Minimum horizontal stress in an inelastic fluid-saturated reservoir and a constitutive instability development during fluid production

We investigate the impact of fluid drainage on the stress–strain state of a fluid–saturated reservoir. Our focus is on the transition from an elastic to an elastoplastic state of the rock mass and the appearance of constitutive instability during plastic yield. We determine the onset of inelastic deformations using the Drucker–Prager yield criterion and Eaton’s solution for an elastic medium. Our findings illustrate that the transition to an elastoplastic state occurs with increasing depth and decreasing pore fluid pressure at a fixed depth. When dealing with inelastic rock deformation, we analytically solve the Prandtl–Reuss equations under uniaxial strain conditions to obtain the distribution of minimum horizontal stress within the reservoir characterized by both hydrostatic and abnormally high pore fluid pressure. Furthermore, for a formation undergoing inelastic deformations, we identify the critical value of the plastic hardening modulus at which material instability emerges. The applied analytical approach relies on the Prandtl–Reuss equations, Darcy’s law, and continuity equation for an incompressible fluid.