Current univariate approach to predict the probability of well construction time has limited accuracy due to the fact that it ignores key factors affecting the time. In this study, we propose a multivariate probabilistic approach to predict the risks of well construction time. It takes advantage of an extended multi-dimensional Bernacchia–Pigolotti kernel density estimation technique and combines probability distributions by means of Monte-Carlo simulations to establish a depth-dependent probabilistic model. This method is applied to predict the durations of drilling phases of 192 wells, most of which are located in the Australia- Asia region. Despite the challenge of gappy records, our model shows an excellent statistical agreement with the observed data. Our results suggested that the total time is longer than the trouble-free time by at least 4 days, and at most 12 days within the 10%–90% confidence interval. This model allows us to derive the likelihoods of duration for each phase at a certain depth and to generate inputs for training data-driven models, facilitating evaluation and prediction of the risks of an entire drilling operation.

目前单变量预测建井时间概率的方法由于忽略了影响时间的关键因素，精度有限。在这项研究中，我们提出了一种多变量概率方法来预测建井时间的风险。它利用扩展的多维 Bernacchia-Pigolotti 核密度估计技术，并通过蒙特卡罗模拟结合概率分布来建立依赖于深度的概率模型。该方法用于预测192口井的钻井阶段持续时间，其中大部分位于澳大利亚-亚洲地区。尽管存在空白记录的挑战，但我们的模型与观察到的数据显示出极好的统计一致性。我们的结果表明，在 10%–90% 的置信区间内，总时间比无故障时间长至少 4 天，最多 12 天。该模型使我们能够推导出特定深度每个阶段的持续时间的可能性，并生成用于训练数据驱动模型的输入，从而促进对整个钻井作业风险的评估和预测。