Study on Build-up Rate of Push-the-bit Rotary Steerable Bottom Hole Assembly

Journal of Applied Science and Engineering, Vol. 20, No. 3, pp. 401 408 (2017) DOI: 10.6180/jase.2017.20.3.15 Study on Build-up Rate of Push-the-bit Rotary Steerable Bottom Hole Assembly Heng Wang*, Zhi-Chuan Guan, Yu-Cai Shi and De-Yang Liang School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, P.R. China Abstract Rotary steerable drilling is an effective technique for drilling directional wells. Given the currently inadequate understanding about the variation of build-up rate for rotary steerable bottom hole assembly under different drilling condition, a build-up rate prediction model needs to be established. Aimed at push-the-bit rotary steerable bottom hole assembly, a continuous beam model was applied to study the mechanical properties. Further considering drill bit cutting anisotropy, the build-up rate prediction method was built. Effects of configuration parameters on build-up rate were analyzed. Results showed that build-up rate decreases with the increasing of distance between bit and steering pads. There was an optimal distance between bit and near-bit stabilizer to obtain a maximum build-up rate. With lower flexural rigidity and longer length of flex sub, the build-up rate is much higher. Smaller diameter of near-bit stabilizer diminished build-up rate. However, smaller diameter of upper stabilizer improved build-up rate. And build-up rate became bigger when distance between the two stabilizers extended. The study can provide theoretical basis for optimal configuration design of push-the-bit rotary steerable bottom hole assembly to get higher steering ability. Key Words: Rotary Steerable Drilling, Mechanical Property, Cutting Anisotropy, Build-up Rate, Configuration 1. Introduction Rotary steerable drilling is now one of hot research topics in drilling engineering field. With the superiority in drilling rate improvement, borehole quality and horizontal section extending ability, it has become more and more widely used in drilling horizontal, extended reach and multilateral wells [1,2]. Currently, there are two types of rotary steerable system (RSS): push-the-bit and point-the-bit RSS [3]. When well control instructions are given, the RSS will carry out the instructions to achieve well control goal. The determination of control instructions rely on rotary steerable bottom hole assembly (RSBHA) build-up capability. So it is of great importance to understand the build-up rate of RSBHA. *Corresponding author. E-mail: wanghengupc@163.com Several methods have been developed for predicting build-up rate of bottom hole assemblies (BHAs). Karisson et al. first presented three point geometry method to calculate BHAs build-up rate [4]. Liu et al. put forward a correctional three point geometry in consideration of the position of bent angles and the radial clearance between bottom stabilizer and borehole wall [5]. Sugiura analyzed the driving mechanism of push-the-bit RSBHA and gave out the build-up rate calculation formula based on the geometry method [6]. The three point geometry method is simple to understand and easily calculated. But it ignores the effect of drilling parameters to BHAs deformation. Birades et al. took BHAs equilibrium curvature as inclination gradient of drilling [7]. The core was when bit side force became zero, the borehole curvature would maintain a constant value and that is the equilibrium curvature. Compared with three point geometry,

402 Heng Wang et al. equilibrium curvature method considered the effect of borehole parameters and drilling parameters to BHAs build-up rate. Su et al. pointed out the actual build-up rate is lower than equilibrium curvature. Then limiting curvature model was established by multiplying a factor to equilibrium curvature [8]. Instances proved Su s viewpoint right. However, the difference of bit cutting property was not considered into those methods. Researches and engineering showed bit cutting property played an important role in well trajectory building [9 11]. To reveal the influence of bit cutting property to BHAs drilling tendency, bit cutting anisotropy index was put forward which represented the capability of bit side cutting [12]. The bigger index value was, stronger the capability of bit side cutting would be. Shi and Xia established tendency angle model to reflect the drilling tendency using bit cutting anisotropy index [13,14]. But it needs a quantitative relation between cutting anisotropy index and BHAs build-up rate for evaluating the BHAs build-up capability. In this paper, focus was concentrated on push-the-bit RSBHA of the two types of RSBHA. Firstly, a continuous beam model was built to characterize the mechanical properties of push-the-bit RSBHA where bit side force and tilt angle could be obtained when configuration parameters, borehole parameters and drilling parameters were given. Then build-up rate prediction method was established according to tendency angle model. Instance was given out to verify the validity and accuracy of this method. Then the effect of configuration parameters to push-the-bit RSBHAs build-up rate was analyzed. This will be beneficial to optimal RSBHA configuration design to attain a higher build-up capability. 