optimization and application of wob for deflection control ... 2 china petroleum exploration vol....

CHINA PETROLEUM EXPLORATION

Volume 21, Issue 2, March 2016

Received date: 07 Sep. 2015; Revised date: 10 Oct. 2015. Corresponding author. E-mail: [email protected] Foundation item: NSFC “Fluid-solid coupling theory-based research on borehole instability mechanism of underbalanced horizontal well” (51474186); “Multi-field coupling theory-based research on borehole instability mechanism of shale gas horizontal well” (51574202). Copyright © 2016, Petroleum Industry Press, PetroChina. All rights reserved.

Optimization and application of WOB for deflection control while fast drilling with a conventional drilling assembly

Shui Guohuang1, He Shiming1, Deng Xiang2

1. Petroleum and Gas Engineering College, Southwest Petroleum University;

2. Downhole Service Company, CNPC Chuanqing Drilling Engineering Company Limited

Abstract: In China, to achieve deflection control while fast drilling with a conventional drilling assembly, easing the bit in lightly

with a high weight on bit (WOB) pre-bending passive anti-deviation technique are often combined to achieve hole deflection con-

trol in complex formations. However, low WOB may lead to low rate of penetration (ROP), and a high WOB pre-bending passive

anti-deviation technique may make the drill string become unstable, thereby causing underground complexities. For the purpose

of balancing the relationship among deflection control during fast drilling, ROP and drill string instability, it is necessary to select

an optimal WOB. This study is based on the vertical and horizontal bending beam and column bending theory, and a WOB opti-

mization model was built to evaluate deflection control and straight drilling (with a conventional drilling assembly in vertical

well), and considers the influences of formation deflection force on well deflection and the minimum comprehensive bit force. A

relevant computer program was prepared in addition to conducing a field test in Well BUCS-44 of the Maysan Oilfield in Iraq.

The results show that different ranges of WOB is applicable to formations with different deflections. In high and steep structures,

drill tools with a high angle drop capacity are used, and under the condition of a pre-bent drill string, high WOB can be adopted to

address the contradiction between ROP and deviation control and straight drilling. In addition, an optimal WOB is selected by

fully considering the deflecting features in formations and those of drill tool itself. In this way, instability of drill string can be

avoided, and deflection control during fast drilling can also be achieved. This study has a certain significance in guiding on-site

deflection control.

Key words: deflection control while fast drilling, critical WOB, conventional drilling assembly, deflection control, vertical

and horizontal bending beam method

Well deflection control is an ubiquitous problem in drill-ing engineering. Many innovative active deflection control technologies (such as VDS and SDD) have been developed abroad for application with fast drilling, however, these are too costly for use in most wells[1–4]. Instead, conventional drilling assemblies are commonly used.

In easily-inclined formations like a high-steep mountain front formation, the well deflection is particularly out-standing due to the natural deflecting force of the formation. It may impede the discovery of geologic target through all E&P stages including, logging, well cementation, well completion and production. The development of deep res-ervoirs and unconventional oil & gas resources places re-quires a higher well bore quality. Therefore, well deflection control capacity restricts the quality and economic benefits of oil & gas exploration and development to a certain extent. Currently, in WOB anti-deviation control, light easing of the bit and high WOB pre-bending anti-deviation techniques are often adopted. The former technique is to control well de-flection by sacrificing rate of penetration (ROP), thus pre-venting deviation to the cost of slower drilling. The latter

technique allows the drill string to bend and achieve effec-tive well deflection control through controlling the bit’s an-gle of rotation, however high WOB is bound to lead to an unstable drill string and potentially cause downhole acci-dents.

