Modular Dynamic Simulation Model for Comminution Circuits

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10.1016/j.ifacol.2016.10.090
© 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
A Modular Dynamic Simulation Model for
Comminution Circuits
?
B. Légaré
⇤
J. Bouchard
⇤⇤
´
E. Poulin
⇤⇤⇤
⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: benjamin.legare.1@ ulaval.ca)
⇤⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: jocelyn.bouchard@gmn.ulaval.ca)
⇤⇤⇤ LOOP, E4m, Department of Electrical and Computer Engineering,
Université Laval, Quebec City, Canada,
(e-mail: eric.poulin@gel.ulaval.ca)
Abstract: Properly controlling comminution circuits is generally acknowledged to be highly
profitable for any mining site’s bottom line. On the other hand, the process control prob-
lem of comminution circuits is challenging due to circulating loads and non-linear trans-
port/transformation rates. As the performance and robustness of the control system highly rely
on a good understanding of the process dynamics, characterizing the deterministic behavior
requires a certain level of operation disruption (bump tests). For a grinding circuit, it implies
a↵ecting the throughput and product size distributions. The management team can be reluctant
to risk obvious consequences on downstream processing stages i.e. inadequate mineral liberation,
reduction of product quality, and perhaps even recovery losses. Process simulation becomes in
this case an attractive tool to design, assess, and pre-commission advanced control strategies.
This paper presents a phenomenological dynamic simulator for comminution circuits developed
in Matlab/Simulink R©. The block model programming allows changing plant layout or control
loops easily, and is flexible for future extensions or model upgrades as any block can be simply
added to the library or replaced with its updated version. The flexibility of the modular
approach allows testing any control system, from basic PID loops to advanced control schemes.
A simulation case study shows how the simulation model can capture the behavior of an actual
circuit once properly calibrated.
Keywords: Comminution, grinding, phenomenological models, dynamic simulation, process
control.
1. INTRODUCTION
According to the estimations of Tromans (2008), com-
minution processes accounted for 29.3% of the total mining
energy in the USA, which corresponded to 0.39% of the
national energy consumption. For mining oriented coun-
tries like Canada and Australia, comminution represents
respectivelly 1.86% and 1.48% of the total energy expen-
diture of the country. This mineral processing stage is
essential for the extraction and recovery of most metals as
the fragmentation liberates the ore from the valueless rock.
The most widely used types of equipment are crushers and
grinding mills. Considering that the relative efficiency of
grinding mills ranges from 3 to 26 % (Tromans, 2008),
great improvements and cost reductions can be achieved
through a better overseeing of comminution operations.
Among the various approaches put forward to tackle this
issue, process control o↵ers a well recognized potential, but
faces difficulty to penetrate, partly because the benefits
?
The authors acknowledge financial support from BBA inc.,
NSERC, FQRNT, and the implication of the industrial partner’s
metallurgical team.
are difficult to predict prior to implementation. Moreover,
developing a control system requires periods of time during
which the circuit will be moved away from the nominal
operating regime for model identification and commission-
ing purposes. The management team can be reluctant to
risk the consequences on downstream processing stages,
which can lead to punctual production losses. More than
one design can also be on the drafting table, and not
all of them can be tested in practice as they all involve
important research and development costs. The use of
dynamic simulation at the engineering stage of a control
system, or to assess the impact of a change of operating or
control strategy can certainly help mitigate some of these
hurdles.
Comminution processes modeling is in constant evolution.
Powell and Morrison (2007) reviewed the latest develop-
ments, ongoing work, and future trends. They concluded
that the next generation of process models will be of a
more fundamental type and usable for equipment design.
Powell and McBride (2006) proposed a solution scheme
to introduce breakage considerations into models based
on discrete element methods (DEM). Despite these recent
17th IFAC Symposium on Control, Optimization and Automation in
Mining, Mineral and Metal Processing
Vienna, Austria. Aug 31 - Sept 2, 2016
Copyright © 2016 IFAC 19
A Modular Dynamic Simulation Model for
Comminution Circuits
?
B. Légaré
⇤
J. Bouchard
⇤⇤
´
E. Poulin
⇤⇤⇤
⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: benjamin.legare.1@ ulaval.ca)
⇤⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: jocelyn.bouchard@gmn.ulaval.ca)
⇤⇤⇤ LOOP, E4m, Department of Electrical and Computer Engineering,
Université Laval, Quebec City, Canada,
(e-mail: eric.poulin@gel.ulaval.ca)
Abstract: Properly controlling comminution circuits is generally acknowledged to be highly
profitable for any mining site’s bottom line. On the other hand, the process control prob-
lem of comminution circuits is challenging due to circulating loads and non-linear trans-
port/transformation rates. As the performance and robustness of the control system highly rely
on a good understanding of the process dynamics, characterizing the deterministic behavior
requires a certain level of operation disruption (bump tests). For a grinding circuit, it implies
a↵ecting the throughput and product size distributions. The management team can be reluctant
to risk obvious consequences on downstream processing stages i.e. inadequate mineral liberation,
reduction of product quality, and perhaps even recovery losses. Process simulation becomes in
this case an attractive tool to design, assess, and pre-commission advanced control strategies.
