Abstract

Interaction of rock cutting tool (rotating under load roller cone bit) with the rock (slaughter) plays a major role in the drilling. To study this interaction is necessary to create a mathematical model of the drilling process, taking into account the essential elements and factors that affect the bottom groove. The paper proposes a new mathematical model of the "bit-slaughter", which allows to describe the main stages of the process of drilling a well. The model includes a system of two differential equations, the first of which describes the rotational movement of the bit, and the second – the translational movement of bit in view of its rotational movement and deeper wells. The developed model systems "chisel-slaughter" allowed to analyze the effect of a force on a system of "bit-slaughter" and link them to the characteristics of the actuators, carrying out the drilling process.

Keywords

Mathematical model, differential equations, fluctuations, stability, control, well, slaughter, bit, drill string, the load time.