Advertisement

Analysis and optimization of control algorithms for RSSTSP for horizontal well drilling

  • Li Gang Zhang
  • G. R. Liu
  • Wei Li
  • Shi Bin Li
Open Access
Original Paper - Exploration Engineering
  • 253 Downloads

Abstract

Steering control algorithm plays an important role in a rotary steerable system for horizontal well drilling, including the determination of the well trajectory, vibrations, stability, durability among other variables. This work develops a control algorithm for three static push-the-bit rotary steerable systems (RSSTSP) (TSP is the abbreviation of “three static push-the-bit”). Based on the structure, mechanism, and working process of the RSSTSP, mechanical and mathematical models are proposed to determine the required steering force (amplitude and direction) to move the drill bit from a point to another. Additional equations are constructed to overcome the non-uniqueness and then compute the optimal forces for the three pads to achieve the required steering force. Moreover, a new control algorithm of RSSTSP is developed, considering the steerability, stability, durability, favorable area, unfavorable area, maximum usable magnitude of steering force. The proposed control algorithm is also applied to a new RSSTSP and tested on a GU-693-P102 well for validation. It is found that each pad force changes smoothly, the drilling tool is stable, and the well trajectory is consistent with the design, demonstrating that our proposed control algorithm is robust and effective for RSSTSP for horizontal well drilling.

Keywords

Horizontal well drilling Rotary steerable system (RSSTSPControl algorithm Steering force Pad force Dogleg 

Introduction

With the technological development for unconventional oil and natural gas productions, the numbers of horizontal and three-dimensional multi-target directional wells have increased significantly (Ozkan et al. 2011; Jia et al. 2014; Orem et al. 2014). Drilling equipment not only needs to meet requirements for desired drilling trajectory, but also needs to work reliably in more complex stratum and harsher operating conditions, which presents significant challenges on the drilling technology (John et al. 2000; Kaiser and Yu 2015; Ikonnikova et al. 2015). In recent decades, rotary steerable systems (RSS) have developed very rapidly, in their capability to provide continuous rotation, constant steering, and smoother boreholes (Weijermans et al. 2001; Drummond et al. 2007; Hakam et al. 2014). RSS ensure steering the borehole when drill string is rotating, and are usually used together with a logging while drilling (LWD) system. Geological parameters are analyzed in real time, and then precise control of the directional trajectory is achieved based on geological conditions (Haugen 1998; Tribe et al. 2001; Torsvoll et al. 2010). So far, Schlumberger’s PowerDrive, Baker Hughes’ AutoTrak, and Halliburton’s Geo-Pilot have been the main representative technologies (Stuart et al. 2000; Tribe et al. 2001; Bian et al. 2011; Wang et al. 2014). RSS can be divided into static bias and dynamic bias according to different bias units and can also be divided into push-the-bit and point-the-bit approaches according to different directing principles. PowerDrive and AutoTrak belong to “push-the-bit,” while Geo-Pilot belongs to “point-the-bit” type. PowerDrive is of dynamic bias, while AutoTrak is of static bias (Schaaf 2000; Fontenot et al. 2005; Wang et al. 2014). This article focuses on three static push-the-bit (RSSTSP) like AutoTrak systems. RSSTSP have three stretching pads, which press against the well bore thereby causing the bit to press on the opposite side resulting in a direction change (Niu et al. 2013; Wang et al. 2014, Marck and Detournay 2016). Steering control algorithm plays an important role in any RSSTSP, and a robust control algorithm is the key factor to achieve the desired control effects (Seifabad and Ehteshami 2013; Hakam et al. 2014; Kremers et al. 2015).Because many of these techniques are not available to the public, the research papers for control algorithm for RSSTSP are very few in the published literature. Zhang and Yu analyzed the configuration and deviation principle of RSSSTP (Zhang 2000). Cheng and Jiang studied control method, using biasing displacement vector (Cheng et al. 2010). Du and Liu studied multi-solution and uncertainty for controlling three pad forces. Models were established with two pads and adapted to adjust and control magnitude and orientation of steering force vector, and another pad extended to wellbore without force (Du et al. 2008). Due to non-unique solutions, Li et al. (2015) proposed to use three pads working at the same time, where one pad force should have a maximum or minimum value determined by relative position of pad and steering forces. The aforementioned papers mainly deal with how to calculate steering force. However, vibrations, stability, and durability were not considered. Therefore, based on the structure and work process of RSSTSP, this work develops mechanical and mathematical models for the steering force and pad force. A new control algorithm is developed considering factors of steerability, stability, durability, “favorable area,” and “unfavorable area.”

