Drillstring Buckling Prediction and Its Impact on Tool-Joint Effects in Extended Reach Wells

The mechanism of buckling has been extensively studied in pipes and tubings. But these studies more often has been restricted to continuous or straight body pipes. In reality most pipes and other drillstring elements have end couplings or connections known as tool joint. Tool joint presence changes the annular geometry, hydraulics and stress distribution of the pipe or tubulars in the wellbore. Modelling drillstring in highly deviated wells with no regards to the tool joint effects has been a major source of error in many drilling mechanics analysis. This has often led to misleading information on buckling and bending of the pipe which could lead to drilling and completion problems and costly well interventions. Thus it becomes necessary to model tool joint effect in the drillstring as it is subjected to downhole forces and stresses. In this study, emphasis is made on the determination of tool joint effect on pipe buckling for highly deviated extended reach wells (ERWs). WellPlan T&D spreadsheet software was used for the simulation. The simulation was runned for pipe with tool joint and the same pipe with the tool joints removed. Results show that jointed pipes has similar buckling behaviour with continuous straight body pipes with buckling starting from sinusoidal buckling mode and gradually entering the helical buckling mode for both types of pipes. Furthermore, result revealed that tool joint presence increases the critical buckling force by an average of 28.9% for helical as well as (AWA) sinusoidal buckling modes.


Introduction
With the increasing complexity of petroleum geological formations, and the decreasing oil price, it becomes paramount to optimize AWA gas operations. One area of this optimisation is in drilling and completions [1]. Drilling in oil and gas asset development requires high investment cost [2,3]. Owing to this, operators seek ways to efficiently reach target depths at least overall drilling costs [3]. The development of longer reach or ERWs enables maximum contact with reservoirs allowing more drainage area and requiring less number of platforms on new development assets. ERWs are wells in which the horizontal departure is at least two times the true vertical depth [1,4]. These high angle wells prove very challenging to drill and complete especially during tripping and sliding operations. The complexity of ERWs becomes more pronounced as the well becomes threedimensional in shape, in this case, both the azimuth and inclination is changing continuously with the wellbore path.
In ERWs, Excessive torque and drag, buckling of drillstring and tubulars are commonly encountered due to complex wellpath, and also due to doglegs and tortuosities which are usually connected with extended reach drilling (ERD) architectures. Engineers are faced with the challenge of designing safe operational practices and windows to ensure that acceptable design factors are met at least operating costs [1,5]. In ERWs, due to high angle, there is tendency for high compression generated in the drillstring during tripping and sliding operations. At some point, these compressive forces may rise and exceed the critical buckling loads leading to buckling of the drillstring or tubulars. It is then advisory to evaluate pre-buckling and post-buckling periods in the pipe elements. This will serve to check if the pipe will be able to withstand forces downhole so as to reach target depth on prevalent circumstances given the drag, torque and stress encountered by the pipe as it travels.
While a great number of researches have been conducted to evaluate buckling in vertical, inclined and curved wellpaths, nearly all have focused on straight body pipe configurations by applying a simplistic approach; little has been done by researchers to investigate the effect of buckling on jointed pipes (i.e. pipes with tool joints). Tool joints' presence changes the annular geometry of the pipe thus leading to reduced radial clearance. In this situation, the contact of the wellbore wall with the jointed pipes is usually at the tool joints especially in curved wellbore sections. Tool joints cause casing wears due to torque and drag forces and buckling [6]. This results from interaction between the pipe tool joints and the casing string. Due to complex trajectories as encountered in extended reach wells, the degree of such contact might increase leading to additional loads on the casing when buckled.
Many studies have been conducted on the subject of buckling. Most of these were extensively done for completely straight body pipes neglecting tool joints or couplings. Only a few recent studies focus on the determination of equations for buckling of jointed pipes. One of the earliest pioneering works on buckling was conducted by [7]. Lubinski formulated mathematical equations for effect of sinusoidal buckling in pipes for vertical wells. Later on that year Lubinski and Athouse went further to formulate equations for helical buckling of pipes in vertical wells. Paslay and Bogy (1964) worked oncircular pipes and their work helped in determining circular pipes' stability when constrained in a cylinder that is inclined [8]. Ziegler (1977) studied shaft buckling using end torque. He considered only fixed-fixed boundary conditions. His analyses demonstrated that buckling is not caused only by compression but can be caused by tension when the pipe is under applied torque [9]. Mitchell (1982); Mitchell (1986) contributed immensely to buckling analyses. He applied boundary conditions AWA friction effects and revolutionilize the subject of buckling [10][11]. Mitchell (1988) proposed stability criterion for sinusoidal AWA helical buckling [12]. Mitchell (1999); Mitchell (2000) developed analytical connections for buckling of pipe with connectors. The equations described 3D buckling of pipe. He provided the contact force between the connector and wellbore [13][14]. In 2006, Mitchell and Miska went further to develop the equations for pipes helical buckling with connectors AWA torque [15]. Recently Menand et al., (2008) utilized simplified quasi-static models to study friction effect on critical load value with drill pipes that are rotating [16]. Menand et al., (2008); Gao and Liu (2013) recently provided new concepts for buckling limit factor that considers wellbore tortuosity, borehole stability and shape that is used to better calibrate buckling equations [16][17]. Gao and Huang (2015); Gao et al., (2002) revealed the instability of sinusoidal buckling but showed that helical buckling is stable in vertical wellbores [18][19].
The topic of tool joint effects on pipe buckling has only attracted recent attention. Mitchell (1999) gave 3D beam column equations for a buckled pipe that is helical in configuration and as well has connectors (tool joints and couplings). The equation includes the contact force between the connector and the wellbore [13]. Mitchell (2000) extended his 1999 work by analyzing lateral buckling of pipes with connectors for horizontal wells [14]. Later on, Gao (2006) used energy method to analyze pipe helical buckling with tool joints and demonstrated that the tool joints presence increase the buckling loads by 20-40% while pipe pads reduce the contact force by 10-30% [20]. Tikhonov et al., (2000) provided experimental evidence to collaborate tool joint effects on buckling/post buckling behaviour of drill pipes constrained in straight horizontal wellbores [21]. Duman et al., (2003a) experimentally determined tool joint effect on axial AWA and contact force transfers in horizontal wellbores [22].

