Finite element analysis for wellbore stability of transversely isotropic rock with hydraulic-mechanical-damage coupling

The finite element analysis (FEA) technology by hydraulic-mechanical-damage (HMD) coupling is proposed in this paper for wellbore stability analysis of transversely isotropic rock, developed basing on the recently established FEA technology for isotropic rock. The finite element (FE) solutions of numerical wellbore model, damage tensor calculation and Pariseau strength criterion for transversely isotropic rock are developed for researching the wellbore failure characteristics and computing the collapse and fracture pressure of laminated rock as shale reservoirs. The classic Biot constitutive for rock as porous medium is introduced to establish a set of FE equations coupling with elastic solid deformation and seepage flow. To be in accord with the inclined wellbore situation, the coordinate transformation for global, wellbore, in-situ stress and transversely isotropic formation coordinate systems is established for describing the in-situ stress field and the results in laminated rock. To be in accord with the practical situation, a three-dimensional FE model is developed, in which several other auxiliary technologies are comprehensively utilized, e.g., the typical Weibull distribution function for heterogeneous material description and adaptive technology for mesh refinement. The damage tensor calculation technology for transversely isotropic rock are realized from the well-developed continuum damage variable of isotropic rock. The rock is subsequently developed into a novel conceptual and practical model considering the stress and permeability with the damage. The proposed method utilizing Pariseau strength criterion fully reflects the strength parameters parallel or perpendicular to bedding of the transversely isotropic rock. To this end, an effective and reliable numerically three-step FEA strategy is well established. Numerical examples are given to show that the proposed method can establish efficient and applicable FE model and be suitable for analyzing the state of pore pressure and stress surrounding wellbore, furthermore to demonstrate the effectiveness and reliability of the instability analysis of wellbore failure region and the safe mud weight computation for collapse and fracture pressure of transversely isotropic rock.