This paper presents a phenomenological dynamic simulator for comminution circuits developed
in Matlab/Simulink R©. The block model programming allows changing plant layout or control
loops easily, and is flexible for future extensions or model upgrades as any block can be simply
added to the library or replaced with its updated version. The flexibility of the modular
approach allows testing any control system, from basic PID loops to advanced control schemes.
A simulation case study shows how the simulation model can capture the behavior of an actual
circuit once properly calibrated.
Keywords: Comminution, grinding, phenomenological models, dynamic simulation, process
control.
1. INTRODUCTION
According to the estimations of Tromans (2008), com-
minution processes accounted for 29.3% of the total mining
energy in the USA, which corresponded to 0.39% of the
national energy consumption. For mining oriented coun-
tries like Canada and Australia, comminution represents
respectivelly 1.86% and 1.48% of the total energy expen-
diture of the country. This mineral processing stage is
essential for the extraction and recovery of most metals as
the fragmentation liberates the ore from the valueless rock.
The most widely used types of equipment are crushers and
grinding mills. Considering that the relative efficiency of
grinding mills ranges from 3 to 26 % (Tromans, 2008),
great improvementsand cost reductions can be achieved
through a better overseeing of comminution operations.
Among the various approaches put forward to tackle this
issue, process control o↵ers a well recognized potential, but
faces difficulty to penetrate, partly because the benefits
?
The authors acknowledge financial support from BBA inc.,
NSERC, FQRNT, and the implication of the industrial partner’s
metallurgical team.
are difficult to predict prior to implementation. Moreover,
developing a control system requires periods of time during
which the circuit will be moved away from the nominal
operating regime for model identification and commission-
ing purposes. The management team can be reluctant to
risk the consequences on downstream processing stages,
which can lead to punctual production losses. More than
one design can also be on the drafting table, and not
all of them can be tested in practice as they all involve
important research and development costs. The use of
dynamic simulation at the engineering stage of a control
system, or to assess the impact of a change of operating or
control strategy can certainly help mitigate some of these
hurdles.
Comminution processes modeling is in constant evolution.
Powell and Morrison (2007) reviewed the latest develop-
ments, ongoing work, and future trends. They concluded
that the next generation of process models will be of a
more fundamental type and usable for equipment design.
Powell and McBride (2006) proposed a solution scheme
to introduce breakage considerations into models based
on discrete element methods (DEM). Despite these recent
17th IFAC Symposium on Control, Optimization and Automation in
Mining, Mineral and Metal Processing
Vienna, Austria. Aug 31 - Sept 2, 2016
Copyright © 2016 IFAC 19
A Modular Dynamic Simulation Model for
Comminution Circuits
?
B. Légaré
⇤
J. Bouchard
⇤⇤
´
E. Poulin
⇤⇤⇤
⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: benjamin.legare.1@ ulaval.ca)
⇤⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: jocelyn.bouchard@gmn.ulaval.ca)
⇤⇤⇤ LOOP, E4m, Department of Electrical and Computer Engineering,
Université Laval, Quebec City, Canada,
(e-mail: eric.poulin@gel.ulaval.ca)
Abstract: Properly controlling comminution circuits is generally acknowledged to be highly
profitable for any mining site’s bottom line. On the other hand, the process control prob-
lem of comminution circuits is challenging due to circulating loads and non-linear trans-
port/transformation rates. As the performance and robustness of the control system highly rely
on a good understanding of the process dynamics, characterizing the deterministic behavior
requires a certain level of operation disruption (bump tests). For a grinding circuit, it implies
a↵ecting the throughput and product size distributions. The management team can be reluctant
to risk obvious consequences on downstream processing stages i.e. inadequate mineral liberation,
reduction of product quality, and perhaps even recovery losses. Process simulation becomes in
this case an attractive tool to design, assess, and pre-commission advanced control strategies.
This paper presents a phenomenological dynamic simulator for comminution circuits developed
in Matlab/Simulink R©. The block model programming allows changing plant layout or control
loops easily, and is flexible for future extensions or model upgrades as any block can be simply
added to the library or replaced with its updated version. The flexibility of the modular
approach allows testing any control system, from basic PID loops to advanced control schemes.
