A review of vertical drill-string mathematical modelling

Abstract

This work aims to elucidate the fundamental concepts and approaches for modelling the vertical rotary drilling system and analysing drill string vibrations through a comprehensive literature review. It offers a detailed examination and critical discussion for the discrete and distributed mathematical modelling vibration along with associated boundaries conditions for low and high frequency oscillations. Additionally, this study discusses experimental models and their actual applications, highlighting their role in validating theoretical models and improving drilling performance. This study presents a thorough overview of existing literature on vertical drill string vibration problems, making it a valuable resource for researchers in the field. The study not only synthesizes existing knowledge but also seeks to guide future research efforts in addressing and mitigating the complex challenges associated with drill string vibrations.