SPE 151235

Modeling Dynamic Behavior of Bottomhole Assemblies Containing an Underreamer G. Ishak, SPE, Tesco Corporation; J. Daily, and S. Miska, SPE, University of Tulsa; and R. Mitchell, SPE, Halliburton

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Deepwater Drilling and Completions Conference held in Galveston, Texas, USA, 20–21 June 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Reaming while drilling can be a more economical drilling technique than conventional drilling. Downhole failures can occur

for a variety of reasons, and failure as a result of excess dynamic loading on the bottom hole assembly (BHA) components

may be the most mysterious. One of those mysteries is the static and dynamic distribution of axial load between the bit and

the reamer. This paper presents an approach using the explicit finite element method to model the static and dynamic

interactions between the bit, the reamer and the formation of the BHA.

The results for axial displacement from the explicit finite element method are compared to theoretical results for a self-

weighted column. Also, the axial vibrations are compared to the theoretical natural frequencies. Once the comparison showed

the explicit FE method gives the same theoretical results, the model is expanded to better reflect actual downhole conditions.

The model includes a bit and a reamer from which the interaction can be studied with an emphasis on axial loading. A weight

dependent velocity boundary condition is used to model formation penetration of the bit and reamer. This models the

relationship between the axial load on the reamer and the bit. This so-called drill-ahead model can be used to better

understand the dynamics of the BHA.

Results from this study show the amplitude of the axial oscillating force on the reamer was greater than that of the force

on the bit. Drilling with a more aggressive reamer will decrease the side forces on these components for the case studied. In

addition, for a change of load at the top of the model, the reamer can take more of the transient load than the bit.

Introduction Simultaneous drilling and underreaming is a technique that opens a drilled pilot hole to a larger diameter for the installation

of close tolerance casing strings and to insert and extract drilling assemblies. Because of excessive dynamic loading on the

bottom hole assembly (BHA) components, downhole failures can occur. Therefore, to decrease the damage to these

components and to increase the drilling efficiency, there is a need for a better understanding of the dynamic BHA interactions

with the formation. If an adequate model can be built of the dynamic BHA behavior, then drilling engineers can study the

effect of parameters including rate of penetration (ROP), weight on bit (WOB), weight on reamer (WOR), BHA

configuration, inclination angle, and size of the pilot hole and reamed hole.

This paper provides a better understanding of the dynamics of BHAs by addressing axial loading for a BHA with a bit

and reamer. The study of the statics and dynamics of the BHA included in this paper consists of modeling the lower part of

the drillstring. Most failures occur in the BHA because of excessive loading and vibrations. The explicit finite element

method implemented in Abaqus 6.10 was used for modeling the BHA. Explicit three dimensional, linear beam elements were

used to model the neutral axis of the drill string. The finite element formulation also includes axial deformation. Each node

has six degrees of freedom: axial displacement, two components of transverse displacement, and three rotations. These nodes

are also attached to a connector element that models the wellbore.

The following sections provide: a literature review, a description of the model, comparison to closed form solutions, a

description of a drill-ahead routine, results of the dynamic interactions in the BHA and, finally, some remarks about the

results.

Literature review Information taken from the Drilling Information Management System (DIMS) in (1987) indicates that the company expects

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double the amount of non-productive time when dealing with underreaming operations compared to conventional drilling

operations. Drilling larger holes improves cementing operations and enables the running of closer tolerance casing strings.

Burgess et al. (1992) discuss the dynamic problems that cause failure in the BHA tool components. Modeling of drill

string vibrations showed high shocks are associated with transverse vibrations of the BHA, which may lead to failure. A

model of the transverse vibration response of the BHA was developed to improve the design and the location of the tools in

the drill string.

Another SPE paper is written about the chaotic motion of stabilized drill collars by J.D. Jansen (1992). Lateral vibration

of the stabilized part of a BHA results in large side forces on the bit and may influence the directional tendency of the

assembly. Lateral vibration may cause failure of components and damage the wellbore wall. This paper shows the

complicated lateral vibrations of stabilized bottom hole assemblies.

