DEM AS A TOOL FOR DESIGN AND OPTIMISATION OF MINERAL PROCESSING EQUIPMENT

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DEM AS A TOOL FOR DESIGN AND OPTIMISATION OF 
MINERAL PROCESSING EQUIPMENT 
 
 
Paul W. Cleary 
CSIRO Mathematical and Information Sciences, Private Bag 10, Clayton, Vic, 3169. Australia. 
E-mail: Paul.Cleary@csiro.au 
 
 
ABSTRACT 
 
DEM application in mineral processing has for many years been heavily focused on simulating mills of 
various types. This method can be used to simulate many other aspects of mineral processing operations and 
can be used both to enhance understanding of the underlying flows and of issues such a breakage, wear, 
blockage, product degradation, segregation and mixing. The application of DEM to four important classes of 
non-comminution problems and equipment commonly found in or near mineral processing plants are 
described. These are: 
! Particle transport (examples include a conveyor belt and an inclined screw conveyor) 
! Sampling (assessment of sample bias for cross-stream samplers) 
! Separation (the efficiency of vibrating screens) 
! Storage and reclaim (discharge from a multi-port hopper and segregation in a splitter bin with asymmetric 
ingoing and outgoing conveyor belts, apron feeders and impact plate). 
 
Keywords: Discrete element method, sampling, storage, particle transport, separation. 
 
INTRODUCTION 
 
Particle scale simulation of industrial particle flows using DEM (Discrete Element Method) offers the 
opportunity for better understanding flow dynamics leading to improvements in equipment design and 
operation that can potentially lead to large increases in efficiency, throughput or product quality. DEM has 
been used for modelling many industrial applications, particularly milling (Mishra and Rajamani, 1992, 
1994, Rajamani and Mishra 1996, Cleary 1998a, 2001a&b, Cleary et.al. 2001, Morrison et.al. 2001, and 
others), flows in rotating drums (Ristow 1994 and Cleary 2000 and many others), operation of dragline 
excavators (Cleary, 2000) and hopper flows (Holst, 2000). In mineral processing, DEM has been 
concentrated on mills because of their critical importance. However DEM also offers the opportunity to 
improve many other parts of mineral processing operations. These areas often do not receive the attention 
that the key comminution equipment commands, but can become critical when they fail or under-perform. 
Importantly their assessment/improvement using DEM is often much more feasible because of smaller 
problem sizes and the absence of poorly understood physics such as breakage. 
 
THE DEM METHOD 
 
DEM simulation involves following the motion of every particle in the flow and modelling each collision 
between the particles and between the particles and their environment (e.g. the walls of a bin or the belt on a 
conveyor). Industrial applications place heavy demands on the geometrical capabilities of DEM codes. In 
three-dimensions, boundary objects are defined here by triangular finite-element surface meshes. Such 
meshes can be produced using any reasonable mesh generator from solid models generated in suitable CAD 
packages. This provides enormous flexibility in specifying three-dimensional environments with which the 
particles interact. The particles are modelled here as spheres. 
 The general DEM methodology and its variants are well established and are described in review articles 
by Barker (1994), Campbell (1990) and Walton (1994). Here we use a conventional implementation that is 
described in more detail in Cleary (1998a&b). 
 
Proceedings: XXII International Mineral Processing Congress 29 September – 3 October 2003 
Chief Editors: L. Lorenzen and D.J. Bradshaw Cape Town, South Africa 
ISBN: 0-958-46092-2 Produced by: Document Transformation Technologies 
Briefly, the particles are allowed to overlap and the amount of overlap ∆x, and normal vn and tangential vt 
relative velocities determine the collisional forces via a contact force law. We use a linear spring-dashpot 
model. For more complex models see Schäfer (1996) and Walton (1994). The normal force: 
 
 F −= (1) nnnn vCxk +∆
 
consists of a linear spring to provide the repulsive force and a dashpot to dissipate a proportion of the relative 
kinetic energy. The maximum overlap between particles is determined by the stiffness kn of the spring in the 
normal direction. Typically, average overlaps of 0.1-0.5% are desirable, requiring spring constants of the 
order of 104 - 106 N/m in three dimensions. The normal damping coefficient Cn is chosen to give the required 
coefficient of restitution ε (defined as the ratio of the post-collisional to pre-collisional normal component of 
the relative velocity), and is given in Cleary (1998b). The tangential force is given by: 
 