2. RSBHA Mechanical Model The steering principle of push-the-bit rotary steerable drilling tool can be summarized as: when a well control instruction is given, the three steering pads will extend to the borehole wall, pushing the drill string to the other side of wellbore and generating lateral forces on the bit and stabilizer. Then bit will generate side cutting and drill towards orientation of resultant steering force [15]. The directional drilling is as shown in Figure 1. Under different borehole parameters and drilling parameters condition, RSBHA will be in different stress state where bit lateral force and tilt angle change with the variation of those parameters. So it is necessary to calculate bit lateral force and tilt angle when a certain condition is given. Continuous beam theory is an effective method solving this question. It is assumed that the bottom hole is a section of arc located in the plane of a certain space. Then the three-dimensional force of RSBHA can be solved separately in two two-dimensional planes called inclination plane P and azimuth plane Q. To obtain the value of bit lateral force and tilt angle, we should analyze the stress state of the string span between bit and near-bit stabilizer as shown in Figure 2. The string span is mainly affected by weight on bit (WOB), weight per meter of string, steering force, bit lateral force and bending moment at near-bit stabilizer. According to the continuous beam theory [16], relationship between bit lateral force, tilt angle and the influencing parameters can be derived. The theory considers a multi- Figure 1. Directional drilling of push-the-bit RSBHA.

Study on Build-up Rate of Push-the-bit Rotary Steerable Bottom Hole Assembly 403 Figure 2. Mechanical properties of drill bit. stabilized bottom hole assembly in borehole as a continuous beam-column with many supports. And then the beam-column can be divided into several simply-supported beam-columns by separating the sections at each stabilizer. In the case of inclination plane P, bit lateral forceis expressed as Equation (1): (1) Equation (1) was obtained according to the force balance principle for the string span between bit and near-bit stabilizer. Where N bp is the component force on P plane of bit lateral force, called deviation force, KN; P b is WOB, KN; q 1 is weight per meter of the string span between bit and near-bit stabilizer, KN/m; M 1P is the bending moment on P plane at near-bit stabilizer, KN m; M 1P is a unknown value, it needs resolved by three moment equations. L 1 is the length of string span between bit and near-bit stabilizer, m; L 11 is the distance between steering pads to bit, m. F P is the component force on P plane of resultant steering force and y 1 is the ordinate value of near-bit stabilizer s center in an arc borehole. They can be expressed as: (2) (3) where p is the tilt angle in P plane, rad; EI 1 is the flexural rigidity of string span between bit and near-bit stabilizer, KN m 2 ; X(u 1 ), Z(u 1 ) are the amplification factors. k is a stability factor resulting from the effect of axis forces applied at both ends of simply-supported beam-column and can be expressed as: (5) Azimuth force N bq and tilt angle Q on azimuth plane Q can also be gotten with the similar analysis. 3. Build-up Rate Prediction Method Drill bit plays an important role in well trajectory formation. RSBHAs build-up rate will be different with the change of bit side cutting capability which can be evaluated by the index of bit cutting anisotropy. On the basis of equilibrium curvature, we further take bit cutting anisotropy index into consideration and establish push-the-bit RSBHA build-up rate prediction method. Establish the geodetic coordinate system O-NED taking wellhead O as the origin. Taking bottom hole center o as the origin, establish bottom hole coordinate system o-xyz and bit coordinate system o-x y z separately. The coordinates are shown as Figure 3. In the bottom hole coordinate system, x axis points in the tangent direction of the borehole axis and z axis points towards high side direction of borehole. The direction of y axis is determined by right-hand rule. Bit coordinate system is where F is the resultant steering force, KN; is tool face angle, rad; K P is the borehole curvature in P plane, /30 m; is the gap value of near-bit stabilizer to borehole wall, m. Bit tilt angle can be obtained by the superposition of influencing components and is expressed as Equation (4): (4) Figure 3. Geodetic, bottom hole and bit coordinates system.

