KONA Powder and Particle Journal No. 40 (2023) 262–276/https://doi.org/10.14356/kona.2023011 Original Research Paper

A Hybrid PBM-DEM Model of High-Pressure Grinding Rolls
Applied to Iron Ore Pellet Feed Pressing †Victor A. Rodriguez 1, Túlio M. Campos 1, Gabriel K.P. Barrios 1,
Gilvandro Bueno 2 and Luís Marcelo Tavares 1*
1 Department of Metallurgical and Materials Engineering, Universidade Federal do Rio de Janeiro, Brazil
2 Vale S.A., Complexo de Tubarão, Brazil

Abstract
Mathematical models of high-pressure grinding rolls (HPGR) have attracted great attention, owing to their role inoptimization of operating machines as well as in the design and selection of new ones. Although population balance
models (PBM) and the discrete element method (DEM) have been used in this task, both suffer from important
limitations. Whereas PBMs have challenges associated to the prediction of operating gap and to the validity ofseveral of its assumptions in different formulations in the literature, application of DEM has its own challenges, inparticular when fed with distributions containing large amounts of fines. This work proposes a hybrid approach inwhich the coupling of DEM to particle replacement models and multibody dynamics is used to predict operating
gap, throughput and power, as well as providing information along the rolls length that is used in PBM to predictthe product fineness. The hybrid approach is then compared to both DEM and a PBM (Modified Torres and Casali),demonstrating similar results to the later when applied to simulating a pilot-scale machine operating under different
conditions, but improved prediction when applied in scale-up to an industrial-scale HPGR.
Keywords: high-pressure grinding rolls, discrete element method, population balance method, modelling,simulation

1. Introduction

Since the introduction of the high-pressure grindingrolls (HPGR) technology, various authors have proposed
different approaches to its mathematical modelling, which
may be classified as predominantly empirical, phenomenological or mechanistic.
Schönert (1988) was the first to propose relationships
among key performance variables, involving geometricalvariables of the HPGR such as rolls diameter and length;
operating variables as rolls velocity, working gap, nipangle, working pressure and material variables such as
flake density. Based on experimental evidence, Austin et al.
(1993; 1995) and Morrell et al. (1997), proposed relationships to predict the porosity of the product flakes, as well as
the working gap as a function of the specific grinding force,
including a correction factor for the effects of rolls surface,feed top size, scale of the machine, moisture content androlls speed.
In regard to prediction of product fineness, Klymowsky†*

Received 18 April 2022; Accepted 23 May 2022
J-STAGE Advance published online 2 July 2022
Corresponding author: Luís Marcelo Tavares;
Add: COPPE/UFRJ, Cx. Postal 68505, CEP 21941-972, Rio deJaneiro, Brazil
E-mail: tavares@metalmat.ufrj.br
TEL: +55 21 2290-1544 (ext. 246)

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and Liu (1997) and Morrell (2004; 2010; 2022) developed
work indices that characterize empirically the relationshipbetween the energy that is applied by an HPGR to a particle
bed and the resultant product fineness. Application of the
HPGR work index to predict the specific energy consumed
by the machine demands the use of correction factors thatreflect the effect of top feed particle size, fines, moisture
content, mode of operation (open- or closed-circuit), material strength, and roll surface. More recently, Chelgani etal. (2021) and Tohry et al. (2021) proposed yet another empirical approach that is based on the so-called Explainable
Artificial Intelligence (EAI). Although it requires large databases originated from monitoring variables in industrialscale plants, it demonstrated to be able to predict accurately the 80 % passing size in the product and the powerdraw using linear and nonlinear multivariable assessment,
being useful in optimizing a machine in operation. These
approaches may be regarded as predominantly empiricalsince they do not rely on a consistent description of theunderlying physics of machine operation.
Phenomenological models have been widely used to
predict the HPGR product particle size distribution. Different authors have developed approaches based on the selfsimilarity concept (Fuerstenau et al., 1991; Lim et al.,1996), different formulations of the population balance
model (PBM) (Austin et al., 1993; Dundar et al., 2013;

Copyright © 2023 The Authors. Published by Hosokawa Powder Technology Foundation. This is an open accessarticle under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

Thivierge et al., 2022), including those considering different breakage zones (pre-crushing, edge and compression
zones) and mechanisms (Daniel and Morrell, 2004; Morrell
et al., 1997), which are often characterized using the pistonand-die, besides laboratory- and pilot-scale HPGR tests(Rashidi et al., 2017).
Torres and Casali (2009) proposed a PBM formulationof the HPGR that refined the description of the edge andcentral products, relying on an empirical parabolic variation of axial pressure profile along the rolls. In their model,
the specific breakage rates are a function of the specificenergy input. As such, good predictions of product fineness
rely on the ability of the model to properly predict HPGR
throughput and power. Based on a large number of experiments, Campos et al. (2019a) identified some limitationsof the Torres and Casali approach when applied to a pilotscale HPGR processing iron ore pellet feed. The authors
proposed modifications of the expressions originally used
to describe HPGR throughput, associated to the material
ejection from the edge of the rolls, as well as to the power
consumption equation. Additional modifications were also
proposed and validated in industrial-scale HPGRs, including a breakage saturation model and an equation to accountfor variations of the axial pressure profile (Campos et al.,2021a).
One important application of mathematical models is in
sizing and scale-up of HPGRs (Daniel and Morrell, 2004;
Morrell et al., 1997; Schönert, 1988), where limitations
are recognized when they deal with prediction of HPGR
throughput (Banini et al., 2011), working gap and productfineness (Daniel and Morrell, 2004). Many of the mentioned scale-up studies are based on HPGR testing in pilotand industrial-scale machines. However, experimental tests
require a large mass of material even at the laboratory scale(Rashidi et al., 2017). The piston-and-die test is adopted bymany researchers to study interparticle breakage and obtain
information of the compressibility and breakage responseof the particle bed. Models based on the PBM and pistonand-die tests include the description of the energy absorption in different size classes of a compressed particle bed(Liu and Schönert, 1996) and the creation of new surface
area and particle bed porosity (Dundar et al., 2013; Esnault
et al., 2015) to describe the HPGR product particle size distribution. In addition, the piston-and-die test has also beenused to predict and scale-up HPGR performance variables(Davaanyam et al., 2015; Hawkins, 2008; Nadolski et al.,2011; Pamparana and Klein, 2021).
The application of mechanistic models to simulate
comminution machines has been increasing in recent years.
Mechanistic models are meant to describe in detail theeffect of operating and design variables since they can decouple material from machine contributions in the process.
This is accomplished by both characterizing and modellingin detail each of the breakage mechanisms, almost invari-

