A novel 1.5-D solution method for solving 2-D advection–dispersion-reaction equations in layered media: application to a triple-domain PRB system considering arbitrary source distributions

Permeable reactive barrier (PRB) is a promising technology for groundwater remediation. The variation in the concentration of contaminant source upstream the PRB is a key consideration for analyzing the remediation process. However, the concentration variation in the upstream aquifer has yet to be considered in existing analytical models. This paper develops a new 2-D analytical model for contaminant transport through an upstream aquifer-PRB-downstream aquifer (UA-PRB-DA) system, and an arbitrary distribution of source concentration is considered in the UA. A novel analytical approach (1.5-D solution method) is presented to obtain exact solution to 2-D advection–dispersion-reaction equations (ADREs) for contaminant transport through the UA-PRB-DA system. The solution has been validated against an analytical solution, a semi-analytical solution and numerical results. The results show that our solution produces the 2-D transport characteristics well through the PRB system. Both the evolutions of the upstream contaminant concentration and the downstream transport can be captured. Under the effect of advection, the contaminant plume in the UA continuously approaches the PRB, and its distribution pattern changes constantly. A higher flow velocity accelerates the remediation upstream of the PRB, but may bring a risk to the downstream aquifer. The effect of flow velocity on the reacted contaminant amount in the PRB is associated with elapsed time. The proposed solution is a valuable tool for designing groundwater remediation and contaminant barriers and the benchmark for numerical models.