How Heat Extraction Reshapes Subsurface Stresses: A Three‐Dimensional Analytical Study of Layered Geothermal Reservoirs

ABSTRACT This paper presents a three‐dimensional (3D) analytical solution for deformation and stress changes inside and outside a geothermal reservoir that is under a prescribed temperature change, derived based on the Hankel transform and thermoelastic constitutive equations. The geothermal reservoir is bounded between two isothermal layers, with different mechanical moduli considered. Unlike most existing analytical models that are restricted to one‐dimensional (1D) or two‐dimensional (2D) frameworks, assume homogeneous rock properties, or ignore interlayer stiffness differences, the proposed solution innovatively captures 3D thermoelastic responses, explicitly accounts for distinct mechanical moduli between the reservoir and bounding isothermal layers, and integrates boundary effects. The solution is based on Navier's static equilibrium equations and derived under the boundary conditions of stress and deformation continuity at the interfaces between rock layers. Considering a uniform temperature change within the geothermal reservoir, this study analyzes the influence patterns of key parameters, including the thickness‐to‐diameter ratio of the temperature‐varying volume, the stiffness ratio of rock layers on reservoir compaction and stress changes inside and outside the reservoir. The magnitude and orientation variations of principal stresses around the geothermal reservoir are presented. Studies indicate that subsurface heterogeneity and the thickness‐to‐diameter ratio of the temperature‐varying volume have significant effects on stress redistribution, reorientation, and reservoir compaction. Additionally, results also reveal the influence of boundary effects on reservoir compaction. Practically, this 3D analytical solution is able to serve as a quantitative tool to assist in estimating reservoir compaction magnitude and understanding stress reorientation patterns, providing a reference for evidence‐based decisions in geothermal reservoir management.