{ }∫ += ttttnt vCdtvkFF ,min µ (2) 
 
where the vector force Ft and velocity vt are defined in the plane tangent to the surface at the contact point. 
The integral term represents an incremental spring that stores energy from the relative tangential motion and 
models the elastic tangential deformation of the contacting surfaces, while the dashpot dissipates energy 
from the tangential motion and models the tangential plastic deformation of the contact. The total tangential 
force Ft is limited by the Coulomb frictional limit µFn,, at which point the surface contact shears and the 
particles begin to slide over each other. 
 The discrete element algorithm has three main stages: 
! A search grid is used to periodically build a near-neighbour interaction list that contains all the particle 
pairs that are likely to experience a collision in the short term. Using only particle pairs in this list reduces 
the contact detection calculation to an O(M) operation, where M is the total number of particles. Industrial 
simulations with up to 500,000 particles are now possible in reasonable times on current single processor 
workstations. 
! For pairs of particles or particles and objects in the near-neighbour list, the closest distance between them 
is calculated in order to determine if they are in contact. The contact forces between each pair of 
interacting particles and/or boundary objects are then evaluated in their local reference frame using the 
spring-dashpot model and then transformed into the simulation frame of reference. 
! All the forces and torques on the interacting particles and objects are summed and the resulting equations 
of motion are integrated. Time integration is performed using a second-order predictor-corrector scheme 
and typically uses between 15 and 25 time steps to integrate accurately each collision. This leads to small 
time steps (typically 10-4 to 10-6 s depending on the controlling length and time). 
Quantitative predictions of boundary stresses, wear rates and distributions, collision forces, energy 
spectra, power consumption, torques and flow rates, sampling statistics, mixing and segregation rates and 
many other quantities can be made from the information available in DEM simulations. For more details on 
the simulation method and on the data analysis see Cleary (1998c). 
 
TRANSPORT 
 
Larger particulate solids, such as ore or coal from mines, flowing into or from stockpiles and into 
elements of the grinding circuit are commonly transported using conveyor belts. In some circumstances 
within plants, particulate solids can also be transported by screw conveyors. Both modes of transport can be 
easily modelled using DEM, which allows detailed knowledge of transport rates, size segregation, particle 
degradation and boundary wear to be assessed. 
 
Conveyor belts 
Figure 1 shows the loading of a 1.2 m wide conveyor belt at 1500 tph. The belt speed is 6 m/s. The head 
pulley is 1 m in diameter, the idler spacing is 3 m and the idler pitch is 45o. The particle size distribution 
(PSD) is 15 – 60 mm. The particles are generated above the belt at the given mass flow rate, with the 
specified PSD and any degree of segregation in any direction. The particles then fall onto the belt and are 
accelerated by the frictional forcesexerted by the rapidly moving belt. Their initially low speed is shown as 
blue. After 3-4 m of travel the particles have accelerated to the belt speed (shown as green). As they reach 
the head pulley they fly off the belt on parabolic trajectories as they accelerate under gravity (changing from 
green through yellow and orange to red). 
The camera view is rotated during the belt loading process to give a range of views of the conveyor 
configuration. This loading process corresponds to the lower section of any conveyor interchange 
arrangement where the particulates are fed onto the belt. DEM simulation allows predictions to be made for 
the damage to the belt, the degradation of the solids and the distribution of the particulates upon the belt. The 
degree of spread of the solids as the belt trough becomes shallower during the approach to the head pulley 
can also be examined. This demonstrates that full scale belts can now be modelled using DEM for realistic 
belt speeds and tonnage rates. 
 
 
 
 
Figure 1. DEM prediction of the loading and discharge of a conveyor belt. The particles are coloured by speed and 
show the acceleration of the falling stream up to the belt speed and then further acceleration under gravity as they flow 
over the head pulley. 
 
