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.

中文翻译：

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非弹性流体饱和油藏中的最小水平应力和流体生产过程中的本构失稳发展

我们研究了流体排放对流体饱和储层应力应变状态的影响。我们的重点是岩体从弹性状态到弹塑性状态的转变以及塑性屈服过程中本构不稳定的出现。我们使用 Drucker–Prager 屈服准则和伊顿弹性介质解来确定非弹性变形的开始。我们的研究结果表明，随着深度的增加和固定深度处孔隙流体压力的降低，会发生向弹塑性状态的转变。在处理非弹性岩石变形时，我们在单轴应变条件下解析求解 Prandtl-Reuss 方程，以获得以静水压力和异常高孔隙流体压力为特征的储层内最小水平应力的分布。此外，对于经历非弹性变形的地层，我们确定了出现材料不稳定的塑性硬化模量的临界值。所应用的分析方法依赖于普朗特-罗伊斯方程、达西定律和不可压缩流体的连续性方程。