Wellbore instability is an important consideration during both drilling and production of hydrocarbon reservoirs. The optimal well trajectory must be determined during the design phase to avoid wellbore shear failures. This study makes two fundamental contributions towards improving contemporary wellbore shear models. For the first time, the analytical wellbore shear models are formulated implicitly to significantly improve the computational efficiency and obtainable accuracy. The stability problem is resolved with the bisection method and an optimisation algorithm, where Powell’s method and the Nelder-Mead method have been implemented here. The second contribution is to account for the depletion of various formations, especially coal, in the stability models. Three stress models, namely those of Gray, Shi and Durucan, and Cui and Bustin, were used to develop stress paths for a depleted coal reservoir. The results were quantified via the maximum allowable pressure (MAP), which indicates the wellbore pressure required to avoid wellbore failure and thus guide corresponding operational decisions.

The results of this work show that implicit methods significantly improve computational efficiency over the conventional iterative method used in the literature and industry. In particular, it was found that Powell’s method saves greater than 95% of the computation time for sandstone and coal case studies, respectively. In terms of stability during depletion, a higher depletion pressure resulted in an increased MAP. For a drilling application, this means that a greater overbalance pressure is required. While in a production application, a lower maximum drawdown pressure would be expected. The Gray model indicates the largest impact on stability prediction for depleted coals, and the Cui and Bustin model is the most conservative among the three stress models. The proposed numerical framework provides an efficient tool to determine the optimal well trajectory for different formations (e.g. coal, clastic rock) experiencing depletion before or after drilling.

井筒不稳定性是油气藏钻井和生产过程中的重要考虑因素. 最佳井轨迹必须在设计阶段确定，以避免井筒剪切失效。这项研究对改进当代井筒剪切模型做出了两个根本性的贡献。首次隐式建立解析井筒剪切模型，显着提高了计算效率和可获得的精度。稳定性问题通过二分法和优化算法得到解决，其中鲍威尔方法和 Nelder-Mead 方法在这里已经实现。第二个贡献是在稳定性模型中考虑各种地层的枯竭，尤其是煤。三个应力模型，即 Gray、Shi 和 Durucan 以及 Cui 和 Bustin 的模型，被用于开发枯竭煤储层的应力路径。结果通过量化最大允许压力（MAP），表示避免井筒失效所需的井筒压力，从而指导相应的操作决策。

这项工作的结果表明，与文献和工业中使用的传统迭代方法相比，隐式方法显着提高了计算效率。特别是，发现 Powell 方法为砂岩节省了 95% 以上的计算时间和煤炭案例研究，分别。就耗尽期间的稳定性而言，较高的耗尽压力会导致 MAP 增加。对于钻井应用，这意味着需要更大的过平衡压力。在生产应用中，预计最大下降压力会更低。Gray 模型表明对贫煤稳定性预测的影响最大，Cui 和 Bustin 模型是三个应力模型中最保守的。所提出的数值框架提供了一种有效的工具来确定不同地层（例如煤、碎屑岩）在钻井之前或之后经历枯竭的最佳井轨迹。