Stick-slip vibrations modeling is an important topic within drillstring dynamics. Thus, a number of mathematical models has been suggested to describe behavior of drillstrings under torsional. Most of the models take similar approach with regard to, for instance, drillstring discretization, definition of external forces and velocity-weakening effect.
Commonly, research papers focus on the models’ core — mathematical expressions that describe stick-slip oscillations and inherent to it negative damping. The results are usually presented in terms of downhole rotational velocity or displacement and reaction forces at various surface rotational velocities and applied external forces. However, little attention is paid to discussion and justification of selected model configuration, which includes definition of the following 1) total simulation time, time step, number of masses/elements, etc., 2) initial conditions and boundary conditions, and 3) numerical solver to obtain solution in time. This paper reviews commonly used configurations for stick-slip vibrations modeling and discusses selection criteria provided in the references. It also presents case studies to evaluate effect of the above-mentioned configuration properties on simulations outcome. A simple in-house 1DOF torsional dynamics model was used for that purpose, where one explicit and one implicit numerical solvers were applied to obtain solution in time.
Three case studies are presented, which compare performance of two numerical solvers with respect to convergence and stability. The results from the case studies show, for example, that applied explicit numerical solver (Central Difference Method) introduces numerical damping, while implicit solver (Newton-Raphson Method) does not. Central Difference Method provides convergence when initial force is applied, while damping function has to be defined in case of Newmark-Raphson method to obtain convergence. Stability of the explicit numerical solver is determined by the time step, while selected implicit solver is unconditionally stable. A reasonably small time step has to be selected though to improve the accuracy of the results.
Presented literature review and outcome from the case studies can be used by researchers within this area to select suitable configuration parameters for their models and critically evaluate the outputs. In addition, presented results have application in automated drilling where configuration parameters and calibration factors are updated in real time by control algorithms for continuous modeling of drillstring state with regard to stickslip. Understanding the effects of mentioned properties on system dynamics helps to select suitable combination of operational parameters to stabilize the drillstring.