Screw feeders and screw conveyors 
Screw conveyors are used to transport particulate solids over short to medium distances. They have the 
advantage of being closed and can be operated at significant inclinations. Figure 2 shows a 45° inclined 
screw conveyor with a constant pitch screw rotating at 150 rpm. The screw draws down particulates from the 
hopper and transports them in a 200 mm diameter cylindrical tube up 3 m to the discharge point from which 
they fall freely at mass flow rate of 16 kg/s. Typically, the discharge would be into another hopper or into a 
processing unit of some kind. 
Screw conveyer performance is affected by the design of the screw and hopper, the rotational speed of the 
screw, the screw inclination, and the material properties and size distribution of the bulk material. In this 
case, we are principally interested in the nature of the draw down from hopper and whether this is even 
across the length of the hopper. To examine this issue, the particles are coloured in vertical strata determined 
by their initial positions in the hopper at the time the screw starts to rotate. The first frame of Figure 2 shows 
the particulates soon after screw motion commences. The particles have initially fallen into the screw trough. 
After 10 s of operation, particles are discharging from the conveyor. Note that the material around the 
screw is predominantly blue and green and that there is little of the red/orange material drawn down yet. 
In the hopper the red/orange particles fill a much larger proportion than at the start and are clearly flowing 
down the angled free surface towards the left side of the hopper. The colour distributions in the hopper and 
the screw both demonstrate that this constant pitch screw has a strong predisposition to draw down from the 
back of the hopper. This is very undesirable and can lead to many processing problems. In a similar way, the 
effect of variable core sizes, variable pitch and screw blade spacing can be evaluated and optimal screws can 
be designed for specific materials in order to ensure that the draw down is uniform across the feed hopper. 
 
 
 
Figure 2. Inclined screw conveyor reclaiming from a hopper. 
 
SAMPLING 
 
Bulk sampling of materials is commonly performed using a sampling device that passes through the 
stream of material flowing from the head pulleys of conveyor belts. The accuracy of the sampling is very 
difficult and expensive to establish experimentally. DEM modelling allows any bias to be simply and 
cheaply evaluated. Previously Robinson and Cleary (1999) performed a detailed parametric study using 2D 
DEM to establish the sensitivity of the sampling to the details of the particles and the sampling system taking 
account of the complex multi-body interactions that occur at the cutter opening. 
Here the analysis of a real sampler system is performed in 3D. The geometry modelled includes the 
conveyor up to the head pulley and the cutter, which consists of two parallel vertical blades with connecting 
structures. The sampling configuration is shown in Figure 3. The left column shows the top view looking in 
the direction of the cutter and the right column shows a view from underneath and slightly to the side. The 
top pair of frames show the state as the cutter blade just starts to enter the particle stream falling from the 
head pulley. As the blades pass through the stream, some particles pass between the blades and fall to the 
bottom of the cutter and discharge as a separate sample stream. This is the material sample and is collected in 
the same way as for the real sampler. The particle size distribution and the composition of the sample are 
then known. The critical question is: how representative is this sample of the original stream of particulates. 
The biggest advantage of DEM for this application is not so much its ability to predict the composition of 
the sample taken, but its ability to determine what the reference sample should be. The reference sample is 
the imaginary sample to which the real sample is compared in order to assess the bias. It consists of all the 
particles that should have been sampled if the multi-body interactions with the cutter had not changed their 
trajectories and pushed them away from the cutter. Obtaining reference samples from experiments is 
extremely expensive and involves crash stopping the conveyor, manually digging up and analysing 
extremely large amounts of material from the belt. In the DEM simulations, a computational sample plane is 
simply placed across the stream of particles just after they leave the belt at the head pulley. The trajectories 
of all the particles are assessed here and ones that should be sampled are re-coloured yellow and form the 
reference sample. Congestion of the particle flow at the sampler opening leads to many yellow particles 
escaping the sample. These are the prime contributors to sample bias. At the end of the simulation, the actual 
sample is compared to the reference sample. This is repeated fives times to give good statistical accuracy for 
the bias estimate (biases of more than 1% can be easily identified). In this case the sampler has an aperture of 
only 2.5 times the particle topsize and a significant bias of several percent was identified. 
 
 
 
 
Figure 3. Cross belt sampler shown during operation from above and below views. The material is originally coloured 
blue and then re-coloured as yellow particles if they belong to the reference sample and should be sampled. 
 
Figure 4 shows the sampler passing through the stream of particles in a side view with the particles 
coloured by speed. The acceleration of the particles under gravity can be seen in the change of colour from 
green (the 6 m/s belt speed) to red as they pass the sampler. The effect of the interaction of the stream with 
the sampler is to significantly slow the particles that are in close proximity to the sampler. They are shown as 
dark blue and are moving at speeds of less than 1 m/s. This demonstrates that the sampler blades do not just 
separate the stream into sub-streams with the central sub-stream being directed into the sampler, but also 
significantly impede and disrupt the particle flow. This leads to sample volumes of only about 70% of the 
theoretical perfect sample. Current sampling theory suggests that for samples that are below 90% of the 
theoretical value, there is a strong chance of bias occurring. This is certainly true for this case. 
 