ably using the Discrete Element Method (Weerasekara etal., 2013). However, simulation of large-scale industrial
comminution machines using DEM deals with challenges
that include the large number of elements (up to several
million particles), boundaries containing large numbers ofelements, wide particle size ranges and need to couple withother tools describing the additional relevant physics of thesystem, which include particle breakage, dynamic geometry interactions, solid-fluid interactions, etc. (Cleary, 2004).
In particular, laboratory- and pilot-scale DEM simulations of HPGRs allowed to describe the effect of feed size
distribution, roll dimensions and speed, applied specificforce, besides features such as lateral confinement, rollwear profile and feed segregation. These have then beenused to predict performance variables that include throughput, working gap, power consumption and compressive
force profile along the rolls, besides skewing (Barrios andTavares, 2016; Cleary and Sinnott, 2021; Nagata et al.,2020; Quist and Evertsson, 2012; Rodriguez et al., 2021;
2022a; 2022b).
However, prediction of size distribution of the product remains a great challenge in DEM simulations of HPGRs. In
this regard, two publications are worth mentioning. Herbst
and co-workers (2011) combined Metso’s proprietary Fast
Breakage simulation approach in DEM, experimental datafrom piston-and-die tests and the energy-based population
balance model as alternatives to ore characterization andequipment selection by HPGR pilot-plant testing. The
validated physics-based model was then successfully used
to predict the performance of industrial-scale HPGRs using
the proposed energy-based scale-up method. Althoughpromising, their approach did not account for the axial
force and throughput distribution along the rolls.
Cleary and Sinnott (2021) simulated an industrial-scale
HPGR using DEM including a particle replacement model(PRM) to predict the variation of flow, pressure and particle
breakage response along the rolls. Yet, the authors recognized that it is not possible to include all fine particles in the
DEM simulations owing to the large computational effort,
so that a minimum cut-off size was applied to represent the
HPGR product, representing the fines as additional mass inthe finest resolved size class. While good predictions werereached, such approach is not suitable to predict HPGR
operation with very fine feeds.
The present work proposes a hybrid modelling approach, through which HPGR throughput and power aredescribed as a function of roll axial position for a given set
of design and operating conditions through coupled DEMMBD-PRM simulations (Rodriguez et al., 2022a; 2022b),
whereas size reduction is also predicted as a function ofroll axial position using PBM considering the breakage
distribution and selection functions. The approach has been
applied to a base case, consisting of a pilot-scale HPGR in
size reduction of iron ore pellet feed with 80 % passing size

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as fine as 103 μm, from which model parameters have been
fitted. The approach was validated by comparing model
predictions to data from the HPGR operating under different specific forces and roll velocities. The greatest potentialof the model has then been demonstrated by predicting theperformance of an industrial-scale HPGR based on breakage parameters calibrated at pilot-scale.

2. Modelling background
2.1 Proposed hybrid model

The model consists of linking outputs from DEM
simulations to the population balance model (PBM).
This later is represented by the energy-specific selection
function proposed by Herbst and Fuerstenau (1980), a nonnormalizable breakage distribution function used byCampos et al. (2019a) and selected expressions proposedby Torres and Casali (2009). Following this approach,
DEM simulations allow to capture the effect of design andoperating variables on the HPGR performance, while the
PBM model allows dealing with the entire range of particle
sizes fed to the machine.
As presented in detail in recent publications by theauthors (Rodriguez et al., 2022a; 2022b), outputs provided
by the DEM simulations correspond to total power (PDEM),
total throughput (QDEM), compressive axial force profile in
the region between the gap and the nip angle (Fk), and axial
mass flowrate profile in the region between the gap and thenip angle (Vk).
Following the PBM approach proposed by Torres andCasali (2009), the roll length is discretized in NB sections.
In each of the k sections, the mass of material contained inevery size class i is given by:
v z,k

i 1
d
wi, k  z  S j,k bij w j,k  z  Si,k wi,k  z
dz
j 1

(1)

where wi,k is the fraction of material in size class i andsection k, z is the distance between the beginning of the(1)
compression
zone and the extrusion zone, vz,k is the material flow velocity in the z direction for each section k, Si,k isthe breakage rate for each size class i and section k, and bij
is the breakage function in distributed form.
Two functions must be known in order to solve the resulting system of differential equations: bij and Si,k. Campos
et al. (2019a) and Faria et al. (2019) observed that, forsome Brazilian iron ores, the non-normalizable breakage
function proposed by King (2001) was required to describe
their response, being given by:
γ

β

x 
x 
Bij   i   1     i 
 xj 
 xj 
γ

Bi–1,j – Bij. The specific selection function can be calculated using the polynomial equation given by Herbst andFuerstenau (1980):
 sE x 
  x ln  iE   ξ1 ln  i   ξ 2 ln  i sx
 1  x1 
 1 

(3)

where s1E (t/kWh), ξ1 and ξ2 are the parameters to be fitted
from a base case, xi is the representative size given by(3)xi  xi 1xi and x1 is a reference size. In the present workx1 was[21]set to 1 mm. Following the Torres and Casali modelling approach, Eqn.
4 calculates the breakage rates (Si,k),
[22]
[23]
giving[24][24]
P
S i, k  siE k(4)Mk
where Pk and Mk are the power profile and the mass ofsolids profile along the roll length gathered from the DEM(4)simulations.
Power profile is hereby calculated by normalizing the compressive force profile (Fk) and multiplying
it by the total HPGR power, with both variables gatheredfrom the DEM simulation (Eqn. 5). The throughput profile in Eqn. 6 is then calculated on the basis of the total
throughput and mass flowrate of solids profile from DEM:
(5)

Fk
Pk  PDEM

NB j 1F j
Vk
Qk  QDEM(6)N j B1V j(5)
where PDEM is power consumption (kW), QDEM is total
throughput (t/h), and Fk is the compressive force profile(6) predicted by DEM. Given their direct relationship to(kN)
power, compression forces (Fk), provided by DEM simulation, are used in Eqn. 5. In the hybrid model approach, themass flowrate profile of solids (Vk) is then defined on thebasis of the mean particle residence time (λk) and the total
mass (Mk) in each block (k) along the rolls:
Vk 