A simulation case study shows how the simulation model can capture the behavior of an actual
circuit once properly calibrated.
Keywords: Comminution, grinding, phenomenological models, dynamic simulation, process
control.
1. INTRODUCTION
According to the estimations of Tromans (2008), com-
minution processes accounted for 29.3% of the total mining
energy in the USA, which corresponded to 0.39% of the
national energy consumption. For mining oriented coun-
tries like Canada and Australia, comminution represents
respectivelly 1.86% and 1.48% of the total energy expen-
diture of the country. This mineral processing stage is
essential for the extraction and recovery of most metals as
the fragmentation liberates the ore from the valueless rock.
The most widely used types of equipment are crushers and
grinding mills. Considering that the relative efficiency of
grinding mills ranges from 3 to 26 % (Tromans, 2008),
great improvements and cost reductions can be achieved
through a better overseeing of comminution operations.
Among the various approaches put forward to tackle this
issue, process control o↵ers a well recognized potential, but
faces difficulty to penetrate, partly because the benefits
?
The authors acknowledge financial support from BBA inc.,
NSERC, FQRNT, and the implication of the industrial partner’s
metallurgical team.
are difficult to predict prior to implementation. Moreover,
developing a control system requires periods of time during
which the circuit will be moved away from the nominal
operating regime for model identification and commission-
ing purposes. The management team can be reluctant to
risk the consequences on downstream processing stages,
which can lead to punctual production losses. More than
one design can also be on the drafting table, and not
all of them can be tested in practice as they all involve
important research and development costs. The use of
dynamic simulation at the engineering stage of a control
system, or to assess the impact of a change of operating or
control strategy can certainly help mitigate some of these
hurdles.
Comminution processes modeling is in constant evolution.
Powell and Morrison (2007) reviewed the latest develop-
ments, ongoing work, and future trends. They concluded
that the next generation of process models will be of a
more fundamental type and usable for equipment design.
Powell and McBride (2006) proposed a solution scheme
to introduce breakage considerations into models based
on discrete element methods (DEM). Despite these recent
17th IFAC Symposium on Control, Optimization and Automation in
Mining, Mineral and Metal Processing
Vienna, Austria. Aug 31 - Sept 2, 2016
Copyright © 2016 IFAC 19
A Modular Dynamic Simulation Model for
Comminution Circuits
?
B. Légaré
⇤
J. Bouchard
⇤⇤
´
E. Poulin
⇤⇤⇤
⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: benjamin.legare.1@ ulaval.ca)
⇤⇤ LOOP, E4m, Department of Mining, Metallurgical and Materials
Engineering, Université Laval, Quebec City, Canada,
(e-mail: jocelyn.bouchard@gmn.ulaval.ca)
⇤⇤⇤ LOOP, E4m, Department of Electrical and Computer Engineering,
Université Laval, Quebec City, Canada,
(e-mail: eric.poulin@gel.ulaval.ca)
Abstract: Properly controlling comminution circuits is generally acknowledged to be highly
profitable for any mining site’s bottom line. On the other hand, the process control prob-
lem of comminution circuits is challenging due to circulating loads and non-linear trans-
port/transformation rates. As the performance and robustness of the control system highly rely
on a good understanding of the process dynamics, characterizing the deterministic behavior
requires a certain level of operation disruption (bump tests). For a grinding circuit, it implies
a↵ecting the throughput and product size distributions. The management team can be reluctant
to risk obvious consequences on downstream processing stages i.e. inadequate mineral liberation,
reduction of product quality, and perhaps even recovery losses. Process simulation becomes in
this case an attractive tool to design, assess, and pre-commission advanced control strategies.
This paper presents a phenomenological dynamic simulator for comminution circuitsdeveloped
in Matlab/Simulink R©. The block model programming allows changing plant layout or control
loops easily, and is flexible for future extensions or model upgrades as any block can be simply
added to the library or replaced with its updated version. The flexibility of the modular
approach allows testing any control system, from basic PID loops to advanced control schemes.
A simulation case study shows how the simulation model can capture the behavior of an actual
circuit once properly calibrated.
Keywords: Comminution, grinding, phenomenological models, dynamic simulation, process
control.
1. INTRODUCTION
According to the estimations of Tromans (2008), com-
minution processes accounted for 29.3% of the total mining
energy in the USA, which corresponded to 0.39% of the
national energy consumption. For mining oriented coun-
tries like Canada and Australia, comminution represents
respectivelly 1.86% and 1.48% of the total energy expen-
diture of the country. This mineral processing stage is
essential for the extraction and recovery of most metals as
the fragmentation liberates the ore from the valueless rock.
