ANALYSIS OF MATHEMATICAL MODELS OF WELL DRILLING

Abstract

This article presents a comprehensive review of mathematical models used to describe well drilling processes under conditions of variable rock strength, which are characteristic of complex and heterogeneous geological formations. In environments where lithological transitions are accompanied by abrupt fluctuations in the strength and deformation properties of rocks, traditional approaches to predicting the rate of penetration and selecting optimal drilling parameters become insufficiently effective. Therefore, models that account for the dynamic behavior of the drill bit and its interaction with heterogeneous media gain particular relevance. The study considers four main classes of models: physical-mechanical, energy-based, kinematic, and empirical. Each group is systematized based on input parameters, predictive accuracy, adaptability to changing geological conditions, and practical applicability in engineering tasks. Special attention is given to modern intelligent approaches, such as neural networks, fuzzy logic systems, and hybrid algorithms capable of self-learning and real-time operation. The article concludes that building multi-component models combining physical principles with machine learning methods is essential. Such integration significantly improves the reliability of engineering forecasts, minimizes operational risks, and ensures the stability and efficiency of drilling operations in lithologically variable and geomechanically uncertain environments.