Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool

Transcription

1 Journal of Applied Science and Engineering, Vol. 20, No. 4, pp (2017) DOI: /jase Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool Hong Zhang 1,2,3, Yijing Feng 4, Zhengxin Xiang 1,2 and Ding Feng 1,2 * 1 Hubei Engineering Research Center of Oil and Gas Drilling and Completion Tools, Yangtze University, Jingzhou, Hubei , P.R. China 2 Hubei Cooperative Innovation Center of Unconventional Oil and Gas, Yangtze University, Wuhan, Hubei , P.R. China 3 Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, China Three Gorges University, Yichang, Hubei , P.R. China 4 School of Mechanical and Transportation Engineering, China University of Petroleum, Beijing , P.R. China Abstract The build-up rate and steering force of the wellbore trajectory control tool has a close relationship with its shaft deformation, which mainly depends on the eccentric movement of the shaft and its flexural deformation. In combination with the working principle of the shaft of the tool, the deformation motion of the shaft was analyzed first, based on which, the flexural equation of the shaft at the static bias state was deduced as well as its angle equations, bearing reaction equations and bending moment equations. According to the deduced equations, the mechanical model of the shaft was established and optimized. To test and verify the reliability and feasibility of the model, the lab simulation experiment was carried out by using the dynamic simulation test bench of the wellbore trajectory control tool, and the bit deflection angle was acquired. A comparison was made between the data from the model and the one from the experiments. The results show that the data measured in experiments is very close to the data derived from the theoretical equations, thus verifying the feasibility of the established mechanical model of the shaft, which provides reference for the shaft design of the wellbore trajectory control tool. Key Words: Deformation Movement, Mechanical Model, Lab Testing, Wellbore Trajectory Control Tool, Shaft, Bias Units 1. Introduction As the oilfield development enters the late period and the development is increasingly difficult, the using of slide steering drilling tools in directional drilling wells, especially in extended reach wells and long horizontal wells, shows many shortcomings and deficiencies. Rotary steering drilling technology, which was developed in 1990s, can overcome those shortcomings and deficiencies effectively. Currently, it represents a hot spot *Corresponding author. fengd0861@163.com and direction of the development of directional drilling tools. The technology has experienced three stages of development, which are the slide steering drilling stage, ground control steering drilling stage and automatic rotary steering drilling stage [1 3]. Rotary steering drilling system includes the Push-the-bit system and the Pointthe-bit system. From the point of view of commercial applications in recent years, although the commercial application of the Push-the-bit system is earlier, the Pointthe-bit system has an advantage over Push-the-bit system, because the Point-the-bit system has so many advantages such as high trajectory control accuracy, good