(7)

Mk
λk

The solution of Eqn. 1 allows calculating the fraction
retained in each size class of every block (k) following the(7) and Casali model approach, which is based on the
TorresReid’s analytical solution (Reid, 1965):i
P pi,k  Aij, k exp  s Ej k 
Qk 

j 1

(8)

where Aij,k is a matrix given by:

for xi  ωx x η x 
Bij   i   i   1     i 
ω
x


(2)-1
 j
 xj 

(2)β

for xi  ωwhere γ, β, ϕ, ω and η are fitting parameters and bij =0 i 1 bil S l, kAij, k  l  j
Alj, kS i, k  S j , k

 IP
i 1
 f i  l 1Ail , k

(8)

(2)-2
264

2

(9)


i  j
i  j
i  j (9)

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

where is the fraction retained in each size class i in the feed.
Finally, the overall product size distribution is calculated
from the weighted average product size distributions ofeach section k and is given as:

piHPGR 

1

NB

(10)

 pi,k Qk
QDEM
k 1

2.2 Modified Torres and Casali model(10)
In the present study, the Modified Torres and Casali(MTC) model (Campos et al., 2019a) represents the purely
phenomenological model that is compared to the proposed
hybrid approach. A summary of its main expressions andthe comparison with the corresponding ones in the hybrid
model is presented in Table 1. Throughput and powermodels in the Modified Torres and Casali model required
fitting four parameters (φ, υ and τ for the throughput modeland κ for the power model). That was done on the basis ofa selected base case. The throughput profile is assumed as
uniform. On the other hand, whereas the Torres and Casali(2009) model assumes a parabolic pressure profile along
the rolls, the MTC model allows for different profiles,
given evidence from both experiments and DEM simulations (Cleary and Sinnott, 2021; Rodriguez et al., 2021).

3. Materials and methods
3.1 Experimental

In the present study, the material selected is an iron ore
concentrate processed in the production line of the Com-

plexo the Tubarão (Vitoria, Brazil) and used in the production of iron ore pellets. The iron ore concentrate, originallyfrom the Itabira region, in the Iron Quadrangle from Minas
Gerais (Brazil), is essentially composed of hematite withminor amounts of quartz as contaminant (Campos et al.,2019b).
Experiments consisted in both pilot-scale tests and an industrial survey. Pilot-scale tests were carried out in an RPR
03.6 – 100/32 roller press manufactured by KHD Humboldt Wedag AG with 1 m-diameter rolls (Fig. 1). A sample
of 100 tons was collected from the production line in the
HPGR feed located in the pre-grinding stage (Campos etal., 2019b). The feed moisture content was 7.5 %, which
is very similar to the value practiced in industrial-scale
operations, although close to the maximum value allowablefor pressing iron ore concentrates (Van der Meer, 1997).
A total of eight experiments were carried out varying thespecific force (2.5 and 3.5 N/mm2) and the peripheral
roll velocity (0.20, 0.35, 0.50 and 0.70 m/s). Throughput,
power consumption, specific energy, operating gap, rollvelocity and operating pressure were obtained from thesupervisory system. During each test, a sampling apparatus
was introduced underneath the rolls to collect samples fromfive parallel sections of the discharge. The apparatus wasintroduced manually and allowed characterizing the axial
variation of the product fineness along the rolls (Campos
et al., 2019b). Additional pilot-scale tests were carriedout with a blend composed of iron ore concentrates fromthe Iron Quadrangle, normally used to feed the pelletizing

Table 1 Summary of expressions and approaches used for estimating the key performance variables in both the Modified Torres and Casali model(Campos et al., 2019a; Campos et al., 2021a) and the proposed hybrid model.

Model
Throughput

Modified Torres and Casali

Hybrid approach100 
Q  LU g ρg xg  100  δ Mass flow sensor underneath the working gap in DEM
simulationsτχg  U δln    υD  U max φThroughput profileUg 

xcUρa 
xg ρg

{31}

Uniform, with step bypass flow

{32}
Power consumption
Power distribution
along the rolls καip P  2Fsin 
U
 2 

Pk 

4 100 1  cos nπ  μ n 2π 2
sin nπy k 2n eπ n 1{33}
Breakage modelpiHPGR 

1 NB
 pi, kN B k 1

Eqn. 7 Extracted from NB sections positioned in thecompression zone (i.e. between the working gap andnip angle) along the rolls in the DEM simulations. Eachsection moves as a plugP  4πτ DEMU
Force profile extracted from NB bins located in thecompression
zone (i.e. between the working gap and nip{34}
angle) along the rolls in the DEM simulations
piHPGR 

1NB pi,k Qk
QDEM
k 1

{35}

D: roll diameter, L: roll length, U: roll velocity, Ug: material velocity; ρa: bulk density ρg: flake density, xc: critical size, xg: operating gap,
δ: the percentage of material ejected by the edge of the rolls; F: compressive force, αip: nip angle, τDEM: torque on the rolls extracted
from DEM simulation, ω:{36}angular velocity of the roll, κ: nip angle parameter, φ,{37}υ and τ: throughput model parameters, μ: power profile
parameter, ȳk: normalized average position, NB: number of sections along the roll length. *Only used in simulations of industrial-scalemachines

265Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

Fig. 1

Pilot-scale HPGR (left) and industrial-scale HPGR (right) used in the experimental campaigns.

Table 2 Summary of the main design and operating conditions of
HPGRs in the experimental campaigns.

