1. 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 SYSTEM
Dr. Masood Ghasemi, Dr. Xingyong Song
Texas A&M University
Department of Engineering Technology and Industrial Distribution
Aakash Bajpai
University of Maryland, Baltimore County
Department of Mechanical Engineering
Future Work
Simulation
𝑚1
𝑚 𝑏, 𝐼 𝑏
𝑚 𝑏 𝑔
𝑚1, 𝐼1
𝑚2, 𝐼2
𝑚2 𝑔
𝑚1 𝑔
𝑙2
𝑙1
𝑘1 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 =
𝜋2
𝐸𝐼
𝐾𝑙
=
𝜋2
𝐸𝐽
2𝐾𝑙
𝐸𝑞. 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 − 𝑚1 𝑔
𝐸𝑞. 4𝑑 ത𝑇𝑏(𝑡) =
2𝑇𝑏
𝑎2
=
𝐸∗
𝐸∗ − 𝜀
𝜇𝛾𝜎𝜅𝑑∗
−𝜁𝜀(𝑑 𝑡 − 𝑑∗
)
𝑑∗
→ 0
Simplifies to
ത𝑇𝑏 = 𝜁 ത𝐹𝑏
𝐸𝑞. 4𝑐 ത𝐹𝑏(𝑡) =
𝐹𝑏
𝑎
=
𝐸∗
− 𝐸0
𝐸∗ − 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.