Dynamics of Mechanical Automatic Vertical Drilling System with a Novel Hydraulic Balanced Turbine

The automatic vertical drilling system (VDS) adopts downhole closed-loop control, through ground monitoring, a large closed-loop control on the ground and downhole is formed to keep the wellbore in a vertical position. The Mechanical Automatic Vertical Drilling System (MVDS) which working in full mechanical mode has been more economical, safety and reliability. We proposed and developed a novel MVDS with high control accuracy in this paper. A new type of Hydraulic Balance Turbine (HBT) is presented and applied to MVDS, used to drive the upper disc valve to reduce the frictional resistance and the influence of the bottom drilling tool vibration. This can achieve a “soft” connection between eccentric platform and the upper valves, eliminate the effect of the friction between the upper valve and the lower valve, and optimize the control ability. After HBT optimization, the stable angle is closer to the low side, which can make the control of MVDS more accurate. The same conclusion was verified by laboratory tests as well.

inability to reach planned depth because of torque and drag.
Currently, there are mainly three kinds of typical VDS tools, including the Baker Hughes Verti-Trak system, Schlumberger Power-V system, Halliburton Sperry-sun V-Pilot system [2,6,8]. All of them have sensitive and expensive electronic components [9] which has low reliability under complex conditions such as high temperature (more than 200℃) and extreme vibration in ultra-deep wells [10][11][12][13].
(a) Schematic of a drilling system for a vertical borehole configuration (b) Schematic of working principle of MVDS FIGURE 1. Schematic of a drilling system for a vertical borehole configuration (a) and the working principle of MVDS (b), When the VDS works, it will generate a pushing force to push against the high side of the wellbore and then return inclined boreholes to verticality. The eccentric block turn to the low side of the hole under the action of gravity, drives the upper disc valve to stabilize in the expected position. Due to the lower disc valve rotates with the bottom hole drilling tool, when one of its three valve holes rotates to the upper disc valve hole, the corresponding hydraulic flow channel is connected and pushed the pads to the high side of the borehole.
In recent years, the Mechanical Automatic Vertical Drilling System (MVDS) [14][15][16] which working in full mechanical mode and more economical, safety and reliability has gradually attracted attention. Especially in today's low oil price economic situation [17], it has become the best choice for "deviation control and fast drilling". The working principle of MVDS as shown in Fig.1, (a) is the schematic of a drilling system for a vertical borehole configuration, When the VDS works, it will generate a pushing force to push against the high side of the wellbore and then return inclined boreholes to verticality. In MVDS, as show in the Fig.1 (a) and (b), there has an eccentric block, which could stable at the low side of the wellbore under the influence of gravity. When the borehole and drilling tool is inclined, the eccentric block turns to the low side of the hole under the action of gravity, which drives the upper disc valve to stabilize in the expected position. The lower disc valve rotates with the bottom hole drilling tool and the drill bit. When one of its three valve holes rotates to the upper disc valve hole, the corresponding hydraulic flow channel is connected. The pads will be pushed to the high side of the borehole by internal and external drilling fluid differential pressure. After a period of time, it is turned off, the next one is turned on, and in this way the full-rotation dynamic correction is realized. Eccentric platforms as shown in Fig.1(b) are now widely applied in MVDS. However, due to the friction between the upper and lower valves, as well as the vibration caused by bottom hole assembly [18][19], the well deviation control accuracy is low, which is a key factor to restrict the development of MVDS.
In this paper, a novel Hydraulic Balance Turbine (HBT) is installed at MVDS, the balance moment generated by the HBT is used to stabilize the upper disc valve at a predetermined position. This can achieve a "soft" connection between eccentric platform and the upper valves, eliminate the effect of the friction between the upper valve and the lower valve, and optimize the valve control ability. Therefore, deviation precision will be improved greatly.
The paper is organized as follows. The conceptual design and geometric features of the new turbine using MVDS are presented in Section 2. Subsequently in Section 3, the mechanical model of HBT and the mathematical methods of simulation based on FE methods is presented. Then, the mathematical model of dynamic characteristics of eccentric block torsion is established. Next, the main results of the paper are given in Section 4, the dynamic characteristics of eccentric block torsion and the optimization effect of HBT were obtained.
Finally, Section 5 draws conclusions and gives a summary of the most important outcomes of this work with suggestions for the future work.

