Numerous models have been proposed to address the time-delayed wellbore collapses or untimely mud losses that have been widely reported in the field. There is still reluctance in applying them in real-time field operations due to their complex mathematical appearance. In this technical note, we address the effective stress solutions for short- and long-term wellbore stability analysis. We present the poroelastic, porothermoelastic, and porochemoelastic wellbore effective stress solutions at $t\to 0^{+}$ and $t\to \infty$. The concise expressions of these solutions are simple to implement into computational codes for the ease of engineering field data interpretation. We also improve a generic algorithm for calculating mud weight windows. Application of the asymptotic solutions and the algorithm in an example with a random set of data indicates that the long-term collapse and fracturing mud weights can be 32.5% higher and 25.6% lower than the short-term ones, respectively. Conventional time-independent elastic models cannot capture these behaviors.

已经提出了许多模型来解决已在该领域广泛报道的延时井筒塌陷或不合时宜的泥浆流失。由于其复杂的数学外观，仍然不愿意将它们应用于实时现场操作。在本技术说明中，我们讨论了用于短期和长期井筒稳定性分析的有效应力解决方案。我们提出了多孔弹性、多孔热弹性和多孔化学弹性井筒有效应力解决方案，网址为$吨\to 0^{+}$和$吨\to \infty$. 这些解决方案的简洁表达很容易实现到计算代码中，以便于工程现场数据解释。我们还改进了计算泥浆重量窗口的通用算法。渐近解和算法在随机数据集的示例中的应用表明，长期塌陷和压裂泥浆的重量可以分别比短期的高 32.5% 和低 25.6%。传统的与时间无关的弹性模型无法捕捉这些行为。