Structure and work process of RSSTSP

RSSTSP has three support pads: pad 1, 2, and 3, which are spaced 120° apart from each other, as shown in Fig. 1a, with coordinated movements for rotating spindle, drill string, and bit rotating. The pads are relative static to the rotating outside sleeve. The pads are driven by drilling fluid and stretched out to press against the well bore, thereby causing the bit to press on the opposite side causing a direction change. The support force for each pad is expressed as F1, F2, F3, respectively, as shown in Fig. 1b. The resultant force F of three pad forces forms the total steering force, leading to desired changes in inclination and azimuth, as shown in Fig. 1c.
Fig. 1

Schematic of the structure and pad forces of a typical RSSTSP

The RSSTSP works as follows: The value and direction of steering force are first determined based on the current actual point and the expected point on the ground. The steering force is then transmitted downhole. Based on steering force, each pad force is next determined in accordance with predetermined control algorithms downhole. Lastly, the pads are pushed out by applying hydraulic pressure, and the expected steering force and well trajectory are realized. In the whole process, a robust algorithm for steering force and pad force is the key factor for achieving the desired control effects.

Maximum usable steering forces (A max)

For a given hydraulic pressure applied, the static bias pad has a maximum or minimum support force (Fmax or Fmin). Because the three pads are 120° apart, the range of the steering force is in a hexagon, as shown in Fig. 2a, b. The hexagon shall have an inner circle and an outer circle, as shown in Fig. 2c.
Fig. 2

Inner circle and outer circle hosting the hexagon of maximum pad force

For a given position of the three pads, if the maximum usable magnitude of steering force (Amax) is within the inner circle and outer circle touching the hexagon, it can only be realized at a point on the hexagon, as shown in Fig. 3. If the steering force is within the inner circle, it can be achieved everywhere. In the actual operation, in order to achieve a steering force in all directions at any time, the steering force must be adjustable in 360°. Therefore, the steering force should be limited in the range within the inner circle. Thus, the maximum usable magnitude of steering force is not Fmax, but Amax shown in Fig. 3.
Fig. 3

Vector geometry of the maximum steering force

The maximum usable magnitude of steering force can be expressed as follows:
$$ A_{\hbox{max} } = \frac{\sqrt 3 }{2} \times (F_{\hbox{max} } - F_{\hbox{min} } ), $$
(1)
where Fmax is the maximum support force of the pad, Fmin is the minimum support force of the pad, and Amax is the maximum usable magnitude of steering force. It is necessary to consider the constraint of Amax in the control algorithm, so as to achieve a desired dogleg, build rate, or walk rate in the actual operations.

Amplitude and direction of the required steering force

Consider a RSSTSP used in a drilling operation. The amplitude and its direction of the required steering force should be determined based on the current point and orientation of the drill bit and the target point and orientation one would want the drill bit to be.

Amplitude of the required steering force (A k )

Assume that the current drill bit is at point A (XA, YA, ZA), and the actual hole inclination angle and azimuth angle are αA and βA. The targeted position is at point C (XC, YC, Z C ), and the expected inclination angle and azimuth angle are αC and βC. The tangent lines at points A and C intersect at point D, and the normal lines of points A and C intersect at point O, as shown in Fig. 4.
Fig. 4

Current position “A” and targeted position “C”

