1016 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
of the system entropy is at its maximum. With more than ~
17 milling steps, the entropy reduction becomes negative,
reflecting an increase in entropy, meaning that the entropy
reduction of the separation process cannot compensate for
the increase in entropy by the comminution of the particles.
SUMMARY AND OUTLOOK
Statistical entropy analysis is already used in various fields
of the raw material sector, including waste management
and primary and secondary resources. Until now, the
analysis was based only on one of the three dimensions
of concentration of components, partition in separation
processes or disperse properties as size and liberation.
With this contribution, we introduce a uniform frame-
work that can consider all of these dimensions, increasing
the precision of entropy analysis. Further, using statistical
entropy to describe disperse particle properties enables for
the first time to describe comminution. Using simulated
particles, we showed that an ideal liberation breakage does
not increase the system’s entropy, as the additional disor-
der due to an increased number of particles is compensated
by liberation. Separation increases the entropy of a system
due to the uncertainty in which product the system’s mass,
the component or the particle is recovered. However, this
uncertainty can be eliminated by additional information,
such as measuring the mass split with a balance or analyzing
the product phases. If the separation entropy surpasses the
entropy produced by comminution, the entropy of a mate-
rial stream can be reduced. A couple of comminution and
separation are optimized by choosing the number of mill-
ing steps with the highest decrease in entropy for a fixed
separation scenario.
The introduced entropy notation can be easily extended,
including additional dimensions. One example might be
to include the microstructure of particles, considering the
number of grains in one mineral phase in a particle. As a
next step, the entropy concept should be applied to actual
data from a process plant rather than using simulated data.
REFERENCES
Ballantyne, G.R., Powell, M.S., 2014. Benchmarking com-
minution energy consumption for the processing of
copper and gold ores. Miner. Eng. 65, 109–114. doi:
10.1016/j.mineng.2014.05.017.
Brunner, P.H., Rechberger, H., 2003. Practical Handbook of
Material Flow Analysis.
Buchmann, M., Schach, E., Leißner, T., Kern, M., Mütze,
T., Rudolph, M., Peuker, U.A., Tolosana-Delgado, R.,
2020. Multidimensional characterization of separa-
tion processes—Part 2: Comparability of separation
efficiency. Miner. Eng. 150, 106284. doi: 10.1016
/j.mineng.2020.106284.
Figure 5. Entropy decrease by separation in dependency on the actual milling cycles—figure adapted from (Schach et al.,
2024)
of the system entropy is at its maximum. With more than ~
17 milling steps, the entropy reduction becomes negative,
reflecting an increase in entropy, meaning that the entropy
reduction of the separation process cannot compensate for
the increase in entropy by the comminution of the particles.
SUMMARY AND OUTLOOK
Statistical entropy analysis is already used in various fields
of the raw material sector, including waste management
and primary and secondary resources. Until now, the
analysis was based only on one of the three dimensions
of concentration of components, partition in separation
processes or disperse properties as size and liberation.
With this contribution, we introduce a uniform frame-
work that can consider all of these dimensions, increasing
the precision of entropy analysis. Further, using statistical
entropy to describe disperse particle properties enables for
the first time to describe comminution. Using simulated
particles, we showed that an ideal liberation breakage does
not increase the system’s entropy, as the additional disor-
der due to an increased number of particles is compensated
by liberation. Separation increases the entropy of a system
due to the uncertainty in which product the system’s mass,
the component or the particle is recovered. However, this
uncertainty can be eliminated by additional information,
such as measuring the mass split with a balance or analyzing
the product phases. If the separation entropy surpasses the
entropy produced by comminution, the entropy of a mate-
rial stream can be reduced. A couple of comminution and
separation are optimized by choosing the number of mill-
ing steps with the highest decrease in entropy for a fixed
separation scenario.
The introduced entropy notation can be easily extended,
including additional dimensions. One example might be
to include the microstructure of particles, considering the
number of grains in one mineral phase in a particle. As a
next step, the entropy concept should be applied to actual
data from a process plant rather than using simulated data.
REFERENCES
Ballantyne, G.R., Powell, M.S., 2014. Benchmarking com-
minution energy consumption for the processing of
copper and gold ores. Miner. Eng. 65, 109–114. doi:
10.1016/j.mineng.2014.05.017.
Brunner, P.H., Rechberger, H., 2003. Practical Handbook of
Material Flow Analysis.
Buchmann, M., Schach, E., Leißner, T., Kern, M., Mütze,
T., Rudolph, M., Peuker, U.A., Tolosana-Delgado, R.,
2020. Multidimensional characterization of separa-
tion processes—Part 2: Comparability of separation
efficiency. Miner. Eng. 150, 106284. doi: 10.1016
/j.mineng.2020.106284.
Figure 5. Entropy decrease by separation in dependency on the actual milling cycles—figure adapted from (Schach et al.,
2024)