Research on Rotation Speed Equation of Drilling Bit Based on Intrusion Theory

Rotation speed of drill bit directly affects the progress of drilling and the evaluation of oil and gas reservoirs [1,2]. In view of this, a lot of research were carried out to establish a standardized calculation method for drill speed [3-5]. However, some shortcomings need to be noticed for these works, i.e., the neglected Intrusion Theory. Therefore, the rotation speed equation of drill bit would be established based on the Intrusion Theory.

Based on the Intrusion Theory, the momentum theorem was applied to establish the rotation model of drill bit, seeing Eq.(1).

Eqs.(2) - (3) were substituted into Eq. (1), and then drill speed equation Eq.(4) was obtained:

where F is horizontal force produced by screw drill torque, dm is moment, m is the quality of drill bit, ΔP is pressure drop at inlet and outlet of screw motor, q is displacement per revolution of screw motor, ηm is mechanical efficiency

Figure 1 shows the predicted and actual rotational speed of drill bit in Wells I and II.

Figure 1: The comparison chart of predicted speed and actual speed of drill bit.

a. In this paper, the standardized calculation equation for predicting drill speed was established based on the Intrusion Theory.
The predicted speed obtained by bit speed equation is basically the same as the actual drilling bit speed, which proves the accuracy of rotation speed prediction equation.

1. Tong AP (2015) Research on dynamic characteristics of composite drilling string. Southwest Petroleum University, China.
2. Shao DD (2013) Analysis of drill string dynamic characteristics in horizontal well hole. University of Petroleum of China, China.
3. Liu ZZ (1996) Present situation of downhole power drilling tool reducer at home and abroad. Petroleum Machinery, USA, 6: 43-47.
4. Liu JB, Wei HS, Zhao JF, Zhang H, Zhang NP (2015) New 3D drilling speed equation considering the influence of bit speed. Petroleum Drilling Technology 43(1): 52-57.
5. DHZeuch (2019) Recent studies from Yangtze University, Fracture failure analysis and research on drive shaft of positive displacement motor. NewsRx, USA.