The most widely used types of equipment are crushers and
grinding mills. Considering that the relative efficiency of
grinding mills ranges from 3 to 26 % (Tromans, 2008),
great improvements and cost reductions can be achieved
through a better overseeing of comminution operations.
Among the various approaches put forward to tackle this
issue, process control o↵ers a well recognized potential, but
faces difficulty to penetrate, partly because the benefits
?
The authors acknowledge financial support from BBA inc.,
NSERC, FQRNT, and the implication of the industrial partner’s
metallurgical team.
are difficult to predict prior to implementation. Moreover,
developing a control system requires periods of time during
which the circuit will be moved away from the nominal
operating regime for model identification and commission-
ing purposes. The management team can be reluctant to
risk the consequences on downstream processing stages,
which can lead to punctual production losses. More than
one design can also be on the drafting table, and not
all of them can be tested in practice as they all involve
important research and development costs. The use of
dynamic simulation at the engineering stage of a control
system, or to assess the impact of a change of operating or
control strategy can certainly help mitigate some of these
hurdles.
Comminution processes modeling is in constant evolution.
Powell and Morrison (2007) reviewed the latest develop-
ments, ongoing work, and future trends. They concluded
that the next generation of process models will be of a
more fundamental type and usable for equipment design.
Powell and McBride (2006) proposed a solution scheme
to introduce breakage considerations into models based
on discrete element methods (DEM). Despite these recent
17th IFAC Symposium on Control, Optimization and Automation in
Mining, Mineral and Metal Processing
Vienna, Austria. Aug 31 - Sept 2, 2016
Copyright © 2016 IFAC 19
20 B. Légaré et al. / IFAC-PapersOnLine 49-20 (2016) 019–024
progresses, the particle balance model (PBM) approach is
currently the most accepted and widely spread technique
to simulate comminution processes.
The published simulators are basically of two types, either
steady-state or dynamic. Examples of steady-state simu-
lators are JKSimMetTM, USIM PACTM, ModSim (King,
2012), and the one developed by Sosa-Blanco et al. (1999).
These are appropriate for design purposes and circuit diag-
nosis. However, as they do not allow simulating transient
states, they are inadequate to study the process variability.
Dynamic simulators are more appropriate to assess the im-
pact of input variability and process control performances.
Only two commercial mineral processing dynamic simula-
tors are known to the authors: IDEASTM by Andritz Au-
tomation and HSC Sim c© by Outotec Research. However,
a lot of academic applications have been developed using
Matlab/Simulink R©. le Roux et al. (2013) proposed and
validated a novel and simple non-linear model, Sbárbaro
(2010), Liu and Spencer (2004), and Rajamani and Herbst
(1991a) proposed more standard modeling approaches
based on PBM as introduced by Epstein (1947).
The number of successful simulation examples of process
control applications proved the relevance of dynamic simu-
lator development. Rajamani and Herbst (1991b), Lestage
et al. (2002), Duarte et al. (2002), Remes et al. (2010),
and le Roux et al. (2013) all demonstrated how grinding
circuit simulation can be used to develop advanced control
strategies. Other focused their e↵ort on controlling specific
types of equipment. Salazar et al. (2014) and Steyn and
Sandrock (2013) have developed model-based predictive
controllers for semiautogenous mills and fully autogenous
mills respectively, and Neesse et al. (2004) addressed the
hydrocyclone control problem in a grinding circuit. All
the above-mentioned studies may not have been possible
without the use of dynamic simulators.
This paper presents an update to the modular dynamic
simulation model for comminution circuits initially pub-
lished by Sbárbaro (2010). The core of the paper is com-
posed of Sections 2 and 3, which introduce the various
models and block-programming simulation environment.
Section 4 briefly discusses the issue of model parameter
calibration and section 5 presents results of a simulation
case study for an actual comminution circuit.
2. MODELS
2.1 Mill modelling
Mixing and transport. The multi-segment flow model
schematized in Fig. 1, which is composed of a transport
delay Vd followed by three continuously stirred reactors
(CSTR) with internal classification, allows simulating both
rod and ball mills.
The first two CSTRs are identical. Their fixed volume Vf
is expressed as a fraction of the grinding media interstitial
volume. The last CSTR exhibits a variable volume Vv to
account for dynamic fluctuations of the volumetric mill
content. The volumetric discharge rate of the last CSTR
D (m3/h), corresponding to the mill discharge, is inspired
by the Torricelli’s theorem and thus proportional to the
square root of the slurry volume Vv i.e.