2 436 Hong Zhang et al. hole cleaning, high displacement extension ability, high mechanical rotating speed and high drilling efficiency [4 6]. Now the Point-the-bit technology is monopolized by foreign oilfield service companies such as Schlumberger Anadrill, Halliburton Sperry-Sun [7 9]. In China, the principle prototype of the wellbore trajectory control tool with the high build-up rate is developed by Yangtze University and CNOOC Research Center, which is made with a drill pipe as downhole drive power source and a deceleration device with annular structure. The prototype is a new adjustable Point-the-bit drilling tools with infinitely variable speed, which mainly consists of the rotary shaft, non-rotary housing, bias units with two eccentric rings, cantilever bearing, electromagnetic clutch, dynamic seal and fulcrum ball bearing [10,11]. The wellbore trajectory control tool works with mechanical power transmission and stationary housing, on which there are bias units which can make the shaft offset. When the direction of wellbore trajectory needs to be changed in the drilling process, bias units receive the control instruction to make the shaft bent, and then the axis of the shaft deviate from its original direction to make the bit drill along with the new direction to achieve the direction control. When the wellbore trajectory control tool works in its normal state, the shaft has been suffering from alternating stress of high intensity and is prone to fatigue failure, so it is necessary to analyze the mechanical behavior of the shaft. 2. Analysis of Deformation Motion of the Shaft The rotatory shaft of the tool made from high-strength stainless steel materials, is directly connected with the drill pipe. So it can ensure a certain flexural deformation and has the high strength at the same time. The function of steering and building mainly depends on a set of bias units between non-rotary housing and rotatory shaft, which can make the shaft bent and make an eccentric motion. Then an inconsistent dip angle with the wellbore axis is provided for the bit to point to the steering direction. Figure 1 shows the deviation principle of the steering drilling tool. Bias units are composed of outer eccentric ring, inner eccentric ring and their respective driving devices, the combined movement of which can make the shaft achieve the eccentric motion with any angle [12]. The magnitude and direction of the shaft offset can be determined by the control of offset driving devices over two eccentric rings. Inner eccentric ring is embedded in the internal wall of the outer eccentric ring, and the shaft is embedded in the internal wall of the inner eccentric ring. The external wall of the outer eccentric ring is always concentric with the housing of the wellbore trajectory control tool, and the internal wall center of the outer eccentric ring is the rotation center of the outer eccentric ring. The distance between the two centers is e. Similarly, the external wall of the inner eccentric ring is constantly concentric with the internal wall of the outer eccentric ring and the internal wall center of the inner eccentric ring is the rotation center of the shaft. The distance between the two centers is the same e. Schematic diagram of eccentric displacement and trajectory of the shaft center is shown in Figure 2. When the inner eccentric ring and the shaft remain relatively stationary, and the outer eccentric ring rotates alone, in the tool housing constraint, the outer eccentric ring drives the shaft to do circular motion with the rotation center of the housing center O 1 and the radius of e. The offset range of the shaft is a torus space. When the outer eccentric ring and the tool s housing remain relatively stationary, and the inner eccentric ring rotates alone, the inner eccentric ring drives the shaft to do circular motion with the rotation center of the internal wall center of the outer eccentric ring O 2 and the radius of e. The offset range of the shaft is another torus space. When Figure 1. The deviation principle of the wellbore trajectory control tool.

3 Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool 437 Figure 2. Schematic diagram of eccentric displacement and trajectory of the shaft center. the inner eccentric ring and the outer eccentric ring rotate together, motion trajectory of the internal wall center of the outer eccentric ring is still the circle with the rotation center of the housing center O 1 and the radius of e because of the tool housing constraint. However, the external wall center of the inner eccentric ring O 2 is not stationary on account of the motion of the internal wall center of the outer eccentric ring, which does circular motion in the rotation center of the housing center O 1 and in the radius of e. Therefore, the inner and outer eccentric ring drive the shaft move together to achieve 360 stepless deflection in one spatial dimension. The circle in the center of O 3 and in the radius of 2e is the trajectory of maximum eccentric displacement of the shaft center. 3. Study on the Mechanical Model of the Shaft The drilling pressure is transferred indirectly for the well trajectory control tool, which varies with the soft and hard degree of stratum when drilling. If it is transferred by the shaft directly, the force applied to the shaft by bias units must be adjusted in real time in order to achieve the same deflection angle, which means keeping the designed build-up rate under different bit pressure, and the difficulty of control and the complexity of bias units will be increased. Therefore, in order to control the shaft easily and reduce the complexity of bias units, drilling pressure should be transferred by housing of the tool, bypass the control section of the shaft, and be transmitted from bearing to shaft at the lower fulcrum and finally applied to the bit. 3.1 Conditions for Establishing Mechanical Model of the Shaft In order to study the behavior of the shaft and establish reasonable mechanical model, the following assumptions are made: 1) in the process of directional drilling, the shaft goes forward in the state of flexural deformation, so a reasonable dynamic mechanical model should be established. 2) in this model, not only the load on the shaft in the drilling process should be considered, but also the torque, rotary speed and other parameters the bottom hole assembly passed, as well as the environmental impact in the drilling process. This paper mainly takes the eccentric motion and the flexural deformation of the shaft while the torque and rotational speed have a little impact on the deflection angle of the shaft and other engineering parameters [13]. So the model established assumed to work on the condition that the shaft works with a constant torque and constant speed. Combined with the structure of the wellbore trajectory control tool, when the bias units are under a fixed offset state, condition for establishing mechanical model of the shaft is shown as the Figure 3. The direction of the coordinate system is on the right of the figure. The shaft Figure 3. The mechanical model of the shaft in the condition of static offset.

