An Analytical Solution for Linear Elastic Geomechanical Responses in a Layered Vertical Transversely Isotropic Medium

ABSTRACT The isotropic homogenous assumption in the conventional Geertsma model is often contradicted by reality because the rock properties in the overburden are typically anisotropic and often can be quite different from the reservoir. Thus, we present an analytical solution that extends Geertsma's solution and can consider layered subsurface, including anisotropic elasticity. Namely, five independent parameters are assigned in each anisotropic layer in this analytical model. The derived functions are expressed in terms of both displacements and stress fields accounting for any number of layers. Different from the original Geertsma model, this model also describes horizontal stress changes inside the reservoir. We assess the analytical solution's performance, advantages, but also limitations by comparing it to finite-element numerical modelling results in three cases. The results of the analytical solution agree well with those of the numerical solution for both fully anisotropic and isotropic cases. It is also learned that side-burden has a minor impact on stress and displacements for the case with anisotropic surrounding around a depleted isotropic reservoir. The analytical solution enables us to achieve sufficiently accurate results with low computational cost and be focused on the essential features of the Geertsma-type geomechanical problems. INTRODUCTION Pore pressure changes due to fluid injection for underground carbon storage or depletion for hydrocarbon production can cause stress redistribution in the subsurface. Therefore, a quantitative understanding of the geomechanical changes in the subsurface is essential for safe drilling and carbon storage processes. ‘Stress path’ is commonly used to help understand the changes in the stress state within the rocks around or inside an injected or depleted reservoir. For the overburden, the stress path coefficient κov is defined as the ratio between total horizontal stress change ΔSr and total vertical stress change ΔSz for an axisymmetric model: (Equation) The value of κov corresponds to different stress change scenarios. For example, three values of κov −0.5, 0, and 1 correspond to constant mean stress (CMS) change, uniaxial stress change, and isotropic stress change, respectively. Studying the stress path is crucial for safe reservoir operation and can help design monitoring strategies to prevent geomechanical instability and other risks.