difference method and the experimental data. The results indicate that the Neumann boundary is better than the infinite extraction boundary, and the analytical solution with the infinite boundary is a special case of the proposed solution. The proposed analytical solution is relatively simple and can be used for a quick preliminary calculation to evaluate the experimental results and to evaluate more complex numerical methods.