Constructal design of permeable reactive barriers: groundwater-hydraulics criteria

Abstract

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.

Use of Vegetable Fibers for PRB to Remove Heavy Metals from Contaminated Aquifers—Comparisons among Cabuya Fibers, Broom Fibers and ZVI

“…This type of test is essential for a correct dimensioning of a PRB, as it allows the kinetics of degradation of the pollutant considered, and then the thickness of the barrier to be defined. Indeed, the optimal thickness of reactive materials in a PRB is a trade-off between maximizing the removal efficiency and longevity and minimizing construction costs, namely minimum dimensions and cost of the reactive material [ 77 , 78 , 79 ]. In any case, it is advisable to determine the minimum thickness of reactive materials for a PRB longevity of not less than 10 years.…”

Constructal law of design and evolution: Physics, biology, technology, and society

“…88,89 Microreactors were developed by Mathieu-Potvin and Gosselin 90 and Chen et al 91 Microfluidic structures were studied by da Silva and coworkers. 92,93 Constructal design continues to be used in more classical applications such as shell and tube heat exchangers, 94 furnaces, 95 reactors [96][97][98][99] and distributors, [100][101][102] and maximum heat transfer density. 103,104 Boiling in dendritic channels was proposed by Bonjour and coworkers 105,106 and Liu et al 107 Industrial applications of constructal design were reported for steam generators, 108,109 steam turbines, 110 furnaces for heating streams of solid metal, 111,112 cross-flow heat exchangers, 113 and solar power plants.…”

Removal of Heavy Metals from Contamined Aquifers by Vegetable Fibers. Comparisons among Cabuya Fibers, Broom Fibers and ZVI

“…This type of test is essential for a correct dimensioning of a PRB, as it allows the kinetics of degradation of the pollutant considered, and then the thickness of the barrier to be defined. Indeed, the optimal thickness of reactive materials in a PRB is a trade-off between maximizing the removal efficiency and longevity and minimizing construction costs, namely minimum dimensions and cost of the reactive material [55][56][57]. In any case, it is advisable to determine the minimum thickness of reactive materials for a PRB longevity of not less than 10 years.…”