Effective Tension Is Given by
-are the hydrostatic pressures at a depth, D, of a column of mud for outer and inner sections of the pipe.

The True Tension Is Given by
When the drill string is rotating off-bottom, the weight on bit ()*+) is zero.
If the drill string is on bottom, then is a compressive force equal to )*+ Where: ! " =weight per foot of the drill string in air in lb/ft,, L -Length of drill string hanging below point in feet, #=inclination in degrees, ' ( =bottom pressure force, '. =buckling stability force. The bottom pressure force is a compressive force due to fluid pressure applied over the cross sectional area of the bottom component.
∆ !" ! =the change in force due to a change in area.
The force due to fluid pressure applied is at the bottom of the pipe. The bottom force should be equal to the stability force at the bottom of the pipe. This bottom force is applied throughout the pipe uniformly, whereas the buckling stability force is calculated using the same equation but with different depths. The depth of interest when calculating bottom force is the bottom of the wellbore while in buckling stability force, the depth is the depth of the tubular in the wellbore The force necessary to buckle a pipe is given by the buckling force. This is a compressive force, equal but opposite in sign to the\ effective force.
Buckling analysis is analyzed with regards to the well type. The critical angle is the angle above which the hole is no longer considered to be vertical. The critical inclination angle determines if the wellbore path is vertical or deviated and is given by If > > > ? wellbore is deviated If > < > ? wellbore is vertical

Critical Buckling Force for Deviated Wellbore
i. Sinusoidal buckling ii. Helical buckling Where: F a = critical helical buckling force, lbs F V = critical sinusoidal buckling force, lbs > = g ℎ ℎ , g