Feed
Delay
Fixed volume
Reactor 1
Fixed volume
Reactor 2
Fixed volume
Reactor 3
Variable volume
Classification
Classification
Classification
Product
Breakage
Breakage
Breakage
Fig. 1. Mill schematic flow model diagram
D = ✏⌦
p
Vv (1)
where ⌦ (m1.5/h) represents a flow conductivity coeffi-
cient, and ✏ (le Roux et al., 2013), a unitless empirical
rheology factor given by
✏ =
�
1− s2.5v
� ⇣
1−
⇣
100(sv−1)
⌘⌘
(2)
as a function of the slurry volumetric solids content sv.
The original rheology factor proposed by le Roux et al.
(2013) was modified here to avoid discontinuity and allow
the slurry to flow even at high solids fractions.
Classification is an essential part of the flow model to
predict a mill charge since particles of di↵erent sizes do not
exhibit the same residence time. It also allows representing
a higher solids fraction inside the mill than that of the
feed and product as observed in practice. The classification
function
Ci = exp

−
✓
Xi −Xmin
X
◆�
(3)
provides the probability of a particle to leave the reactor
for each i th size class.  is the classification sharpness
ranging from 0.5 to 3, and X is the classification size
parameter. Both are set according to operating conditions:
• internal CSTRs in ball mills: X = 40% of top size
ball diameter, and  = 0.5;
• internal CSTRs in rod mills: X = P90 (sieve dimen-
sion larger than 90% of the particles) in the CSTRs,
and  = 1.2;
• grate discharge mills: X must match the grate aper-
ture, and  = 3 at the mill discharge in the variable
volume CSTRs.
Particles of the minimum size Xmin are believed to flow
with water without any restriction. The subtraction of
Xmin in the exponent numerator of (3) ensures that
behavior.
IFAC MMM 2016
Vienna, Austria. Aug 31 - Sept2, 2016
20
 B. Légaré et al. / IFAC-PapersOnLine 49-20 (2016) 019–024 21
This simple structure allows adequate representation of
any kind of responses for conventional mills, e.g. longer
delays observed in rod mills, and charge fluctuations
typical of both grate discharge (fast) and overflow (slow)
mills.
Fragmentation. The PBM approach consists of applying
mass balance equations to all the particle size classes in
every CSTR. Fragmentation is modelled using a selection
function S, representing the probability of a particle to
break during a certain period of time (i.e. a breakage rate),
and the breakage function B, representing the relative cu-
mulative distribution produced by primary parent classes
in every product child classes. Fragmentation occurs in
all three mixers assuming a first order kinetic reaction.
The mass balance equation describing the evolution of the
mass of particles in each size fraction (M) inside a reactor
is described by
@M
@t
= F−P− S M+B S M (4)
F, P and M are vectors of the mass fraction in each size
class respectively for the feed, product, and charge inside
the CSTR. Both the selection and breakage functions
are square matrices. The product P is determined by
the mixing and transport model. The selection function
elements are defined as
Sj,j =
S0X
↵
j
(1 + (Xj/Xm)σ)
(5)
giving the breakage rate of each j th particle size class
(Klimpel and Austin, 1984). The parameters S0, ↵, and
σ are calibrated from survey data and X is the geometric
average particle size within a class. Xm is expressed as a
function of the grinding media top size diameter Db in mm
as defined by Erdem and Ergün (2009)
Xm = 0.2971 exp [0.0346Db] (6)
The breakage function was initially presented by Austin
and Luckie (1972) in this form and a detailed analysis of
the function physical meaning was done by Kelly and Spot-
tiswood (1990). The expression of the breakage function
Bi,j =
8
<
:
φi
✓
Xi−1
Xj
◆β
+ (1− φi)
✓
Xi−1
Xj
◆γ
for i ≥ j
0 for i < j
(7)
with
φi = φ0
✓
Xi
X1
◆δ
(8)
provides the cumulative relative size distribution following
the breakage of every j th size class particle. The parame-
ters β, γ, δ, and φ0 are determined by laboratory testwork
from size distribution data. The parameter φi depends on
the parent particle size and allows taking into account non
normalized breakage function occurring when the relative
size distribution from the breakage of a particle is function
of its size. The cumulative distribution is expressed as a
ratio of the child size class to the parent class. For example,
the breakage function of a particle of 1000 mm breaking
in three size classes of 100 mm, 10 mm, and 1 mm will
be expressed as the fraction of the mass below a tenth,
hundredth and a thousandth of the initial size.