404 Heng Wang et al. formed through bottom hole coordinate by turning an angle value of P around y axis, and then turning Q around z axis [17]. The x axis points towards bit axis and y, z point towards bit side direction. We can get the bit force value F(x, y, z) =[P b N bp N bq ] T in the bottom hole coordinate system and tilt angle P, Q by the push-the-bit RSBHA mechanical analysis model above. Then convert the bit force into bit coordinate system, we can get an equation as follows: (6) where F(x, y, z ) is the bit force in bit coordinate system, KN; [k 1 ] is the transformation matrix of bottom hole coordinate and bit coordinate system. According to the definition of bit cutting anisotropy index, drilling speed components of bit in bit coordinate system can be described as follows: (7) (8) (10) where A P, A Q is the inclination tendency angle in plane P and azimuth tendency angle in plane Q, collectively called tendency angle, rad; V x, V y, V z is the drilling speed component in x, y and z axis separately, m/h; B is the inclination angle at bit, rad; The tendency angle represents the included angle value of bit resultant velocity direction and borehole axis direction in P and Q plane separately. Inclination tendency angle is as Figure 4 shows. When the tendency angle A P, A Q comes close to zero, RSBHA will be at an equilibrium state where build-up rate will maintain a constant value. We call the borehole curvature at present as the ultimate build-up rate of RSBHA. If the value of A P, A Q isn t equal to zero, then we give another borehole curvature until tendency angle comes close to zero. This method built for predicting push-the-bit RSBHA can be called equilibrium tendency method. 4. Instance Analysis In order to verify the reliability of the build-up rate prediction model of push-the-bit RSBHA, we take the experimental well gas storage-1-c1 drilling data of Chuanqing Drilling & Production Technology Research Institute to compare with the result of the prediction model. where V(x, y, z ) is the drilling speed of bit in bit coordinate system, m/h; I b is the bit cutting anisotropy index; V l, V a is the drilling speed component in side direction and axis direction of bit coordinate system separately, m/h; F l, F a is the bit lateral force and axis force in bit coordinate system, KN. Then convert the drilling speed components back to bottom hole coordinate system: (9) where V(x, y, z) is the drilling speed of bit in bottom hole coordinate system, m/h. Tendency angle can be expressed as: Figure 4. Inclination tendency angle.

Study on Build-up Rate of Push-the-bit Rotary Steerable Bottom Hole Assembly 405 The steering parameters in drilling experimental well section are as Table 1 shows. Push-the-bit RSBHA: 215.9 mm PDC bit 0.34 m + 192 mm adapter 430 411 0.39 m + 178 mm rotary steerable system 411 410 13.17 m + inverted valve 411 410 + 165.1 mm non-magnetic drill collar 411 410 + 165.1 mm drill collar 411 410 + 127 mm drill string. Drilling parameters: WOB is 60 KN and drilling fluid density is 1.27 g/cm 3. Bit cutting anisotropy index is 0.036. Table 2 gives out actual build-up rate of push-the-bit RSBHA as well as prediction value of limiting curvature and equilibrium tendency method. Table 2 shows that compared with actual build-up rate, the equilibrium tendency method gives a calculating value within the margin of error. Because limiting curvature is an effective means for predicting BHAs build-up rate, so results of the two methods are put together to have a comparison. It can be seen equilibrium tendency method has a lower error than limiting curvature method in most cases except well section 694 732 m. Actually, BHA s build-up rate is also affected by the formation property which is difficult to predict [12]. Under the same steering force condition, the build-up rate will become much bigger with the decrease of formation resistance ability to bit lateral cutting. It is known that Table 1. Experimental steering parameters Well section/m Resultant steering force/kn Tool face angle/ the formation property may get changed during different drilling depth. So, we surmised that formation property varied in well section 694 732 m. Though an occasional smaller error showed in this well section using limiting curvature method it can t illustrate that the limiting curvature method was much better because neither limiting curvature method nor equilibrium tendency method took formation property into consideration. On the whole, the calculation results proved the method built in this paper correct and reliable for evaluating build-up rate of pushthe-bit RSBHA. 