Let the changes in inclination angle and azimuth angle be ΔαAC and ΔβAC, and the average inclination angle of points A and C be α0. The γ of points A and C can be calculated as follows:
$$ \gamma = \frac{{30 \times 360\left| {\sin \frac{{\sqrt {\Delta \alpha_{\text{AC}}^{2} + \Delta \beta_{\text{AC}}^{2} \cdot \sin \alpha_{0}^{2} } }}{2}} \right|^{{}} }}{{\pi \sqrt {(X_{\text{C}} - X_{\text{A}} )^{2} + (Y_{\text{c}} - Y_{\text{A}} )^{2} + (Z_{\text{C}} - Z_{\text{A}} )^{2} } }}, $$
(2)
where \( \Delta \alpha_{\text{AC}} = \alpha_{\text{C}} - \alpha_{\text{A}} \), \( \Delta \beta_{\text{AC}} = \beta_{\text{C}} - \beta_{\text{A}} \), \( \alpha_{0} = \frac{{\alpha_{\text{A}} + \alpha_{\text{C}} }}{2}_{{}} \), γ is the dogleg, αA is the inclination angle of point “A,” αc is the inclination angle of point “C,” and αo is the average inclination angle.
The γ max of RSSTSP is usually known and supplied by manufactures under Amax. The work efficiency of RSSTSP is defined as follows:
$$ A_{k} = \frac{\gamma }{{\gamma_{\hbox{max} } }} \times 100\% , $$
(3)
where γmax is the dogleg when working under Amax.

If the value of A k is greater than 100%, it would not be drilled to the target point. In this situation, it is necessary to redesign well trajectory and redetermine target point until the value of A k is less than 100%.

It can also be expressed using the amplitudes of the steering forces in relation to its maximum usable magnitude, as follows:
$$ A_{k} = \frac{F}{{A_{\hbox{max} } }} \times 100\% , $$
(4)
where F is the steering force.

Therefore, once A k is obtained, the amplitude of the steering force F can be calculated using Eq. (4).

Direction of steering force (α k )

The direction angle of steering force (α k ) is defined as clockwise rotation angle from high side to the direction of steering force in the bottomhole plane. The steering force could be broken up into build force and walk force, as shown Fig. 5.
Fig. 5

steering force distribution in bottomhole plane

The “+” indicates increase in “build force” or “walk force,” and the “−” indicates decrease in “build force” or “walk force.” Build rate and walk rate are also determined by steering force and the direction angle of steering force α k .

With the current point (A) and expected point (C) shown in Fig. 4, the expected build rate (∆α) and the walk rate (∆β) can be obtained using
$$ \Delta \alpha = 30 \times \frac{{\alpha_{\text{c}} - \alpha_{\text{A}} }}{{\Delta D_{m} }}, $$
(5)
$$ \Delta \beta = 30 \times \frac{{\beta_{c} - \beta_{A} }}{{\Delta D_{m} }}, $$
(6)
where Δα is the expected build rate, βA is the azimuthal angle of point “A,” βc is the azimuthal angle of point “A,” βo is the average azimuthal angle, and Δβ is the expected walk rate.
The relations between dogleg γ and α K , Δα and Δβ (Lapeyrouse et al. 2002) are shown in Fig. 6.
Fig. 6

Diagram for calculating dogleg

Figure 6 shows graphic relationship between α K Δβ, α0, and Δα. According to the changes in the inclination and azimuth, α K can be divided into following nine cases:
$$ _{\text{k}} = \left( {\begin{array}{*{20}c} {\begin{array}{*{20}c} {0,\left( {\Delta \alpha > 0\text{,}\Delta \beta = 0} \right), \left( 1 \right)} \\ {\begin{array}{*{20}c} {\arctan \left( {\frac{\Delta \beta \times \sin \alpha 0}{\Delta \alpha }} \right),\left( {\Delta \alpha > 0\text{,}\Delta \beta > 0} \right), \left( 2 \right)} \\ {90, \left( {\Delta \alpha = 0\text{,}\Delta \beta > 0} \right), \left( 3 \right)} \\ {\arctan \left( {\frac{\Delta \beta \times \sin \alpha 0}{\Delta \alpha }} \right) + 180,\left( {\Delta \alpha < 0,\Delta \beta > 0} \right),\left( 4 \right)} \\ \end{array} } \\ {180,\left( {\Delta \alpha < 0\text{,}\Delta \beta = 0} \right),\left( 5 \right)} \\ {\arctan \left( {\frac{\Delta \beta \times \sin \alpha 0}{\Delta \alpha }} \right) + 180,\left( {\Delta \alpha < 0\text{,}\Delta \beta < 0} \right),\left( 6 \right)} \\ \end{array} } \\ {270,\left( {\Delta \alpha = 0\text{,}\Delta \beta < 0} \right), \left( 7 \right)} \\ {\arctan \left( {\frac{\Delta \beta \times \sin \alpha 0}{\Delta \alpha }} \right) + 360,\left( {\Delta \alpha < 0\text{,}\Delta \beta < 0} \right), \left( 8 \right)} \\ {None,\left( 9 \right)} \\ \end{array} } \right) $$
(7)
  1. 1.