Drilling practices show that the lateral force of bit and the natural deflecting force of formation are two major fac-tors that impact well deflection control. The lateral force of the bit, belonging to drill string mechanics, is controllable. Currently, there are many studies on drill string mechanics. For example, Walker et al. studied the stress and deforma-tion of drill string with the “principle of minimum potential energy”[5]. Milleim et al. established a calculation model for the stress and deformation analysis of bottomhole assembly (BHA) and solved it with finite element[6]. Su Yinao ana-lyzed drill string mechanics with crossbar bent continuous beam law[7]. Gao Deli proposed a high WOB anti-deviation technique on the basis of weighted residual method[8]. However, these drill string mechanics theories only deal with changing the laws of stress and deformation of the drill string, lateral force on bit, and angle of rotation, without

2 CHINA PETROLEUM EXPLORATION Vol. 21, No. 2, 2016

considering the impact of formation deflecting force on well deflection. As an objective law, the formation deflection characteristics also impact the control of well deflection. Hoch et al. firstly proposed the concept of formation de-flecting force[9]. Yang Xunyao revised the calculation for-mula of natural deflecting force of formation on the basis of the study of Hoch et al.[10]. Gao Deli et al. reverse engi-neered the formation deflecting force by using the log data[11], which is relatively consistent with real-world sce-narios. Combining the formation’s natural deflecting char-acteristics with drill string mechanics, with the goal of achieving a high quality well bore, is the key to the deflec-tion control during fast drilling of vertical well. By combining research results of drill string mechanics and formation natural deflecting characteristics, a WOB optimi-zation model for deflection control during fast drilling was established and its accuracy was verified through field data.

1. WOB optimization model for deflection control during fast drilling

WOB anti-deviation is one of the key technologies for well deflection control. Three principles should be followed to this technique. First, the drill string itself is allowed to bend correspondingly under pressure. Second, the compre-hensive impacts of formation deflecting force and lateral force of bit on well deflection are considered. Third, the contradiction between ROP and deflection control while straight drilling is considered, and objective factors are taken full account to change passive control into active con-trol.

1.1. Determination of objective function

There is a combined action of formation deflecting force Fa and lateral force of bit pa in the plane along the well de-flection direction in the downhole coordinate system. The BHA mechanics analysis model is shown in Fig.1. It shows that the magnitude of resultant force determines the increase and decrease of well deflection. Therefore, the comprehen-sive force on the bit in the well deflection plane is selected as the objective function.

Fig. 1 BHA mechanics analysis model

B 1 1 1 1a a B

1 1 2

p e M q LF F p Kp

L L (1)

a BF Kp (2)

B 1 1 1 1a

1 1 2

p e M q Lp

L L (3)

where, F - comprehensive force on the bit; Fa - formation deflecting force; pa - lateral force of bit; K - natural deflecting characteristic parameter of for-

mation; pB - WOB; e1 - radial clearance between primary stabilizer and

bore hole; L1 - drill string length from bit to stabilizer; M1 - inner bending moment of drill string at primary

stabilizer; q1 - horizontal uniformly distributed load of drill string.

The natural deflecting characteristic parameter K reflects the magnitude of formation deflecting capacity, which is mainly caused by an imbalance of rock breaking speed re-sulting from formation anisotropy and different occur-rence[12]. Yang Xunyao analyzed the impact of formation factors on well deflection based on the study of Lubinski et al. and proposed the specific calculation formula of K[10]:

[cos cos sin sin cos( )][cos sin cos( ) sin cos ]

(1 )

hK

hc h

(4)

tg

[tan sin( ) cos( )][ sin( ) cos( )]x z

x z

F Fh

F F

(5)

2 21 2 3 2 3

1

2

3

( tan tan )

cos cos sin sin cos( )

sin sin( )

cos sin cos( ) sin cos

c g g g g g

g

g

g

(6)

where, h - drillability anisotropy index of formation; α - well deflection angle; β - formation dip angle; - borehole azimuth; γ - formation updip azimuth;

Shui Guohuang et al., Optimization and application of WOB for deflection control while fast drilling with a ... 3

Fx - x-axis bit force component in borehole axis co ordinate system;

Fz - z-axis bit force component in borehole axis co-ordinate system;

Δα - well deflection angle increment; Δ - borehole azimuth increment.