Variables

Pilotscale
study

Scale-up study
Pilot

Industrial

Roll diameter (m)

1.0

1.0

1.4

Roll length (m)

0.32

0.32

1.6

Specific force (N/mm2)

2.5–3.5

2.5

2.5

Operating pressure (bar)37.0–52.0 40.0

60.9

Rolls velocity (m/s)

0.20–0.70 0.32

1.30

Operating gap (mm)6.8–8.2

13.8

6.0

Maximum roll velocity (m/s) 0.90

0.90

1.95

Feed 80 % passing size (μm) 103

143

143

Feed % passing 45 μm

28

26

26

Feed BSA (cm2/g)

450 ± 10490 ± 10 470 ± 10

plant in question (Campos et al., 2021a). A previous study
demonstrated relatively minor differences in pressing response between the samples (Campos et al., 2021b), making comparisons valid between them. Operating conditions
and main feed characteristics are presented in Table 2.
In addition, industrial-scale data were obtained from asurvey on an HPGR manufactured by KHD/WEIR (Fig. 1).
The machine has 1.4 m-diameter rolls, with 15.9 mm diameter studs, and cheek plates. During the survey the HPGR
operated at a specific compressive force of 2.5 N/mm2
and roll velocity of 1.3 m/s. Performance variables of the
HPGR were captured using the supervisory system. Samples from the feed and product were collected from belt
cuts for size analysis.
Particle size distributions from samples of the feed andproduct were measured by laser scattering in a Malvern
MastersizerTM 2000 (Malvern Instruments Inc), whereas
Blaine specific surface area (BSA) was measured in a PCBlaine-Star (Zünderwerke Ernst Brün GmbH).

266

3.2 Coupled DEM-MBD-PRM simulations

Simulations using DEM were carried out coupled tomultibody dynamics (MBD), describing the translation of
the movable roll, and particle replacement method (PRM),
following the approach proposed and adopted as part ofearlier studies by the authors (Rodriguez et al., 2021;
2022a). In the present work, DEM simulations were carriedout using the commercial software Altair EDEM version
2020.3. The Hertz–Mindlin contact model was used, inwhich the normal force component is described on thebasis of Hertz contact theory, whereas the tangential force
model is based on Mindlin-Deresiewicz work (Mindlin
1949; Mindlin and Deresiewicz 1953). Furthermore, theseparticles are allowed to break owing to the use of a spherebased particle replacement (PRM) strategy, recently proposed by Tavares et al. (2021) and coded in an application
programming interface (API). Finally, a two-way coupledmodel based on MBD and DEM was implemented to calculate the dynamics of the floating roll as initially proposed
elsewhere (Edwards et al., 2013; Barrios and Tavares,
2016). Since this DEM-MBD coupling was embedded in
the EDEM software, the use of co-simulation tools became
unnecessary.

3.2.1 Material properties

Due to the large number of particles demanded in HPGR
simulations, the authors selected a coarser particle size
distribution, with a top size 8 mm, to represent the ironore pellet feed. This approach was already successfully
used in this application in previous studies (Rodriguez etal., 2021; 2022a). From this and bench-scale tests, which
included measurement of the static and dynamic angles
of repose (Rodriguez et al., 2022a), material and contact
parameters were calibrated (Table 3). Addition material
properties were estimated on the basis of a piston-and-die
test, resulting in the selection of values of Poisson’s ratioof 0.25, particle density of 3,011 kg/m3 and shear modulus of 2 GPa (Rodriguez et al., 2022a). Finally, valuesof breakage model parameters were taken from previous
publications (Rodriguez et al., 2021; 2022a). The same set

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276
Table 3 Hertz–Mindlin contact parameters used in the DEM simulations.

CoefficientOre-steelOre-oreRestitution

0.15

0.20

Static friction

0.49

0.55

Rolling friction

0.47

0.51

of material, contact and breakage parameters were used tosimulate both pilot- and industrial-scale HPGRs.

3.2.2 Equipment setup

At first, computer Aided Designs (CAD) of the HPGR
units simulated were generated. The translational dynamics
in the floating roll was described by a force controlled in
the longitudinal direction “x”, while only the kinematicsof the rotating movement in both rolls with a fixed angular velocity was described. Being a one-dimensionalmodel, it does not allow for skewing of the rolls, studied
by Rodriguez et al. (2022b). The rolls movement started
only when DEM particles filled the hopper from a particle
factory located above the rolls. From this point on in thesimulation, new particles were added continuously until
steady-state conditions were reached, and then analysis
were performed.
The hopper level is an important aspect in DEM simulation of HPGRs, since particles located in this region
only apply pressure to the particle bed sitting between therolls (Cleary and Sinnott, 2021; Nagata et al., 2020). In
the present study, the recommendation from Cleary and
Sinnott (2021) was followed, where the minimum mass inthe hopper (mhopper) is given by:mhopper  LhW 2 ρaf(11)

where Lh is the length along the diameter of the rolls andW the width of the feed hopper, and ρaf is the bulk density(11)of the feed. During simulations, this minimum mass ofparticles filling the hopper was maintained approximately
unchanged.
Even though the present approach already used virtual
particles that are larger than those in the real operations(upscaled particles), maintaining the hopper level to meet
Eqn. 11 imposes a major computational challenge when
dealing with simulations of industrial-scale machines. As
such, in order to reduce the number of elements requiredin the simulation, the final portion of the hopper silo wasfilled with particles of even coarser size (60 mm diameter)and density (10,000 kg/m3)—called column-pressure particles—so as to match the same pressure that would havebeen generated by piling up additional feed particles. Fig. 2
illustrates this scheme, where these column-pressure particles are placed without interfering with the rolls. It is worth
mentioning that, although these particles move downwards

Fig. 2 Representation of industrial HPGR simulation using the coupled DEM-MBD-PRM with both feed (upscaled) particles and columnpressure particles.

as rolls rotate, the short simulation times required to reachsteady state conditions prevented them from ever contacting the rolls.

3.2.3 Measurement of key variables in DEM
simulations

As part of the hybrid simulation approach, the DEM
simulations directly provide throughput and power of the
HPGR, as informed in Table 1. Indeed, total throughput
between the rolls was estimated with a cylindrical geometry sensor positioned underneath the working gap. The
total power was calculated based on the torque required torotate the rolls multiplied by the rotation frequency. The
mass flowrate in each block (Vk) and axial compressive
force (Fk) profiles were estimated from a grid bin locatedin the compression zone, presented in detail elsewhere(Rodriguez et al., 2022a).
With the aim of providing an additional comparison withboth phenomenological and hybrid approaches, the size
distribution from the DEM simulations using PRM wasalso computed. The approach used to obtain the particle
size distribution using the Tavares PRM can be found elsewhere (Tavares et al., 2021).