II. Novel HBT in Mechanical Vertical Drilling Tools
In MVDS, because of the friction resistance between the upper and lower disc valves and the vibration of the bottom drilling tool [18][19], the deviation control accuracy of the MVDS is difficult to improve, which has become the main factor restricting its development. The main factors affecting the accuracy of deviation control are as follows: firstly, due to the friction resistance of the upper and lower disc valves, the eccentric platform cannot be stabilized at the low side of the well [15]; Secondly, the centralized force of the pads cannot be stabilized at the high side of the well due to the vibration of the bottom drillstring [20][21][22][23].
In addition to the friction resistance between the upper and lower disc valves, the friction resistance between the mechanical structures, bearings and the damp effect of drilling fluid [24] will also affect the platform, but the friction resistance between the upper and lower disc valves is the most significant, and it is difficult to quantify and compensate the friction resistance at the beginning of the design due to the influence of bottom drilling tool dynamics [18,25].
In this paper, a novel HBT is installed at MVDS as shown in Fig.2 (b), the balance moment generated by the HBT is used to stabilize the upper disc valve at a predetermined position. The eccentric platform is only controlled by the liquid flow nozzle to drive the HBT. The "soft" connection between the eccentric platform and the upper disc valve is realized, so that the eccentric platform is not affected by the friction resistance of the upper and lower disc valve, and the abnormal oscillation of the eccentric platform will not be transmitted to the upper disc valve, which makes the thrust force as shown in fig.1 (a) more stable. The HBT optimizes the performance of the control mechanism of MVDS. The advantages as following two aspects: firstly, it effectively avoids the influence of the frictional resistance of the upper and lower disc valves, as well as the influence of stick-slip vibration of the bottom drilling tools [18]; secondly, utilizing the follow-up and hysteresis characteristics of the HBT, can cushion the vibration of the eccentric block, effectively reduce the influence of the swing of the eccentric block on the upper plate valve, and improve the stability of the control. As shown in Fig.2, the hydraulic turbine is installed between the upper and lower disc valves, the hydraulic impact of the nozzle provides the driving force.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  In the new design, the eccentric platform control the up disc valve with a nozzle to drive the HBT stable in the low direction of the wellbore, then the vibration of the tool caused by pads will not affect the stability of the eccentric platform. The "soft" connection between the eccentric platform and the upper disc valve is realized.
The working principle of the HBT is shown in Fig. 3, where (a) depicts the balance state of the turbine, where the turbine torque is balanced and the turbine is stable. When the nozzle moves to other positions driven by the control mechanism, the hydraulic impact of the nozzle will provide the driving torque, as shown in Fig. 3 (b). Finally, the turbine will restore to its

Bearings
Under the impact of nozzle jet, the turbine overcomes the frictional resistance torque and then moves. The ability of the hydraulic turbine to overcome the frictional resistance torque is called the start-up performance of the turbine. When the nozzle moves driven by the eccentric platform, the turbine will move along with the nozzle, as shown in the Fig.1 (c). We call this characteristic of the turbine dynamic following performance. When the nozzle deviates from the balance position, the turbine will gradually stabilize at the position shown in Fig. 3 (a). At this time, the hydraulic moment tends to be balanced. The anti-disturbance performance of the turbine is defined as the dynamic balancing performance of the HBT.
Whether the turbine can overcome frictional resistance and follow the nozzle rotation depends on the turbine torque. This paper studies the factors affecting the turbine impact torque, and provides a theoretical basis for the optimal design of the balance turbine.

1) Static analysis of eccentric platform
When the inclination angle of the well exists, the eccentric block will generate an eccentric torque that always points to the low side of the well. As shown in the Fig.4, let F E is the eccentric force of the eccentric block during the movement.
Gravity G produces two components for an eccentric block, F r and F a . The component F E of F r generates an eccentric force, thereby providing an eccentric torque. The eccentric torque T E will be calculated by the following: wherein, r 1 and r 2 are inside and outside radius of eccentric block, m; ρ is the material density of the eccentric block, kg/m 3 ; g is gravitational acceleration, 9.8m/s 2 ; l is the length of the eccentric block, m. Friction resistance torque comes mainly from two aspects: One is the frictional resistance torque generated by axial and radial bearings; The second is the frictional resistance caused by the relative rotation of the upper and lower disc valves.
Assuming that the radial bearing friction is F TB , the axial thrust bearing friction is F AB , and the relative motion resistance of the disc valve is   T  T  T  + , the eccentric block will turn to the lower side of the wellbore, in fact, the frictional resistance of the disc valve is the main factor.
As shown in the Fig.5, because the upper disc valve has an arc hole for overcurrent, we divide the friction torque into three parts, the area of S1 and S2 was ignored during the calculation and the calculation formula as follows: wherein D is outer diameter of upper disc valve, mm; P  is coefficient of friction between disc valves;  is opening angle of arc hole of upper disc valve; P l is the pressure on the upper disc valve during drilling fluid flow.