WOB optimization aims to minimize the comprehensive force on the bit. Essentially, the comprehensive force can be reasonably controlled by adjusting the WOB; the design is reasonable, as long as it can stabilize or reduce deviation. Assuming that formation deflecting force Fa and lateral force of bit pa are on the same straight line and in the oppo-site direction, it can be derived from Formula (1) that the comprehensive force F determines the increase and decrease of well deflection. Specifically, F>0 (Fa>pa) corresponds to deviation increase, F=0 (Fa=pa) corresponds to deviation stabilization, and F<0 (Fa<pa) corresponds to deviation de-crease.

1.2. Constraints

1.2.1. Constraints for drill string instability Bending of downhole drill string is the main reason for

well deflection[13]. In view of drill string mechanics, WOB is divided into three types based on the curvature of the drill string (Fig.2), i.e. critical WOB for primary bending (Curve I), critical WOB for secondary bending (Curve II), and critical WOB for tertiary bending (Curve III).

Fig. 2 Bending deformation of the drill string

Calculation formulas for above-mentioned three types of WOB can be expressed as: 1 1 m m2.04p l q mq (7)

2 2 m m4.05p l q mq (8)

3 3 m m5.07p l q mq (9)

3

m

EIm

q (10)

where, p1, p2 and p3 refer to the critical WOB for primary bending, secondary bending and tertiary bending respec-tively, N; l1, l2 and l3 refer to the length of drill string for primary bending, secondary bending and tertiary bending respectively, m; qm refers to the gravity of per unit length of drill string in drilling fluid, N/m; EI refers to the flexural ri-gidity, N·m2.

Between the critical WOB for primary bending, and the critical WOB for secondary bending, the bending shape of the drill string becomes two half-waves from one half-wave. Thus, the position of the upper point of contact changes and the change of bit’s angle of rotation is uncertain. In this scenario WOB is deemed unnecessary. Limited by drill string strength, WOB shall be smaller than the critical WOB for tertiary bending. In summary, constraints for drill string instability are defined as:

B 1

2 B 3

0 p p

p p p

≤ ≤

≤ ≤ (11)

It can be seen from Formula (11) that, for a given BHA, critical WOB should not fall between the critical WOB for primary bending and the critical WOB secondary bending, nor be any higher than the critical WOB for tertiary bend-ing. 1.2.2. Constraints for deflection control while fast drill-ing

Anti-deviation and fast drilling are contradictive in well deflection control. In order to balance the contradiction be-tween ROP and deflection control while straight drilling, it is considered through investigation and analysis [14] that high WOB drilling is not suitable when the formation dip angle β is bigger than 20°, and WOB can be appropriately increased to promote ROP when the formation dip angle is smaller than 20°. The constraints are as shown in Formula (12):

B 1 2 B 3

B 1

0 or ( 20 )

0 ( 20 )

p p p p p

p p

≤ ≤ ≤

≤

< <

< < (12)

2. Determination of optimal WOB for deflec-tion control during fast drilling

2.1. Method to determine optimal WOB for deflection control during fast drilling

The pF chart was drawn for WOB and force on bit ac-cording to the above-mentioned function and constraints[15]. The pF chart takes pB as the horizontal axis and F (includ-ing formation deflecting force and lateral force of bit) as the


vertical axis. It can be derived from Formula (2) that, given a specific formation and BHA, the formation natural de-flecting characteristic parameter is a constant and the for-mation deflecting force is a line crossing the origin; lateral force of bit can be obtained through the vertical and hori-zontal bending beam method[1618]. According to the relation among formation deflecting force, lateral force of bit and critical WOB for drill string bending, the pF chart can be discussed with respect to the following situations:

(1) The critical WOB of formation deflection is smaller than the critical WOB for primary bending.

