3691
Dynamic Simulation for Tumbling Mills Using
Analytical Solutions
Weiguo Xie
Department of Chemical Engineering, University of Minnesota Duluth, USA
ABSTRACT: In recent years, dynamic simulations for tumbling mills have attracted more attention due to
the higher demands for process optimization and control. In this research, an advanced dynamic simulation for
tumbling mills has been developed using analytical solutions. It can be seen that the analytical method is more
accurate since it does not require the input of a time step, on the contrary, the choice of a time step is most
critical for traditional numerical methods and it leads to inevitable errors. Furthermore, the analytical method
saves the computational time because the required iterative methods by numerical techniques are avoided.
Keywords: Dynamic simulation, tumbling mills, analytical solutions, numerical methods
INTRODUCTION
The minerals processing industry plays a vital role in energy
transition to sustainable energy in the coming decades as
higher demand on minerals will be inevitable. However, it
is also facing the simultaneous challenges of decreasing ore
grades and increasing mineralogical complexity, which tend
inherently to lead to increased energy usage and reduced
yields. The energy consumption of comminution processes
far exceeds the energy consumption of other processes.
Liberation of the valuable mineral grains from the host
(gangue) minerals is a key requirement for any subsequent
separation technology, but the high-energy requirements
of the size reduction operations required to achieve this
makes this one of the key bottlenecks in terms of improv-
ing the overall efficiency and profitability of these processes.
Grinding mills, which feature in most comminution cir-
cuits, take the biggest section of the energy consumption
pie in comminution, arousing researchers’ interests in the
optimization of grinding circuits.
Steady–state simulators have been applied in the pro-
cessing industries for many decades. There are, however,
very few dynamic simulators available to describe the
processes in these industries. Steady–state simulators can
perform mass and energy balance across the circuit, which
can be used to test the impact of different operating and
feed conditions. In real operations, the dynamics of the
system, especially those induced by feed operations, can
have a significant impact on the performance that is not
captured by the steady-state predictions. In general, this
variability reduces the performance below what the steady
state simulations predict. In addition, dynamic simulations
are far more useful in the tuning and optimization of con-
trol systems than steady state simulations. This is especially
true when a dynamic simulator is combined with efficient
techniques for the utilization of the large amount of both
live and historic data that these plants generate. Dynamic
behavior of grinding circuits was initially addressed in the
1970s (Lees and Lynch, 1972), with further insights being
gained over the last 50 years, but there are comparatively
few equipment scale models for these dynamics. Some of
these models include a dynamic version of the SAG mill
model (Valery and Morrell, 1995 Salazar, et al., 2009 Yu,
Dynamic Simulation for Tumbling Mills Using
Analytical Solutions
Weiguo Xie
Department of Chemical Engineering, University of Minnesota Duluth, USA
ABSTRACT: In recent years, dynamic simulations for tumbling mills have attracted more attention due to
the higher demands for process optimization and control. In this research, an advanced dynamic simulation for
tumbling mills has been developed using analytical solutions. It can be seen that the analytical method is more
accurate since it does not require the input of a time step, on the contrary, the choice of a time step is most
critical for traditional numerical methods and it leads to inevitable errors. Furthermore, the analytical method
saves the computational time because the required iterative methods by numerical techniques are avoided.
Keywords: Dynamic simulation, tumbling mills, analytical solutions, numerical methods
INTRODUCTION
The minerals processing industry plays a vital role in energy
transition to sustainable energy in the coming decades as
higher demand on minerals will be inevitable. However, it
is also facing the simultaneous challenges of decreasing ore
grades and increasing mineralogical complexity, which tend
inherently to lead to increased energy usage and reduced
yields. The energy consumption of comminution processes
far exceeds the energy consumption of other processes.
Liberation of the valuable mineral grains from the host
(gangue) minerals is a key requirement for any subsequent
separation technology, but the high-energy requirements
of the size reduction operations required to achieve this
makes this one of the key bottlenecks in terms of improv-
ing the overall efficiency and profitability of these processes.
Grinding mills, which feature in most comminution cir-
cuits, take the biggest section of the energy consumption
pie in comminution, arousing researchers’ interests in the
optimization of grinding circuits.
Steady–state simulators have been applied in the pro-
cessing industries for many decades. There are, however,
very few dynamic simulators available to describe the
processes in these industries. Steady–state simulators can
perform mass and energy balance across the circuit, which
can be used to test the impact of different operating and
feed conditions. In real operations, the dynamics of the
system, especially those induced by feed operations, can
have a significant impact on the performance that is not
captured by the steady-state predictions. In general, this
variability reduces the performance below what the steady
state simulations predict. In addition, dynamic simulations
are far more useful in the tuning and optimization of con-
trol systems than steady state simulations. This is especially
true when a dynamic simulator is combined with efficient
techniques for the utilization of the large amount of both
live and historic data that these plants generate. Dynamic
behavior of grinding circuits was initially addressed in the
1970s (Lees and Lynch, 1972), with further insights being
gained over the last 50 years, but there are comparatively
few equipment scale models for these dynamics. Some of
these models include a dynamic version of the SAG mill
model (Valery and Morrell, 1995 Salazar, et al., 2009 Yu,