    Full working to advance the inclination, while the azimuth is not changed.

     
  2. 2.

    Both the inclination angle and azimuth angle are all advanced.

     
  3. 3.

    Full working to increase azimuth, while the inclination is not changed.

     
  4. 4.

    The inclination angle decreased, while the azimuth angle increased.

     
  5. 5.

    Full working to decrease inclination angle, while the azimuth angle is not changed.

     
  6. 6.

    The inclination angle and the azimuth angle all decreased.

     
  7. 7.

    Full working to decrease azimuth, while the inclination is not changed.

     
  8. 8.

    The inclination angle and the azimuth angle all decreased.

     
  9. 9.

    No working. The inclination and the azimuth were controlled by BHA.

     

A new algorithm for pad forces (F 1, F 2, F 3)

Non-uniqueness for pad forces

When the amplitude A k and the direction α k of the required steering force F are determined, a control algorithm is then needed to adjust each pad force to achieve the required steering force. The control variables are these three pad forces. These force vectors constitute a planar concurrent force system in the bottomhole plane, as shown in Fig. 7.
Fig. 7

Three pad forces adjusted to achieve the required steering force F

Figure 7 shows two programs which adjust three pad forces (F1, F2, F3) or (F1′, F2′, F3′) to achieve the same required steering force F. F12 is the resultant force of F1 and F2. F12′ is the resultant force of F1′ and F2′. The relation between F and F1, F2, F3 can be expressed as follows:
$$ \left\{ \begin{aligned} &F\cos \alpha_{k} = F_{1} \cos \alpha_{1} + F_{2} \cos (\alpha_{1} + 240) + F_{3} \cos (\alpha_{1} + 120) \hfill \\ &F\sin \alpha_{k} = F_{1} \sin \alpha_{1} + F_{2} \sin (\alpha_{1} + 240) + F_{3} \sin (\alpha_{1} + 120) \hfill \\ \end{aligned} \right. $$
(8)

The angle (α1) between pad 1 and high side is measured by the RSSTSP system. Once F and α k are determined, there are three unknown parameters F1, F2, and F3. However, there are only two equations in Eq. (8). The solutions are thus not unique. To determine F1, F2, and F3, an additional equation must be established.

An additional equation for optimal pad force

When a RSSTSP starts to work, in order to prevent pad damages, forces exerted on each pad should be limited. Initially, the three pads should start simultaneously with the same forces. The initial force can be set as,
$$ F_{\text{ini}} = \frac{{F_{\hbox{max} } + F_{\hbox{min} } }}{2}, $$
(9)
where Fini is the pad force at the initial working time.
When the RSSTSP starts to steer the drill bit to a target point, we require a steering force F and direction α K . One has to decide on whether each of the pad forces is in a “favorable” or “unfavorable” area. Such a decision is made by assessing the direction of each of the pad forces F1, F2, and F3, in relation to the required steering force. If the angle between a pad force and the required steering force is within (− 30°, 30°), the pad force plays a positive role in achieving the required steering force, as shown in the hexagon in Fig. 8. In such cases, the pad force falls in the “favorable” area, and the force of the pad should be:
Fig. 8

