Analytical solution approach for geomechanical response of 3-D geological model

Understanding geomechanical response to pore pressure changes in subsurface structures is crucial for safe drilling and carbon storage operations. One of the most recognized analytical geomechanical models to understand overburden geomechanical responses to reservoir pore pressure changes is Geertsma's analytical solution, which used the 'nucleus of strain' concept to quantify displacements and changes in stress field in the surroundings as a result of reservoir depletion. However, the Geertsma solution is limited to isotropic conditions, no contrast between reservoir and surroundings, and homogeneous pore pressure changes, which do not fully capture heterogeneity and anisotropy of real-world subsurface with horizontally layered structures. Shale, as one of the most common caprock, exhibits vertically transverse isotropic (VTI) properties. Our work aims to enhance the ability of analytical modelling to accommodate more realistic scenarios for considering topographic changes in the subsurface. It is based on a semi-analytical solution that extends the Geertsma solution to accommodate static VTI properties with five independent elastic stiffnesses in the surroundings of the reservoir. This extension significantly enhances the ability of the model to represent the vertical stiffness variations characteristic of realistic subsurface conditions. We have applied the extended Geertsma solution through linear superposition to adapt our model for practical use in scenarios with inhomogeneous pore pressure distributions and 3-D variations in rock stiffness. We validated deformation results from our linear superposition approach by comparing them with those from a finite element numerical method under multiple scenarios. This helped evaluate the performance of the approach and identify its key limitations. After validation, we applied our approach to the Valhall field, which is known for its significant subsidence and considering complex topography. The practical application highlighted the approach's capability to accurately model realistic subsidence changes, demonstrating its utility for complex geomechanical assessments and the potential to be linked with geophysical monitoring.