4 438 Hong Zhang et al. does not bear the drilling pressure and is supported by the cantilever bearing and focal bearing on both ends (i.e. point 1 and 2 in the Figure 3), and its total length is L. P is the action force. B is the point of action. The distance between P and 1 is L 2, and the distance between P and 2 is L 1. O is the rotation point of the lower support, and also is the origin of the coordinate system. is the rotation angle of the shaft around the point O. The outer diameter of shaft is D, and its inner diameter is d. R 1 is reaction force of the lower support, R 2 is reaction force of the upper support and M 2 is bending moment of the upper support reaction. 3.2 Establishment of Mechanical Equations of the Shaft Assume that the equation of deflection curve of the shaft is: y = f (x) (1) The equation of rotation angle for each point on the shaft is: (2) In the static offset condition, the magnitude and direction of the force P applied on the shaft have been identified, and then in the constant force condition the equation is as follows: (5) When the line of deflection heaves down, M(x)ispositive. On the other hand, the second derivative curve 2 d y which heaves down in the selected coordinate system is also positive; on the contrary, M(x) is negative 2 dx and d 2 y is also negative. So the symbols in the both 2 dx sides of equation (5) are the same, the equation (5) can be written as: (6) Under the condition of static bias, the assumption of boundary conditions is as follows: 3.3 Solution of Mechanical Equations of the Shaft According to assumptions of the shaft boundary conditions and the solution of the equation (6), the equation of deflection curve and deflection angle of the shaft in the static bias state can be obtained as follows: (3) In above equation, (x) is the curvature radius of the shaft, m; M(x) is the bending moment of the shaft, N m; E is the Young s modulus of the shaft, Pa; I is the moment of inertia of cross section of the shaft, m^4. The following equation can be got through the analysis: (7) (8) (4) From the equation (3) and equation (4), the equation (5) is as follows: And the reaction force equation of the shaft at the focal bearing position is as follows:

5 Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool 439 (9) And the equation of bending moment of the shaft at the static bias state is as follows: (10) According to the above equations, the following parametric equations are obtained which can be the calculation basis for engineering design. When x equals 0, the equation of rotation angle of the shaft at the focal bearing position can be obtained through equation (8): (11) Deflection equation at P point can be got through equation (7): (12) Bending moment equation at P point can be obtained from the equation (10): (13) Bending moment equation at the cantilever bearing position can be obtained through the equation (10): (14) 3.4 Optimization of Mechanical Model of the Shaft In the directional drilling process with the wellbore trajectory control tool, the shaft is in the state of continuous rotation to drive the bit to build up, and the shaft bears the maximum force at the point of the cantilever bearing and action of the biasing force, which is directly related to the service life of the shaft. Under the prerequisite of satisfying the engineering design requirements, how to minimize the biasing force and the bending moment of the shaft to make the shaft axis curve as smooth as possible, and how to reduce the bending moment of the cantilever bearing support position as much as possible, all need to analyze and optimize the force of the whole main shaft under static bias state in order to extend the service life of the whole system. The most critical engineering parameter of the wellbore trajectory control tool is the deflection angle of the shaft at the lower support, which is identified before the engineering design. The target for shaft optimization is that, under the premise of ensuring, as far as possible to reduce the biasing force P to minimize the deflection and bending moment of the action point and bending moment M 2 of the cantilever bearing, and decrease bias mechanism design requirements Optimization Equations Assume that is constant and equals 0, represents eccentric rings installation position and equals L 1 /L, the shaft size and material are determined which means Young s modulus E and moment of inertia I are constant, and other conditions remain unchanged as mechanical model mentioned above. Substituting 0 and into the equation (11), the equation (15) is as follows: (15) Substituting 0 and into the equation (13) and (14), the equation (16) and (17) are as follows: (16) (17) Substituting 0 and into the equation (12), deflection equation at P point can be obtained as follows:

6 440 Hong Zhang et al Optimization Solution (18) From equation (15), when equals 1, the force P is 3 minimized with the range of 0 < < 1, which is (19) According to the equation (16), the value of M 1 increases as the value of increases. The first derivative of M 2 can be got from the formula (17): (20) In the range of 0 < <1,M 2 ( ) > 0, so bending moment M 2 of the cantilever bearing increases as the value of increases. The deflection change of the shaft itself can be simplified as the deflection change at the reaction point P. So analysis results can be obtained from the first derivative of of the formula (18) as follows: In the range of < <1, y x L1 ( ) 0, 3 the value of y x L1 ( ) decreases as the value of in- creases. In the range of 0 < < , y x L1 ( ) 3 > 0, so the value of y x L1 ( ) increases as the value of increases. As can be seen from the above analysis, the action point P should be as close as possible to the focal bearing position when the engineering design permits. Assume that the action point P is fixed, then is constant, and also design deflection angle of shaft end is 0. According to the formula (15), (16) and (17), the values of P(L), M 1 (L) andm 2 (L) decrease as the value of L increases, while according to the formula (18), the value of yx L 1 (, L) increases as the value of increases Calculation and Comparative Results For the wellbore trajectory control tool, some parameters of the shaft are known that Young s modulus of E equals pa, outer diameter D of shaft equals 70 mm, inner diameter d of shaft equals 40 mm, and design deflection angle 0 of shaft end is constant. Based on the above analysis, substitute these parameters into above equations, calculating results are shown in Table 1, influence laws of biasing mechanism installation position on P and M 2 are shown in Figure 4 and Figure 5. As shown in Table 1, Figure 4 and Figure 5, when L keeps constant and the value of decreases, the value of M 2 increases and the value of P first decreases then increases. When equals 1/3, the value of P is the smallest, which means the action point P should be set close to 1/3 of the length of the shaft at the bit end as far as possible under the premise to ensure bearing life, the design difficulty of the bias mechanism can be reduced and the shaft can work in a state of smaller deflection and less force and its service life can be extended. When keeps constant and the value of L increases, the value of P and M 2 all decrease. That means if the force required to reach the design deflection angle 0 exceeds the maximum bias force P provided by the biasing mechanism, or the bending moment M 2 the cantilever bearing sustains is too large and affects its service life, the value of L should be increased to reduce bias mechanism design requirements Table 1. Contrast of calculating results L (m) P (kn) M 2 (kn m) L=3.5m L=4m / /