Six areas of favorability based on the angle between the directions of each pad force and the required steering force

$$ F_{\text{f}} = \frac{{F_{\hbox{max} } + F_{\hbox{min} } }}{2} + \frac{{F_{\hbox{max} } - F_{\hbox{min} } }}{2}A_{K} , $$
(10a)
where Ff is the pad force on the favorable area and the second term on the right-hand side of Eq. (10a) is the augment of the pad force. On the other hand, if the angle between the pad force and the opposite direction of steering force is within (− 30°, 30°), the pad force plays a negative role in achieving the required steering force. In such cases, the pad force falls in the unfavorable area. The pad force takes big value in favorable area and takes small value in the “unfavorable” area, and the force of the pad should be:
$$ F_{\text{uf}} = \frac{{F_{\hbox{max} } + F_{\hbox{min} } }}{2} - \frac{{F_{\hbox{max} } - F_{\hbox{min} } }}{2}A_{K} , $$
(10b)
where the second term on the right-hand side of Eq. (10b) is the reduction of the pad force. The Fuf is the pad force on the unfavorable area. The bottomhole plane can now be divided into six areas, as shown in Fig. 8. At any point in time, the steering force (determined in “Maximum usable steering forces (Amax)” section) should fall in one of these six areas. The favorable or unfavorable area for one of the pad forces can then be easily determined.

For example, if the required steering force falls in area 1 (in which there is no pad), then area 4 (in which there must be a pad) is an unfavorable area. We thus set the pad force in area 4 with an unfavorable force: F1 = F uf, which gives an additional equation to Eq. (8), so that a set of solutions for all the pad forces can be uniquely found. If the steering force falls in area 2 (in which there is a pad), then area 2 is the favorable area. In this case, a favorable force should be assigned to pad 2: F2 = F f, which gives an additional equation. If the steering force is in area 3, then area 6 is the unfavorable area and F3 = Fuf becomes an additional equation. If the steering force is in area 4, then area 4 is the favorable area and F1 = Ff gives as an additional equation. If the steering force is in area 5, then area 2 is the unfavorable area and F3 = Fuf becomes an additional equation. If the steering force is in area 6, then area 6 is the favorable area and F2 = Ff becomes an additional equation.

A new algorithm for pad forces

We are now ready to develop a new algorithm for computing the pad forces. For convenience, we define a \( \alpha_{K}^{'} = \alpha_{K} - \alpha_{1} \), which is the relative direction of \( \alpha_{K} \) with respect to \( \alpha_{1} \), as shown in Fig. 9.
Fig. 9

Relative direction (α K ) with respect to direction α1

As a general convention, α1 and α k are all defined as clockwise positive. The relative steering force direction \( \alpha_{K}^{'} \) is also defined as clockwise positive with respect to pad 1, and it can be expressed in the following two cases.
$$ \left\{ {\begin{array}{*{20}l} {\alpha_{K}^{'} = \alpha_{K} - \alpha_{1} ;} \hfill & {\alpha_{\text{K}} \ge \alpha_{1} } \hfill \\ {\alpha_{K}^{'} = \alpha_{K} - \alpha_{1} + 360;} \hfill & {\alpha_{K} < \alpha_{1} } \hfill \\ \end{array} } \right. $$
(11)

According to the relative status of the steering force, one of the pads can be determined in either the favorable and unfavorable areas, following the procedure detailed in “Direction of steering force (α k )” section. Hence, there are six possible situations.