Dewey and Miller (1996) showed the value of underreaming and drilling in the same time. The paper shows the

advantages of underreaming while drilling focusing on two things: efficiency and cost effectiveness. Csonka et al. (1996)

give another example of the cost effectiveness of reaming while drilling offshore wells in Australia. Hyatt et al. (1997)

published a paper on an underreamed well drilled in Egypt. Miller and Childers (2003) describe a concentric reamer as a

replacement of the bi-center bit to enlarge the holes and argue that it is still a cost effective solution for hole enlargement

despite the mechanical problems occurring in these underreamers. Courville, Childers, and Miller (2004) published a paper

that presents the main issue of wellbore enlargement in deep water which facilitates a multiple casing program. In this paper

it is shown that the new concentric reamer technology is reliable and it gives a high quality wellbore. Mason et al. (2007)

provide an example of extended–reach wells drilled from the Chirag Platform. In this paper, the authors present the

advantages and disadvantages of drilling and underreaming in addition to a hole cleaning. Vibration, torque and drag

analyses are also shown. Jones and Sugiura (2008) discuss the use of a rotary steerable system (RSS) used for directional

drilling was successfully applied in five wells. The RSS resulted of less vibration during the drilling and hole enlargement

operations while not affecting the stability of the BHAs. These papers describe the use of concentric underreamers as part of

the BHA as a cost-effective method of hole enlargement.

Recently, Meyer-Heye et al. (2010) published about weight distribution during simultaneous drilling and reaming. For

optimization purposes, it is necessary to know the weight and torque distribution on the reamer as well as on the bit. In this

paper, the authors showed an analytical method to calculate the load distribution on the BHA based on the penetration

parameter and mechanical specific energy. Then the authors show the effect of different formation changes and drilling

parameters on the rate of penetration and weight distribution. Finally, their conclusions stated the weight distribution varies

with different tool penetration parameters and cross sectional areas drilled by each tool while the torque distribution is

independent of the tool penetration parameter, the reamer is damaged while taking too much weight and torque due to high

depth of cut. The reamer efficiency is less than the bit due to higher lateral vibration. They suggest that to increase the

efficiency of the reamer, it should be stabilized above

Using the method of the transfer function matrix, J.R. Bailey and S.M. Remmert (2010) published a paper to improve the

drilling efficiency, increase the footage per day and reduce the tool damage by managing drilling vibrations by optimizing the

BHA design. They used a frequency domain lateral dynamic model to predict the vibrations on the BHA and redesign it to

decrease them and increase drilling efficiency.

Model Development for Axial Motion Beginning with 1D models, it is important to show that finite element analysis (FEA) matches the known analytical solutions

very closely, and then to show a transition to 3D and present the drill-ahead model. The drill-ahead model will show the

dynamic interactions of a drillstring with the formation, focusing on the axial motion and addressing the weight distribution

problem.

One of the primary vibrations to which the BHA is subjected is the axial vibration; consequently, axial vibrations are

one of the causes of the premature wear and failures of the BHA components. Subjected to various boundary conditions, a

governing equation that describes the behavior of an axial rod as presented by (Inman 2007) as follows:

( ) ( ) ( )

( )

where F is the axial force, ρ is the density of the material, g is the acceleration due to gravity, A is the cross sectional area as a

function of x, and w(x, t) is the deflection of the rod in the x direction. If the boundary conditions are such that each end is

pinned and the static deformation is desired, then the following equation describes the axial displacement.

( )

( )

where E is the Young’s modulus of elasticity, and l is the length of the bar. As an example, consider a 12,000 inch drillstring

composed of tubulars with an outside diameter (OD) of 8.25 in. and an inside diameter (ID) of 3 in. The drillstring has a

density of 0.000741 lb-s2/in4 , and a modulus of elasticity of 30,000,000 psi. The maximum displacement occurs in the center

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and has a value of -0.172 inches. Figure 1 shows the axial deflection of the drillstring w(x) for this example, as calculated by

Eq. (2):

Fig. 1—Axial deformation of the drillstring.