3.3 PBM parameter estimation

The proposed Hybrid model was implemented in
MatlabTM (version R2021a, Mathworks Inc.), which is theplatform also used in predictions using the Modified Torres
and Casali model. Initially, the parameter optimization
was performed on a base case test, which consisted in
the pilot-scale experiment with a peripheral roll velocityof 0.35 m/s and specific compressive force of 2.5 N/mm2(reference test #1 in Table 4). Breakage function parameters (Eqn. 2) were estimated as part of previous studies

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by Campos et al. (2019a), being also used in the present
work. The three remaining parameters in Eqn. 3 were thencalibrated from reference test #1.
Parameter optimization for DEM simulations, used in
power and mass flowrate predictions in the Hybrid model
was conducted as part of an earlier work (Rodriguez etal., 2022a), whereas in the case of the Modified Torres
and Casali model, reference tests #1 and #2 (Table 4)
were used. Two parameters from the throughput model(Table 1) were kept constant and equal to values from aprevious study (φ = 100 and τ = 0.1), since they were foundto be valid for a range of machines (Campos et al., 2019a).
The single fitting parameters for the nip angle model (κ)
and the remaining parameter for the throughput model(υ) were then calibrated on the basis of the reference tests
in Table 4. This was used to ensure that the model wasproperly calibrated to capture variations when the HPGR
was operating under different conditions. In order to ensure
a parabolic pressure profile as assumed by Campos et al.
(2019a), parameter μ from Table 1 was set to 0.05. From
the fitted parameters, prediction of the remaining pilotscale experiments as well as the industrial-scale survey was
performed.
The optimal parameters were fitted using the function
fminsearch from MatlabTM (version R2021a, MathworksInc.), which allows finding the minimum of unconstrained
multivariable function using the derivative-free method.
The objective function consisted of the sum of squaresof the differences in the logarithms of the experimental
and fitted cumulative particle size distribution values ofreference test #1.
Comparison between predictions by the different models and the experimental results were carried out fromcomputations of the relative absolute deviation given by
εABS = 100|varExp – varCalc|/varExp, where varExp is the exTable 4 Operating conditions of the reference tests.

Variable

Reference test
#1

#2*

Specific force (N/mm2)

2.5

3.5

Operating pressure (bar)

38.6

48.5

Operating gap (mm)

8.2

7.4

Roll peripheral velocity (m/s)

0.35

0.50

Throughput (t/h)

19.9

26.8

Power consumption (kW)

47.2

66.1

Specific energy (kWh/t)

2.37

2.47

Passing 45 μm in product (%)

52.3

52.0

Product BSA (cm2/g)

800

820

*Additionally used to calibrate the power and throughput
model in the Modified Torres and Casali model.

perimental variable and varCalc is the calculated variable.
Besides power, throughput and product size distribution,
Blaine specific surface area (BSA) was also analyzed. Predictions of BSA from simulated product size distributions
were computed using the approach described elsewhere(Campos et al., 2019b).

4. Results and discussion
4.1 Parameter fitting

Different base cases were used for predictions ofthroughput and power in each approach. The DEM-MBDPRM approach, used in the proposed Hybrid model, wasable to make predictions of power and throughput of thepilot HPGR campaign. In that procedure, Rodriguez et al.
(2022a) based their results on reference test #2 (Table 4).
No particular calibration was carried out using industrial
data. On the other hand, selected parameters of the power
and throughput equations (Table 1) for the Modified Torres
and Casali model (Campos et al., 2019a; Campos et al.,2021a) were calibrated from reference tests #1 and #2 inTable 4, resulting in the values of υ = 155 and κ = 3.2. The
different values for these parameters from those previously
fitted on the basis of data from pressing dry pellet feed fines
may be attributed to the effect of moisture content.
In predicting size reduction, the optimal parameters
fitted for the Hybrid model and the Modified Torres andCasali model are shown in Table 5. Both the non-normalizable breakage and the selection functions are illustrated inFig. 3, which show that nearly identical specific selection
functions were obtained from the parameter optimization
procedure. The results compared to the experimental data
are presented in Fig. 4, demonstrating that good agreement
was reached between model and experiments, with valuesof the objective function of 0.038 for the Hybrid modeland 0.040 for the MTC model. Results allow to conclude
that the non-normalizable breakage function parametersproposed in a previous study (Campos et al., 2019a) remain
valid in the present work. A closer examination of predicted product BSA shows that good agreement between

Table 5 Fitted selection and breakage function parameters.

Equation

Parameter

MTC

Hybrid model

Breakage function(Eqn. 2)

γ

0.896

0.896

β

5.461

5.461

ϕ

0.857

0.857

η

0.46

0.46

ω (mm)

0.013

0.013

ξ1

–0.491–0.492

ξ2–0.191–0.190s1E (t/kWh)

0.260

0.247

Selection function(Eqn. 3){38}
268

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

fitted and predicted values for size reduction was obtained,
since absolute deviations from measurements were 0.7 %and 0.5 % for the Modified Torres and Casali and Hybrid
models, respectively. It is worth mentioning that values ofBreakage function

1

0.1

0.01

0.001

0.0001
0.001

0.01

0.1

1

10

Particle size (mm)Selection function (t/kWh)

1

0.1

0.01
MTC model
Hybrid model
0.001
0.001

0.01

0.1

1

10

Representative size (mm)Fig. 3 Non-normalizable breakage function of selected feed particle
sizes (top) and comparison between specific selection function fitted for
the Hybrid model and for the Modified Torres and Casali (MTC) model(bottom).

10

1

0.1
0.001

Feed
ExperimentHybrid model
MTC model
0.01

0.1

4.2 Pilot-scale HPGR simulations

Based on thecalibrations from Section 4.1, both mod[24]elling approaches were applied to predict the remaining
pilot-scale tests (Table 2) pressing iron ore concentrates.
Initially, Fig. 5 compares measured and predicted throughputs, highlighting the good agreement between both model
approaches and experiments. As discussed by Rodriguez etal. (2022a), good predictions were achieved using DEMMBD-PRM simulations with average absolute deviationof 7.2 %, with larger overestimations for tests at higher
throughputs (peripheral roll velocity of 0.70 m/s). Predictions of the Modified Torres and Casali model, on the other
hand, show a smaller deviation of 4.6 %, underestimating
values for roll peripheral velocity of 0.70 m/s.
A comparison between measured and predicted power
consumptions in the pilot-scale HPGR using the Hybrid
model and the MTC model is presented in Fig. 6 (top).
Very good agreement is evident between the Hybrid modeland experiments, with mean absolute deviations of 7.9 %.
Likewise, the MTC model, with κ = 3.2 fitted based on
the two pilot-scale tests (Section 4.1), also exhibited good
agreement with experiments, with mean deviation of
9.5 %. Likewise, similar deviations of the specific energy
predictions were observed in Fig. 6 (bottom), being equal
to 7.2 % for the Hybrid model and 8.2 % for the MTC
model. Those estimates are very important for both approaches since the predicted product size distributions are
directly influenced by them.
Fig. 7 shows experimental results and predictions of
product size distribution from two selected tests run at theroll peripheral velocity of 0.50 m/s. Reasonable agreement
is evident, demonstrating the acceptable ability of both
50

Predicted throughput (t/h)

Cumulative passing (%)

100

the specific selection function in Table 5 differ from thosereported in earlier studies (Campos et al., 2019a) primarily
due to setting x1 = 1 mm in Eqn. 3.

