On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion

Pavan Cornelissen; Bernard J. Meulenbroek; Jan-Dirk Jansen

doi:10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8

On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion

Pavan Cornelissen, Bernard J. Meulenbroek, Jan-Dirk Jansen^*

^*Corresponding author for this work

Research output: Book/Report › Report › Scientific

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Abstract

This note provides the derivation of closed-form expressions for elastic displacements, strains, and stresses inside an inclusion. Jansen et al. (2019) and Wu et al. (2021) obtained correct expressions for the stresses inside an inclusion, but their derivation of these expressions contained mistakes. In this note, the correct derivation of expressions for the stresses inside an inclusion is presented and some of the results of the aforementioned studies are clarified.

Original language	English
Publisher	Delft University of Technology
Number of pages	12
DOIs	https://doi.org/10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8
Publication status	Published - 2023

Bibliographical note

This note provides corrections to results published in:

J.D. Jansen, P. Singhal, and F.C. Vossepoel. Insights from closed-form expressions for injection- and production-induced stresses in displaced faults. Journal of Geophysical Research - Solid Earth, 124:7193{7212, 2019. URL https://doi.org/10.1029/2019JB017932.

H. Wu, V. Vilarrasa, S. De Simone, M. Saaltink, and F. Parisio. Analytical solution to assess the induced seismicity potential of faults in pressurized and depleted reservoirs. Journal of Geophysical Research - Solid Earth, 126: e2020JB020436, 2021. URL https://doi.org/10.1029/2020JB020436.

Funding

This publication is part of the project ‘Science4Steer: a scientific basis for production and reinjection strategies to minimize induced seismicity in Dutch gas fields’ (with project number DEEP.NL.2018.046) of the research programme 'DeepNL' which is financed by the Dutch Research Council (NWO).

Keywords

inclusion theory
poroelasticity
Fubini
Leibniz integral rule

Access to Document

10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8Licence: CC BY

On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusionFinal published version, 269 KBLicence: CC BY

Cite this

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title = "On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion",

abstract = "This note provides the derivation of closed-form expressions for elastic displacements, strains, and stresses inside an inclusion. Jansen et al. (2019) and Wu et al. (2021) obtained correct expressions for the stresses inside an inclusion, but their derivation of these expressions contained mistakes. In this note, the correct derivation of expressions for the stresses inside an inclusion is presented and some of the results of the aforementioned studies are clarified.",

keywords = "inclusion theory, poroelasticity, Fubini, Leibniz integral rule",

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note = "This note provides corrections to results published in: J.D. Jansen, P. Singhal, and F.C. Vossepoel. Insights from closed-form expressions for injection- and production-induced stresses in displaced faults. Journal of Geophysical Research - Solid Earth, 124:7193{7212, 2019. URL https://doi.org/10.1029/2019JB017932. H. Wu, V. Vilarrasa, S. De Simone, M. Saaltink, and F. Parisio. Analytical solution to assess the induced seismicity potential of faults in pressurized and depleted reservoirs. Journal of Geophysical Research - Solid Earth, 126: e2020JB020436, 2021. URL https://doi.org/10.1029/2020JB020436.",

year = "2023",

doi = "10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8",

language = "English",

publisher = "Delft University of Technology",

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AU - Cornelissen, Pavan

AU - Meulenbroek, Bernard J.

AU - Jansen, Jan-Dirk

N1 - This note provides corrections to results published in: J.D. Jansen, P. Singhal, and F.C. Vossepoel. Insights from closed-form expressions for injection- and production-induced stresses in displaced faults. Journal of Geophysical Research - Solid Earth, 124:7193{7212, 2019. URL https://doi.org/10.1029/2019JB017932. H. Wu, V. Vilarrasa, S. De Simone, M. Saaltink, and F. Parisio. Analytical solution to assess the induced seismicity potential of faults in pressurized and depleted reservoirs. Journal of Geophysical Research - Solid Earth, 126: e2020JB020436, 2021. URL https://doi.org/10.1029/2020JB020436.

PY - 2023

Y1 - 2023

N2 - This note provides the derivation of closed-form expressions for elastic displacements, strains, and stresses inside an inclusion. Jansen et al. (2019) and Wu et al. (2021) obtained correct expressions for the stresses inside an inclusion, but their derivation of these expressions contained mistakes. In this note, the correct derivation of expressions for the stresses inside an inclusion is presented and some of the results of the aforementioned studies are clarified.

AB - This note provides the derivation of closed-form expressions for elastic displacements, strains, and stresses inside an inclusion. Jansen et al. (2019) and Wu et al. (2021) obtained correct expressions for the stresses inside an inclusion, but their derivation of these expressions contained mistakes. In this note, the correct derivation of expressions for the stresses inside an inclusion is presented and some of the results of the aforementioned studies are clarified.

KW - inclusion theory

KW - poroelasticity

KW - Fubini

KW - Leibniz integral rule

UR - https://doi.org/10.1029/2019JB017932

UR - https://doi.org/10.1029/2020JB020436

U2 - 10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8

DO - 10.4233/uuid:e2f21e31-3221-4d61-bb97-c74bdd3567a8

M3 - Report

BT - On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion

PB - Delft University of Technology

ER -

On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Insights From Closed-Form Expressions for Injection- and Production-Induced Stresses in Displaced Faults

Matlab files used to produce the figures in the publication: On the Derivation of Closed-Form Expressions for Displacements, Strains and Stresses Inside Poroelastic Reservoirs

Cite this

On the derivation of closed-form expressions for displacements, strains and stresses inside a poroelastic inclusion

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Research output

Insights From Closed-Form Expressions for Injection- and Production-Induced Stresses in Displaced Faults

Datasets

Matlab files used to produce the figures in the publication: On the Derivation of Closed-Form Expressions for Displacements, Strains and Stresses Inside Poroelastic Reservoirs

Cite this