7 Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool 441 Figure 4. The influence law of eccentric rings installation position on P. 4.1 Test Method for the Bit Deflection Angle As shown in Figure 7, in order to conveniently observe the process of angle building and measure the deflecting parameters, a laser pointer has been fixed on the shaft nose by a magnetic base. There is a target at a certain distance from the laser pointer, on which many arithmetic diameter circles are depicted. At the beginning of the test, the laser point is set to be coincident with the center of target. When the shaft is slightly deformed, the laser point will show a significant offset on the target. is deflection angle of the bit. The distance between focal bearing and laser pointer is l 1. The distance between laser pointer and the center of target is l 2. The offset distance of the laser spot on the target is m. The deflection angle is calculated by trigonometric function with the values of l 1, l 2 and m. The equation is shown as follows: (21) Figure 5. The influence law of eccentric rings installation position on M 2. and extend the service life of cantilever bearing. 4.2 Test Procedure of the Bit Deflection Angle Before the test, the tool should be adjusted to the reference position through the control program, which means the thicker side of the internal eccentric ring faces down and the thicker side of the external eccentric ring faces up. The laser point should be set to be coincident with the center of target and the maximum eccentric displacement and tool face angle of the shaft should be in- 4. Lab Testing In order to further verify the reliability and feasibility of above mechanical analysis on the shaft of the wellbore trajectory control tool, the lab simulation experiment was carried out by using the test bench of the tool. The magnitude of the drill bit deflection angle was tested and verified by comparing with theoretical calculation value. The test bench of the tool mainly contains two parts: the principle prototype and the measurement andcontrol system.asshowninfigure6,itisusedto simulate the process of downhole drilling with the tool, and to test basic parameters of the tool and related equipment. Figure 6. Test bench of the wellbore trajectory control tool with the high build-up rate. Figure 7. Schematic diagram of test method of bit deflection angle.

8 442 Hong Zhang et al. put. While deflection is finished, the tool face angle and the laser point offset can be measured. By changing the length of l 2 and after a number of trial, test data of m and l 2 are obtained as shown in Table 2. In Table 2, the tool face angle is always maintained at about 0 degree and the maximum error is 2 degree. The length of l 1 in Figure 7 is measured to be equal to mm. According to different values of l 2 and m, several sets of deflection angles of the bit can be calculated and then the mean deflection angle value can be obtained. Through the test, deflection angle of the bit is equal to Theoretical Calculation of the Bit Deflection Angle As shown in Figure 3, for the prototype of the wellbore trajectory control tool, L 2 is equal to 1795 mm, L 1 is equal to 590 mm. So polar second moment of area of the shaft can be got: I = mm 4. Maximize the deflection of the shaft y = 6 mm. According to formula (8), (12) and (15), = can be obtained. 4.4 Result Analysis Comparison between the test value and theoretical calculation one of the bit deflection angle shows the two values are very close, where error between them is and proximity is up to about 98%. After analysis, it is found that the errors are caused by the following reasons: 1) Lack of processing accuracy on the tool leads to errors of test data; 2) The laser point is coincided with the center of the target by manual adjustment which is not accurate enough; 3) In the process of measurement the laser point rotates in a circle with a very small radius, which causes the error of the measurement of the laser pointer s practical position; 4) There exist errors in measurement of distance. Above errors are in the allowable range. 5. Conclusions (1) Combined movement of eccentric rings inside the wellbore trajectory control tool implements the eccentric motion with any angle in three-dimensional space. The mechanism of deformation of the shaft motion is analyzed and the shaft eccentricity trajectory is obtained. (2) The wellbore trajectory control tool uses an indirect drilling pressure transmission method, which indirectly passes the drilling pressure from tool housing to the shaft. Based on the analysis of the shaft mechanical behavior, the flexural equation of the shaft at the static bias state is deduced as well as its angle equations, bearing reaction equation and bending moment equations. The mechanical model of the shaft is established and optimized, and optimization suggestions are given. (3) The lab simulation experiment was carried out by using the dynamic simulation test system of the tool. The result shows that the data measured in experiments is very close to the data derived from the theoretical calculation and their proximity is up to about 98%. As a result, the reliability and feasibility of the mechanical model of the shaft established is verified. Acknowledgments Supported by Open Fund (No. OGE ) of Key Laboratory of Oil & Gas Equipment AMinistry of Education (Southwest Petroleum University), Open Fund Table 2. Test data of m and l 2 Eccentric displacement (mm) Tool face angle ( ) Rotation angle of internal eccentric ring ( ) Rotation angle of external eccentric ring ( ) The length of l 2 (mm) The measures values of tool face angle ( ) The laser point offset m (mm)