Torque Created by Helical Buckling
When helical buckling has occurred in a pipe it creates torque which is given as: Torque caused by buckling is usually small and can be neglected. But in cases where there tubing diameter is small and the radial clearance is large, the buckling induced torque may be considerably large when compared with the make-up torque for the connections

Additional Side Force Due to Buckling
Once buckling has occurred, there is an additional side force due to increased contact between the wellbore and the string. For the soft string model, the following calculations are used to compute the additional side force. These calculations are not included in a stiff string analysis because the Stiff String model considers the additional force due to buckling in the derivation of the side force.
i. Sinusoidal Buckling Mode Total Contact force in sinusoidally buckled pipe is given as Total Contact force in helically buckled pipe is given as Where:EI − stiffness of pipe bending ? −radial distance existing between constraining pipe and borehole wall

Buckling In Pipes with Tool Joints
Pipes with tool joints have discontinuous flow conduits. As such there is reduced radial clearance, increased weight, and more pressure loss at the tool joint sections. For curved wellbores, the tubular makes contact with the wellbore at the tool joint leading to increased contact force at the tool joint.
In buckling analysis, there is variation of tool-jointed pipes with straight body pipe because of tool joint effects. As such the following pipe parametres are changed: the crosssectional area, diameter or radius, radial clearance and pipe weight. These parametres affects the subsequent parametres that requires their input for their determination. i

. Radius of pipe with tool joints
When there is tool joints then radius r of the pipe is given by: = 0.95 ' + 0.05 ~ Where: ii. Diameter of pipe with tool joints When there is tool joints then diameter D of the pipe is given by: D † ‡ and D † ‡ are the diameter of pipe body in inhes, A ‡ and A W are the outer and inner pipe wall cross sectional area, in H D ‹ ‡ and D ‹ ‡ are outer and inner diameter of pipe tool joint, inch

iv. Radial clearance for Pipe with Tool Joints
The radial clearance for pipe with tool joint differs from that of straight body pipes Note: It is assumed that the tool joint length is 5% of the entire pipe length.
Radial clearance (in) for section with too joint is given using the relations below: For pipe body For tool joint Effective radial clearance combining the straight pipe body section and the tool joint section is Where ?v =radial clearance, in r •Ž0 = effective radial clearance, in r •Ž0 is utilized when tool joint effect is considered r •Ž‹ = radial clearance between wellbore wall and tool joint, in.
‚ u =Hole diameter, in ‚ ' =outer diameter of drill string section without tool joint, in. ‚~=Outer diameter of tool joint, in.
OD=drill string element outer diameter v. Moment of Inertia for Pipe components with tool joint For components with tool joints, the constraints, 0.95 and 0.05 are used to assume 95% of the component is length body and 5% is tool joint body.
A pipe with tool joints has straight pipe body and tool joint sections. Two moments are evaluated: a) Moment of inertia for circular pipe for straight pipe body length b) Moment of inertia for circular pipe for tool joint section of the pipe '~= Total moment of inertia for pipe length and tool joint vi. Critical sinusoidal force for pipe with tool joint Where F stj =critical force to initiate sinusoidal buckling for pipe with tool joint,lbf F s =critical force to initiate sinusoidal buckling for pipe without tool joint,lbf

Drill String Elements
The drill string elements data for this study is given in table 1 below and the model was validated using the stated data of table 1.

Hole Data
The hole data also utilized for the modeling are given below for both openhole and cased hole:

Simulation
The simulation was done using wellPlan T&D spreadsheet software design for torque and drag analyses in wellbores. The simulation procedure is summarized in the diagram below.