40
30
20
10
0

1

Particle size (mm)Fig. 4 Comparison of fitted and experimental product size distributions of base case (reference test #1).

MTC model
Hybrid model

0

10

20

30

40

50

Experimental throughput (t/h)
Fig. 5 Comparison between measured and predicted throughput in thepilot-scale HPGR using the Hybrid and the Modified Torres and Casali
models.

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Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276
100

120

Predicted power (kW)100

Cumulative passing (%)

MTC model
Hybrid model

80
60
40

10

1

Feed
ExperimentHybrid model
MTC model

20
0

0.1
0.001
0

20

40

60

80

100

0.1

1

100

4
MTC model
Hybrid model

Cumulative passing (%)

Predicted Specific energy (kWh/t)

Experimental power (kW)

3

2

1

1

2

3

4

Experimental Specific energy (kWh/t)
Fig. 6 Comparison between measured and predicted power (top) andspecific energy consumption (bottom) in the pilot-scale HPGR for the
Modified Torres and Casali and Hybrid models. Filled markers correspond to the base cases used in model calibration.

modelling approaches in predicting product size distribution when operating conditions are varied. In applicationof HPGRs to iron ore concentrate pressing, it is routine
to check the percent passing the 45 μm sieve to assess thecoarser part of the product size distribution, whereas theBlaine specific surface area (BSA) is strongly influenced
by its finer portion. As such, Fig. 8 presents a comparison
between experimental and predicted values for both indicesfor all tests performed in the pilot-scale HPGR. In general,
Hybrid model predictions are in only reasonable agreementwith experiments, with values of average absolute deviations of 5.5 % and 6.2 % for passing in 45 μm and the BSA,
respectively. Marginally higher deviations were observed
for the MTC model, where average absolute deviations of
5.9 % were obtained for the percentage passing the 45 μm
sieve and 6.7 % for the BSA.
A more detailed inspection is also possible from Fig. 9
with a relationship between specific energy consumption
and the product BSA. Unlike expected, experimental BSA
values did not show clear trend with specific energy. In

270

0.01

Particle size (mm)

120

10

1

0.1
0.001

Feed
ExperimentHybrid model
MTC model
0.01

0.1

1

Particle size (mm)Fig. 7 Comparison between predicted and experimental product size
distributions in the pilot-scale HPGR with roll peripheral velocity of
0.5 m/s and specific compressive forces of 2.5 N/mm 2 (top) and 3.5 N/
mm 2 (bottom).

general, although recent works showed no improvementin size reduction given the increment in roll peripheral
velocity (Campos et al., 2019b; Van der Meer and Leite,2019), it is worth mentioning that HPGR operations withhigh moisture content as in the present work would provide
some acceleration on the compression zone and increase
the proportion of material ejected from the edge of therolls. These features can, at least in part, be responsible forthe dispersion of the data in Figs. 8 and 9.
On the other hand, Fig. 9 shows that results from thetwo models exhibited a clear and direct improvement in the
BSA with the increase in specific energy. These results canbe explained by the modelling approach adopted in bothmodels, which relies on breakage rates (Eqn. 4) that arecalculated from the product of the specific selection function and the ratio between the power consumption and theholdup. As such, although DEM provides a more detailed
description, the use of the PBM limits the capability of themodel in providing improved descriptions of the effect ofoperating variables when compared to the phenomenological (MTC) model.

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276
70
65

2.5

60

Power (kW)Predicted < 45 µm (%)

3.0

MTC model
Hybrid model

55
50
45

2.0
1.5
1.0

40

0.5

35

0.0
-18

30

30

35

40

45

50

55

60

65

70

Experimental < 45 µm (%)

10.0

Mass flow (t/h)

Predicted BSA (cm2/g)

MTC model
Hybrid model

1000
900
800
700

400
400

600

800

1000

1200

Experimental BSA (cm2/g)
Fig. 8 Comparison of experimental and predicted passing the 45 μm
sieve (top) and the BSA (bottom) using both the Hybrid and the Modified Torres and Casali models. Filled markers correspond to the basecases used in model calibration.

950

BSA (cm2/g)

900
850

Campos et al. (2019b)
Experiments
MTC model
Hybrid model

800
750
700
650
600
0.0

0

6

12

18

2.5 N/mm2 - 0.35 m/s (MTC model)
3.5 N/mm2 - 0.50 m/s (MTC model)
2.5 N/mm2 - 0.35 m/s (Hybrid model)
3.5 N/mm2 - 0.50 m/s (Hybrid model)

-12

-6

0

6

12

18

Roll axial position y-axis (cm)

500

1000

-6

1.0

0.1
-18

600

-12

Roll axial position y-axis (cm)

1200
1100

2.5 N/mm2 - 0.35 m/s (MTC model)
3.5 N/mm2 - 0.50 m/s (MTC model)
2.5 N/mm2 - 0.35 m/s (Hybrid model)
3.5 N/mm2 - 0.50 m/s (Hybrid model)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Specific energy (kWh/t)
Fig. 9 Relationship between product BSA and specific energy consumption for the tests carried out in the pilot-scale HPGR. For comparison, data are also included for the experimental campaign carried out
by Campos et al. (2019b).

Fig. 10 Comparison between the Hybrid model and MTC model ofthe power (top) and mass flowrate (bottom) profiles for the pilot-scale
HPGR. Vertical dotted lines identify the projection of the rolls length.