9 Study on Deformation Motion and Mechanical Model of the Shaft of the Wellbore Trajectory Control Tool 443 (No. 2016KJX12) of Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, National Natural Science Foundation of China (No ) and the Project of Middle-aged and Young Talents of Educational Committee in Hubei Province (No. Q ). References [1] Downton, G., Hendrics, A., Klausen, T. S. and Pafitis, D., New Directions in Rotary Steerable Drilling, Oilfield Review, Vol. 12, No. 1, pp (2000). [2] Weijermans, P., Ruszka, J., Jamshidian, H. and Matheson, M., Drilling with Rotary Steerable System Reduces Wellbore Tortuosity, Society of Petroleum Engineers, pp (2013). doi: / MS [3] Pastusek, P., Brackin, V. J. and Lutes, P. J., A Fundamental Model for Prediction of Hole Curvature and Build Rates with Steerable Bottomhole Assemblies, SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, October 9 12 (2005). doi: /95546-MS [4] Noynaert, S. F., AIMR (Azimuth and Inclination Modeling in Realtime): A Method for Prediction of Dogleg Severity based on Mechanical Specific Energy, Texas A&M University (2013). [5] Sugiura, J., Bowler, A. and Lowdon, R., Improved Continuous Azimuth and Inclination Measurement by Use of a Rotary-steerable System Enhances Downhole-steering Automation and Kickoff Capabilities Near Vertical, SPE Drilling & Completion, New Orleans, Louisiana, USA, September 30 October 2 (2013). doi: / PA [6] Edwin, F., Ariel, T., Neil, D. G., Kate, M., Sivaraman, N., Richard, H., Ke, L., Stephen, J. and Fred, S., The Best of Both Worlds-A Hybrid Rotary Steerable System, Oilfield Review, Vol. 23, pp (2011). [7] Sugiura, J., Optimal BHA Design for Steerability and Stability with Configurable Rotary-steerable System, SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, October (2008). doi: / MS [8] Iyoho, A. W., Rask, J. H., Wieseneck, J. B. and Grant, L. S., Comprehensive Drilling Model Analyzes BHT Parameters, SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, October 4 7 (2009). doi: / MS [9] Hobbs, G., Stinson, R., Alvord, C., Anyanwu, O. N., Klotz, C., Mohammad, M. and Huges, B., First Field-testing of a New Rotary Steerable Drilling Liner Technology on Alaska North Slope, IADC/SPE Drilling Conference and Exhibition, Fort Worth, Texas, USA, March 4 6 (2014). doi: / MS [10] Feng, D., Wu, L., Wang, J. W., Liu, X. H., Zhang, H. and Li, H. X., Research on Eccentric Displacement of the Trajectory Control Tool of High Build-up Rate Wellbore, International Conference on Information Technology and Management Innovation, Guangzhou, China, November (2012). [11] Feng, D., Liao, Z. W., Zhang, H., Shi, L., Xia, C. Y. and Wei, S. Z., The Study of Load Distribution for Combination Bearing in Wellbore Trajectory Control Tool, International Conference on Electrical, Automation and Mechanical Engineering, Phuket, Thailand, July (2015). doi: /eame [12] Feng, D., Xiao, A., Liao, Z. J., Xie, Y., Ruan, C. and Wang, J. W., Loading and Axial Deformation of Finite Element Analysis of Down-hole Strings Used for Hydraulic Fracturing, Applied Mechanics and Materials, Vol. 318, pp. 3 6 (2013). doi: /www. scientific.net/amm [13] Guevara, A., Sandoval, J., Guerrero, M. and Manrique, C., Milestone in Production Using Proactive Azimuthal Deep-resistivity Sensor Combined with Advanced Geosteering Techniques: Tarapoa Block, Ecuador, SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico, April (2012). doi: / MS Manuscript Received: Dec. 27, 2016 Accepted: Apr. 13, 2017

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