Results and Discussions
The result for simulation analyses using WellPlan T&D software for torque and drag analysis are given below. The results show the force variations with depth in sinusoidal and helical buckling mode for various well operations such as tripping in, tripping out and sliding. The results are given for drillstring with tool joint and comparisons were made for tool-jointed drillstring and straight body drillstring or drill string

Effect of Tripping out on Buckling
During trip, there was axial or translational movement of the pipe but no rotational movement. Thus the pipe is not rotating and only drag is experienced. For trips torque is considered to be zero because there is no rotational movement. The weight of the drillstring measured during tripping out is the pickup weight (PUW) which is the downward force on the weight indicator as the drill string is pulled out of the hole.
From figure 2, it can be observed that none of the pipe sections were subjected to buckling either sinusoidal or helical during tripping. This was because the pipe was in tension and the axial and effective tensile forces were very high. Onsite of buckling was not experienced. For tripping out, the force distributions without tool joints are depicted in figure 2 with axial and effective force at the surface being231636.3 lbf and 187309.2 lbf respectively.

Effect of Tripping in on Buckling
In trip in, there is axial motion of the drillstring into the well. Thus only drag is experience and no torque occurs because there is no rotation of the drillstring. In trip in the drag force has a negative sign while the weight of the drillstring appears less than the buoyed weight of the drillstring at the depth considered. From figure 3, it can be observed that the drag force on the pipe is lower and negative. The force on the pipe sections are in tension and are not able to induce buckling on the pipe sections. Thus none of the pipe element is buckled at any depth. For tripping in, the force distributions without tool joints are depicted in figure 3 with axial and effective forces at the surface being 164070.6 lbf and 119743.5 lbf respectively.

Sliding
In sliding or slide drilling, there is rotation but the rotation is not from the surface. Thus the rotary table is not being turned. Turning is at the point of contact in the wellbore usually at the swivel or mud motor. There is not high rotary

Effect of Drillstrngwith and Without Tool Joints on Buckling
To evaluate tool joint effects on buckling, the utilized drillstring elements were used as depicted above except that all the drillstringelements were considered to be continuous and straight when simulation was run without tool joints. This was necessary for effective comparison of the critical buckling force for jointed and continuous or straight body drillstring elements or pipes. Figure 5 shows the critical forces required to initiate sinusoidal and helical buckling for continuous straight body drillstring type and also tool-jointed drillstring configurations. From figure 5, it can be observed that higher compressional force is required to buckle drillstring with tool joint than straight body elements. In continuous straight body drillstring type AWA tool-jointed drillstring configurations, the shape of buckling is from top to bottom and follows both the sinusoidal AWA helical variation incorporated to the trajectory.

Figure 5. Analyses of Forces distribution for tool-joint and straight body pipes for all buckling modes.
The figure reveals change in transfer efficiency of the axial force with the difference existing between the bottom and that of top load which is related to the friction forces' magnitude between wellbore wall and the pipe.  [22][23].
During the process of unloading, there is a reversal of the pipe movement direction AWA that friction forces. Thus, there exist a point at which thetop force is lower than thebottom force, and at that point negative values are recorded as revealed in figure 5.
It is important to evaluate the ratio of the critical force for initiating buckling in straight body and tool jointed pipes.  Table 2 show that there is increase in critical force to buckle a tool jointed pipe or drillstring element than a straight pipe or drillstring element. From table 2 it can be observed that the average critical buckling force ratio for pipe with tool and pipe without tool joint is 1.28. This means that the critical force needed to initiate buckling for a tooljointed pipe is 1.28 times the force needed to initiate buckling in straight body pipe. This is in consonance with the findings of Mitchel that predicts that the critical force to sinusoidally buckle a tool-jointed pipe must be more than or equal to 0.9955 times the critical force to sinusoidally buckle a straight body pipe.

Conclusion
The following conclusion were drawn from the study 1. Buckling of pipe is affected by hole operations such as tripping in, tripping out, sliding etc. 2. The highest surface weight is recorded during tripping out operation.
3. Buckling behaviour of jointed pipes resembles that of continuous pipes. They are both initially subjected to sinusoidal buckling and then gradually reaches the helical buckling mode as axial force increases. 4. The presence of tool joint increases the critical buckling force by an average of 28.9% for both helical and sinusoidal buckling modes. 5. The ratio of critical buckling force of continuous straight pipe to tool jointed pipe is around 1.28.

Appendix
Survey information for the well.