The problem of flow by-pass at permeable reactive barriers

Klammler, Harald; Hatfield, Kirk

doi:10.2495/geo080021

Cited by 5 publications

(5 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 3c represents a situation of flow divergence around the reactor, where a potentially contaminated portion of flow entering the collector drain does not flow through the reactor but immediately re‐enters the aquifer (i.e., leakage from the collector drain indicated by the darkly shaded area outside capture zone where some stream lines connect collector and distributor drains through the aquifer). As opposed to flow by‐pass (Klammler and Hatfield 2008b), where leakage from a drain occurs asymmetrically due to a flow component q y , flow divergence may occur for q y = 0 due to an elevated reactor resistance and is symmetric about the x ‐ (and y ‐) axis. This latter situation is studied by Klammler and Hatfield (2009a), who give the condition R ≤ γ/γ ’ ( for absence of flow divergence, where γ/γ ′≈ [ k 2 /(1 − k 2 )] 1.1 is an approximation with a maximum error of ±5% for 0.1 < k 2 < 0.9, independent of the actual PRB type (i.e., including FG).…”

Section: Resultsmentioning

confidence: 99%

“…Previously developed PRB monitoring approaches (Klammler and Hatfield 2008a, 2009a) are also directly applicable to flow field solutions for DG PRBs presented. Klammler and Hatfield (2008b, 2009b) use PRB flow field solutions to study the problems of flow by‐pass and aquifer travel time distributions of groundwater and contaminants toward the reactor. Kacimov and Klammler (unpublished data) apply the present approach in a mathematically interesting PRB shape optimization context.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Solutions for Flow Fields near Drain‐and‐Gate Reactive Barriers

2010

View full text Add to dashboard Cite

Permeable reactive barriers (PRBs) are a popular technology for passive contaminant remediation in aquifers through installation of reactive materials in the pathway of a plume. Of fundamental importance are the degree of remediation inside the reactor (residence time) and the portion of groundwater intercepted by a PRB (capture width). Based on a two-dimensional conformal mapping approach (previously used in related work), the latter is studied in the present work for drain-and-gate (DG) PRBs, which may possess a collector and a distributor drain ("full" configuration) or a collector drain only ("simple" configuration). Inherent assumptions are a homogeneous unbounded aquifer with a uniform far field, in which highly permeable drains establish constant head boundaries. Solutions for aquifer flow fields in terms of the complex potential are derived, illustrated, and analyzed for doubly symmetric DG configurations and arbitrary reactor hydraulic resistance as well as ambient groundwater flow direction. A series of practitioner-friendly charts for capture width is given to assist in PRB design and optimization without requiring complex mathematics. DG PRBs are identified as more susceptible to flow divergence around the reactor than configurations using impermeable side structures (e.g., funnel-and-gate), and deployment of impermeable walls on drains is seen to mitigate this problem under certain circumstances.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Analytical Solutions for Flow Fields near Drain‐and‐Gate Reactive Barriers

2010

View full text Add to dashboard Cite

show abstract

“…In this manner, seepage through elliptical and rectangular PRBs has been studied in detail; see [9,10,15,23]. In the constructal approach, the design starts not from a given shape but from a given criterion (see [24][25][26] for other hydrogeological/geotechnical/petroleum engineering applications): we specify d (or Q) and determine what is the best shape of a PRB accomplishing the mission of plume interception.…”

Section: Model and Constructal Design Of A Highly Conductive Prbmentioning

confidence: 99%

“…Hydraulics of groundwater plays an important role in the design of PRBs (e.g., [8][9][10][11][12][13][14]). In particular, the position of the PRB with respect to the vector V 0 (the magnitude of which is V 0 ), the shape of the interface CME (denoted L) and the pair (m b , k b ) should be designed in such a manner that the PRB extends hydraulically across (i.e., transversal to the ambient flow) the targeted contamination plume, intercepts as much of the plume as possible (as quantified in the flow rate Q passing through the PRB), and retains the intercepted water in contact with the reactive material as long as possible.…”

Section: Introductionmentioning

confidence: 99%

Constructal design of permeable reactive barriers: groundwater-hydraulics criteria

et al. 2011

View full text Add to dashboard Cite

Unidirectional, steady-state, Darcian flow in a confined homogeneous aquifer is partially intercepted by a permeable reactive barrier (PRB), the shape of which is optimized with the following hydraulic criteria: seepage flow rate through a PRB (equivalent to the width and frontal area of the intercepted part of the plume in 2-D and 3-D cases, correspondingly) and travel time of a marked particle through the PRB interior along streamlines. The wetted perimeter, cross-sectional area and volume of the reactive material are selected as isoperimetric constraints. The PRB contour is modeled as either a constant head line (if the reactive material is much more permeable than the aquifer) or as a refraction boundary (if the reactive material has an arbitrary permeability), on which the hydraulic head and normal flux components in the barrier and aquifer are continuous. In the former case, the complex potential domain of the flow is a tetragon and a broad class of PRBs can be studied. In the latter case, analytical solutions are available for ellipses and ellipsoids (only these classes of shapes are considered in optimization). In the 2-D case and constant head PRB, a novel shape-control technique through the kernels of singular integrals is implemented: the Zhukovskii function is introduced; a Dirichlet boundary-value problem is solved for this function by setting the orientation (with respect to the incident flow direction) of the Darcian velocity vector on the PRB contour as a control function. Unlike similar controls for impermeable airfoils in aerodynamic design, the kernel has two 123 320 A. R. Kacimov et al. discontinuities, which reflect the flow topology near a hinge (stagnation) point and the PRB tip. The integral is evaluated for V-shaped and curve-shaped PRBs and parametric expressions for the contours are obtained resulting (for the latter case) in a "pointy banana" shape. In the class of a V-shaped PRB, it is proved that a straight-line barrier minimizes the perimeter if the plume width is fixed. In 2-and 3-D refracting PRBs, the Pilatovskii (ellipse) and Poisson (ellipsoid) solutions for the flow field inside and outside the PRB are used for obtaining explicit formulae for the magnitude of the velocity, which is uniform inside the PRB. Simple expressions for the longest travel time within the PRB and the discharge intercepted by it are obtained. The ellipse/ellipsoid axes ratio/ratios are used as control variables in optimization. Extrema are obtained and analyzed for different PRB-aquifer conductivity ratios and for varying angles between the incident velocity vector and the ellipse/ellipsoid axes.

show abstract

“…In analogy to the effect of flow divergence, which is due to an elevated reactor hydraulic resistance and may occur even for design flow direction, possible mixing of captured and bypassing flow inside the gravel pack may conduct contamination around the PRB. The problem of flow bypass is studied in more detail by Klammler and Hatfield [2008b]. In Figure 8 the flow fields for a PRB with VEWs of b / a = 2, w / a = 1 and infinite k r are shown for flow in the x direction (Figure 8a), y direction (Figure 8b) and arbitrary flow direction (Figure 8c).…”

Section: Analysis Of Flow Fields and Performance Monitoringmentioning

confidence: 99%

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

Klammler

Hatfield

2009

Water Resources Research

View full text Add to dashboard Cite

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.

show abstract

The problem of flow by-pass at permeable reactive barriers

Cited by 5 publications

References 6 publications

Analytical Solutions for Flow Fields near Drain‐and‐Gate Reactive Barriers

Analytical Solutions for Flow Fields near Drain‐and‐Gate Reactive Barriers

Constructal design of permeable reactive barriers: groundwater-hydraulics criteria

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

Contact Info

Product

Resources

About