10 Citations (Scopus)

Abstract

A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.

Original languageEnglish (US)
Pages (from-to)103-122
Number of pages20
JournalJournal of Engineering Mathematics
Volume92
Issue number1
DOIs
StatePublished - Jun 1 2015

Fingerprint

Conductivity
Analytical Solution
Fluid
Fluids
Fluxes
Confocal
Pressure Gradient
Flow Pattern
Pressure gradient
Dimensionless
Flow patterns
Superposition
Simplicity
Vertical
Numerical Solution
Entire
Converge

Keywords

  • Finite fracture conductivity
  • Fluid production mechanism
  • Porous media flow
  • Pressure gradient singularity

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Analytical solution and mechanisms of fluid production from hydraulically fractured wells with finite fracture conductivity. / Jin, Yan; Chen, Kangping; Chen, Mian.

In: Journal of Engineering Mathematics, Vol. 92, No. 1, 01.06.2015, p. 103-122.

Research output: Contribution to journalArticle

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abstract = "A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.",
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AU - Jin, Yan

AU - Chen, Kangping

AU - Chen, Mian

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N2 - A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.

AB - A comprehensive study of the physical mechanisms of fluid production from a well intersected by a narrow elliptically shaped vertical fracture with finite fracture conductivity is carried out using a newly obtained analytical solution. The flow pattern, flux density distribution along the fracture surface, and fluid production rate are analyzed systematically with respect to finite fracture conductivity. The simplicity of the new analytical solution reveals many physical insights not attainable from existing analytical or numerical solutions. It is shown that the nearly singular pressure gradient developed at the fracture tip induces the reservoir flow to converge to and focus at the tip region, promoting flux density along the entire fracture surface and enhancing the production rate. It is established that the flow in the reservoir is a superposition of two basic flows, a confocal elliptical flow responsible for the fluid production, and a redistributive nonproducing flow induced by a finite fracture conductivity that draws fluids out of the fracture from the part near the tip and redeposits them back to the part of the fracture close to the wellbore. An explicit analytical formula for the fluid production rate is also derived that exhibits a simple dependency on the dimensionless fracture conductivity.

KW - Finite fracture conductivity

KW - Fluid production mechanism

KW - Porous media flow

KW - Pressure gradient singularity

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