The objective of this research is to scale a drilling system to a lab

scale rig that reproduces the physical behavior of drilling systems. The

project aims to mimic torsional stick-slip oscillations specifically. Stick-

slip occurs when the depth of cut increases and the bit sticks, then after a

torsional buildup in the drillstring, the bit breaks out and spins at a

uncontrolled higher angular velocity. The scaling of the system was done

with non-dimensional ratios such as in Eq. (1a) and (1b).

The CAD model was created for the rig using mostly off the shelf materials from

McMaster-Carr, Amazon and other sources. They were selected based on material

properties. The structure went through a static load stress test to check for its ability to

handle the loads applied. The design is then exported from SOLIDWORKS® and

imported to MATLAB®, where sensors track linear/angular position and velocity

(Fig. (2)). With an integrated bit-rock interaction code model developed my Dr.

Masood Ghasmei, we may examine the physical behavior of the drilling system.

Fig. (3) SOLIDWORKS® drilling design is converted to a MATLAB Simulink® design.

Abstract

References

Design As the demand for energy rises, so does the need for resources and

the means to extract them safely and efficiently by means of down-hole

drilling. These large mechanical systems often encounter obstacles; the

drillstring of the drilling rig encounters lateral, torsional, and axial

vibrations which can cause serious damage and possibly failures to a

system. To minimize these effects, control algorithms are developed and

then tested on lab-scale drilling rig models. This paper develops the

systematic method of part selection, design, and simulation of a

customizable lab-scale drilling system. The physical parameters are

created in SOLIDWORKS® and the system is simulated using MATLAB

Simulink®. The goal of the project is to reproduce physical behavior of

drilling systems using a lab scale model for further research on

understanding and mitigating detrimental effects.

Conclusions

Acknowledgements

DESIGN AND SIMULATION OF A LAB-SCALE DOWN-HOLE DRILLING SYSTEMDr. Masood Ghasemi, Dr. Xingyong Song

Texas A&M UniversityDepartment of Engineering Technology and Industrial Distribution

Aakash Bajpai University of Maryland, Baltimore County

Department of Mechanical Engineering

Future Work

Simulation

𝑚1

𝑚𝑏, 𝐼𝑏

𝑚𝑏𝑔

𝑚1, 𝐼1

𝑚2, 𝐼2

𝑚2𝑔

𝑚1𝑔

𝑙2

𝑙1𝑘1 𝑐1

𝑘2 𝑐2

𝑇𝑏 𝐹𝑏

𝑇 𝐹

𝐸𝑞. 1𝑎 𝑘∗ =𝑘

ത𝑘=

𝑘𝑙

𝑚𝑔=

𝑘𝑙

𝜌𝐴𝑙𝑔=

𝑘

𝜌𝐴𝑔=

𝐸𝐴

𝜌𝐴𝑔𝑙=

𝐸

𝑙𝜌𝑔

𝐸𝑞. (1𝑏) 𝑘∗ =𝑘

ത𝑘=𝑘𝑑(𝑡)

𝐹𝑏=𝐸𝐴𝑑(𝑡)

𝑙𝐹𝑏

𝐸𝑞. 3𝑎 𝐹𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔 =𝜋2𝐸𝐼

𝐾𝑙=𝜋2𝐸𝐽

2𝐾𝑙𝐸𝑞. 3𝑏 𝐹𝑏=

𝐹𝑏𝑢𝑐𝑘𝑙𝑖𝑛𝑔

𝑆𝑎𝑓𝑡𝑒𝑦 𝐹𝑎𝑐𝑡𝑜𝑟

The system is assumed to be in an inertial

reference frame. This means that we have a

steady drilling state and acceleration is zero.

The axial dynamics of the drillstring is broken

into a lumped parameter model of three rigid

inertial masses connected by springs and

dampers. The lengths are dictated by the mass

of the segments which are scaled down from the

full scale system, depicted in Fig. (1). An

example of the resulting differential equations

is in Eq. (2).

Fig. (1) Schematic of lumped

parameter axial model.

𝐸𝑞. 2 𝑚1 ሷ𝑥1 + c ሶ𝑥1 − ሶ𝑥2+ k 𝑥1 − 𝑥2 = 𝐹 −𝑚1𝑔

𝐸𝑞. 4𝑑 ത𝑇𝑏(𝑡) =2𝑇𝑏𝑎2

=𝐸∗

𝐸∗ − 𝜀𝜇𝛾𝜎𝜅𝑑∗−𝜁𝜀(𝑑 𝑡 − 𝑑∗)

𝑑∗ → 0Simplifies to

ത𝑇𝑏 = 𝜁 ത𝐹𝑏

𝐸𝑞. 4𝑐 ത𝐹𝑏(𝑡) =𝐹𝑏𝑎

=𝐸∗ − 𝐸0𝐸∗ − 𝜀

𝜎𝜅𝑑∗−𝜀(𝑑 𝑡 − 𝑑∗)

Based on the force, geometry, desired rate of penetration, blade length and frictional

values; The torque and force needed to drill through a selected material can be

calculated with the bit-rock interaction equations in Eq. (4a)-(4d) [Detournay et al.]

𝐸𝑞. 4𝑎 𝐸∗ = 𝜀 + 𝜇𝛾𝜎𝜅 𝐸𝑞. 4𝑏 𝐸0 = (1 − 𝜇𝛾𝜁)𝜀

Fig. (2) Simulink Model actuates the drill in the Mechanics explorer. Displacement readings (inset).

𝑦1(𝑡)−𝑦2(𝑡)

(m)

Start Up Readings

Research Objectives

Previous work of lab scale systems focuses on artificially creating vibrations.

Methods include using an off center masses (lateral vibration) or a an oscillating brake

at the end of the drill string (torsional vibration). This system in contrast attempts to

naturally recreate these vibrations. Failure criteria were needed to outline the ranges of

material properties, geometries and loadings. Due to the flexible nature of soft PVC the

drillstring would likely bow outward and fail due to buckling before shearing or axial

pressure. This leads to the use of the Euler’s Buckling Equation in Eq. (3a). Use of a

safety factor arrives to the maximum allowable weight through the system, Eq. (3b).

The system is customizable with a 10.1 HP topdrive. It can be

outfitted with any drill string up to a meter in length and can apply large

amounts of weight on bit. It is also designed using off-the-shelf parts and

can successfully simulate oscillations of the lumped parameter model.

FEM may be used to analyze the system, which provides more

precise results than the current lumped parameter approach. Also, a

closed loop control system can be integrated into the system.

The current design only considers vertical drilling and it may be

upgraded to include directional drilling. Finally, the SOLIDWORKS®

model can be used to build the physical lab-scale drilling system.

Detournay, Richard, Shephard. “Drilling response of drag bits: Theory

and experiment”. Int J Rock Mech Min Sci 45 (1347-1360), Jan. 2008.

This material is based upon work supported by the Research

Experiences for Undergraduates Program under National Science

Foundation under Grant No. 1263293. Any opinions, findings, and

conclusions or recommendations expressed in this material are those of

the author(s) and do not necessarily reflect the views of the National

Science Foundation.