Nonlinear Vibration Mechanism Analysis And Vibration Control Strategy Design Of Oil Well Drill-string System

Exploration of oil or gas wells is usually carried out by the drill-string system which includes many parts.The driving force is provided by the top drive at surface.The drive torque transfer and the mud transmission from the rotary table to the bit are implemented by the drill-string.The bottom-hole assembly(BHA)is located at the lowest part of the drill-string and includes the drill-collar,the stabilizer and the bit.And the rock is broken by the bit.Due to slenderness and small cross section of the drill-string,low inertia of the BHA,and the nonlinear torque-on-bit(TOB)between the bit and the rock,the insufficient driving force,it is easy prone to stick-slip vibrations of the drill-string.The undesired stick-slip vibrations of the drill-string are harmful.The stick-slip vibrations may lead to failure in the drill pipe sections and connections or may lead to a mechanical failure of the bit.In extreme cases,stick-slip vibrations may lead to a complete standstill of the bit or may lead to fractures of the drill pipe.Therefore,it is of great significance to study the mechanism of the stick-slip vibrations and design the controller to eliminate them.In this paper,theoretical analysis,numerical simulation and practical experiments were combined to study the nonlinear vibration mechanism and to design control scheme for the drill-string system.Based on the proposed control algorithm,a control system was developed to suppress the stick-slip vibrations of the drill-string.(1)Based on investigation,the main components of the drilling machine and their functions were introduced.The lateral vibration,longitudinal vibration and torsional vibration during the drilling process were summarized.Based on the force analysis,the dynamic model of the drill collar and stabilizer was established.Through numerical simulation,the precession law of the drill collar caused by the lateral vibration,such as chaotic vibration,reverse vibration and rubs of backward whirl,were described.The influences of the drill collar speed,equivalent additional mass of drilling fluid,eccentricity and friction on the motion of the drill collar were analyzed.(2)The nonlinear TOB was modeled by a Karnopp friction model.A multi-degree-offreedom model(multi DOF model)and a two-degree-of-freedom model(2DOF model)of the drill-string system were established respectively.The calculation method of the parameters of the drill-string system was summarized.For the first time,the three-dimensional phase trajectory of the phase difference,the top drive speed and the bit speed were used to reveal the nonlinear characteristics of the stick-slip vibrations of the drill-string.The effects of drill-string length,drive speed,drilling pressure and system damping on the stick-slip vibration of the drill-string were analyzed.(3)Based on the 2DOF model,the mechanism of self-excited vibration of the drill-string excited by the nonlinear TOB was studied and the mechanism of forced vibration of the drill-string induced by periodic rubbing was revealed.The stability of the stick-slip vibration of the drill-string was qualitatively analyzed,and the frequency of the stick-slip vibration of the drill-string was solved.The equivalent damping torque formula of the drill-string system and the energy variation formula of the drill-string system were proposed.The stability of the balance state of the drill-string system was analyzed.The mechanism of nonlinear self-excited vibration of the drill-string system was explained.The influence of the disturbance torque difference on the stick-slip vibrations of the drill-string was analyzed.The motion of the bit speed was revealed when the rubbing frequency was close to the natural vibration frequency of the drill-string system,which explained the cause of the stick-slip vibrations of the drill-string when drilling in shallow stratum or loose stratum.(4)Based on the 2DOF model of the drill-string system and the stick-slip vibration mechanism of the drill-string,active control algorithms were designed to improve the damping of the closed-loop control system.The control target of eliminating the stick-slip vibrations was described and the state space of the drill-string system was constructed.A full-dimensional observer and a reduced-dimensional observer were designed respectively.The full-dimensional observer not only could estimate all state variables of the drill-string system,but also could estimate the nonlinear disturbance torque between the drill bit and the rock.The reduced-dimensional observer could estimate the bit speed and its construction was simple.An adaptive sliding mode controller was designed to suppress the stick-slip vibrations of the drill-string.A reference governor was designed to modify the original reference input for controller according to the changing friction torque,which hadn’t been considered before in this field.Based on the reference governor,a full-dimensional state PI controller was designed to suppress the stick-slip vibrations of the drill-string.According to the working environment of the drill-string system,a new type of speed compensation feedback controller was designed to suppress the stick-slip vibrations of the drill-string.By simulations,three control schemes were compared and analyzed.(5)This paper is not only limited to the theoretical research of the stick-slip vibration control algorithm,but also developed the stick-slip vibration control system with independent intellectual property rights.The overall design of the control system of the drill-string was described.The hardware and software design process of human-computer interaction unit,control algorithm unit and communication interface module were introduced respectively.Based on the actual drill-string system,the communication between the control system and the converter was tested.The designed stick-slip vibration control system was applied to the drilling field.The actual top drive torque and top drive speed during the drilling process were collected,and the vibration signal was analyzed by frequency spectrum.The performance of the proposed observers was verified with the acquired vibration signal as an input.The designed control system was applied to the actual drilling platform.The experimental results show that the control system can effectively suppress the fluctuation of the top drive torque and the stick-slip vibrations of the drill-string.The excellent control performance of the control system not only investigates the practicability of the control algorithm and the state observer,but also proves the correctness of the vibration mechanism and the rationality of the2 DOF model.Therefore,the designed control system can effectively eliminate the stick-slip vibrations of the drill-string and can be applied to the drilling field.