A Comparison of Analytical and Experimental Procedures to Verify a Lumped Drill String Element Model

Abstract

A study of axial vibrations in a vertical drill string is conducted using a spring-mass-damper model with n coupled elements. The main motivation behind this is to describe the axial vibrations using a simple mathematical model that allows for a substantial interpretation and application of control theory. In other words, the analytical model describing the test segments in this thesis can easily apply to other vertical drill string models, with a few adjustments. The study attempts to answer the following research question:

To what extent can the lumped element model be used to replicate and predict axial vibrations in a vertical drill string?

The analytical model is derived and tested on the following three scenarios. The first scenario considers only the transient state of the model. It divides into overdamped, critically damped, and underdamped systems. This scenario features both physical experiments and numerical simulations. Results from experiments and numerical simulations are presented graphically in order to identify similarities between the two systems. The second scenario considers the step response as the driving force, and the last scenario introduces a sinusoidal driving force. Only numerical simulations are presented in the last two scenarios.

It is found that the lumped element model cannot be verified on the basis of a comparison of the experimental results and the analytical model for the transient state. The analytical model cannot replicate and predict axial vibrations in a vertical drill string.