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
Earth and Space Science Open Archive This preprint has been submitted to and is under consideration at Water Resources Research. ESSOAr is a venue for early communication or feedback before peer review. Data may be preliminary.Learn more about preprints preprintOpen AccessYou are viewing the latest version by default [v1]Saturated Water Storage in Shallow Perched Aquifer With Evapotranspiration From the Phreatic Surface and Unsaturated Lacunae: the Saint-Venant Theory RevisitedAuthorsFaritAvkhadievAnvar RKacimoviDSee all authors Farit Avkhadievobachevsky Institute of Mathematics and Mechanics, Kazan Federal Universityview email addressThe email was not providedcopy email addressAnvar R KacimoviDCorresponding Author• Submitting AuthorSultan Qaboos UniversityiDhttps://orcid.org/0000-0003-2543-3219view email addressThe email was not providedcopy email address
Abstract An analytical solution is obtained for steady 2‐D potential seepage flow from a nonclogged and nonlined soil channel into a highly permeable porous layer, with phreatic surfaces tapering toward a horizontal interface with a subjacent low‐permeable formation. Along this boundary, a vertical component of the Darcian velocity vector equals the formation saturated hydraulic conductivity. The image of the physical flow domain in the hodograph plane is a circular polygon, a triangle or digon in a limiting case of a “phreatic jet” impinging on the low‐permeable substratum. The polygon is mapped onto an auxiliary half plane, where the complex physical coordinate and complex potential are reconstructed by the Polubarinova‐Kochina method, i.e., by solution of a Riemann BVP. The seepage flow rate from the channel, free surfaces, and a saturated (water‐logged) area are found for different thicknesses of the top layer, channel widths, and conductivity ratios of the two strata. In particular, the earlier results of Brock, Kirkham, and Youngs, which are based on a numerical solution, Dupuit‐Forchheimer (DF) approximation, and approximate potential model, are confirmed in the full 2‐D models. Sufficiently far from the channel, the phreatic surface and interface make a wedge. For a sufficiently deep substratum, three zones are analytically distinguished: an almost vertical 1‐D descending flow, an almost wedge‐configured 1‐D flow, and an essentially 2‐D zone in between, where neither a standard infiltration theory nor DF analysis are valid.
Abstract A study is made of a steady, two‐dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens‐shaped static volume of a heavier saline water (DNAPL‐dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh‐Sedov integral representation of a mixed boundary‐value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small‐thickness bedrock‐spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed‐curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary‐value problem.
A porous barrier bounded by two confocal ellipses is filled with material of a hydraulic conductivity different from the ambient one in order to control the flow rate inside. Optimization problems are solved by describing the flow through a medium consisting of zones of different properties. For three-component composites, viz. three zones demarcated by two confocal ellipses, an explicit rigorous solution of refraction problems for potential fields of Darcian 2-D saturated flows is used. An aquifer, an elliptical 'core' and an elliptical annulus, which serves as a liner of the core, have contrasting hydraulic conductivities (control variables). The magnitude of the velocity in the core, total flow rate, travel time along streamlines, hydraulic gradient in the core are objectives in optimization. A single maximum of the magnitude of velocity in the 'core' is found at a certain conductivity of the annulus, similarly to the Strack circular annulus refracting a unidirectional flow. This maximum can be higher or lower than the velocity at infinity, i.e. the liner can amplify or lessen the incident flow. Applications to in situ ore leaching, permeable reactive barriers, porous waste repositories, aquifer permeameters and formation damage due to suffusion in the vicinity of pumping wells are discussed.Abbreviations: ISL: in situ leaching; RAF: reduction–amplification factor.
An optimal shape design problem for an empty drainage ditch is solved and it is shown that a semicircle intercepting saturated seepage from two constant potential rays is a contour of constant Darcian velocity and of maximal excavated volume at a given flow rate and ditch width. The corresponding family of isobars belongs to the class of conchoids of Nicomedes. The optimal flow is generated by a hydrodynamic dipole placed in a gravitational field.
