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

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

Cornelissen, P. (TU Delft Reservoir Engineering)
Meulenbroek, B.J. (TU Delft Mathematical Physics)
Jansen, J.D. (TU Delft Civil Engineering & Geosciences)

Civil Engineering & Geosciences

2023

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.

inclusion theory
poroelasticity
Fubini
Leibniz integral rule

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

Delft University of Technology

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.

Institutional Repository

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© 2023 P. Cornelissen, B.J. Meulenbroek, J.D. Jansen