3832 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
models for grinding mills and classifiers were implemented.
Verification was carried out by simulating two selected
hypothetical multicomponent grinding circuits, one being
a cement grinding circuit mimicking intergrinding of com-
ponents such as clinker, limestone and gypsum and the
other a wet grinding circuit with a blend of Brazilian iron
ores.
MODELLED CIRCUITS
Dry Cement Grinding Circuit
The dry cement grinding circuit was selected following
the modeling approach proposed by Carvalho and Tavares
(2006) and Carvalho et al. (2007). The unit operations
within this circuit are a two-compartment ball mill with
3.8 m (internal diameter) × 14.4 m (length), a bucket eleva-
tor and a third-generation dynamic classifier. In the circuit,
the fresh feed, consisting of a mixture of clinker, limestone
and gypsum, is blended with the recycle stream from the
classifier and directed to the mill, which is responsible for
size reduction. The discharge from the mill is conveyed to a
dynamic classifier through a bucket elevator. The fine prod-
uct from the classifier represents the final product of the
circuit, while the coarse product forms the recycle stream,
closing the circuit.
It is important to state that the validation of the math-
ematical models of the individual unit operations and the
calibration of parameters with process data were carried out
in the work of Carvalho (2007) and Carvalho et al. (2007),
which focused on single-component grinding (clinker).
The present work then builds on this to analyze a hypo-
thetical multicomponent scenario, where three different
constituents of cement were processed simultaneously, thus
composing the material streams of the circuit with materi-
als such as clinker, gypsum, and limestone. These compo-
nents differ in their grindabilities and densities. For this
operation, the mean residence time of material in the mill
is about 8 min.
Three case studies were selected to analyze the circuit.
In the first one, the density effect of the components on the
classification was disregarded in order to observe only the
effect of varying the specific breakage rate, thus mimicking
a classifier whose performance is independent of material
density. In the second case study, the scenario was reversed,
with the density effect being applied to the classifier, whereas
the specific breakage rate was maintained constant. In the
third case study, both density and specific breakage rate var-
ied for each component, applying both effects. For all cases,
the initial feed to the circuit was 50 t/h, composed of equal
parts of each component. The initial hold-up composition
was assumed to be uneven among the three components in
order to assess the convergence to a steady state from these
initial conditions.
Wet Iron Ore Grinding Circuit
The closed wet grinding circuit studied is in one of the pel-
letizing plants of Complexo de Tubarão, Vale S.A (Vitória,
Brazil). The grinding circuit contains a cluster with six
hydrocyclones that classify the discharge of a 5.1 m (internal
diameter) × 10.31 m (length) overflow ball mill equipped
with two 4.5 MW motors (Figure 1). The mean residence
time of material in the mill for this operation is about 17
min. Liners corresponded to rubber bar-plates, which were
in their midlife (Faria et al., 2019 Carvalho et al., 2021).
In the present work a mixture of two lithologies has been
considered, represented in this case by their corresponding
breakage parameters, density and feed size distribution. In
this scenario two itabirite iron ores, that present different
breakage behavior, have been considered: Fábrica Nova
(FN) and Conceição (CC).
Implementation of the Mathematical Models in Dyssol
In order to describe both circuits, mathematical models
needed to be implemented for ball mills, air classifiers and
hydrocyclones in Dyssol. Additionally, models of auxiliary
units were also implemented for post-processing of simula-
tion results.
The ball mill models have been implemented for the
cases of single and multiple chambers, where each mill
chamber is represented as a perfect mixing reactor which
contains a given mass of material being ground inside,
referred to as hold-up. This approach is commonly used in
mills with a considerable length, as seen in Muanpaopong
et al. (2023). The comminution response in the mill is
governed by the classic population balance model (PBM)
(Ramkrishna &Borwanker, 1973 Carvalho et al., 2024),
expressed in its version that associates mass fractions with
particle size classes. The PBM for comminution in its size-
discrete and continuous unsteady operation can be written
for the size class i as
[
dt
d M^thpik
W thp
thM^thp
b s p
,ik in in out ik
ik
j
i
ijk jk jk
1
1
=
-
-sik
=
-/
^th]
^thp
^
^th
^thM^th
^th
^^thW R
T
SW
S
S
S
S+
S
V
X
W
W
W
W
W
(1)
The variation of mass in each size class i of component
k is determined by the feed rate of that class entering the
mill Win(t)pin,ik(t), minus its discharge rate Wout(t)pik(t),
plus the rate of generation given by the breakage of particles
contained in coarser sizes
models for grinding mills and classifiers were implemented.
