Generalized poroelastic wellbore problem

Amin Mehrabian, Younane N. Abousleiman

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity.

Original languageEnglish (US)
Pages (from-to)2727-2754
Number of pages28
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Volume37
Issue number16
DOIs
StatePublished - Nov 1 2013

Fingerprint

pore pressure
stress field
poroelasticity
fluid
Pore pressure
plane strain
porous medium
boundary condition
probe
permeability
disturbance
Fluids
sampling
Transient analysis
Porous materials
Earth (planet)
Boundary conditions
Sampling
effect
comparison

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Materials Science(all)
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials

Cite this

@article{b9fa0053368f4208b2abcfdd90fd997e,
title = "Generalized poroelastic wellbore problem",
abstract = "This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity.",
author = "Amin Mehrabian and Abousleiman, {Younane N.}",
year = "2013",
month = "11",
day = "1",
doi = "10.1002/nag.2160",
language = "English (US)",
volume = "37",
pages = "2727--2754",
journal = "International Journal for Numerical and Analytical Methods in Geomechanics",
issn = "0363-9061",
publisher = "John Wiley and Sons Ltd",
number = "16",

}

Generalized poroelastic wellbore problem. / Mehrabian, Amin; Abousleiman, Younane N.

In: International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 37, No. 16, 01.11.2013, p. 2727-2754.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Generalized poroelastic wellbore problem

AU - Mehrabian, Amin

AU - Abousleiman, Younane N.

PY - 2013/11/1

Y1 - 2013/11/1

N2 - This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity.

AB - This paper presents a novel analytical solution to the transient, z-dependent, and asymmetric problem of an infinite wellbore drilled into a fluid-saturated porous medium. The formulations are based on Biot's linear theory of poroelasticity, in which the dependency of poroelastic field variables to spatial coordinates as well as time domain is considered in the most general form. This gives flexibility to the solution in cases that cannot be analyzed using the conventional plane strain or symmetric models. One such case is when calculating the stress variations around an inclined wellbore where the far-field stresses are acting over a finite vertical section. The results of our solution to this case with a three-dimensional state of far-field stress are used to analyze the stability of inclined wellbores passing through abnormally stressed formations. The presented solution is capable of finding expressions for fundamental solutions with stress or flow boundary conditions at the wellbore. These solutions are here adopted to analyze the pressure disturbances generated by multiprobe formation tester, a standard wireline device that is designed for downhole fluid sampling as well as estimating the directional permeabilities of subsurface earth formations. A comparison with the conventional solution for the relevant pressure diffusion equation indicates that the poroelastic effect is relatively significant in relation to the transient response of the pore pressure. Further, it is shown that the finite dimensions of sink probe would, to a great extent, contribute to the formation's pore pressure variations at its immediate proximity.

UR - http://www.scopus.com/inward/record.url?scp=84885434674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885434674&partnerID=8YFLogxK

U2 - 10.1002/nag.2160

DO - 10.1002/nag.2160

M3 - Article

AN - SCOPUS:84885434674

VL - 37

SP - 2727

EP - 2754

JO - International Journal for Numerical and Analytical Methods in Geomechanics

JF - International Journal for Numerical and Analytical Methods in Geomechanics

SN - 0363-9061

IS - 16

ER -