Analytical expressions for the hydraulic design of continuous permeable reactive barriers

Craig, James R.; Rabideau, Alan J.; Suribhatla, R. M.

doi:10.1016/j.advwatres.2005.05.006

Cited by 25 publications

(29 citation statements)

References 13 publications

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“…This may be attributed to the fact that simple CW PRBs allow flow through the sides of the reactor, which is not considered as flow by-pass according to the present definition. In this context it is required to recall the discussion about major and minor capture widths for simple CW PRBs as given in [6,7]. 3 shows α f in dependence of k 2 and e 2 for the PRB configurations of figs.…”

Section: Resultsmentioning

confidence: 99%

“…2 and 3 graphically represent results from eqns (3), (6) and (8) and allow for easy determination of the angle α f at which flow by-pass first occurs. The dimensionless parameters k and e facilitate an efficient and closed form representation of results for α f and are given by [7,8] for the range of PRB types discussed.…”

Section: Resultsmentioning

confidence: 99%

“…1(b)) and negligible hydraulic losses in the reactor. The respective relationship is described by eqn (6), where e for each k is determined from [8] for a hydraulic resistance R = 0 [-] of the reactor. Since k is the same for simple CW PRBs and CW PRBs with impermeable side walls of equal aspect ratio, fig.…”

Section: Resultsmentioning

confidence: 99%

“…The problem of flow by-pass as defined by Craig et al [6] is concerned with deviations of the ambient groundwater flow direction from the general design direction perpendicular to a PRB and the resulting effect that some of the captured flow may leave the reactor through the up-gradient side of the PRB without crossing the reactor. This may lead to contaminant divergence around a PRB and, hence, non-compliance with remediation goals.…”

Section: Introductionmentioning

confidence: 99%

“…Fig. 1(a) corresponds to the particular case of a simple CW PRB, where flow can enter and leave through the side walls (see related discussion about major and minor capture widths in [6] and Klammler and Hatfield [7]). The flow fields of fig.…”

Section: Introductionmentioning

confidence: 99%

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The problem of flow by-pass at permeable reactive barriers

Klammler

Hatfield

2008

WIT Transactions on the Built Environment

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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. An analytical approach in two dimensions has been introduced that allows for the determination of the flow fields and capture zones near PRBs of different types. The present work uses this approach to investigate the problem of flow by-pass, which is when a portion of flow both enters and leaves the PRB through the upgradient side of the reactor without crossing it. This occurs when a significant ambient flow component exists parallel to the PRB and may lead to contaminant flow divergence around the PRB. Maximum permissible deviations of the ambient groundwater flow direction are defined for a range of PRB types in order to avoid by-pass. Results show for rectangular continuous wall reactors, deviations in the design ambient groundwater flow direction become even more important as the reactor becomes more elongated perpendicular to that direction. This undermines the typical engineering assumption that a PRB longer than the transverse width of the plume is sufficient for plume intercept and treatment. The addition of perpendicular funnel arms or velocity equalization walls at the reactor acts favorably against flow by-pass. For drain and gate PRBs, susceptibility to flow by-pass may be reduced by increasing the separation of collector and distribution drains. An increase in the hydraulic resistance of the reactor increases the possibility of flow by-pass.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The problem of flow by-pass at permeable reactive barriers

Klammler

Hatfield

2008

WIT Transactions on the Built Environment

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Current awareness

2006

Hydrol. Process.

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Constructal design of permeable reactive barriers: groundwater-hydraulics criteria

et al. 2011

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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.

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Analytical expressions for the hydraulic design of continuous permeable reactive barriers

Cited by 25 publications

References 13 publications

The problem of flow by-pass at permeable reactive barriers

The problem of flow by-pass at permeable reactive barriers

Current awareness

Constructal design of permeable reactive barriers: groundwater-hydraulics criteria

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