Semi-Analytical Solutions of One-Dimensional Multispecies Reactive Transport in a Permeable Reactive Barrier-Aquifer System

At many sites it has become apparent that most chemicals of concern (COCs) in groundwater are persistent and not effectively treated by conventional remediation methods. In recent years, the permeable reactive barrier (PRB) technology has proven to be more cost-efficient in the long-run and capable of rapidly reducing COC concentrations by up to several orders of magnitude. In its simplest form, the PRB is a vertically emplaced rectangular porous medium in which impacted groundwater passively enters a narrow treatment zone. In the treatment zone dissolved COCs are rapidly degraded as they come in contact with the reactive material. As a result, the effluent groundwater contains significantly lower solute concentrations as it re-enters the aquifer and flows towards the plane of compliance (POC). Effective implementation of the PRB relies on accurate site characterization to identify the existing COCs, their interactions, and their required residence time in the PRB and aquifer. Ensuring adequate residence time in the PRB-aquifer system allows COCs to react longer, hence improving the probability that regulatory concentrations are achieved at the POC.

In this study, the Park and Zhan solution technique is used to derive steady-state analytical and transient semi-analytical solutions to multispecies reactive transport in a permeable reactive barrier-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. Also, like the single-species Park and Zhan solution, the solutions presented here were derived using the total mass flux (third-type) boundary condition in PRB-aquifer system. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethylene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway.

Lastly, the solutions in this study are not restricted solely to the PRB-aquifer model. They can also be applied to other types of dual domain systems with distinct flow and transport properties, and up to four other species reacting in serial or parallel degradation pathways. Although the solutions are long, the results of this study are novel in that the solutions provide improved modeling flexibility. For example: 1) every species can have unique first-order reaction rates and unique retardation factors, 2) higher order daughter species can be modeled solely as byproducts by neglecting their input concentrations, 3) entire segments of the parallel degradation pathway can be neglected depending on the desired degradation pathway model, and 4) converging multi-parent reactions can be modeled. As part of the study, separate Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways. The spreadsheet programs are included as supplementary material.