Situation 1:

The steering force is in area 1, as shown in Fig. 10.
Fig. 10

Steering and pad forces when α K  > 330 or α K  ≤ 30

In Fig. 10, F1F, F2F, and F3F are the force components in the directions of F, respectively, for F1, F2, and F3. F1f, F2f, and F3f are the force components in the normal direction of F, respectively, for F1, F2, and F3. At this situation, \( \alpha_{K}^{'} > 330^{^\circ } \) or \( \alpha_{K}^{'} \le 30^{^\circ } \), and pad 1 is in a unfavorable area. Then, supplying F1 = Fuf into Eq. (8), we obtain:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} \cos (\alpha_{K}^{'} - 180) + F_{2} \cos (\alpha_{K}^{'} - 300) + F_{3} \cos (\alpha_{K}^{'} - 60) = A_{\hbox{max} } A_{K} } \hfill \\ {F_{1} \sin (\alpha_{K}^{'} - 180) + F_{2} \sin (\alpha_{K}^{'} - 300) + F_{3} \sin (\alpha_{K}^{'} - 60) = 0} \hfill \\ {F_{1} = F_{\text{uf}} } \hfill \\ \end{array} } \right. $$
(12)
Equation (12) now has unique solutions, and the result is as follows:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{uf}} } \hfill \\ {F_{2} = F_{\text{uf}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} - 60)A_{K} } \hfill \\ {F_{3} = F_{\text{uf}} + \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} + 60)A_{K} } \hfill \\ \end{array} } \right. $$
(13)

Situation 2:

The steering force is in area 2, as shown in Fig. 11.
Fig. 11

Steering and pad forces when 30 < α K  ≤ 90

In this situation, pad 3 is in a favorable area, and \( 30 < \alpha_{K}^{'} \le 90^{^\circ } \), which gives an additional equation of F3 = Ff. Therefore, a unique solution can be given as follows:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{f}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} + 60)A_{K} } \hfill \\ {F_{2} = F_{\text{f}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} )A_{K} } \hfill \\ {F_{3} = F_{\text{f}} } \hfill \\ \end{array} } \right. $$
(14)

Situation 3:

The steering force is in area 3, as shown in Fig. 12.
Fig. 12

Steering and pad forces when 90 <α K  ≤ 150

In this situation, pad 2 is in a unfavorable area, and \( 90 < \alpha_{\text{K}} '\le 150^{o} \), which gives F2 = Fuf. The unique solution becomes:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{uf}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (60 - \alpha_{k}^{'} )A_{K} } \hfill \\ {F_{2} = F_{\text{uf}} } \hfill \\ {F_{3} = F_{\text{uf}} + \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} )A_{K} } \hfill \\ \end{array} } \right. $$
(15)

Situation 4:

The steering force is in area 4, as shown in Fig. 13.
Fig. 13

Steering and pad forces when 150 < α K  ≤ 210

In this situation, pad 1 is in a favorable area, and \( 150 < \alpha_{K}^{'} \le 210^{^\circ } \), which supplies F1 = Ff. Then, the solution is obtained as follows:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{f}} } \hfill \\ {F_{2} = F_{\text{f}} + \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (60 - \alpha_{k}^{'} )A_{K} } \hfill \\ {F_{3} = F_{\text{f}} + \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha \alpha_{k}^{'} + 60)A_{K} } \hfill \\ \end{array} } \right. $$
(16)

Situation 5:

The steering force is in area 5, as shown in Fig. 14.
Fig. 14

Steering and pad forces when 210 <α K  ≤ 270

In this situation, pad 3 is in a favorable area, and \( 210 < \alpha_{K}^{'} \le 270^{^\circ } \), which gives an addition equation of F3 = Fuf. Then, the result is found as follows:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{uf}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (60 + \alpha_{k}^{'} )A_{K} } \hfill \\ {F_{2} = F_{\text{uf}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} )A_{K} } \hfill \\ {F_{3} = F_{\text{uf}} } \hfill \\ \end{array} } \right. $$
(17)

Situation 6:

The steering force is in area 6, as shown in Fig. 15.
Fig. 15

Steering and pad forces when 270 < α k ′ ≤ 330

In this situation, pad 2 is in a favorable area, and \( 270 < \alpha_{\text{K}} '\le 330^{o} \), which leads to an addition equation of F2 = Ff. Then, the result becomes:
$$ \left\{ {\begin{array}{*{20}l} {F_{1} = F_{\text{f}} - \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (60 - \alpha_{k}^{'} )A_{K} } \hfill \\ {F_{2} = F_{\text{f}} } \hfill \\ {F_{3} = F_{\text{f}} + \frac{2\sqrt 3 }{3}A_{\hbox{max} } \sin (\alpha_{k}^{'} )A_{K} } \hfill \\ \end{array} } \right. $$
(18)

Integrating the steer capability, stability, durability, favorable area, unfavorable area, maximum usable magnitude of steering force, a new control algorithm of RSSTSP can easily be written using Eqs. (12)–(18).