Explicit Finite Element Modeling Explicit FEA models static loading by using a time forward integration scheme to propagate stress waves in a material.

Therefore, to determine static values sufficient time must pass and simple analysis may take may steps to complete. While

this is computationally inefficient, it does enable the model to capture transient effects during loading.

To model the axial deformation modeled by Eq. 2, model comprising 1000 elements was used. The only load was gravity

in the vertical direction that is applied gradually. When loads are applied suddenly in explicit analysis the results contain high

frequency content that manifests itself as shock waves. Therefore, a smooth transition over 1 second to full strength gravity is

used to model the static deflection. This results in the displacement of the middle node in the column as shown in Figure 2.

The first second shows the smooth step as gravity is applied to the model. The end of the smooth step results in a

displacement of the middle node of about -0.172 inches, which matches the theory predicted in Eq. (2). However, the model

does not contain any damping so the results show a small vibration about an equilibrium point. These small vibrations are

shown in the expanded bubble of Fig. 2. By determining the duration of a cycle, frequency of vibration was 52.665 radians

per second. More complex digital signal processing techniques may be needed to extract frequency information for complex

models.

Fig. 2—Axial deformation of the middle node from an Abaqus/Explicit analysis.

The natural frequencies obtained from solving Eq. (1) are as follows:

√

( )

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where the frequencies are in radians per second. The first natural frequency is 52.677 rad/s, which compares to the results

from the transient dynamic model. This relatively simple example shows the explicit dynamic solution obtained from

Abaqus/Explicit contains both static and dynamics results. Both the static deformations and linear vibrations from FEA were

verified against closed-form solutions.

Transient Dynamic Models: Drill-Ahead Model Actual BHAs have sufficient complexity where closed-form solutions are often unrealistic. To perform a finite element

analysis, the domain is broken into discrete elements and the elements are connected by nodes. The shape of the element

approximates the position of the neutral axis of the drilling tubular. Each element is modeled as a line segment. Each node

has six degrees of freedom: translation in three enumerated orthogonal directions, as well as rotation around the

corresponding axes. Cutting structures and other points of interest (e.g., stabilizers) are modeled with nodes and additional

point masses where needed. The additional stiffness from the external material of the specialty structures is not included in

the computation. The wellbore is defined using a connector element that allows for radial movement. The radial movement

has a stop criterion which constrains the deformation away from the neutral axis, thus simulating the wellbore.

Because of the nature of drilling, the axial boundary conditions at the cutting structures must be dynamic. In other words,

the boundary of the model is moving as a result of cutting material away. The rate of removal drives the rate of penetration

(ROP), which is essentially the velocity of the bit or the reamer. To explore how the ROP affects the dynamic behavior of the

BHA, a simple drill-ahead model was implemented that defines the ROP as being proportional to the weight on the cutting

structure (i.e., WOB or WOR).

The overall length of the model is 1,000 ft. The diameter of the pilot hole is 12.25 in., and the diameter of the reamed hole

is 14-in. The bit is modeled as a point mass at the first node of the finite element model. Following the bit, 90 ft of slick drill

collars (OD=8.25 in., ID=3 in.) are modeled using elementary linear beam elements. Next, a 4-ft stabilizer (OD=12.125 in.)

section is included. Above the first stabilizer is another 90 ft section of drill collars (OD=8.25 in., ID=3 In.). At 184 ft above

the bit, the reamer is modeled using a point mass. Above the reamer, two additional 90 ft sections of drill collars are used

with a 13.95 in. OD stabilizer splitting those sections. The remainder of the BHA is modeled using heavyweight drillpipes

(OD= 7.0 in., ID =4.0 in.). All sections are assumed to be straight cylinders. A schematic is shown in Figure 3.