4.3 Axial variation in pilot-scale HPGR

Similarities and important differences appear on how
the two model approaches deal with the axial variation of
power and mass flow in the HPGR, as illustrated in Fig. 10.
Regarding the power profile, as mentioned in Table 1, aparabolic pattern is associated to the MTC model with thehighest value at the centre of the rolls, vanishing to zero towards the edges. DEM simulations show a similar pattern,
but with a more marked drop towards the edge of the rolls.
Greater differences are found in the throughput profiles,
whereas the MTC model gives uniform values between
the rolls and a marked step increase at the by-pass region,
due to the material ejected beyond the length of the rolls(Fig. 10 bottom). On the other hand, the mass flowrates inthe Hybrid model do not show the by-pass effect, since its
values are computed within the particle bed. In addition,
this approach results in higher values towards the centre of
the rolls and lower values towards its edge.
As explained in Section 3.1, samples were collectedunderneath the rolls to capture the axial variation of theparticle size distribution along the rolls. This is an important aspect in HPGR operation since products with coarser
particle sizes are known to appear close to the edge of therolls (Campos et al., 2019b; Lubjuhn and Schönert, 1993;

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Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

Passing in 45 µm (%)

2.5 N/mm2

90
80
70

1600

Feed
ExperimentHybrid modelHybrid model (average)
MTC model

1400
1200

BSA (cm2/g)

100

60
50
40

800
600
400

30
20
-18

1000

-12

-6

0

6

12

200
-18

18

Roll axial position y-axis (cm)Passing in 45 µm (%)

3.5 N/mm2

90
80
70

1800

Feed
ExperimentHybrid modelHybrid model (average)
MTC model

1600
1400

60
50

1200

30

400
-6

0

6

12

Roll axial position y-axis (cm)

0

6

12

18

18

Feed
ExperimentHybrid modelHybrid model (average)
MTC model

800
600

-12

-6

1000

40

20
-18

-12

Roll axial position y-axis (cm)

BSA (cm2/g)

100

Feed
ExperimentHybrid modelHybrid model (average)
MTC model

200
-18

-12

-6

0

6

12

18

Roll axial position y-axis (cm)Fig. 11 Comparison between experimental and predicted values for the percentage passing of the 45 μm sieve and BSA using the Hybrid and theModified Torres and Casali models for pilot-scale tests at a peripheral roll speed of 0.50 m/s.

Morrell et al., 1997; Torres and Casali, 2009), in spite ofefforts that have been made to prevent it (Van der Ende etal., 2019; Herman et al., 2013). In order to check the abilityof the models to describe the variation of product size
distribution along the length of the rolls, predictions of selected tests are compared to experiments in Fig. 11 for thepilot-scale HPGR operating at the roll peripheral velocityof 0.50 m/s. Good agreement is evident for both test conditions simulated, in particular for the Hybrid model. Also, as
already discussed by Campos et al. (2019a), the parabolic
shape profile demonstrates a reasonable description for thepilot-scale HPGR studied in pressing iron ore concentrates.

4.4 HPGR Scale-up

At first, a snapshot of the DEM-MBD-PRM simulationof the industrial scale HPGR is presented in Fig. 12.
Around 2.5 million particles were processed in the simulation, in which the reduction in particle size becomes
clear as the bed of particles move towards and throughthe gap. A summary of the simulation results is presented
in Table 6, which shows that the Hybrid model provided
reasonable predictions of total power, with a deviation of
17.8 % from the experimental results, with an even closer

272

Fig. 12 3D rendered DEM simulation image of the industrial-scale
HPGR with particles colored by size operating at specific force of 2.5 N/
mm 2 and roll velocity of 1.30 m/s. Column-pressure particles coloredin gray.

prediction of throughput, with a deviation of only 2.0 %.
Greater deviations are, however, observed when comparing
predictions using the modified Torres and Casali model toexperiments, with 12.3 % deviation in the case of power

Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

Table 6 Key variables of industrial-scale HPGR with both modelingapproaches, with deviations (%) from experiments in parentheses

MeasureSurveyMTCPower (MW)

1.17

1.31 (12.3) 1.37 (17.8)

Throughput (t/h)

520

905 (74.1)

Spec. energy (kWh/t)

2.24

1.45 (35.5) 2.70 (20.2)

Prod. % <45 μm

48.842.5 (13.1) 52.0 (6.6)

Prod. BSA (cm2/g)

890

680 (23.5)

hypothetical case was then simulated. This condition
consisted in matching the experimental specific energy
in each model and make prediction of the industrial test.
These results are presented as dashed lines in Fig. 14, with
reductions in absolute deviations to 6.2 % and 6.9 % for the
MTC and Hybrid models, respectively.
A final comparison is shown in Fig. 15, where predictions

Cumulative passing (%)

100

10
Feed
ExperimentHybrid model1
0.001

Cumulative passing (%)

and 74.1 % in the case of throughput. This significant
overestimation of throughput may be explained by thegreater proportion of material ejected by the bypass zone
in the model prediction. Similar mass transfer in the centreof the roll was predicted by both models, with around 9 %larger from that estimated from the DEM simulation as partof the hybrid model.
A comparison of the pressure profiles in pilot- andindustrial-scale HPGRs predicted using DEM, shownin Fig. 13, demonstrates that the pressure profile in theindustrial-scale machine is more constant in the central
portion of the rolls. Indeed, the DEM simulation was able
to capture this effect that was already reported experimentally by some authors (Campos et al., 2021b; Morley,2010).
On the basis of the parameters calibrated from a basecase test from the pilot-scale test campaign, presented in
Section 4.1, predictions of product size distribution of
the industrial HPGR survey were carried out using boththe Hybrid and the Modified Torres and Casali models.
Predictions are presented in Fig. 14, where the Hybrid
model shows good agreement with experiments, with anaverage absolute deviation of 8.0 %. The poor predictionof throughput (Table 6), which directly affects the specificenergy, led to the high value of absolute deviation (15.8 %)for the Modified Torres and Casali model. An additional

1
0.001

100

Predicted < 45 µm (%)

Relative compressive force (-)

0.8
0.6
0.4

0.0
-0.55

Pilot scale
Industrial scale
-0.35

-0.15

0.05

Feed
Experiment
MTC model
0.01

0.25

1

0.1

Particle size (mm)Fig. 14 Comparison of predicted and experimental product size distribution using the Hybrid (top) and the Modified Torres and Casali models(bottom) of the industrial HPGR operating at 2.5 N/mm 2 and 1.30 m/s.
Dashed lines correspond to hypothetical case matching the experimental specific energy in each model.

