This paper studies vertical stress redistributions around wellbores and reservoirs due to yielding and plastic deformations. The analyses in this paper compare between predictions of elastic, poroelastic, elastoplastic, and poroplastic material models. Two elastoplastic models are used: 1) The Drucker Prager Model (DP), and 2) The Mohr Coulomb Model (MC); while The Modified Cam Clay Model (MCC) is used as the poroplastic model. Although all models are calibrated to the behavior of an analogue shale using drained triaxial compression tests; the models give different predictions in other modes of shearing and other drainage conditions. Two geomechanical problems are considered in the paper: 1) The Wellbore Stability Problem, and 2) The Reservoir Depletion Problem; both of which are analyzed using the finite element commercial software ABAQUS. The wellbore problem considers an undrained vertical wellbore in uniform horizontal stress conditions using a 2D plane strain model. Analyses show that the MC model gives safe predictions and comparable results of vertical stress redistribution to that of the MCC model. The reservoir problem considers a circular disc-like reservoir using a 2D axisymmetric model. The initial stress distribution is considered; once assuming constant far field stresses, and also including the effect of variation due to gravity. Vertical stress redistribution is significant when plastic pore collapse is considered by using the MCC model for reservoir material. Analysis shows that assuming constant far field stresses is a good approximation to the reservoir depletion problem.
The geomechanical analysis of wellbores and reservoirs usually includes the assumption of constant vertical stresses. The safe mud window for stable wellbores is determined to prevent the hoop stresses from causing a breakout, ignoring possible change in vertical stresses. Dunayevsky et al.  formulated a semi-analytical solution to the thick wall cylinder problem. In this solution the vertical stresses are assumed constant. Zoback  formulated the DARS (Deformation Analysis in Reservoir Space) methodology to measure the stress path and compaction of a depleting reservoir. This stress path is considered in the reservoir space where only horizontal stresses vary with pore pressures. The idea of constant vertical stresses is plausible because at any given level the vertical stresses would be the weight of the overburden which is not expected to change. If the theory of elasticity is applied to the reservoir depletion problem, the vertical stresses do not change for infinitely long reservoirs. Segal and Fitzgerald  stated that for a reservoir of aspect ratio 10:1, the change in vertical stress can be ignored as predicted by the theory of elasticity.