Accurate wellbore trajectory prediction is a paramount challenge in subsurface engineering, governed by complex interactions between the drilling assembly and heterogeneous geological formations. This research establishes a comprehensive, mathematically rigorous framework for trajectory prediction that moves beyond empirical modeling to a geomechanically-informed, data-driven surrogate approach.The study leverages Log ASCII Standard (LAS) and wellbore deviation (DEV) data from 14 wells in the Gulfaks oil field, treating petrophysical logs not merely as input features, but as proxies for the mechanical properties of the rock that fundamentally govern drilling dynamics. A key contribution of this work is the formal derivation of wellbore kinematic models, including the Average Angle method and Dogleg Severity, from the first principles of vector calculus and differential geometry, contextualizing them as robust numerical integration schemes. The core of the predictive model is a Gated Recurrent Unit (GRU) network, for which we provide a complete, step-by-step derivation of the forward propagation dynamics and the Backpropagation Through Time (BPTT) training algorithm. This detailed theoretical exposition, often omitted in applied studies, clarifies the mechanisms by which the network learns temporal dependencies. The methodology encompasses a theoretically justified data preprocessing pipeline, including feature normalization, uniform depth resampling, and sequence generation. Trajectory post-processing and error analysis are conducted using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the Coefficient of Determination (R2).

翻译：精确预测井眼轨迹是地下工程领域的一项关键挑战，其受控于钻具组合与异质地质构造之间复杂的相互作用。本研究建立了一个全面且数学严谨的轨迹预测框架，超越了经验建模，转向一种基于地质力学信息的数据驱动代理方法。该研究利用了来自Gulfaks油田14口井的测井ASCII标准（LAS）数据和井斜（DEV）数据，将岩石物理测井曲线不仅视为输入特征，更将其作为从根本上控制钻井动力学的岩石力学性质的代理指标。本工作的一个关键贡献是从矢量微积分和微分几何的第一性原理出发，形式化地推导了井眼运动学模型，包括平均角法和狗腿严重度，并将其定位为稳健的数值积分方案。预测模型的核心是一个门控循环单元（GRU）网络，我们为其提供了前向传播动态和随时间反向传播（BPTT）训练算法的完整、逐步推导。这一详细的理论阐述（在应用研究中常被省略）阐明了网络学习时间依赖性的机制。该方法包含一个理论依据充分的数据预处理流程，包括特征归一化、均匀深度重采样和序列生成。轨迹后处理和误差分析使用平均绝对误差（MAE）、均方根误差（RMSE）和决定系数（R2）进行。