FIGURE 5. Schematic of upper disk valve structure
Then the total frictional torque between the upper and lower disc valves is, The formula for calculating the friction torque T P between disk valves can also be simplified as: wherein is the S P is the area of disc valve except circular hole, also is the area of effect of fluid pressure differential, In the process of working operation of MVDS, if the eccentric block can reliably move to the lower side of the wellbore, need to satisfy the following:

2) Dynamics of eccentric platform
Assuming the equivalent total frictional resistance is F f , R T is the equivalent friction radius. Obviously, total friction torque wherein R T can be considered as the distance from the centroid of the eccentric block to the center of rotation, can be expressed as follows: The direction of the friction resistance depends on the relative movement direction of the eccentric platform and the tool body, so the direction of the friction force is always opposite to the direction of the eccentric force. The motion of the eccentric platform can be expressed as: wherein m is the mass of the eccentric block, is the angular acceleration. Substituting formulas (3) and (13) to (15) can be obtained: According to the different movement modes of the eccentric platform, Equation (15) can be rewritten as follows: ,sin 0 ,sin 0 ,sin 0 ,sin 0 wherein t  is the rotary angular velocity of drillstring; ω e is the rotational angular velocity of eccentric platform.
The eccentric platform will eventually stabilize at an angle , which we call the stable angle. At the stable angle position, the eccentric force and the friction force meet the opposite direction and have the same magnitude. It can be seen that the larger the eccentric force or the smaller the friction, the smaller the stability angle. Therefore, in the design process, the friction should be reduced as much as possible to improve the control accuracy of the drilling tool.
In this paper, the classical Coulomb friction model is used to analyze the dynamics of eccentric platform. The classic Coulomb model states that the friction force F f can be calculated as, where 0 is universal representation of any coefficient of friction, W is the magnitude of the normal contact force and v̇t is the tangential contact velocity. Obviously, this friction model

B. Numerical simulation model of HBT
To verify the feasibility of the new design of this paper, the three-dimensional analysis model of HBT is established in software of Solidworks. Conventional turbine design is complex [27][28][29], in order to make the design of the turbine simple and efficient, projection modeling method is used for the blade. The blade profile is only controlled by the outer angle of the blade. The design parameters of HBT as shown in  The steady operating performance of the turbine was evaluated using a set of dimensionless coefficients which are characterized in terms of the torque coefficient C t , input power coefficient , turbine efficiency  and flow coefficient  .
The definitions related to these parameters are expressed as follows: where P  is the total pressure drop between the inlet and outlet of the turbine; T o is the output torque; and Q and  denote the air volumetric flow rate and liquid density, respectively. s and  represent the number of rotor blades and the angular velocity of the turbine, respectively. Also, v r and r u are mean axial flow velocity and circumferential velocity, respectively; s indicates the area of each annular blade.
A flow simulation was carried out using the software of ANSYS Fluent 19.0, which uses the finite-element numerical method for solving the Reynolds-averaged Navier-Stokes equations by means of the pressure-based solver. The whole 3D geometry model of the turbine was established using ANSYS Workbench (specific parameter values can be obtained in Section 3.3), and grids were generated using the pre-processing software ICEM-CFD.
The k-ε reliable model is chosen as the fluid analysis model, the second-order upwind model is used for discretization, the simple solution algorithm is selected, and the pressure discretization scheme is presto. CFD simulation analysis model and meshing are shown in Fig.7， Fig.8 illustrates

