3756 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
every time step by computing the forces acting on the par-
ticles. Early models of the ball mills (Mishra and Rajamani,
1992, 1994) and (Rajamani and Mishra, 1996) for SAG
mills were mainly in 2D and were used to predict the
charge motion. 3D models of slices of grinding mills were
used to investigate the charge motion (Herbst and Nordell,
2001 Cleary, 2001). Full 3D models of a Hardinge pilot
scale SAG mill were developed by Cleary (2004, 2009) and
Morrison and Cleary (2008).
These models were using just rocks without the presence
of slurry. Slurry has an important role in the transport of the
fine solids and influences the breakage and the dynamics of
the ore inside the mill. A numerical method that is often
used to simulate the slurry flow is the Smoothed Particle
Hydrodynamics (SPH) (Monaghan, 1992, 1994, 2005).
One-way coupled DEM +SPH model for a SAG mill was
introduced by Cleary, Sinnott and Morrison (2006). Fully
coupled models off mills were given by Cleary, Hilton and
Sinnott (2017).
The discharge system of a grinding mill can be con-
sidered as two distinct processes. The first process consists
of the presentation of the slurry and ore to the grate, and
subsequently the flow through the grates into the pans.
The second process is the discharge of the slurry and sol-
ids from the pans. Both processes have great potential in
limiting the discharge rate and therefore the mill through-
put. Coupled DEM +SPH model of the second process
has been reported by Lichter, Suazo, Noriega et all. (2011)
and Ciutina and Soriano (2014). DEM model of the flow
through the grate and discharge system of just rocks has
been presented by Gutierrez, Ahues, Gonzalez and Merino
(2018) and Asakpo, Heath and Chaffer (2018). These
last two papers presented the effect of different pulp lifter
designs on the discharge efficiency. The charge composi-
tion of rock size distributions and slurry content have a sig-
nificant influence on the flow through the grate openings,
Morrell and Stephenson (1996) provides a mathematical
model of the observed relationships between hold-up, flow-
rate and grate designs.
The position of the grates’ openings and the open area
of the grates have also significant effect on the discharge
of the ore and slurry. A study of the effect of the radial
position of the openings on the slurry discharge has been
carried out on a laboratory scale mill with grate-only design
by Latchireddi and Morrell (2003). Similar study on open
grates discharge has been presented by Bordi, Heath and
Pasternak (2017). Both papers highlighted the importance
of the grates position and open area on the discharge rates
of the mill.
This paper also analyzes the effect of radial position
of the openings on the discharge performance of a AG
mill, but the simulation is using DEM coupled with SPH
method. The simulations of seven different positions of
the grates’ openings for both radial and curved pulp lifter
designs are compared in terms of discharge rates, hold-up
in the pans and trunnion and flowrates through grates in
both directions. The open area of the grates, the mill speed,
the filling level, the size distribution of the ore inside the
mill and the percentage of solids by weight inside the mill
are kept unchanged between these configurations in order
to evaluate only the effect of the radial position of the open-
ings on the discharge efficiency.
NUMERICAL MODELS
The simulations of the mill discharge systems described in
this paper were carried out using a coupled DEM+SPH in-
house software.
DEM is a numerical technique in which the motion
and the interactions of a large number of solid discrete par-
ticles are computed using Newton’s laws of motion. This
method solves the equations of motion of each particle at
every time step by evaluating the sum of the force acting
upon the particle. The interactions between particles are
modeled as a linear spring-dashpot that allows particles to
overlap slightly on collision. The dashpot makes the colli-
sion dissipate energy during contact.
The SPH method is well described by Monaghan
(1992, 1994) and consists in obtaining an approximate
solution of the Navier-Stokes equation of fluid dynamics
by replacing the fluid with a set of discrete particles. These
particles interact with each other through pressure and vis-
cous forces. Each particle interacts to varying degrees with
its neighbors based on the distance between them and a
so-called kernel function which depends on the distance
between fluid particles.
CALIBRATION OF THE MODEL
The model has been calibrated by running a simulation of
a 32-foot diameter AG mill discharge for which audit data
was available. The mill had 36 pans and a radial design for
the pulp lifters. The grates had an opening of 95mm and
the total open area of the grates for the whole discharge was
6.2 m2. The rotational speed for the mill was 76% of critical
speed or 10.4 rpm. The simulation has used the discharge
system comprised of the grates, pulp lifter, discharge cone,
cover and trunnion and 0.5 m slice of the mill attached to
the discharge system. The mill slice includes the shell liners
every time step by computing the forces acting on the par-
ticles. Early models of the ball mills (Mishra and Rajamani,
1992, 1994) and (Rajamani and Mishra, 1996) for SAG
mills were mainly in 2D and were used to predict the
charge motion. 3D models of slices of grinding mills were
used to investigate the charge motion (Herbst and Nordell,
2001 Cleary, 2001). Full 3D models of a Hardinge pilot
scale SAG mill were developed by Cleary (2004, 2009) and
Morrison and Cleary (2008).
