TY - JOUR
AU - Horbiichuk, M. I.
AU - Kropyvnytskyi, D. R.
PY - 2023/02/20
Y2 - 2024/10/04
TI - NUMERICAL METHOD OF CALCULATING THE CRITICAL LOAD ON THE CHILL AT DRILLING WELLS
JF - METHODS AND DEVICES OF QUALITY CONTROL
JA - mpky
VL -
IS - 1(48)
SE - MATHEMATICAL MODELLING FOR THE UNDESTROYED CONTROL PROBLEMS
DO - 10.31471/1993-9981-2022-1(48)-115-126
UR - https://mpky.nung.edu.ua/index.php/mpky/article/view/571
SP -
AB - <p>The paper considers the effect of axial load on the bit on the shape of the drill string. It is determined that increasing this parameter to a critical value will lead to deformation of the drill string, as a result it can cause an accident. To determine the critical value of the axial load, a polygon of forces acting at the lower end of the drill string was constructed, determined by the <sub> </sub>coordinate that is the point of maximum deflection of the drill string, and mathematical dependences were made as a system of differential equations (Cauchy form). An algorithm for determining a given x coordinate has been developed in the MatLab environment, which includes solving a system of differential equations using the Runge-Kutta method and building an interpolation Lagrange polynomial. Graphical dependences of drill string deflection change at different values of bending moment are developed. It has been shown that increasing load on the bit makes the torque to increase, as a result of which the intensity of the curvature of the drill string increases. </p><p> Based on the results of calculations, empirical models for determining the point of maximum deflection of the drill string in the form of a polynomial of the 2nd order were synthesized, the parameters of which were calculated by the method of least squares. The adequacy of the models was checked using a correlation coefficient. The calculated values of the correlation coefficient are close to 1, so it can be claimed that the proposed empirical model adequately describes the "experimental" data.</p><p> A series of machine experiments was performed at different values of the maximum degree of the polynomial and it was determined that for the degree of the polynomial equal to 3, the empirical model, which is a function f (a, x) describes the results with high accuracy and the number of polynomial members is 20.</p><p> It was determined that when drilling a well, the critical load on the bit can be calculated by two factors - the point of maximum deflection of the drill string and the length, which is determined by the difference between the maximum deflection point and the neutral section point.</p>
ER -