Analytical expressions for the hydraulic design of continuous permeable reactive barriers

Various analytical expressions describing the hydraulic behavior of a continuous permeable reactive barrier (PRB) are developed based upon a two-dimensional approximation of the local groundwater flow system. The fully penetrating PRB is represented as an arbitrarily oriented elliptical “analytic element” with a hydraulic conductivity different from that of the aquifer. The validity of this elliptical geometry approximation as a surrogate for rectangular PRB performance is evaluated and put into context. Closed-form expressions for solute travel time distributions along the extent of the barrier and PRB capture zone geometry are evaluated for general barrier dimension (length and width), hydraulic conductivity, and orientation with respect to regional flow. These expressions are used as the foundation of a simple PRB design process, and provide some interesting insights into the hydraulic behavior of continuous permeable reactive barriers.