Evaluation of Wellbore Stability by Small Parameter Perturbation Nonlinear Elastoplastic Model

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Abstract Wellbore instability is a frequent occurrence during drilling and a popular research topic among petroleum workers. Most of the previous studies simplified the hardening stage and ignored or classified it into the elastic stage. Engineering practice shows that the total stress–strain process of rock can more truly reflect the bearing and deformation characteristics of rock. This study establishes a total stress–strain constitutive model by combining the perturbation index equation with the linear elastic equation. Additionally, the physical model of rock around the well is presented using the total deformation theory for the plastic zone. The stress field of the rock surrounding the well is analyzed based on the physical model of the rock surrounding the well, taking into account the influence of rock strength and geostress state. The relationship between rock strength, geostress state, drilling fluid density, and plastic radius is given. The calculation method of drilling fluid density limit is also given. The practical application demonstrates that the stability of a borehole wall can be evaluated by analyzing the size and direction of the plastic radius, as well as the distribution of radial, tangential, and shear stress for various combinations of stress states and rock strengths. The maximum shear stress is always found in the softening zone, which is also the region where wellbore instability is most likely to happen. Therefore, the area within the softening radius is regarded as an unstable area, and the softening radius can be used to determine the range of wellbore instability.