Analytical Solution to Study Depletion/Injection Rate on Induced Wellbore Stresses in an Anisotropic Stress Field

Abstract

During production or injection, the state of stresses within the reservoir as well as around the wellbore changes. It is therefore important to evaluate the impact of the induced stresses on stability of wellbores. This study proposes an analytical solution to estimate the influence of production or injection rate on stresses around a wellbore in an anisotropic stress field. For considering the effect of production/injection rate, pseudo steady state flow was assumed within the reservoir that occurs more frequently than transient or steady state flow in a reservoir with an expanding drainage radius. Until now stress equations have not been developed in which the effect of production/injection rate being included. The results showed that the impact of the depletion and injection rate on induced stresses around the wellbore is significant and should be considered in the geomechanical analysis especially in low permeability reservoirs. Application of the proposed solution on a typical sandstone reservoir showed that in relatively high production rate, the radial and tangential stresses near wellbore decrease whereas the vertical and pore pressure increase. An opposite trend was observed for the effect of injection rate on near wellbore stresses. This results are consistent with field observation and means that in rapid production, the vertical stress will increase and horizontal stresses will decrease leading to surface subsidence.