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

Abstract

Precise wellbore trajectory prediction is a crucial task in subsurface engineering, dictated by nonlinear interactions among the drilling assembly and inhomogeneous geology. This study devises a mathematically well-posed framework for trajectory prediction that transitions beyond empirical modeling to a geomechanically-informed framework. The project makes use of Log ASCII Standard and wellbore deviation (DEV) measurements in 14 Gulfaks oil field wells, viewing petrophysical logs as surrogates to the mechanical properties of the rock that truly dictate drilling dynamics. An important result of the project is the formal derivation of wellbore kinematic models presenting them as proper numerical integration schemes. The heart of the predictive model is a Gated Recurrent Unit (GRU) network. The theoretical justification, often overlooked in practice-oriented works, details the mechanisms by which the network learns the dependencies over time. The methodology comprises a theoretically justified preprocessing of the data, i.e. invariant depth resampling, and sequence formation. The post-processing of the trajectories and the error analysis are carried out by way of MAE, RMSE and R2 methods. The results demonstrate that the GRU model, efficiently learns the implicit, nonlinear function of transformation from geology to directional shift, and succeeds in predicting the azimuth, inclination, and spatial location accurately. The present study can be regarded as the guideline for the construction of physically-based machine learning models for petroleum engineering, in which the network learns a functional description of the local Mechanical Earth Model, and can provide more accurate well planning and real-time geosteering operations.