Energy consumption. Morrell (1993) developed the cal-
culation method for mill power draw based on an estima-
tion of the mill charge behavior. The mill slurry content
given by the flow model is used in the calculation. The
method requires estimating the charge shape and motion
to consider the interaction of the charge with the mill shell.
The eight steps presented by Napier-Munn et al. (1996)
allows successively calculating
(1) charge and pulp densities,
(2) slurry toe and shoulder angles,
(3) charge inner surface radius,
(4) charge eye position, i.e. the radius at which the charge
rotational rate is equal to zero,
(5) cylindrical section theoretical power,
(6) cone end theoretical power,
(7) no-load power, and finally
(8) gross power.
2.2 Size separation
Empirical models are dominant in the classification simu-
lation and two of them are used here to simulate hydrocy-
clones and vibrating screens.
Hydrocyclones. The Plitt model used for simulation is
the one modified by Flinto↵ et al. (1987). The model
was upgraded with a physical limitation on the minimal
water volume and maximal slurry velocity at the under-
flow, essentially to avoid divergence during the calibration
procedure. An inferior limit was added to the by-pass
calculation, based on the volumetric split predicted by
Plitt’s equation, to ensure a minimum 76% water vol-
umetric concentration at the underflow. The underflow
was also restricted to a maximal slurry velocity of 6
m/s and the excess slurry is redirected to the overflow
without any modification on the classification. Future ver-
sion of the toolbox will incorporate Najeswararao model
(Nageswararao, 1995) as well.
Vibrating screens. The model developed by Karra (1979)
is used to determine the cut size based on dimensional
and operational parameters. The classification function
proposed by Rogers (1982) is used to predict the partition
curve.
3. BLOCK-PROGRAMMING SIMULATION
Fig. 2 shows the various simulation blocks of the library,
each one representing a piece of equipment of a comminu-
tion plant, including conveyors, pipes, and sensors. The
simulator runs on Simulink R©R2015a.
The block diagram programming interface allows laying
out blocks and linking them like the pieces of equipment
are in the actual plant. Signal transmission between blocks
was improved from the original version with the addition
of a communication bus. The signal bus contains all the
information requiring to be transmitted. It is structured
IFAC MMM 2016
Vienna, Austria. Aug 31 - Sept 2, 2016
21
22 B. Légaré et al. / IFAC-PapersOnLine 49-20 (2016) 019–024
Fig. 2. Simulink comminution toolbox library
in two signals, one for the water and one for the ore. The
water signal is a scalar giving the water mass flow rate
between pieces of equipment, and the ore signal is a vector
giving the ore mass flow rate in each size class between
pieces of equipment. Both signals can be integrated to
compute the mass inside an equipment, thus conserving
the same information structure, i.e. scalar for the water,
and size classes for the ore.
Information common to every block such as the ore density
or size class definition are entered in the Global Parameter
block.
The structure was also improved by replacing S-Function
blocks by MATLAB Function blocks and the equipments
programming were broken down into multiple standard-
ized sub-blocks to represent
• classification,
• noise addition in measured signals,
• mass accumulation,
• power draw,
• selection and breakage functions,
• intermediate calculations (e.g. volume, delay and to-
tal flow), and
• variable transport delay.
4. PARAMETER CALIBRATION
Légaré et al. (2016) detail the methodology for calibrating
the model parameters, and demonstrate the benefits of
using closed-circuit transient data to improve the accuracy
of simulated results. A two-stage approach is put forward
consisting in
(1) determining breakage function parameters of equa-
tions 7 and 8, which are assumed to be material
specific, using batch laboratory mill tests, and
(2) fitting selection function parameters of equation 5 and
flow model parameters (Vd, Vf , ⌦, and ✏) using closed-
circuit transient data.
Stage 2 is performed using Matlab R© built-in optimization
functions minimizing an ISE type least square criterion
comparing simulation predictions to industrial surveys
data (size distributions, solids and water flow rates). It is
worth mentioning that the optimization algorithm requires
being initiated with estimates obtained using open-circuit
steady-states survey data.
5. SIMULATION ACCURACY
The industrial circuit studied is depicted in Fig. 3. It
consists of a rod mill (RM) followed by a ball mill (BM)
in closed-circuit with hydrocyclones. The model parame-
ters were calibrated in the case study using four di↵erent
data sets, representative of four di↵erent circuit operating
points. The proposed model structure allows simulating
the product size distribution, circulating load, and power
draw accurately. The breakage characteristics was set con-
stant as the survey took place in four consecutive days with
no known significant variation in the ore characteristics.
Despite the constant breakage characteristic, disturbances
can besimulated by varying the S0 parameter of equation
5 and additional work still need to be done to improve this
functionality.