858 (3.6)

1.0

1

10

Hybrid509 (2.0)

0.1

Particle size (mm)

100

90

0.2

0.01

80
70
60

MTC model (Industrial)
Hybrid model (Industrial)
PRM (Industrial)
MTC model (Pilot)
Hybrid model (Pilot)
PRM (Pilot)

50
40
30
20
10

0.45

Relative axial (y-distance)from center of the roll (-)
Fig. 13 Relative compressive force profile along the roll in pilot- andindustrial-scale HPGRs obtained from DEM-MBD-PRM simulations.
Pilot-scale HPGR operating at 2.5 N/mm 2 and rotating at 0.32 m/s.

0
30

35

40

45

50

55

60

65

70

Experimental < 45 µm (%)
Fig. 15 Comparison of experimental and predictions of 45 μm of the
product size distribution in both pilot and industrial scale, including the
PRM.

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Victor A. Rodriguez et al. / KONA Powder and Particle Journal No. 40 (2023) 262–276

of percentage passing the 45 μm sieve for all tests arecompared to those obtained using the particle replacement
model (PRM) in DEM. As demonstrated in the earlier
work (Rodriguez et al., 2022a), the PRM was unable toreach quantitative agreement with experiments. However,
although biased, its predictions were more aligned withexperiments than both Hybrid and the MTC models, thus
demonstrating its great future potential.

5. Conclusions

In order to deal with the limitations of DEM-MBD-PRM
approach in predicting quantitatively the fineness of ironore pellet feed in the HPGR product, a Hybrid model was
proposed. The model used throughput and power, besides
mass flowrate and force profiles predicted along the rolls
obtained from DEM simulations as input to a population
balance model (Modified Torres and Casali model), fitted
on the basis of a base case test.
The approach was able to predict the product particle
size distributions of a pilot-scale HPGR operating at different roll velocities and pressures in size reduction of ironore pellet feed, but with predictions that were comparable
to those obtained using the Modified Torres and Casali
model. Advantages of the Hybrid model in this case would
only appear if changes are made to the machine in question,such as replacement of cheek plates by flanges or changes
in stud patterns, for instance. In these cases, the Hybrid
model would be able to capture their effect, whereas thephenomenological model would not.
The Hybrid model demonstrated to provide superior
predictions of throughput, power and product fineness thanthe phenomenological approach when used to predict theperformance of an industrial-scale HPGR when the models
were fitted using data from pilot-scale tests. This demonstrates the great potential of the Hybrid model to be used inscale-up and design of HPGRs in the future.

Acknowledgements

The authors would like to thank Vale S.A. for financial
and technical support to the research, as well as permission
to publish the work. We also thank the additional financial
support by the Brazilian research agencies CNPq (grant
number 151862/2022-2 and 313425/2021-3), FAPERJ(grant number E-26/202.574/2019) and CAPES (finance
Code 001 and grant number - 88881.188860/2018-01).

Data Availability Statement

The data analysis file and the data supporting the findings of this study are available in J-STAGE Data
(https://doi.org/10.50931/data.kona.20129942).

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Authors’ Short Biographies
Victor Alfonso Rodriguez
Victor Rodriguez received his Materials Engineering degree from Universidad del Valle in Colombia. He then spent four years working as an R&D engineer in a company focused on refining,
manufacturing and recycling precious metals. After that, he joined Universidade Federal do Rio deJaneiro (UFRJ), where he was awarded master’s and doctorate degrees for research dealing withmechanistic modeling and simulation of ball mills and HPGRs, respectively. Victor is currently a
post-doctoral fellow at the Laboratório de Tecnologia Mineral (LTM/COPPE/UFRJ) and his researchinterests include discrete element methods, mechanistic modeling and material characterization.

Túlio Moreira Campos
Túlio Campos is a Metallurgical Engineer graduated at UFRJ and is currently pursuing a master’s degree in Metallurgical and Materials Engineering at the Alberto Luiz Coimbra Institute for
Postgraduate Studies and Engineering Research (COPPE/UFRJ). Túlio is a research assistant at theLaboratório de Tecnologia Mineral (LTM/COPPE/UFRJ) and works with mathematical modelling ofcomminution, process simulations, particle breakage, grinding circuit optimization, multicomponent
operations and digital twin technology. Túlio is interested in developing and applying advanced,
practical and robust process models to improve and integrate total process simulation as a tool for
innovation in the minerals industry.

Gabriel Kamilo Pantoja Barrios
Gabriel Barrios is a Chemical Engineer graduated at Universidad del Valle in Colombia, withmaster’s and doctorate degrees from UFRJ in Brazil. He is currently a post-doctoral fellow at theLaboratório de Tecnologia Mineral of the Alberto Luiz Coimbra Institute for Postgraduate Studies
and Engineering Research (LTM/COPPE/UFRJ). His research interests include particle characterization, mathematical modelling and simulation of mineral processing equipment, simulation using thediscrete element method and geometallurgy. He has experience in experimental work in metallurgicallaboratory, mineral processing plant surveying, and computational simulation.

Gilvandro Bueno
Gilvandro Bueno is a Master Engineer at Vale S.A. He is a Metallurgical Engineer, graduated fromthe Universidade Federal de Ouro Preto and has a master’s degree in Metallurgical and Materials
Engineering from UFRJ. Prior to his current engagement he worked at Taboca Mineração S.A., Votorantim Cimentos S.A. and Samarco S.A., with a total of 30 years of industrial experience in mineral,cement and pelletizing processes.

Luís Marcelo Tavares
Luís Marcelo Tavares is a Professor at UFRJ in Brazil. He received his bachelor’s degree in
Mining Engineering (honors) and his master’s degree from Universidade Federal do Rio Grande
do Sul. He was awarded a Ph.D. degree in Extractive Metallurgy at the University of Utah. He has
been a member of the faculty of UFRJ since 1998, where he is head and founder of the Laboratóriode Tecnologia Mineral and has been Department chairman. His research interests include particle
breakage, advanced models of comminution and of degradation during handling, DEM, physicalconcentration, classification, iron ore processing and development of pozzolanic materials. He is afounding member and currently president of the Global Comminution Collaborative (GCC) and hasreceived several awards from the Brazilian Association of Metallurgy, Materials and Mining (ABM).

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