Capture flows of funnel-and-gate reactive barriers without gravel packs

Permeable reactive barriers (PRBs) are a passive in-situ technology, which is based on the interception and physical, chemical and/or biological remediation of a contaminant plume through installation of reactive material in an aquifer. Previous work of the authors includes analytical approaches in two dimensions (horizontal plane) based on the conformal mapping technique that allows for the determination of the groundwater flow fields and capture zones of PRBs of different types. Solutions assume that the permeability k_r of the reactive material itself is high with respect to the surrounding aquifer permeability k_a or that highly permeable gravel packs are present to equilibrate the hydraulic heads at the up and down-gradient faces of the reactor. Respective results include a simple relationship Q(R) between capture flow Q and reactor Darcian hydraulic resistance R. Based on the same technique, the present work gives an exact solution for funnel-and-gate (FG) and velocity equalization wall (VEW) PRBs without gravel packs for the particular case of k_r = k_a. Furthermore, a numerical finite difference study is performed to show that Q(R) is a good approximation (with errors in the 1% range of maximum capture flow Q(0)) for FG and VEW PRBs of arbitrary geometric configurations and arbitrary values of k_r/k_a, even in the absence of highly permeable gravel packs at the reactor entrance and exit faces.