Robust analytic solution for predicting reservoir elastic strain and stress responses
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Changes in the pore-pressure field of porous media play a critical role in several geomechanics problems involving fluid migration, such as hydrocarbon production and geological CO₂ sequestration. These pore pressure variations trigger mechanical responses, including displacements, strains and stresses. Analytical solutions offer a promising alternative for efficiently predicting mechanical responses with a computational effort much lower than that of sophisticated numerical methods. This work develops an enhanced analytical solution for strains and stresses resulting from internal pressure changes in elastic homogeneous media. The proposed methodology is based on the nucleus of strain approach initially proposed by Geertsma [1]. The numerical evaluation of the proposed solution is carried out through a suitable integration process, following the scheme presented in [2]. The solution is generalized to consider an arbitrary distribution of pore-pressure changes. Numerical examples demonstrate excellent agreement between the proposed solution and both analytical and numerical reference results.
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