Verification was carried out by simulating two selected
hypothetical multicomponent grinding circuits, one being
a cement grinding circuit mimicking intergrinding of com-
ponents such as clinker, limestone and gypsum and the
other a wet grinding circuit with a blend of Brazilian iron
ores.
MODELLED CIRCUITS
Dry Cement Grinding Circuit
The dry cement grinding circuit was selected following
the modeling approach proposed by Carvalho and Tavares
(2006) and Carvalho et al. (2007). The unit operations
within this circuit are a two-compartment ball mill with
3.8 m (internal diameter) × 14.4 m (length), a bucket eleva-
tor and a third-generation dynamic classifier. In the circuit,
the fresh feed, consisting of a mixture of clinker, limestone
and gypsum, is blended with the recycle stream from the
classifier and directed to the mill, which is responsible for
size reduction. The discharge from the mill is conveyed to a
dynamic classifier through a bucket elevator. The fine prod-
uct from the classifier represents the final product of the
circuit, while the coarse product forms the recycle stream,
closing the circuit.
It is important to state that the validation of the math-
ematical models of the individual unit operations and the
calibration of parameters with process data were carried out
in the work of Carvalho (2007) and Carvalho et al. (2007),
which focused on single-component grinding (clinker).
The present work then builds on this to analyze a hypo-
thetical multicomponent scenario, where three different
constituents of cement were processed simultaneously, thus
composing the material streams of the circuit with materi-
als such as clinker, gypsum, and limestone. These compo-
nents differ in their grindabilities and densities. For this
operation, the mean residence time of material in the mill
is about 8 min.
Three case studies were selected to analyze the circuit.
In the first one, the density effect of the components on the
classification was disregarded in order to observe only the
effect of varying the specific breakage rate, thus mimicking
a classifier whose performance is independent of material
density. In the second case study, the scenario was reversed,
with the density effect being applied to the classifier, whereas
the specific breakage rate was maintained constant. In the
third case study, both density and specific breakage rate var-
ied for each component, applying both effects. For all cases,
the initial feed to the circuit was 50 t/h, composed of equal
parts of each component. The initial hold-up composition
was assumed to be uneven among the three components in
order to assess the convergence to a steady state from these
initial conditions.
Wet Iron Ore Grinding Circuit
The closed wet grinding circuit studied is in one of the pel-
letizing plants of Complexo de Tubarão, Vale S.A (Vitória,
Brazil). The grinding circuit contains a cluster with six
hydrocyclones that classify the discharge of a 5.1 m (internal
diameter) × 10.31 m (length) overflow ball mill equipped
with two 4.5 MW motors (Figure 1). The mean residence
time of material in the mill for this operation is about 17
min. Liners corresponded to rubber bar-plates, which were
in their midlife (Faria et al., 2019 Carvalho et al., 2021).
In the present work a mixture of two lithologies has been
considered, represented in this case by their corresponding
breakage parameters, density and feed size distribution. In
this scenario two itabirite iron ores, that present different
breakage behavior, have been considered: Fábrica Nova
(FN) and Conceição (CC).
Implementation of the Mathematical Models in Dyssol
In order to describe both circuits, mathematical models
needed to be implemented for ball mills, air classifiers and
hydrocyclones in Dyssol. Additionally, models of auxiliary
units were also implemented for post-processing of simula-
tion results.
The ball mill models have been implemented for the
cases of single and multiple chambers, where each mill
chamber is represented as a perfect mixing reactor which
contains a given mass of material being ground inside,
referred to as hold-up. This approach is commonly used in
mills with a considerable length, as seen in Muanpaopong
et al. (2023). The comminution response in the mill is
governed by the classic population balance model (PBM)
(Ramkrishna &Borwanker, 1973 Carvalho et al., 2024),
expressed in its version that associates mass fractions with
particle size classes. The PBM for comminution in its size-
discrete and continuous unsteady operation can be written
for the size class i as
[
dt
d M^thpik
W thp
thM^thp
b s p
,ik in in out ik
ik
j
i
ijk jk jk
1
1
=
-
-sik
=
-/
^th]
^thp
^
^th
^thM^th
^th
^^thW R
T
SW
S
S
S
S+
S
V
X
W
W
W
W
W
(1)
The variation of mass in each size class i of component
k is determined by the feed rate of that class entering the
mill Win(t)pin,ik(t), minus its discharge rate Wout(t)pik(t),
plus the rate of generation given by the breakage of particles
contained in coarser sizes