Field tests

The new control algorithm is applied to a RSSTSP and carried out a field test in a GU-693-P102 well. The RSSTSP has Fmax = 20KN, and Fmin = 0.7KN. If α1 = 30, the pad forces (F1, F2, F3) are changing with the α k based on the new control algorithm, and the outcome is plotted in Fig. 16.
Fig. 16

Output of the pad forces controlled using the present algorithm for given different α k

It is shown that each pad force changes smoothly and decreases with decreasing A k , which reduces drill bit vibration and improves the stability and durability of the RSSTSP system. The design track and the well trajectory of GU-693-P102 are shown in Fig. 17, where the blue line is the design track and the red line is the well trajectory achieved using the present control algorithm. A is the target spot, and B is the termination spot.
Fig. 17

Well trajectory achieved using the present algorithm against the design track

The results demonstrate the well is consistent with design track as designed. The maximum dogleg rate is 5.92°/30 m, and well trajectory is smooth. It validates that our proposed control algorithm is robust and effective for RSSTSP systems.

Inclusions

  1. 1.

    According to the current and targeted build and walk rates, this work establishes a method to calculate the work efficiency (A k ) and direction of the required steering force (α K ). The calculated results offer key instructions to transmit from ground to downhole for a RSSTSP drilling process.

     
  2. 2.

    Considering maximum usable magnitude of steering force, steerability, stability, durability, favorable area and unfavorable area, a new algorithm for assigning each pad an optimal force is developed to achieve the required steering force to move the drilling bit from point A to point B.

     
  3. 3.

    The present new control algorithm is applied to a new RSSTSP, and a field test is carried out in a GU-693-P102 well for validation. It demonstrates that the new control algorithm is robust and effective for RSSTSP systems.

     

Notes

Acknowledgements

The research is mainly supported by Natural Science Foundation of Hei Long Jiang Province (No. QC2017042).

