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An analytical solution for linear elastic geomechanical responses in a layered vertical transversely isotropic medium.


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.


Academic chapter/article/Conference paper


  • Research Council of Norway (RCN) / 294369




  • Hong Yan
  • Joonsang Park
  • Rune Martin Holt
  • Audun Bakk


  • Norwegian University of Science and Technology
  • Norwegian Geotechnical Institute
  • SINTEF Industry / Applied Geoscience




American Rock Mechanics Association (ARMA)


57th U.S. Rock Mechanics/Geomechanics Symposium



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