 
 
Figure 4. Cross belt sampler shown during operation from the side with particles coloured by speed. The blue particles 
are slowly moving particles whose motion has been seriouslyimpeded by the interaction of the particle stream with the 
sampler. 
 
This sampling analysis can be performed on essentially any cross belt sampler and potentially on other 
types of samplers as well. It is able to detect small biases and can be used to test alternative sampler designs 
and modes / speeds of operation. DEM simulation is able to show that many sample cutters that satisfy 
existing standards in fact produce significant bias whilst others that do not satisfy the standards have either 
small to undetectable bias. In particular, sampler cutters that are made 4 times the topsize (instead of the 
standard 3 times) and which are moved at twice the speed can have samples that are around 1/3 smaller 
(potentially allowing smaller and therefore cheaper sampling systems to be used) while producing biases that 
are less than the detectable 1% level used here. 
 
SEPARATION 
 
Particle separation using vibrating screens is a common method for dividing mill or crusher output into a 
product stream and a recycle stream. The efficiency of a screen is determined by the size and shape of the 
screen openings, the size and shapes of the particles to be separated and the amplitude and frequency of the 
screen motion. DEM allows screen efficiency to be easily evaluated. Figure 5 shows an 800 mm square 
section of a vibrating screen operating with near vertical motion at around 5 Hz. The bed consists of around 
8000 particles with diameters between 10 and 60 mm. The screen acceleration is enough for the bed to 
separate from the screen deck during the upper part of the screen motion and then to crash back down. Each 
landing of the bed leads to a spurt of finer particles through the screen. The screen motion used here leads to 
a pulsing flow through the deck. The flow of fines is ultimately limited by the percolation/transport rates of 
the fines from the upper to the lower regions of the bed. Poor design of the grate openings for a given 
material can also lead to inefficiencies in the passage of finer particles through the screen. DEM also allows 
wear patterns and relative rates of wear to be assessed. In particular, the evolution of the screen geometry 
according to the calculated wear rates allows predictions of the change in screen open area with the screen 
wear to be made. This is a key to understanding the changes in performance of the screen with time (wear). 
The ability to make such predictions allows designers and end-users to optimize their screens for the 
expected feed size distributions. 
 
 
Figure 5. Panel of a vibrating screen. 
STORAGE AND RECLAIM 
 
Hopper discharge 
Hoppers are an important part of all materials handling operations. DEM simulation can help with 
understanding the flow pattern within complex hopper designs, including segregation effects. Understanding 
these can lead to more uniform mass flow and more uniform composition between the ports and throughout 
the discharge process. The stress distributions on the hopper walls, particularly when different combinations 
of ports are opened and closed (inducing potentially huge and very rapid stress changes) can also be 
evaluated in order to assist with structural design of the hoppers. Figure 6 shows an example of a 4 m high 
and 1.5 m diameter hopper (with a hopper half angle of 30o) and with four symmetric discharge ports. There 
are around 70,000 particles with diameters in the range 25-60 mm. 
 
 
 
Figure 6. Discharge from a four-port hopper. 
 
Separation in a large conveyor splitting bin 
Large splitting bins are used to fulfil a range of functions. They can: 
! act as an interchange between different conveyor belts, 
! provide a buffer for the downstream processing plants, 
! enable an incoming stream to be divided into a number of outgoing streams. 
It is useful to understand the effect of the bin/conveyor geometry on the material characteristics on 
outgoing conveyors. 
Figure 7 shows a complex splitter bin system modelled using DEM. The particles are coloured by size 
with red/large and blue/small. The incoming conveyor is oriented at 45° to the bin and carries rock at 10 m/s 
with a flow rate of 5000 tph into a bin with a 6 m square top and a 6 m height. This stream separates from the 
head pulley and travels on a parabolic trajectory over the bin where it is deflected downward by a large 
central impact plate. 
The structure of the flow around the impact plate is clear. The upper part of the stream is deflected 
upwards and to the sides forming a dense parabolic concentration of particles above the impact point that in 
turn produces a distinctly separate stream of particles on either side. The left one falls towards the back left 
corner of the bin and the other towards the front right corner. The lower part of the incoming stream is 
deflected immediately downwards into the middle of the bin. 
 
 
a) 
 
b) 
 
c) 
 
d) 
 
Figure 7. Splitter bin showing incoming and outgoing conveyors, apron feeders and an impact plate. 
 