Fig.3 is the pF chart when the WOB that corresponds to the case that lateral force of bit is equal to, formation de-flecting force (i.e., the critical WOB of formation deflection (pB)0) is smaller than the critical WOB for primary bending. Easing the bit in with light pressure can be adopted for de-flection control while drilling in high and steep structures, i.e.,

Fig. 3 The relation curve between WOB and force on bit (a)

B B 0 1( )p p p≤ < (13)

When pB=(pB)0, it presents deviation stabilization. When pB<(pB)0<p1, it presents deviation decrease.

Under the geological condition of a relatively small for-mation dip angle, in order to avoid sacrificing ROP, the high WOB pre-bending anti-deviation drilling can be adopted according to the characteristic of the minimum angle of ro-tation of the bit during secondary bending of the drill string and in combination with the bending characteristic of the assembly, i.e., 2 B 3p p p (14)

At this moment, pB=p2+(pB)0, which suggests that secon-dary bending is the original state of drill string, and WOB optimization shall be conducted with the pF chart.

(2) The critical WOB of formation deflecting is between the critical WOB for primary bending and the critical WOB for secondary bending.

Fig.4 is the pF chart when the critical WOB of formation deflecting is between the critical WOB for primary bending

and secondary bending. During the drilling process critical WOB between the primary and secondary bending should be avoided due to potential for drilling string instability. For the purpose of safe drilling, WOB can be selected by the following means according to the change of formation dip angle:

Fig. 4 The relation curve between WOB and force on bit (b)

In high and steep structures, and in order to maintain the stability of drilling tools and meet the technical requirement of deflection control during fast drilling, low WOB drilling should be adopted. WOB must meet the following condi-tion: B 1 B 0( )p p p≤ ≤ (15)

With a relatively small formation dip angle, deflection control is relatively easy. Therefore, in order to balance the contradiction between low WOB and ROP, high WOB pre-bending anti-deviation drilling can be adopted, i.e., B 2p p (16)

When pB=p2, due to secondary bending of drill string, the angle of rotation of the bit is almost 0, and can realize de-flection stabilization while drilling.

(3) The critical WOB of formation deflecting is between the critical WOB for secondary bending and the critical WOB for tertiary bending.

Fig.5 is the pF chart when the critical WOB of formation deflection is between the critical WOB of secondary bending

Fig. 5 The relation curve between WOB and force on bit (c)


and the critical WOB for tertiary bending. In high and steep structures, in order to keep effective deflection control, low WOB should be adopted in combination with constraints. The optimal WOB is as follows: B B 0 2 1( )p p p p (17)

Under the condition of a relatively small formation dip angle, high WOB pre-bending anti-deviation drilling can be adopted, i.e.,

2 B 0 3

B B 0

( )

( )

p p p

p p

(18)

At this moment, the optimal WOB is right the critical WOB (pB)0 of formation deflection, the magnitude of which meets the balance relation between formation deflecting force and lateral force of bit, and balances the contradiction between ROP and deflection control while straight drilling.

2.2. Basic flow of WOB optimization for deflection con-trol during fast drilling

With the above-mentioned WOB optimization method, a deflection control calculation was developed using the C# language. This software can reverse engineer the formation natural deflecting characteristic parameter depending on formation occurrence and physical electrical logging data[19]. Given a BHA, lateral force of bit is derived by the vertical and horizontal bending beam method, and finally the objec-tive function is solved by means of dichotomy. It can also quantify the relation between the critical WOB of formation deflection and the critical WOB of drill string bending, so as to provide the applicable range of corresponding WOB ac-cording to the change in formation dip angle. The logic used by the program is shown in Fig. 6.