The total weight in air of the 1,000-ft BHA is 117,813 lb. When using a drilling fluid with a density of 16.5 pounds per

gallon, the buoyancy factor is 0.7467, and the total weight of the BHA in mud is equal to 87,971 lb. This value was used to

check the equilibrium using the output from the Abaqus simulation.

Fig. 3—Schematic of the drillstring in the wellbore.

Deformed Shape Because this is a transient dynamic analysis, the deformed shapes are always changing. However, the loading is such that

quasi-static solutions can be extracted from the analysis. These shapes are plotted with a high magnification to accentuate the

lateral deformation. The legend of the contour plot for the deformed shape shows the Abaqus variable of SF1, which is the

internal axial force. The results shown in Figure 4 indicate the original vertical drillstring and the contour of the internal axial

force under a load in which the combined WOB and WOR is 80,000 lb. The neutral point (transition from compression to

tension) is allocated approximately 800 ft above the bit. There is a force discontinuity at the reamer because an external axial

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reaction force is present. The vertical line shows the original configuration. The color hued shape shows both lateral

deformation and formation penetration. A step time of 7.000 corresponds to a simulation time of 8.0000 seconds.

Fig. 4—Deformed shape of the drillstring.

Axial Forces The axial force time history is tracked within in Abaqus. Figure 5 shows the complete history of the axial forces for the bit,

reamer, and top node load (labeled as the hook load). There are four distinct phases shown in the time history graphs of

Figure 5 as summarized in the following list.

1. The time from 0 to 2 seconds establishes a load due to gravity of the BHA. The goal of this phase was to suspend the

BHA so no load was on the cutting structures. In the results, the WOR was zero with some forces still on the bit.

2. During the time from 2 seconds to 2.5 seconds the force holding the BHA off the formation was decreased in a smooth

manner so the WOB and WOR would develop. The results show an overshoot for the weight on the reamer with the bit

gradually building the load.

3. From 2.5 to 5 seconds, the load at the top drive is held constant. The assembly is penetrating the formation at rates

proportional to the WOB and WOR. The dynamic interaction is shown by the harmonic forces highlighted in Figure 6.

4. The same sequence as described in the last two steps is repeated to give a total formation load of 80,000 lb from 5 to 8

seconds.

5. At 8 seconds, the top node, where the suspending load was applied, is clamped such that its velocity is zero. The bit and

reamer continue to penetrate the formation at a rate proportional to the force. As the bit and reamer continue to penetrate,

the BHA extends and the load on the top increases. This response is similar to what would be expected if a so-called drill

off test was conducted. At time increases, the force on the bit and reamer become asymptotic to zero and the load at the

top node approaches the entire weight of the BHA.

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Fig. 5—Simulation output showing the effect of transient loading and cutting relief when the inclination angle is near vertical (0.001 deg).

The graph in Figure 5 shows that for each transition time, the reamer has tendency to take more loading than the bit.

Increasing the transition time when the loading is increased on the bit and the reamer will decrease the overshoot of loading

on the reamer. Therefore, it is recommended to avoid sharp changes in the WOB+WOR while operating a rig. This

observation provides insight into why the reamer may seem to fail first in an operation, even when the cutting structures were

matched (i.e., the same ROP/WOB ratio and the same foundation stiffness). Figure 5 also shows that there are harmonic

components in the axial force. An enlargement of Figure 5 the region at approximately 6 to 8 seconds and -40,000 lb

provides Figure 6, which shows the axial vibration occurring at the bit and the reamer. The simulation results show a greater

amplitude (almost doubled) of vibration of the reamer than the bit. The fundamental frequency is approximately 6 Hz.

Fig. 6—Detailed view of the harmonic oscillation associated with the movement of the bit and reamer.

Side Forces It is important to understand side forces because they relate to deviation control and component wear. Impulsive side forces

arise from the dynamic effects of lateral vibrations. In the near vertical wellbore simulation, the side forces are relatively

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small, as shown in Figure 7. The forces within the connector elements that simulate the wellbore are automatically tracked in

Abaqus. The inclination angle has a significant effect on the static side forces of the BHA, as shown in Figure 8 and Figure 9.

