Tong, C.C., Huang, C.-S., Townley, L.R., and Wang, C. (2026), Two new analytical models for three-dimensional transport in a confined aquifer with a Permeable Reactive Barrier: A new adsorptive-reactive Robin matching condition", Water Resources Research, Accepted pending final revision.

Existing analytical models for permeable reactive barriers (PRBs) treat an upgradient aquifer formation with contaminant sources as either a Dirichlet or Robin boundary condition specified at the upgradient face of the PRB. This study develops two new analytical models for three-dimensional transport in a confined aquifer with a PRB. One model applies governing equations to the upgradient and downgradient formations and PRB in between. The other simplified model represents the PRB as a new adsorptive-reactive Robin matching condition including two terms with a coefficient reflecting the effects of adsorption and reaction in the PRB. Analytical solutions satisfying these models are obtained. Results show the coefficient equals PRB’s retardation factor times its thickness divided by the average linear flow velocity. The analytical solutions for dimensionless concentration agree within 5% error under quantitative conditions. Treating an upgradient formation as a Dirichlet boundary condition at PRB’s upgradient face is preferable to treating the formation as a Robin boundary condition. A solution depending on the Dirichlet boundary condition only requires measurements of concentration at the boundary for arbitrary values of Peclet number defined as the ratio of PRB’s thickness to its longitudinal dispersivity. A solution relying on the Robin boundary condition, however, requires measurements of both concentration and concentration gradient when Peclet number is small, and is applicable for large Peclet number when only concentration measurements are available. A handy tool for designing PRB size is provided.