These models were using just rocks without the presence
of slurry. Slurry has an important role in the transport of the
fine solids and influences the breakage and the dynamics of
the ore inside the mill. A numerical method that is often
used to simulate the slurry flow is the Smoothed Particle
Hydrodynamics (SPH) (Monaghan, 1992, 1994, 2005).
One-way coupled DEM +SPH model for a SAG mill was
introduced by Cleary, Sinnott and Morrison (2006). Fully
coupled models off mills were given by Cleary, Hilton and
Sinnott (2017).
The discharge system of a grinding mill can be con-
sidered as two distinct processes. The first process consists
of the presentation of the slurry and ore to the grate, and
subsequently the flow through the grates into the pans.
The second process is the discharge of the slurry and sol-
ids from the pans. Both processes have great potential in
limiting the discharge rate and therefore the mill through-
put. Coupled DEM +SPH model of the second process
has been reported by Lichter, Suazo, Noriega et all. (2011)
and Ciutina and Soriano (2014). DEM model of the flow
through the grate and discharge system of just rocks has
been presented by Gutierrez, Ahues, Gonzalez and Merino
(2018) and Asakpo, Heath and Chaffer (2018). These
last two papers presented the effect of different pulp lifter
designs on the discharge efficiency. The charge composi-
tion of rock size distributions and slurry content have a sig-
nificant influence on the flow through the grate openings,
Morrell and Stephenson (1996) provides a mathematical
model of the observed relationships between hold-up, flow-
rate and grate designs.
The position of the grates’ openings and the open area
of the grates have also significant effect on the discharge
of the ore and slurry. A study of the effect of the radial
position of the openings on the slurry discharge has been
carried out on a laboratory scale mill with grate-only design
by Latchireddi and Morrell (2003). Similar study on open
grates discharge has been presented by Bordi, Heath and
Pasternak (2017). Both papers highlighted the importance
of the grates position and open area on the discharge rates
of the mill.
This paper also analyzes the effect of radial position
of the openings on the discharge performance of a AG
mill, but the simulation is using DEM coupled with SPH
method. The simulations of seven different positions of
the grates’ openings for both radial and curved pulp lifter
designs are compared in terms of discharge rates, hold-up
in the pans and trunnion and flowrates through grates in
both directions. The open area of the grates, the mill speed,
the filling level, the size distribution of the ore inside the
mill and the percentage of solids by weight inside the mill
are kept unchanged between these configurations in order
to evaluate only the effect of the radial position of the open-
ings on the discharge efficiency.
NUMERICAL MODELS
The simulations of the mill discharge systems described in
this paper were carried out using a coupled DEM+SPH in-
house software.
DEM is a numerical technique in which the motion
and the interactions of a large number of solid discrete par-
ticles are computed using Newton’s laws of motion. This
method solves the equations of motion of each particle at
every time step by evaluating the sum of the force acting
upon the particle. The interactions between particles are
modeled as a linear spring-dashpot that allows particles to
overlap slightly on collision. The dashpot makes the colli-
sion dissipate energy during contact.
The SPH method is well described by Monaghan
(1992, 1994) and consists in obtaining an approximate
solution of the Navier-Stokes equation of fluid dynamics
by replacing the fluid with a set of discrete particles. These
particles interact with each other through pressure and vis-
cous forces. Each particle interacts to varying degrees with
its neighbors based on the distance between them and a
so-called kernel function which depends on the distance
between fluid particles.
CALIBRATION OF THE MODEL
The model has been calibrated by running a simulation of
a 32-foot diameter AG mill discharge for which audit data
was available. The mill had 36 pans and a radial design for
the pulp lifters. The grates had an opening of 95mm and
the total open area of the grates for the whole discharge was
6.2 m2. The rotational speed for the mill was 76% of critical
speed or 10.4 rpm. The simulation has used the discharge
system comprised of the grates, pulp lifter, discharge cone,
cover and trunnion and 0.5 m slice of the mill attached to
the discharge system. The mill slice includes the shell liners