MODELING THE STABILITY OF THE DRILLING COLUMN MOVEMENT

In this article, a mathematical model of the movement of a drill string used in the oil and gas industry is constructed and the values of parameters are determined that, at minimal cost, provide a fast and productive result that preserves the stability of the movement of the column. During the project, a model was considered in which the lower part of the drill string in a vertical well is influenced by two loads: the axial force load and the column's own weight. The model in question is multidimensional and periodic. It includes several parameters that affect the stability of the column. Due to the complexity of the multidimensional model, using the Bubnov-Galerkin variable separation method, the model was transformed into a system of second-order ordinary differential equations. By deducing the solution of the mathematical model using the partial discretization method and performing calculations in the C++ programming language and the Matlab application software package, graphical results were obtained. An effective solution to the stability of the drill string was considered by changing the values of various parameters found in the drilling model.

The analysis of the influence of the parameters of the drill string on the amplitude of vibrations is carried out. A significant influence of the rotation frequency and the length of the column was revealed.