Feed
(ore + water)
Rod mill
Pump box
HydrocycloneBall mill
Hydrocyclone 
overflow
Water
addition
Water
addition
Fig. 3. Grinding circuit simplified flow diagram
5.1 Dynamic behaviour
The dynamic response of the studied circuit to a step
change of -18% in the ore and water feed rate is shown
in Fig. 4 and Fig. 5. The simulated responses for both mill
discharges, in terms of P80 (the screen size through which
80% of the particles will pass), follow the expected trends
and are similar to the measured ones. On the other hand,
the hydrocyclone overflow (OF) P80 seems to respond
erratically. However, this is only because the simulator was
fed with fresh feed and water addition measured values,
and the water flow rate to the pump box was oscillating
during the survey. It is interesting to see that the model
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can capture this behavior when the same variations are
introduced. The o↵set between measured and simulated
water addition at the pump box is the result of unmeasured
water addition in the circuit.
The discrepencies between measured and simulated values
of the P80 for mill discharges and hydrocyclone overflow
is mainly attributed to the difficulty of sampling these
streams. The overall trend, i.e. the dynamic behavior, is
nonetheless well simulated, which is the most important
thing for process control applications.
Fig. 4. Flow rates following a -18% step change in ore and
water feed rates
Fig. 5. P80 following a -18% step change in ore and water
feed rates
5.2 Steady-state predictions
The complete cumulative size distributions of the first and
final samples representing the moment when the circuit is
believed to be in a periodic steady-state are shown in Fig. 6
and Fig. 7.
The results confirm a relatively good agreement between
simulated and measured size distributions for both mill
discharges. A slight discrepancy is observed for coarser size
fractions in the circulating load probably because of the
Fig. 6. Cumulative size distribution following a -18% step
change in ore and water feed rates at t = 0
Fig. 7. Cumulative size distribution following a -18% step
change in ore and water feed rates at t = 80
hydrocyclone near roping operation in the actual plant. It
is worth noting that composite samples are used for the
validation of the steady-states, thus minimizing the e↵ect
of sampling errors.
6. CONCLUSION
This paper presented an updated version of a modular sim-
ulation environment for comminution circuits originally
developed by Sbárbaro (2010). The simulator was repro-
grammed with Simulink R©R2015a allowing many upgrades
i.e.
• addition of a bus to improve the signal transmission,
• improved flow models for conventional mills,
• replacement of the S-Function blocks by MATLAB
Function blocks, and
• standardization of the programming structure with
sub-blocks.
Results of a case study show that the simulation model
can capture the actual plant behavior with only minor dis-
crepancies resulting from abnormal operating conditions
for the hydrocyclones (near roping). This issue doesn’t
prevent the simulation to predict the general trends of
process variables accurately, which is the most important
thing for process control applications.
Future work should address the following issues:
• improving the simulation code to reduce the compu-
tational burden,
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• linking the breakage function of the ore to its hardness
and/or composition,
• validating/calibrating the classification functions,
• adding the hydrocyclone Nageswararao’s model, and
• extending the breakage model to include mineral
liberation.
Other models, e.g. for the giratory and cone crushers,
require to be updated to the new standard, and perhaps
upgraded using the work of Evertsson (2000). The mill
model could also be generalized to cover semi-autogenous
and autogenous operations. Lastly, it would certainly be
interesting to develop a model for high pressure grinding
rolls (HPGR) and attrition mills, which have been receiv-
ing increasing attention lately.
The Matlab/Simulink R© comminution toolbox is currently
being integrated to an industrial test-bed reproducing
an entire industrial control system using a PLC (pro-
grammable logic controller), DCS (distributed control sys-
tem), and operator interface. It will be used to develop a
control strategy aiming at minimizing the specific energy
consumption of an actual grinding circuit.
ACKNOWLEDGEMENTS
The authors would like to thank Prof. Daniel Sbárbaro
for sharing the original Matlab/Simulink R© comminution
toolbox files.
REFERENCES
Austin, L.G. and Luckie, P.T. (1972). The estimation of
non-normalized breakage distribution parameters from
batch grinding tests. Powder Technology, 5(5), 267–271.
Duarte, M., Castillo, A., Sepúlveda, F., Contreras, A.,
Gimnez, P., and Castelli, L. (2002). Multivariable
control of grinding plants: A comparative simulation
study. ISA Transactions, 41(1), 57–79.
Epstein, B. (1947). The mathematical description of cer-
tain breakage mechanisms leading to the logarithmico-
normal distribution. Journal of the Franklin Institute,
244(6), 471–477.
Erdem, A.S. and Ergün, S.L. (2009). The e↵ect of ball
size on breakage rate parameter in a pilot scale ball mill.