Fig. 7—Side forces with a near vertical inclination angle.

A plot of the change of the side force magnitude on the reamer and the bit vs. inclination angle and WOB is shown in

Figs. 8 and 9. An investigation of Figs. 8 and 9 leads to two conclusions. First, the side force magnitude at the reamer are

considerably greater than at the bit. Second, the side force magnitude decreases with the increase in WOB and increases with

the increase in inclination.

Fig. 8—Side force at the bit vs. total combined (WOB+WOR) for various inclination angles.

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Fig. 9—Side force at the reamer vs. total combined (WOB+WOR) for various inclination angles.

Penetration Parameter The penetration parameter is defined as the proportionality constant for the drill-ahead model. Three values were selected that

correspond to 15, 45, and 75 ft/hr of penetration at 30,000 lb WOB. Simulations were run to compare the system response to

different ability of the cutter to penetrate the formation and remove cuttings. Simulation results are presented in the appendix

for an inclination angle of 45 degrees. For this case, the simulation results show that, as the penetration parameter of the bit

increases, the side force magnitude on the bit and the reamer also increase. Likewise, as the penetration parameter of the

reamer increases, the side force magnitude on the bit and the reamer decrease. This finding leads to the recommendation that

the reamer be selected to have a greater ability to penetrate than the bit. The use of ROP-limiting bits could help to ensure

that the bit does not “run away” from the reamer. The axial forces on the reamer tend to be lower if the penetration parameter

of the reamer is higher. Finally, it is well known that the location of stabilizers will affect the side force on the reamer.

Conclusions Simultaneous drilling and underreaming has proven to be an economical technique that opens a drilled pilot hole to a larger

diameter to install close tolerance casing strings and to simplify the insertion and extraction of drilling assemblies. However,

because of the potential for different types of formation, the loading on the reamer and the bit can quickly change. This

situation may cause vibration while the assembly is drilling ahead, which may lead to uneven wear or premature failure of the

components of the BHA. Therefore, there is a need for a better understanding of the dynamic of the BHA interactions with

the formation and for a tool to capture such behavior. This paper presented a predictive model to help to explain the axial

dynamics in a BHA generated during simultaneous drilling and reaming operations.

The results indicate that explicit FEA is an adequate solution technique for the boundary value problem describing the

drillstring structure as it compares to closed form solutions. Furthermore, the drill-ahead model enabled study of the transient

interaction between the reamer and the bit. Results also showed the transient history of the side and axial forces on the bit,

reamer, and stabilizers.

From the history of the axial forces, the steady-state dynamic results were extracted by showing the time history of the

forces occurring on the reamer and the bit. The amplitude of the vibrations on the reamer was approximately double that

occurring at the bit for this example study. In addition, the natural frequency was determined, which is important when

avoiding resonance. The axial forces history diagram showed the transient dynamic response from which we concluded that

for each change of top node load, the reamer has tendencies to take more of the load than the bit by observing the overshoot

occurring on it.

The major conclusions of the paper include the following:

FEA using Abaqus is an adequate solution technique for the boundary value problem describing the drillstring

structure. Results were compared to known analytical solution and models, and they provided a close match.

During drilling and underreaming, more vibrations occur on the reamer than on the bit; during each transition of

load, the reamer tends to take more of the load than the bit.

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To decrease the side forces at the reamer, it is recommended to operate with a more aggressive reamer and a less

aggressive bit.

Results and conclusions were made for particular examples in this paper and some of the observations may not be

generalizable.

Acknowledgment

The author would like to thank the faculty of Petroleum Engineering in the University of Tulsa in addition to Tulsa

University Drilling Research Projects and Tesco Corporation for their constant support of this research.

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Appendix This appendix describes the change of side force at the bit and the reamer with respect to the change of penetration parameter.

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