Analytical expressions for the hydraulic design of continuous permeable reactive barriers James R. Craig a, * , Alan J. Rabideau b , Raghavendra Suribhatla b a Department of Civil Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada b Department of Civil, Structural, and Environmental Engineering, University at Buffalo, 212 Ketter Hall, Buffalo, New York 14260, USA Received 22 December 2004 Available online 5 July 2005 Abstract 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 expres- sions 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. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Permeable reactive barrier; Analytic element method; Analytical techniques; Ground-water pollution 1. Introduction A popular technology for remediating contaminated groundwater is the permeable reactive barrier (PRB), which consists of a trench filled with reactive material placed in the path of a contaminant plume. As ground- water passes through the PRB, contaminants are re- moved by local transformation reactions and/or sorption to the PRB material. Regardless of the removal mechanism, PRB performance depends on (1) appropri- ate placement of the barrier to capture the targeted con- taminant plume and (2) sufficient residence time within the PRB to accomplish the desired reaction. Effective de- sign therefore requires an accurate and comprehensive understanding of the groundwater flow regime as affected by the emplaced PRB. Modeling of groundwater flow through a PRB is commonly accomplished using a numerical simulator such as MODFLOW [13]. While straightforward, appli- cation of a finite difference model must be carefully per- formed to avoid numerical artifacts. Modification of the conceptual model (e.g., changing the barrier orientation or dimensions) for sensitivity analysis can be tedious. Due to discretization artifacts, numerical methods are more cumbersome, and can have significant errors if dis- cretization is too coarse or improperly aligned. For aquifers characterized by horizontal regional flow, an appealing option is the analytic element method (AEM), which can simulate both regional and local hydrogeologic features without discretization artifacts [19]. In this paper, we propose the conceptual model 0309-1708/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2005.05.006 * Corresponding author. Tel.: +1 519 888 4567; fax: +1 519 888 6197. E-mail addresses: jrcraig@civmail.uwaterloo.ca (J.R. Craig), rabideau@eng.buffalo.edu (A.J. Rabideau), rms29@eng.buffalo.edu (R. Suribhatla). URL: www.groundwater.buffalo.edu (J.R. Craig). Advances in Water Resources 29 (2006) 99–111 www.elsevier.com/locate/advwatres