3734 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
As described in the previous section, the DEM-SPH
interactions are fully resolved, requiring SPH elements to be
at least a few times smaller than the smallest DEM particle.
From Figure 3a, accounting for the full PSD would impose
a computational restriction due to the number of resulting
SPH and DEM particles to be tracked throughout the sim-
ulation. To avoid explicitly solving for the fines, the PSD
was truncated at 16 mm, and the lower end was lumped
into the water to obtain a slurry. The resulting simulation
PSD, illustrated in Figure 3b, shows that roughly 35% of
ore mass remained to be explicitly computed. The complete
set of operating conditions is summarized in Table 1.
SIMULATION PARAMETERS
From the information provided in Table 1, the initial con-
dition and feed parameters were obtained, as summarized
in Table 2. It is important to note that the slurry density
was estimated based on the mill initial conditions. The
same density was then used for the corrected water feed.
Due to the different ore-to-water ratios, the mass flow rate
was conserved but the volumetric flow rate was not. Since
the total amount of slurry fed to mill during the simulation
represents only a small portion of the initial slurry content,
the effect of the density difference can be disregarded.
The ore and ball particles were computed using the
DEM method, for which the relevant parameters are sum-
marized in Table 3. For steel media or steel ball particles typ-
ical spherical DEM particles are used and where as for rock
or ore particles Spero-polyhedrons DEM particles (shape
shown in Table 3) are used so that an average shape of a
rock/ore particle is captured and represented in the simula-
tion. More details on Spero-polyhedrons DEM particles can
be found in Rocky (2023).
In this set of simulation slurry is modelled using IISPH
method in Rocky. The relevant SPH parameters, used to
solve the slurry part are summarized in Table 4.
RESULTS AND DISCUSSION
Once the validation of lab scale and pilot scale mills were
established, a 6.7m diameter full scall SAG was modelled
using Rocky’s coupled SPH-DEM technique. Here mill
charge with slurry, rocks and balls were modelled with a full
grate and pulp lifter arrangement (Figure 1).
The mill was fed using a typical feeding arrangement
as shown in Figure 4a with adjusted feed mass and PSD
suite SPH-DEM modelling setup which corresponds to
measured feed conditions. The simulation was allowed to
run for number of revolutions to achieve numerical stability
and charge dynamics stability. Figure 4 shows charge flow
Table 1. SAG mill parameters and operating conditions
Parameter Value
Mill parameter, ft 22
Internal diameter, mm 6700
Internal length, mm 2130
Number of liners 44
Average Speed, rpm 12.42
Average Speed, %critical 75.2
Average Mill filling, %19
Average Ball filling, %15
Solids SG, t/m3 2.92
Solids feed rate, tph 203.5
Water feed rate, tph 16.5
Total number of mill revolutions 6
Source: Weerasekara 2019
Table 2. Mill charge and feed parameters
Parameter Value
Balls total mass, ton 52.71
Ore total mass, ton 5.26
Ore mass lumped into water, ton 3.35
Initial water content, ton 5.70
Initial slurry content, ton 9.05
Slurry density, kg/m3 1321.8
Corrected ore feed rate, ton/h 73.8
Slurry feed rate, ton/h 146.2
Table 3. DEM model parameters
Parameter Value
Normal contact force Hysteretic Linear Spring
Tangential contact force Linear Coulomb Spring Limit
Rolling resistance Linear Spring Rolling Limit
Particle-particle friction 0.5
Particle-wall friction 0.3
Ball particle rolling
resistance
0.05
Ore particle shape Sphero-polyhedron
Ball particle shape Sphere
Table 4. SPH model parameters
Parameter Value
Viscosity type Cleary
Viscosity, cP 50
Element Size, mm 5.3
Kernel type Wendland
Kernel factor 1.25
As described in the previous section, the DEM-SPH
interactions are fully resolved, requiring SPH elements to be
at least a few times smaller than the smallest DEM particle.
From Figure 3a, accounting for the full PSD would impose
a computational restriction due to the number of resulting
SPH and DEM particles to be tracked throughout the sim-
ulation. To avoid explicitly solving for the fines, the PSD
was truncated at 16 mm, and the lower end was lumped
into the water to obtain a slurry. The resulting simulation
PSD, illustrated in Figure 3b, shows that roughly 35% of
ore mass remained to be explicitly computed. The complete
set of operating conditions is summarized in Table 1.
SIMULATION PARAMETERS
From the information provided in Table 1, the initial con-
dition and feed parameters were obtained, as summarized
in Table 2. It is important to note that the slurry density
was estimated based on the mill initial conditions. The
same density was then used for the corrected water feed.
Due to the different ore-to-water ratios, the mass flow rate
was conserved but the volumetric flow rate was not. Since
the total amount of slurry fed to mill during the simulation
represents only a small portion of the initial slurry content,
the effect of the density difference can be disregarded.
The ore and ball particles were computed using the
DEM method, for which the relevant parameters are sum-
marized in Table 3. For steel media or steel ball particles typ-
ical spherical DEM particles are used and where as for rock
or ore particles Spero-polyhedrons DEM particles (shape
shown in Table 3) are used so that an average shape of a
rock/ore particle is captured and represented in the simula-
tion. More details on Spero-polyhedrons DEM particles can
be found in Rocky (2023).
In this set of simulation slurry is modelled using IISPH
method in Rocky. The relevant SPH parameters, used to
solve the slurry part are summarized in Table 4.
RESULTS AND DISCUSSION
Once the validation of lab scale and pilot scale mills were
established, a 6.7m diameter full scall SAG was modelled
using Rocky’s coupled SPH-DEM technique. Here mill
charge with slurry, rocks and balls were modelled with a full
grate and pulp lifter arrangement (Figure 1).
The mill was fed using a typical feeding arrangement
as shown in Figure 4a with adjusted feed mass and PSD
suite SPH-DEM modelling setup which corresponds to
measured feed conditions. The simulation was allowed to
run for number of revolutions to achieve numerical stability
and charge dynamics stability. Figure 4 shows charge flow
Table 1. SAG mill parameters and operating conditions
Parameter Value
Mill parameter, ft 22
Internal diameter, mm 6700
Internal length, mm 2130
Number of liners 44
Average Speed, rpm 12.42
Average Speed, %critical 75.2
Average Mill filling, %19
Average Ball filling, %15
Solids SG, t/m3 2.92
Solids feed rate, tph 203.5
Water feed rate, tph 16.5
Total number of mill revolutions 6
Source: Weerasekara 2019
Table 2. Mill charge and feed parameters
Parameter Value
Balls total mass, ton 52.71
Ore total mass, ton 5.26
Ore mass lumped into water, ton 3.35
Initial water content, ton 5.70
Initial slurry content, ton 9.05
Slurry density, kg/m3 1321.8
Corrected ore feed rate, ton/h 73.8
Slurry feed rate, ton/h 146.2
Table 3. DEM model parameters
Parameter Value
Normal contact force Hysteretic Linear Spring
Tangential contact force Linear Coulomb Spring Limit
Rolling resistance Linear Spring Rolling Limit
Particle-particle friction 0.5
Particle-wall friction 0.3
Ball particle rolling
resistance
0.05
Ore particle shape Sphero-polyhedron
Ball particle shape Sphere
Table 4. SPH model parameters
Parameter Value
Viscosity type Cleary
Viscosity, cP 50
Element Size, mm 5.3
Kernel type Wendland
Kernel factor 1.25