On the Derivation of Closed-Form Expressions for Displacements, Strains, and Stresses Inside Poroelastic Reservoirs

On the Derivation of Closed-Form Expressions for Displacements, Strains, and Stresses Inside Poroelastic Reservoirs

Cornelissen, P. (TU Delft Reservoir Engineering; Wageningen University & Research)
Meulenbroek, B.J. (TU Delft Mathematical Physics)
Jansen, J.D. (TU Delft Reservoir Engineering)

2024

We critically review the derivation of closed-form analytical expressions for elastic displacements, strains, and stresses inside a subsurface reservoir undergoing pore pressure changes using inclusion theory. Although developed decades ago, inclusion theory has been used recently by various authors to obtain fast estimates of depletion-induced and injection-induced fault stresses in relation to induced seismicity. We therefore briefly address the current geomechanical relevance of this method, and provide a numerical example to demonstrate its use to compute induced fault stresses. However, the main goal of our paper is to correct some erroneous assumptions that were made in earlier publications. While the final expressions for the poroelastic stresses in these publications were correct, their derivation contained conceptual mistakes due to the mathematical subtleties that arise because of singularities in the Green's functions. The aim of our paper is therefore to present the correct derivation of expressions for the strains and stresses inside an inclusion and to clarify some of the results of the aforementioned studies. Furthermore, we present two conditions that the strain field must satisfy, which can be used to verify the analytical expressions.

analytical solution
Green's function
inclusion theory
Leibniz integral rule
poroelasticity

http://resolver.tudelft.nl/uuid:1200e5a2-966c-44d8-ad2b-0084ac57b721

https://doi.org/10.1029/2023JB027733

2169-9313

JGR Solid Earth, 129 (2)

Institutional Repository

journal article

© 2024 P. Cornelissen, B.J. Meulenbroek, J.D. Jansen