The lower half of the bin is split into two parts by a splitter plate and each side converges to form a long 
slot hopper. Each hopper then discharges onto an apron feeder that moves with speed of 1.5 m/s and which 
draws out material. Each discharge stream then falls around 0.75 m onto a smaller 900 mm conveyor belt. 
The two exit belts are parallel, with gentle but different downhill grades and have speeds of 6 and 7 m/s 
respectively. 
The incoming particle stream is expected to be substantially segregated during its transport along the 
conveyor, with the fines concentrated in the lower region adjacent to the belt. The DEM particles have been 
generated just above the belt with such a vertical size segregation pattern imposed. This is clearly indicated 
by the layer of blue fines visible on the underneath of the stream after it has departed the head pulley in 
Figure 7b. This vertical segregation of the particles is very important since it interacts strongly with the sub-
division of the incoming stream generated by the impact plate into three distinct streams falling into different 
parts of the bin. Since the central downward stream from the impact plate consists predominantly of material 
from the bottom of the incoming stream it then consists of mainly finer particles. Conversely, the two side 
streams (directed into opposite corners of the bin) consist of mostly of coarser particles from the upper parts 
of the incoming stream. The combination of the impact plate and the vertical segregation of the incoming 
stream appears to be an efficient separation mechanism generating multiple streams with different 
compositions into the bin. 
The apron feeders draw their material preferentially from the back of the hoppers with this material 
deposited on the bottom of the belt with smaller amounts of material drawn from the front of the bin 
overlayed on top of this. For the left hopper (as seen in Figure 7c), the coarse material is deposited towards 
the back so this coarse material is removed first and ends up at the bottom of the left outgoing conveyor with 
finer material deposited on top. For the right hopper, the coarse material is deposited towards the front so 
that finer material at the back is removed first and ends up at the bottom of the right outgoing conveyor with 
coarser material deposited on top. This can create an apparent visible surface composition difference 
between the outgoing belt, purely because of the layering of the different sizes produced by the action of the 
apron feeders on oppositely segregated material along the length of the slot hoppers. This is not an overall 
composition difference between the belts, but is a surface difference due to the different layering on the belts. 
This effect is generated by the difference in angle between the incoming and outgoing conveyors. 
A real composition difference can be created though by the choice of location of the impact plate. If the 
impact plate is symmetrically located,so the center of the finer middle stream falling from the impact plate is 
directly over the center of the bin, then equal amounts of the fines will fall into either side of the bin. The 
coarse material is mostly in the two outer streams falling from the impact plate. One stream falls into each 
hopper and so the amount and composition of coarse material in each hopper is essentially the same. The 
overall composition of the material in each hopper is then the same, (even though there are differences in the 
distribution of the coarse and fine within each hopper). 
If the impact plate is placed closer to the incoming conveyor then a larger fraction of the fines will fall 
into the closer hopper (the left one in Figure 7c) and the left hopper will have a finer composition than the 
right one. Conversely, if the impact plate is located further away then more of the finer material will fall into 
the far hopper (on the right in Figure 7c) and this will have a finer composition. The positioning of the 
impact plate is therefore critical as this determines the split of fine material between hoppers. 
 We note here that extreme positions of the impact plate will also start to affect the split of the coarse 
material between hoppers. The sideways position of the impact plate is not important as long as the entire 
incoming stream is deflected by the plate. These observations have been made on the basis of one simulated 
configuration, but the general understanding obtained can be expected to apply for a range of belt speeds and 
tonnages and for variants of the conveyor and bin geometry. The critical aspects required to generate the 
composition variations are the asymmetric orientation of the incoming conveyor, the presence of an impact 
plate and the initially vertically segregated material on the incoming belt. 
 
CONCLUSIONS 
 
DEM simulations of applications relating to the storage, transport, sampling and separation of particulate 
solids have shown that: 
! A broad variety of coarse particulate mineral processing equipment can be successfully modelled. 
! Relevant information relating to the important issues for each of the types of equipment/processes can be 
predicted. This includes flow rates, segregation effects, particle degradation and damage to equipment for 
transport equipment; sample bias for sample cutters; segregation effects, flow rates and wall stresses for 
storage and reclaim equipment and separation efficiency for vibrating screen decks. 
! Enhanced understanding of the particulate flows in the equipment and of the important issues for each 
case. 
 
ACKNOWLEDGEMENTS 
 
The author would like to acknowledge the contributions of Geoff Robinson to the development of the 
capability to analyse cross belt conveyor sampling over the last decade. Also acknowledged is the work of 
Phil Owen in performing the screw conveyor simulations. 
 
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