Analytical solutions for one-phase seepage flows impeded by wellbore seals

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Steady, one-phase, plane and axisymmetric, Darcian seepage in a homogeneous rock adjacent to a partly isolated wellbore with annular seals is analytically studied. Water flows from an isobaric feeding contour and a fracture, which is kept at the same pressure as the feeding contour, to a wellbore. Partial isolation of the wellbore makes its wall a composition of intermittently arrayed no-flow boundaries, which model the wellbore seals, and isobaric surfaces, which model the annular compartments between the seals and a wellbore tubular on which the seals are mounted. Pressure drops from the aquifer (fracture) to the compartments and further to the borehole that generates a hierarchy of flows mathematically equivalent to the Toth [Freeze, R.A., Cherry, J.A., 1979. Groundwater. Prentice Hall, Englewood Cliffs] hydrogeological patterns of regional, intermediate and local groundwater flows on the scale of catchments. Conformal mappings of complex potential domains onto physical planes, where water seepage takes place, are used to tackle the fragments of the full feeding contour-fracture-sealed wellbore system. Explicit rigorous solutions for the flow characteristics (pressure and stream function) enable calculating optimal wellbore isolation with a criterion of minimal water flow rate from the fracture.

Original languageEnglish
Pages (from-to)67-76
Number of pages10
JournalJournal of Petroleum Science and Engineering
Volume64
Issue number1-4
DOIs
Publication statusPublished - Feb 2009

Fingerprint

Seepage
seepage
Seals
water flow
Water
Conformal mapping
Groundwater flow
pressure drop
Boreholes
Aquifers
cliff
Catchments
Pressure drop
groundwater flow
Groundwater
borehole
Rocks
Flow rate
aquifer
catchment

Keywords

  • complex variables
  • fracture
  • one-phase flow
  • seepage
  • stream function

ASJC Scopus subject areas

  • Fuel Technology
  • Geotechnical Engineering and Engineering Geology

Cite this

Analytical solutions for one-phase seepage flows impeded by wellbore seals. / Kacimov, Anvar R.; Marketz, Franz; Pervez, Tasneem.

In: Journal of Petroleum Science and Engineering, Vol. 64, No. 1-4, 02.2009, p. 67-76.

Research output: Contribution to journalArticle

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