Calibrated FEM modelling of rock cutting with PDC cutter
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Calibrated FEM modelling of rock cutting with PDC cutter
Nina Yari 1
Marcin Kapitaniak 1
Vahid Vaziri 1
Lifeng Ma 0
Marian Wiercigroch 1
0 S&V Lab, Department of Engineering Mechanics, Xi'an Jiaotong University , 710049 China
1 Centre for Applied Dynamics Research, University of Aberdeen , AB24 3UE, Scotland , UK
Complexity of bit-rock interactions and formation fracture makes rock drilling a challenging task from modelling perspective. A finite element model is developed which can plausibly capture the rock fractures while it is capable of evaluating drilling forces for various values of Rate of Penetration (ROP), bit angular velocity and cutter configuration. Firstly, experiments on a single cutter rig are performed with various drilling parameters to be compared to the proposed FE model. Prior to detailed numerical simulation, a rigorous computation test on material model characterization and the element size and type is conducted to ensure feasible and reliable simulation results. The cutting forces are analysed for different values of WOB, rake angle, initial depth of cut and cutter speed for a single-cutter linear cutting. The formation fragmentation process and computed results are comparable to laboratory tests.
1 Introduction
Polycrystalline diamond compact (PDC) bits have been
used in in drilling industry from early 1970 [
4, 5
]. PDC
bits consist of a set of PDC cutters on a tungsten carbide
body which shear the rock [
4, 5
]. Rock drilling
modelling is still a challenge due to the rock material
nature and complexity of rock-bit interaction. In order to
enhance the efficiency of drilling and improve the drill
bit performance, a calibrated model which is able to
estimate the drilling forces would be highly beneficial.
In Oil and Gas drilling industry, an axial force is exerted
on the bit due to the drill-string weight which is called
weight on bit (WOB) while the bit is rotated with an
angular velocity (ω) creating a torque on bit (TOB). In
order to investigate drilling forces on each PDC cutter, a
linear single cutter rig was designed and built in drilling
lab within Centre for Applied Dynamics Research
(CADR) at University of Aberdeen. Linear single cutter
rig has been used for a long time by many researchers [
3,
7, 9
] to model rock-cutter interaction. Similar tests have
been performed to assess the unconfined compressive
strength of the rock at very small depth of cuts [
9
].
Numerical simulation methods such as Discrete Element
Method (DEM), Finite Element Method (FEM), Finite
Difference Method (FEM) and Boundary Element
Method (BEM) have been widely used to model rock
fracturing and rock-cutter interaction [
6, 8
]. The aim of
this study is to develop a Finite Element model utilizing
ABAQUS CAE which can simulate the rock fracturing
and predict the cutting forces in different operating
parameters such as the cutter back rake angle, depth of
cut and cutter velocity. The model assists in
understanding the stress and strain field in the region of
rock involved in drilling accompanied by how the cracks
are formed and create a chip in the formation. The FE
models are then tested against the experimental results.
Fig. 1. Linear cutting configuration and the resultant forces.
2 Experiments
This section briefly introduces the linear cutting rig
followed by test results.
2.1 Experimental setup
The linear single cutter rig is a metal shaper machine
which is modified to suit for rock cutting. It consists of a
stationary table which accommodates the rock, a single
PDC cutter (3mm diameter) which is attached to a three
dimensional force sensor moving along the rock length
to cut a groove. The test is conducted under kinematic
control which means the depth of cut and the cutting
velocity is constant. Figure 1 represents linear cutting
parameters. The cutter velocity in direction of the cutting
is equal to rω, where r is the distance of the cutter from
the bit centre. Depth of cut (h) is defined as the bit rate
of penetration per revolution (2π×ROP/ ω). Interfacial
frictional angle (ψ) is the angle between the resultant
cutting force and the resolved force normal to the cutter
[
5
].
Fx
Fy
The corresponding cutting and normal force values for
the experiment of a 3mm single PDC cutter with 20°
back rake angle cutting a groove of 1.3 mm at
500mm/sec velocity in a sandstone sample are
represented in Figure 2. The tests are performed for the
same cutter at different values of depth of cut and the
resultant cutting forces are measured which are
demonstrated in Figure 3.
3 Numerical models
Finite Element Code, explicit ABAQUS CAE is utilized
for modelling the rock cutting. The rock is modelled as a
2D rectangular deformable solid part and the cutter is a
discrete rigid element. The mesh size and type were
selected after a careful mesh sensitivity analysis. The
bottom part of the rock is fully constrained in all
directions while the sides are constrained in Z di (...truncated)