TY - JOUR
T1 - On the Derivation of Closed-Form Expressions for Displacements, Strains, and Stresses Inside Poroelastic Reservoirs
AU - Cornelissen, P.
AU - Meulenbroek, B. J.
AU - Jansen, J. D.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - analytical solution
KW - Green's function
KW - inclusion theory
KW - Leibniz integral rule
KW - poroelasticity
UR - http://www.scopus.com/inward/record.url?scp=85185696402&partnerID=8YFLogxK
U2 - 10.1029/2023JB027733
DO - 10.1029/2023JB027733
M3 - Article
AN - SCOPUS:85185696402
SN - 2169-9313
VL - 129
JO - Journal of Geophysical Research: Solid Earth
JF - Journal of Geophysical Research: Solid Earth
IS - 2
M1 - e2023JB027733
ER -