5. Influencing Factors Analysis From the analysis above, we can see build-up rate is affected by many factors such as BHA s configuration parameters, drilling parameters and bit cutting property. Focus is concentrated on push-the-bit RSBHA s configuration parameters in this paper. The result will benefit for optimal BHA configuration design with a higher steering ability. Push-the-bit RSBHA: 215.9 mm PDC bit + 178 mm rotary steerable tool + 214 mm stabilizer + 127 mm flex sub + 165.1 mm drill collar + 213 mm stabilizer + 165.1 mm drill collar. The configuration is shown as Figure 5. Where L 11, L 1 is the distance from bit to steering pads and near-bit stabilizer separately, m; L 21, L 2 is the length of flex sub and distance between two stabilizers sepa- 670-694 15 0 694-732 15 60 732-751 15 330 751-774.5 15 270 774.5-809.39 22.5 0 Figure 5. Push-the-bit RSBHA configuration. Table 2. Build-up rate comparison of different method Actual build-up Limiting curvature method Equilibrium tendency method Well section (m) rate ( /30 m) Build-up rate ( /30 m) Error (%) Build-up rate ( /30 m) Error (%) 670-694 3.24 3.34-3.09 3.33 2.78 694-732 3.61 3.58-0.72 3.36-6.93-732-751 3.12 3.55-13.820 3.31 6.26 751-774.5 3.15 3.44-9.11 3.27 3.81 774.5-809.39 5.27 4.92-6.71 4.99-5.40-

406 Heng Wang et al. rately, m. When the length of L 11, L 1, L 21, L 2 isn t changed, the basic length is 1.2 m, 2.3 m, 1.68 and 7.9 m separately. Internal diameter of the RSBHA is 57. 2 mm. Drilling parameters: WOB is 60 KN and resultant steering force is 10 KN with tool face angle 0.523 rad. Drilling fluid density is 1.27 g/cm 3. Bit cutting anisotropy index takes 0.1. Inclination angle at bit is 0.523 rad and azimuth angle is 1.57 rad. 5.1 Distance from Bit to Steering Pads and Near-bit Stabilizer Change the distance from bit to steering pads and near-bit stabilizer L 11, L 1. The relationship between build-up rate and L 11, L 1 can be obtained as Figure 6 shows. Figure 6 shows that when the distance from bit to near-bit stabilizer L 1 maintains a certain value, build-up rate will decreases with the increasing of distance from bit to steering pads L 11. This is caused by decreasing of bit lateral force when L 11 becomes larger. When L 11 maintains a certain value, build-up rate will rise first and then go down with the increasing of L 1. The growth rate is larger than reduction speed of build-up rate. An optimal distance from bit to near-bit stabilizer exists achieving the highest steering ability. 5.2 Flexural Rigidity, Length of Flex Sub and Distance between Two Stabilizers Change the flexural rigidity EI of flex sub and change the length of flex sub L 21 and distance between two stabilizers L 2. Then relationship between build-up rate and EI, L 21, L 2 can be obtained as shown in Figure 7 and Figure 8. Figure 7 shows that build-up rate decreases nonlinearly with the increasing of flexural rigidity EI actually the out-diameter of flex sub. And the value tends to stabilize after the first rapid decline. This is because with the increasing of EI, bending moment at near-bit stabilizer will be bigger. Thus, bit lateral force will be lower. Figure 8 shows when the distance between two stabilizers L 2 maintains a certain value, build-up rate will become higher with the increasing of flex sub s length L 21. Flexural rigidity of whole section between two stabilizers will actually decrease with a longer length of flex sub when L 2 maintains a certain value. From a perspective of improving steering ability, lower EI and longer L 21 should be taken. However, the reliability and strength requirements of push-the-bit RSBHA should also be considered which will limit the value of EI and L 21 [18]. Figure 8 also demonstrates that build-up rate will increase slightly with the increasing of L 2 when L 21 doesn t change. It indicates we can properly extend the distance between two stabilizer to get a higher build-up rate. Figure 7. Relation between build-up rate and flexural rigidity of flex sub. Figure 6. Relation between build-up rate and distance from bit to near-bit stabilizer. Figure 8. Relation between build-up rate and distance of two stabilizers.

