A Geomechanically-Informed Framework for Wellbore Trajectory Prediction: Integrating First-Principles Kinematics with a Rigorous Derivation of Gated Recurrent Networks

TL;DR

This work addresses the challenge of predicting wellbore trajectories under complex geomechanical coupling by introducing a geomechanically-informed data-driven surrogate that couples first-principles wellbore kinematics with a GRU network. The method derives kinematic models from physics, provides a complete forward and Backpropagation Through Time formulation for GRUs, and employs a principled data preprocessing pipeline on LAS/DEV data from 14 Gulfaks wells. Key contributions include the formal derivation of the Average Angle and Minimum Curvature methods, a full BPTT treatment for the GRU, and demonstration of accurate inclination, azimuth, and dogleg severity predictions with an interpretable latent MEM in the hidden state. The framework offers practical impact for well planning and real-time geosteering, and points to future work on uncertainty quantification, cross-field generalization, and integration of dynamic drilling parameters.

Abstract

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).

Figures (6)

• Figure 1: Sample Log Data
• Figure 2: Architecture of the GRU-based Trajectory Prediction Model
• Figure 3: Aggregated Prediction Performance on Test Set
• Figure 4: Model Performance Metrics
• Figure 5: Predicted vs Actual Trajectory (View 1)