Hydraulically optimal porous liner around a porous lens: Strack’s problem revisited

Anvar Kassimov, Yurii Obnosov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
JournalISH Journal of Hydraulic Engineering
DOIs
Publication statusAccepted/In press - Jan 1 2018

Fingerprint

liner
Lenses
Hydraulic conductivity
Aquifers
Leaching
Flow rate
ellipse
Travel time
Refraction
Ores
hydraulic conductivity
leaching
Hydraulics
aquifer
reactive barrier
permeameter
potential field
Composite materials
refraction
repository

Keywords

  • erosional stability and suffusion
  • extreme velocity/flow rate/travel time/average hydraulic gradient
  • residence time of groundwater in contamination/remediation
  • Seepage with refraction on aquifer heterogeneities

ASJC Scopus subject areas

  • Environmental Engineering
  • Civil and Structural Engineering
  • Water Science and Technology
  • Fluid Flow and Transfer Processes

Cite this

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abstract = "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.",
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