Study on Build-up Rate of Push-the-bit Rotary Steerable Bottom Hole Assembly 407 5.3 Gap between Stabilizer and Borehole Wall The relationship between build-up rate and gap of stabilizer to borehole wall is as Figure 9 shown. It can be seen that the gap between stabilizer and borehole wall plays an opposite role in affecting push-the-bit RSBHA build-up rate. With the increasing of gap at near-bit stabilizer, build-up rate declines linearly. On the contrary, build-up rate rises linearly with increasing of gap at upper stabilizer. Bigger gap at near-bit stabilizer will cause a larger bit tilt angle resulting decrease of tendency angle when steering force is given. However, bigger gap at upper stabilizer can decrease the bending degree of RSBHA in borehole producing a larger bit lateral force when equal steering force is applied. From a perspective of increasing build-up rate, it is better to have a smaller gap at the near-bit stabilizer that is a larger out-diameter of near-bit stabilizer and a smaller out-diameter of upper stabilizer. But it is much easier to get stuck with a larger out-diameter for near-bit stabilizer. For upper stabilizer, the decrease of out-diameter will reduce the stability of RSBHA resulting severe lateral vibration. So the determination of stabilizers out-diameter should further consider dynamic influencing factors. 6. Conclusions (1) Equilibrium tendency method further considers the effect of bit cutting anisotropy to push-the-bit RSBHA build-up capability compared with equilibrium curvature. Instance proves the method feasible and reliable to predict the build-up rate of push-the-bit RSBHA. (2) Among the configuration parameters, the distance from bit to steering pads, length and flexural rigidity of flex sub have a more obvious effect to build-up rate than the distance from bit to near-bit stabilizer, distance between two stabilizers and stabilizers out-diameter. Build-up rate grows up with the decreasing of distance from bit to steering pads. Flex sub can improve the build-up capacity which goes higher with a longer length and lower flexural rigidity of flex sub. (3) It is better to use longer length and lower flexural rigidity of flex sub from a perspective of increasing Figure 9. Relation between build-up rate and gap of stabilizer to borehole wall. build-up rate. However, the stability and strength requirement of RSBHA needs to be guaranteed. So the optimal configuration parameters should further consider dynamic property of push-the-bit RSBHA. Acknowledgment The authors would like to acknowledge the academic and technical support of China University of Petroleum (East China). This paper is supported by the National Science and Technology Major Project (2016ZX 05022-002) and the Fundamental Research Funds for the Central Universities (16CX06035A). References [1] Albardisi, T., Akhmetov, R., Sanderson, M., et al., Hybrid High Build Rate RSS Improves Challenging Directional Control in a Soft Abrasive Drilling Environment in Oman Drilling Operation, SPE Heavy Oil Conference, Albert, Canada, Jun. 10 12 (2014). [2] Bai, J., Liu, W. and Huang, C. J., Application of Rotary Steering Drilling Technology in Sichuan Shale Gas Reservoir, Drilling and Production Technology, Vol. 39, No. 2, pp. 9 12 (2016). doi: 10.3969/J.ISSN. 1006-768X.2016.02.03 [3] Xue, Q. L., Ding, Q. S., Huang, L. L., et al., The Latest Progress and Development Trend of Rotary Steering Drilling Technology, China Petroleum Machinery, Vol. 41, No. 7, pp. 1 6 (2013). doi: 10.3969/j.issn. 1001-4578.2013.07.001 [4] Karlsson, H., Cobbley, R. and Jaques, G. E., New De-

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