C. Simulation parameters of CFD
In this paper, a novel HBT is installed at MVDS, the balance Boundary layer moment generated by the HBT is used to stabilize the upper disc valve at a predetermined position. The "soft" connection between the eccentric platform and the upper disc valve is realized, so that the eccentric platform is not affected by the friction resistance of the upper and lower disc valve.
The impact torque and impact force of the turbine directly affect the start-up performance of the turbine. The magnitude of the hydraulic torque determines whether the turbine can overcome the system friction torque, which drives the upper disc valve to rotate, and the impact force affects the system friction torque. Therefore, unlike conventional turbines, when the turbine works, it is not necessary to consider the hydraulic efficiency of the blades, and only the torque and impact force of the HBT are important. This paper uses computational fluid dynamics (CFD) software to simulate and analyze the system of nozzle and the HBT to explore the influence of different factors on the turbine force. A flowing fluid follows the law of conservation of mass, momentum and energy. However, it is very difficult to solve the velocity field and pressure field in complex flows accurately. The CFD method can be used to solve the approximate solution to satisfy the engineering application. The accuracy of CFD methods has been verified in many fields [33][34][35]. This paper employed numerical simulation tools to demonstrate the results of the theoretical analysis, and to study the variation of geometric parameters.
The design of the eccentric platform in this paper takes the parameters as shown in the Table 1. According to the structural parameters of the MVDS [15] and   Table 2, No. represents the system parameters corresponding to different simulation tests), and grids were generated using the pre-processing software ICEM-CFD.
where, P is pressure, ρ is fluid density, i   is velocity vector, i f is volume force vector,  is dynamic viscosity.

Work-bench was employed to create a design space and
Standard Response Surface-Full 2nd order polynomial model was used to study the influence of design variables on the turbine efficiency.
As shown in Fig.10 (a), the amplified nozzle jet diffuses at the inlet, the core area of the jet attenuates completely before the outlet of the nozzle, while the jet velocity of the shrinkage nozzle diffuses at the outlet of the nozzle, and the core area of the jet lasts until it contacts the turbine, as shown in Fig. 10 (b).
Therefore, although the inlet velocity of amplified nozzle is equal to the outlet velocity of shrinkage nozzle, the structure of the amplified nozzle leads to the decrease of jet average velocity, and finally the velocity of amplified nozzle jet impacting turbine is much lower than that of shrinkage nozzle, which leads to different toques on turbine. The force of the cylindrical nozzle is more stable than that of the other two nozzles, as shown in Fig.10 (c) which is due to the smaller velocity and the smaller turbulence fluctuation in the flow field.
As shown in Fig.10   (a) Impact torque variation (b) Impact force variation Considering the comprehensive torque and thrust, we choose the cylindrical nozzle as the practical application. In the following simulation and experimental results, we have adopted this structure. When the turbine is in a steady state, the final stop position of the turbine is as shown in Fig.12. At this time, the nozzle is in the balance position, and the turbine is balanced and stationary. When the balance is broken by disturbance, the turbine will provide a recovery torque. VOLUME XX, 2021 The curve of torque, force, and maximum tangential velocity of the turbine without friction is smoother while the curve with friction fluctuates at the tail. This is because the friction force will change abruptly when the velocity direction changes and the calculation is discontinuous due to the time step, which will lead to the instability of the turbine speed and the fluctuation of the turbine speed in the balance position. Turbine torque also fluctuates due to the fluctuation of turbine's position.
When designing the turbine blade, it is necessary to consider comprehensively so as to achieve the optimal relationship between the torque and the impact force. In principle, the greater torque of the turbine is better and the smaller force of the turbine is better. However, considering the strength and durability of the turbine, the turbine blade thickness was set to 4 mm and the fluid velocity was 20m/s. Considering the coupling relationship between the nozzle diameter and the nozzle from the center, when the nozzle diameter is 40 mm, the distance between the nozzle and the center of the turbine is preferably 88 mm. At the same time, the turbine design also needs to cooperate with the parameters of MVDS, borehole size, drilling pressure, drilling fluid type and so on. According the research above, optimized parameters design of the turbine is shown in Table 2.

B. Optimization of Eccentric Block Dynamics
The stable platform included an eccentric block which is not only sensitive to gravity, but also severely affected by vibration of drillstring [15,18,36]. When the eccentric torque of the eccentric block is greater than the friction torque of the bearing and the disc valve, the eccentric block can be started. At this time, the position of the corresponding lower side of the eccentric block is the critical start angle. Starting torque Tq=TE-Tf , for different well inclination angles β, when the torque of the eccentric block is equal to the frictional resistance, the angle φ between the eccentric block and the low side of the well is the starting angle.
As shown in the Fig. 15, when the well is inclined at 6 °, the change curve of Tq, the intersection point of the curve and the x-axis of the abscissa is the starting critical angle. It is convenient to explain that it cannot be started under the x-axis.
The larger the value, the greater the startup acceleration.

