Analytical solutions for the flow fields near funnel‐and‐gate reactive barriers with hydraulic losses

Abstract

Permeable reactive barriers (PRBs) are a passive in situ technology that is based on the interception and physical, chemical, and/or biological remediation of a contaminant plume through installation of reactive material in an aquifer. The present work is an extension and generalization of a previous paper and derives analytical expressions for flow fields toward PRBs in two dimensions on the basis of the conformal mapping approach. Considered is the classic funnel‐and‐gate configuration with perpendicular funnel arms (PFGs) as well as PRBs with velocity equalization walls. While the aquifer is assumed to be homogeneous in a uniform far field, the hydraulic conductivity of the reactive material is allowed to take arbitrary values above or below the aquifer conductivity. At the up‐ and down‐gradient interfaces between reactor and aquifer, highly permeable gravel packs are assumed to establish constant head conditions. The flow fields are analyzed regarding the widths and shapes of respective capture zones as functions of PRB type and dimensions, reactor hydraulic resistance (including flow divergence and longevity), and ambient groundwater flow direction. Expressions for discharge fields are developed as needed for particle‐tracking algorithms. Charts of relative capture width are given to facilitate PRB design and may be included in more comprehensive PRB design/optimization approaches. An efficient approach is presented to estimate reactor conductivity and capture flow from monitoring the hydraulic loss at the reactor. Inherent assumptions and results are validated against numerical flow field solutions and water level field data for the PFG PRB at the Moffett Federal Airfield, California.

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

“…1(a); [3]), impermeable funnel arms are deployed laterally extending into the aquifer in order to increase [4]) may be used to achieve more uniform contaminant residence time distribution across the reactor by avoiding flow singularities (i.e., the blow-up of the magnitude of the hydraulic gradient) near the reactor and, thus, providing largely uniform flow into, across and out of the reactor. While numerical studies are more abundant in literature, e.g., [3,4], previous work by the authors, [5][6][7], investigates different hydraulic aspects of these PRB configurations in a two-dimensional (horizontal) analytical framework by applying the theory of holomorphic functions, in particular, the conformal mapping technique. However, for arbitrary reactor conductivities results are valid only in the presence of highly permeable gravel packs at the up and down-gradient faces of the reactor, which provide for constant hydraulic head distributions throughout the gravel packs and, thus, strictly uniform flow across the reactor.…”

“…1 and the particular case of the reactor hydraulic conductivity k r [L/T] being equal to the surrounding (homogeneous) aquifer conductivity k a [L/T] without, however, assuming the presence of highly permeable gravel packs. Based on this exact solution and results of Klammler and Hatfield [5] for arbitrary k r in the presence of gravel packs, an approximate solution is further presented for the capture flows of FG and VEW PRBs without gravel packs and for arbitrary k r /k a . The performance of the approximation is systematically validated against output from a numerical finite difference model (MODFLOW).…”

“…With k [-] being a PRB shape parameter (so-called affix) in the sense of previous work, e.g., [5][6][7], eqn. 1 may be rewritten as ,…”

“…Knowing that an ambient groundwater flow component q y does not drive any flow across the reactor (i.e., across A'B' in fig. 2), the capture flow Q [L 3 /T] is obtained as [5] .…”

“…In contrast, independent of f/a the dimensionless capture width fig. 5 compares dimensionless capture flows for no gravel packs (thick continuous lines; previous section) and with gravel packs (thick dashed lines; [5]). Maybe not so unsurprisingly, the agreement is very good with a maximum relative difference of approximately 3% for b/a ≈ 0.5 and f/a ≈ 1.…”