A Well in a 'Target' Stratum of a Two-Layered Formation

The Muskat-Riesenkampf Solution Revisited

Yu V. Obnosov, R. G. Kasimova, A. R. Kacimov

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a 'target' layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the 'target' layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.

Original languageEnglish
Pages (from-to)437-457
Number of pages21
JournalTransport in Porous Media
Volume87
Issue number2
DOIs
Publication statusPublished - Mar 2011

Fingerprint

Laplace equation
Hydraulic conductivity
Surveying
Steady flow
Refraction
Drainage
Electrostatics
Flow rate
Hydraulics

Keywords

  • Analytical solution
  • Complex potential
  • Darcian velocity
  • Refraction

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

Cite this

A Well in a 'Target' Stratum of a Two-Layered Formation : The Muskat-Riesenkampf Solution Revisited. / Obnosov, Yu V.; Kasimova, R. G.; Kacimov, A. R.

In: Transport in Porous Media, Vol. 87, No. 2, 03.2011, p. 437-457.

Research output: Contribution to journalArticle

@article{71025257b6b749e39d419bf782c25509,
title = "A Well in a 'Target' Stratum of a Two-Layered Formation: The Muskat-Riesenkampf Solution Revisited",
abstract = "Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a 'target' layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the 'target' layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.",
keywords = "Analytical solution, Complex potential, Darcian velocity, Refraction",
author = "Obnosov, {Yu V.} and Kasimova, {R. G.} and Kacimov, {A. R.}",
year = "2011",
month = "3",
doi = "10.1007/s11242-010-9693-6",
language = "English",
volume = "87",
pages = "437--457",
journal = "Transport in Porous Media",
issn = "0169-3913",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - A Well in a 'Target' Stratum of a Two-Layered Formation

T2 - The Muskat-Riesenkampf Solution Revisited

AU - Obnosov, Yu V.

AU - Kasimova, R. G.

AU - Kacimov, A. R.

PY - 2011/3

Y1 - 2011/3

N2 - Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a 'target' layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the 'target' layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.

AB - Explicit analytical solutions are obtained in terms of hydraulic head (pressure) and Darcian velocity for a steady Darcian flow to a point/line sink and array of sinks with refraction of streamlines on a horizontal interface between two layers of constant hydraulic conductivities. The sinks are placed in a 'target' layer between a constant potential plane and interface. An equipotential surface, encompassing the sink represents a horizontal or vertical well, is reconstructed as a quasi-cylinder or quasi-sphere. The method of electrostatic images and theory of holomorphic functions are employed for obtaining series expansion solutions of two conjugated Laplace equations. If the conductivity of the 'target' layer is less than that of the super/sub-stratum, then there is a minimum of the flow rate into the well of a given size. Applications to agricultural drainage and surface DC-electrical resistivity surveying are discussed.

KW - Analytical solution

KW - Complex potential

KW - Darcian velocity

KW - Refraction

UR - http://www.scopus.com/inward/record.url?scp=79952735739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952735739&partnerID=8YFLogxK

U2 - 10.1007/s11242-010-9693-6

DO - 10.1007/s11242-010-9693-6

M3 - Article

VL - 87

SP - 437

EP - 457

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 2

ER -