FIGURE 15. Torque difference Tq as the eccentric block rotates
When the bottom drillstring does not rotate, the eccentric block rotates downward from 90° from the lower side, as shown in the Fig.16 is the angular velocity  curve for eccentric block before and after optimization, after optimization of HBT, the eccentric block approaches the steady state faster. Since the friction depends on the relative speed of movement, the rotation of the drillstring will greatly affect the stability of the eccentric block [15], the "soft" connection by HBT in this paper will play a more significant role. As shown in the Fig.17,

C. Laboratory test to verify effectiveness
The above simulations verify the effectiveness of the balanced turbine.
Additionally, we built a prototype to test the control accuracy of the proposed MVDS on the laboratory-scale. As shown in the Fig.18, is the prototype of MVDS and eccentric block response test bench. We can test the inductive accuracy of the eccentric block control mechanism in the laboratory, and objectively reflect the dynamic response of the eccentric control mechanism during the action.
During the test, the effects of the rotation of the drill string, the friction between the upper-and lower-disc valves and the bearings on the eccentric platform can be simulated, the rotation motion of the eccentric platform can be measured, and the final stability angle of the eccentric block can be recorded under different well deflection conditions. As the value of the circular hole of the upper valve  can be adjusted according to different designs, therefore, during the work of the eccentric block, the stability angle of the eccentric block will determine the opening radius of the upper disc valve which is very important for the control accuracy.

FIGURE 18. Prototype of MVDS and Eccentric block response test bench
We test that when the drill string is rotated, the eccentric block is at the starting position of 90 °, and the final stability angle is shown in the Fig.19 resistance plays a key role. These influencing factors cannot be fully considered in the theoretical model. Therefore, the error between theoretical calculation and experimental results is larger than when the eccentric block is longer.

D. Inclination and azimuth building calculations
In the process of deviation correction, the value of deviation angle and azimuth angle gradually decreases (as shown in Figure 20.a), and the borehole trajectory formed by drilling is a three-dimensional curve, which has the tendency of drifting to the left [37]. Furthermore, the deviation change rate decreases and the azimuth change rate increases with the increase of vertical depth (as shown in Figure 20.b). That's because as the deviation angle decreases, the tool face angle of MVDS increases. Resulting in the pushing force distributed in the deviation plane decreases gradually, and the pushing force distributed in the azimuth plane increases gradually.

V. Conclusions
We proposed and developed a novel MVDS with high control accuracy in this paper. A new type of Hydraulic Balance Turbine (HBT) is presented and applied to the eccentric platform-disc valve mechanism used in MVDS. In MVDS, because of the friction resistance between the upper-and lowerdisc valves and the vibration of the bottom drilling tool [18][19], the deviation control accuracy of the MVDS is difficult to improve, which has become the main factor restricting its development.
The HBT is used to drive the upper disc valve to reduce the frictional resistance and the influence of the bottom drilling tool vibration on the bias platform to improve the control accuracy. This can achieve a "soft" connection between eccentric platform and the upper valves, eliminate the effect of the friction between the upper valve and the lower valve, and optimize the valve control ability. In this paper, the optimization mechanism of the HBT to control the mechanical performance of the MVDS disc valve mechanism is revealed.
Torque and impact force acting on the HBT are the most important parameters affecting the performance of turbine.
Turbine blade angle, nozzle diameter, blade thickness, fluid velocity and distance from nozzle center to that of the turbine have great influence on the turbine torque, which is the main factor to be considered in HBT design.
Through dynamics analysis of eccentric block, the rotation of the drillstring will greatly affect the final stable angle of the eccentric block. After HBT optimization, the stable angle is closer to the low side, which can make the control of MVDS more accurate. The same conclusion was verified by laboratory tests, As the length of the eccentric block increases, the position of the stable angle from the lower side becomes smaller and smaller. If the threshold of the stability angle in engineering application is not more than 50°, the 3.5m eccentric block needs 3.98 degree well deviation to respond before optimization, however, after optimization, the response accuracy has become 1.25 degrees, and the engineering applications have been greatly improved. However, in this study, we have assumed that the drillstring rotates at a uniform speed. In fact, the drillstring will exhibit complex dynamic forms of motion such as torsion, stick-slip, etc. Further research is required for in-depth analysis of the effect of the tool in mitigating torsional stick/slip vibrations.