Calculation of drillstring vibrations in real time as part of training system

Abstract

A mathematical model of the dynamics of the drillstring in the hole for a real-time system which is based on the model of the long elastic rod in the shell with small bending angle assumption is discussed. The longitudinal, torsional and transverse vibrations of the column in this case are described by a system of nonlinear partial differential equations. This model allows for the simulation tool wear and mechanical complications that can occur during drilling. Based on the FEM and implicit sampling time, the algorithm was implemented with linear complexity depending on the number of finite elements. It allows for calculation of both the real and the accelerated time. The coefficients of the model are set on the basis of incomplete experimental data provided by operators of drilling rigs. For certain geological conditions, equipment and well configuration presented calculations and obtained the dynamics of the various modes, depending on the control parameters: long stop zone, uniform and non-uniform rotation. It is shown that transition in the non-uniform rotation mode drastically reduced the rate of drilling. Simulator system values behaviour (linear and angular speed, column elements load, torque) are in close location with the experimental data. Refs 9. Figs 5.