Minerals Engineering, 22(78), 660–664.
Evertsson, C.M. (2000). Cone crusher performance. Ph.D.
thesis, Chalmers Tekniska Hogskola (Sweden).
Flinto↵, B., Plitt, L., and Turak, A. (1987). Cyclone
modelling: a review of present technology. CIM Bulletin,
80(905).
Karra, V. (1979). Development of a model for predicting
the screening performance of vibrating screens. CIM
Bulletin, 168–171.
Kelly, E.G. and Spottiswood, D.J. (1990). The breakage
function; what is it really? Minerals Engineering, 3(5),
405–414.
King, R. (2012). Modeling and simulation of mineral
processing systems. Society for Mining, Metallurgy, and
Exploration, Inc., Englewood, Colorado, 2nd edition.
Klimpel, R.R. and Austin, L.G. (1984). The back-
calculation of specific rates of breakage from continuous
mill data. Powder Technology, 38(1), 77–91.
le Roux, J.D., Craig, I.K., Hulbert, D.G., and Hinde, A.L.
(2013). Analysis and validation of a run-of-mine ore
grinding mill circuit model for process control. Minerals
Engineering, 4344(0), 121–134.
Légaré, B., Bouchard, J., Clapperton, A., Poulin, E., and
Rojas-Montes, C. (2016). Methodology for the calibra-
tion of a dynamic model for industrial comminution
circuits. CIM, Quebec City. In press. International
Mineral Processing Congress.
Lestage, R., Pomerleau, A., and Hodouin, D. (2002). Con-
strained real-time optimization of a grinding circuit
using steady-state linear programming supervisory con-
trol. Powder Technology, 124(3), 254–263.
Liu, Y. and Spencer, S. (2004). Dynamic simulation of
grinding circuits. Minerals Engineering, 17(1112), 1189–
1198.
Morrell, S. (1993). The prediction of power draw in
wet tumbling mills. Ph.D. thesis, The University of
Queensland.
Nageswararao, K. (1995). A generalised model for hydro-
cyclone classifiers. In AusIMM, 21.
Napier-Munn, T.J., Morrell, S., Morrison, R.D., and Ko-
jovic, T. (1996). Mineral comminution circuits : their
operation and optimisation. Julius Kruttschnitt Mineral
Research Centre, Indooroopilly, Qld.
Neesse, T., Golyk, V., Kaniut, P., and Reinsch, V. (2004).
Hydrocyclone control in grinding circuits. Minerals
Engineering, 17(1112), 1237–1240.
Powell, M.S. and McBride, A.T. (2006). What is required
from DEM simulations to model breakage in mills?
Minerals Engineering, 19(10), 1013–1021.
Powell, M.S. and Morrison, R.D. (2007). The future
of comminution modelling. International Journal of
Mineral Processing, 84(14), 228–239.Rajamani, R.K. and Herbst, J.A. (1991a). Optimal control
of a ball mill grinding circuit1. grinding circuit modeling
and dynamic simulation. Chemical Engineering Science,
46(3), 861–870.
Rajamani, R. and Herbst, J.A. (1991b). Optimal control
of a ball mill grinding circuit2. feedback and optimal
control. Chemical Engineering Science, 46(3), 871–879.
Remes, A., Aaltonen, J., and Koivo, H. (2010). Grinding
circuit modeling and simulation of particle size control
at siilinjrvi concentrator. International Journal of Min-
eral Processing, 96(14), 70–78.
Rogers, R.S.C. (1982). A classification function for vibrat-
ing screens. Powder Technology, 31(1), 135–137.
Salazar, J.L., Valdés-Gonzlez, H., Vyhmesiter, E., and
Cubillos, F. (2014). Model predictive control of semi-
autogenous mills (sag). Minerals Engineering, 64(0),
92–96.
Sbárbaro, D. (2010). Dynamic Simulation and Model-
based Control System Design for Comminution Circuits,
chapter 5, 213–245. Springer, London.
Sosa-Blanco, C., Hodouin, D., Bazin, C., Lara-Valenzuela,
C., and Salazar, J. (1999). Integrated simulation of
grinding and flotation application to a lead-silver ore.
Minerals Engineering, 12(8), 949–967.
Steyn, C.W. and Sandrock, C. (2013). Benefits of opti-
misation and model predictive control on a fully auto-
genous mill with variable speed. Minerals Engineering,
53(0), 113–123.
Tromans, D. (2008). Mineral comminution: Energy effi-
ciency considerations. Minerals Engineering, 21(8), 613–
620.
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Vienna, Austria. Aug 31 - Sept 2, 2016
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