References

  1. Bian JH, Niu WT, Wang LN et al (2011) Study of steering actuator of static “point-the-bit” rotary steerable system. In: Materials science forum, vol 697–698, pp 665–670Google Scholar
  2. Cheng Z, Jiang W, Jiang S et al (2010) Control scheme for displacement vector of three-pad biasing rotary steerable system. Acta Pet Sinica 31(4):675–676Google Scholar
  3. Drummond M, Costa K, Renfrow D et al (2007) Large hole RSS used for shallow kick-off, directional control in soft sediment. World Oil 228(10):39–44Google Scholar
  4. Du JS, Liu B, Xia B (2008) The control scheme for three pad static bias device of push-the-bit rotary steerable system. Oil Drill Prod Technol 30(6):5–10. http://en.cnki.com.cn/Article_en/CJFDTotal-SYZC200806005.htm
  5. Fontenot KR, Lesso B, Strickler RD et al (2005) Using casing to drill directional wells. Oilfield Rev 17(2):44–61Google Scholar
  6. Hakam CE, Davis E, Serdy AM et al (2014) Rotary steerable system with optimized functionally integrated system-specific drill bits reduces drilling days and extends laterals in northeastern US Horizontal shale plays. Icarus 243:129–138CrossRefGoogle Scholar
  7. Haugen J (1998) Rotary steerable system replaces slide mode for directional drilling applications. Oil Gas J 96(9):65–71Google Scholar
  8. Ikonnikova S, Gülen G, Browning J et al (2015) Profitability of shale gas drilling: a case study of the Fayetteville shale play. Energy 81:382–393CrossRefGoogle Scholar
  9. Jia C, Zhang Y, Zhao X (2014) Prospects of and challenges to natural gas industry development in China. Nat Gas Ind B 1(1):1–13CrossRefGoogle Scholar
  10. John E, Chris A, Clive D et al (2000) The application of rotary closed-loop drilling technology to meet the challenges of complex wellbore trajectories in the Janice field. SPE Drill Complet 17(3):151–158Google Scholar
  11. Kaiser MJ, Yu Y (2015) Drilling and completion cost in the Louisiana Haynesville Shale, 2007–2012. Nat Resour Res 24(1):5–31CrossRefGoogle Scholar
  12. Kremers NAH, Detournay E, Wouw NVD (2015) Model-based robust control of directional drilling systems. IEEE Trans Control Syst Technol 24(1):226–239CrossRefGoogle Scholar
  13. Lapeyrouse NJ, Lyons WC, Carter T (2002) Formulas and calculations for drilling, production, and workover, 3rd edn. Elsevier, OxfordGoogle Scholar
  14. Li SB, Wang YQ, Zhang LG, Xu YQ (2015) Analysis and optimization of static push-the-bit rotary steering control scheme. Oil Drill Prod Technol 37(4):12–15. http://www.en.cnki.com.cn/Article_en/CJFDTOTAL-SYZC201504006.htm
  15. Marck J, Detournay E (2016) Influence of rotary-steerable-system design on borehole spiraling. SPE J 21(1):293–302CrossRefGoogle Scholar
  16. Niu WT, Li HT, Wang LN, Li YZ (2013) Static point-the-bit rotary steerable drilling tool. CN202788615 U (Chinese) Google Scholar
  17. Orem WH, Varonka M, Crosby L et al (2014) Organic substances from unconventional oil and gas production in shale. AGU Fall Meeting AbstractsGoogle Scholar
  18. Ozkan E, Brown ML, Raghavan R et al (2011) Comparison of fractured-horizontal-well performance in tight sand and shale reservoirs. SPE Reservoir Eval Eng 14(2):248–259CrossRefGoogle Scholar
  19. Schaaf S, Pafitis D, Guichemerre E (2000) Application of a point the bit rotary steerable system in directional drilling prototype well-bore profiles. In: SPE/AAPG western regional meeting, 19–22 June, Long Beach, CaliforniaGoogle Scholar
  20. Seifabad MC, Ehteshami P (2013) Estimating the drilling rate in Ahvaz oil field. J Pet Explor Prod Technol 3(3):1–5Google Scholar
  21. Stuart S, Demos P, Eric G (2000) Application of a point the bit rotary steerable system in directional drilling prototype well-bore profiles. J Am Board Fam Med: JABFM 27(1):1400–1405Google Scholar
  22. Torsvoll A, Abdollahi J, Eidem M et al (2010) Successful development and field qualification of a 9 5/8 in and 7 in rotary steerable drilling liner system that enables simultaneous directional drilling and lining of the wellbore. Phys Status Solidi 211(2):425–432Google Scholar
  23. Tribe IR, Burns L, Howell PD et al (2001) Precise well placement using rotary steerable systems and LWD measurements. Am J Ophthalmol 56(5):836Google Scholar
  24. Wang R, Xue Q, Han L et al (2014) Torsional vibration analysis of push-the-bit rotary steerable drilling system. Meccanica 49(7):1601–1615CrossRefGoogle Scholar
  25. Weijermans P, Ruszka J, Jamshidian H et al (2001) Drilling with rotary steerable system reduces wellbore tortuosity. Society of Petroleum Engineers, pp 194–203Google Scholar
  26. Xue Q, Leung H, Wang R et al (2016) Continuous real-time measurement of drilling trajectory with new state-space models of Kalman filter. IEEE Trans Instrum Meas 65(1):144–154CrossRefGoogle Scholar
  27. Zhang SH (2000) Drilling extended reach well with rotary steering drilling system. Acta Pet Sinica 21(1):76–80Google Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Petroleum EngineeringNortheast Petroleum UniversityDaqingChina
  2. 2.School of Mechanical EngineeringHebei University of TechnologyTianjinChina
  3. 3.Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiOhioUSA

Personalised recommendations