A Graph-Based Drained Wellbore Stability Analysis in Mohr-Coulomb Rock Formation Under Hydrostatic in Situ Stress Field
Authors: Wang X. , Chen S. L. , Han Y. H. , Abousleiman Y. 
Published: August 2024

ABSTRACT:
This paper focuses on the development of a rigorous analytical solution for the drained wellbore drilling problem in a non-associated Mohr-Coulomb rock formation subjected to hydrostatic in-situ stress field, for a specific case that the axial/vertical stress is strictly the intermediate principal stress in the drilling process. The proposed solution is extended from the graphical analysis-based method recently proposed by Chen in 2024 for the cylindrical cavity expansion problem. The wellbore support pressure versus the contracted borehole radius, i.e., the well-known wellbore drilling curves, are numerically calculated through the radial equilibrium equation in the Lagrangian form. The graphical solution effectively avoids the common yet unnecessary intermediacy assumption for the axial/vertical stress in most existing wellbore drilling analyses. Selective numerical results are presented for the desired wellbore drilling curves and the impacts of some rock mechanical parameters on the calculated curves are also investigated.

1. INTRODUCTION
Wellbore drilling in the petroleum industry is a process whereby natural resources, such as natural gas and oil, can be extracted from the rock formation. Wellbore stability must be maintained during both wellbore drilling and the well construction phase to support the structural integrity an oil and gas well. In the wellbore drilling, the rock mass inside the circular borehole is relaxed progressively and removed eventually, which results in the wellbore contraction. The stress field around the wellbore will also be redistributed, which is therefore necessary to be determined during the drilling process (Risnes et al., 1982).
In the past few decades, the stress field around the wellbore undergoing drilling is primarily obtained based on the linear elasticity or poroelasticity theory (Al-Ajmi & Zimmerman, 2006; Bradley, 1979; Carter & Booker, 1982; Cui et al., 1997; Detournay & Cheng, 1988; Kanfar et al.; 2015; Mehrabian & Abousleiman, 2013). However, the rock mass around the wellbore will develop plastic deformation, which is inevitable in many scenarios (Charlez, 1997; Papanastasiou & Zervos, 2004; Potts & Zdravkovic, 1999). It follows that plastic deformation of rock occurs due to high stresses concentrated near and around the wellbore during active drilling operations (Ito, et al., 1998; Zoback, et al., 2003). The stress distribution determined based on the elastic analysis will be invalid after the rock mass runs into plasticity (Chen, et al., 2011; Huang, et al. 2018). Note that the plastic yielding state of a rock mass depends upon the stress state, the strength properties of the rock mass around the wellbore, and the plastic yield criterion for the rock mass. It should be emphasized that the end of the pure elastic deformation does not indicate the failure of the rock mass around the wellbore. Furthermore, an allowable tolerance plastic yielding around the wellbore induced by the drilling will not affect the wellbore stability but can reduce the collapsed mud weight subsequently the cost of the drilling job. It is, therefore, necessary to evaluate the elastoplastic behavior of the rock mass around the wellbore under the drilling process.