Similarity solution of axisymmetric flow in porous media

L. Li, David Anthony Lockington, Marc B. Parlange, Frank Stagnitti, Dong-Sheng Jeng, John S. Selker, A. S. Telyakovskiy, David Andrew Barry, J-Y Parlange

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14 Citations (Scopus)

Abstract

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

Original languageEnglish
Pages (from-to)1076-1082
Number of pages7
JournalAdvances in Water Resources
Volume28
Issue number10 SPEC. ISS.
DOIs
Publication statusPublished - Oct 2005
Externally publishedYes

Keywords

  • Axisymmetric flow
  • Boussinesq equation
  • Density-dependent flow
  • Drilling mud invasion
  • Groundwater pumping
  • Sparging

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