Fig. 6 Logical functions of the program

3. Field application

Well BUCS-44H is located in the Missan Province in southeastern Iraq, adjacent to the border with Iran, 175 km to Basra in the south and 350 km to Baghdad in the north-west. It is a horizontal well, with a 3300 m deep vertical section. With the actual data of the 1000-1500 m vertical section in the fourth spud-in, the application effect of WOB-based deflection control during fast drilling was ana-lyzed. During drilling of the 720-1000 m section in the third spud-in, bending positive displacement motor (PDM) drill-ing was employed in order to increase ROP, with the as-sembly of φ444.5 mm PDC bit + φ244.5 mm PDM + φ228.6 mm float valve + φ228.6 mm drill collar + φ441.3 mm stabilizer + φ228.6 mm drill collar + φ441.3 mm stabi-lizer + joint drill pipe + φ203.2 mm drill collar (joint + jar) + tool joint (full hole) + φ139.7 mm heavy weight drill pipe

+ φ139.7 mm drill pipe. However, it was discovered that well deflection increased during the drilling process, and later a double-stabilizer assembly with stronger deviation reduction capacity was adopted in the 1000-1500 m section in the fourth spud-in, with the assembly of φ444.5 mm roller bit + tool joint (float valve) + φ228.6 mm non-magnetic drill collar + φ441.3 mm stabilizer + φ228.6 mm drill collar + φ441.3 mm stabilizer + tool joint (731×630) + φ203.2 mm drill collar + φ203.2 mm (joint + jar) + tool joint (full hole 631) + φ139.7 mm heavy weight drill pipe + φ139.7 mm drill pipe.

Fig.7 shows the measured WOB during drilling of Well BUCS-44H by the double-stabilizer assembly in the 1000-1500 m section. It can be seen that the WOB in this section fluctuates in 4.5-7 tf. Fig.8 shows the measured well deflection angle of Well BUCS-44H in the 1000-1500 m section. Both figures reveal that the well deflection angle in


the 1000-1300 m section is relatively big and the WOB is about 4.5 tf; and the well deflection angle in the 1300-1500 m section is relatively small and the WOB is about 7 tf, with obviously reduced deviation.

Optimal WOB was calculated according to the balance principle between formation deflecting force and lateral force of bit, and in combination with formation deflecting

force and drill string bending characteristic; the results are shown in Fig.9. It can be seen that the optimal WOB for the double-stabilizer assembly using theoretical calculations is 6.76 tf, and in the 12221464 m section, formation natural deflection characteristic parameter tends to decrease. There-fore, the formation deflection force decreased on the whole. Namely, in the pF chart, the critical WOB (pB)0 of formation

Fig. 7 Measured WOB for Well BUCS-44H

Fig. 8 Measured well deflection angle for Well BUCS-44H

Fig. 9 Results of the optimal WOB calculation


deflection shifts rightwards on the whole and WOB may be added to realize deflection control while fast drilling. The WOB used in the 12221464 m section is around 7 tf. Fig.8 shows the most obvious deviation decrease effect in this section, while the optimal WOB through theoretical calcula-tion is 6.76 tf. This confirms the accuracy of the WOB op-timization model, and indicates that it offers valuable in-sight into site deflection control during fast drilling.

4. Conclusions and suggestions

(1) WOB, formation deflecting force, lateral force of bit and the bending state of the drill string affect one another. Therefore, WOB can be adjusted during the drilling process to achieve effective control of the formation deflecting force, bit’s angle of rotation, lateral force of bit and bending state of the drill string, thus controlling well deflection changes and providing the necessary data for adopting the WOB de-flection control technique.

(2) Drilling tools with different deviation reduction ca-pacities were analyzed using the WOB optimization model. The results show that, in high and steep structures, a drilling assembly with a stronger deviation reduction capacity can realize deflection control while fast drilling under the condi-tion of high WOB, which balances the contradiction be-tween deflection control and ROP and can help promote a positive ROP.

(3) Computer software was written to provide calcula-tions according to this method of determining optimal WOB . Comparative analysis was made on the measured drilling data and theoretically calculated results of Well BUCS-44H in the Missan Oilfield, Iraq. The results show that the optimal WOB technique is applicable to use when drilling in complex formations. However, in the future studies, this application should be verified in the formations of different blocks in order to confirm the reliability of the proposed WOB optimization model.

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