1012 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
substances. New analytical measurement techniques, such
as SEM-based mineral liberation analysis, allow for the cal-
culation of multidimensional partition curves, taking more
than one particle property for the analysis of a separation
process into account. Statistical entropy was introduced as
a measure of separation efficiency that considers the whole
distribution of partition values to characterize multidimen-
sional separation processes (Buchmann et al., 2020 Schach
et al., 2019).
To describe comminution as one of the most energy-
intensive processes in the resource sector (Ballantyne and
Powell, 2014), Peuker et al. introduced an excess entropy
term in addition to conventional SEA, allowing the descrip-
tion of disperse particle properties as size and intergrowth
(Peuker et al., 2020). Fernandes et al. applied SEA, includ-
ing this extensive entropy term, to the comminution of
a gold-copper ore, taking different milling times and size
fractions into account (Fernandes et al., 2021). However,
the authors could not find a direct correlation between the
excess entropy term and the particle size.
Until now, statistical entropy analysis for processes for
raw materials takes only one of the following dimensions
into account: bulk concentrations, partition values from
separation processes or the disperse properties of particle
systems relevant for comminution. However, processing
routes for raw materials, including primary and secondary
materials, include all those aspects, and their relation to
each other determines the overall process efficiency. This
contribution introduces a standard notation for the statisti-
cal entropy analysis containing all the previously mentioned
dimensions. Describing those dimensions can improve
entropy analysis accuracy as part of, e.g., life cycle assess-
ment. Further, with the ability to describe comminution
and separation with one consistent measure, we showcase
how to use entropy analysis to optimize both processing
units simultaneously. Such a joined optimization could
reduce overgrinding and increase process efficiency.
METHODOLOGY
To understand the differences and relations between the
definitions of statistical entropy mentioned above, we have
to consider three levels of aggregation of a system mass
N000. The first level is the level of batches. A batch is a
homogeneous amount of material treated in a processing
plant in a homogeneous way. One process unit has one or
more input batches representing the feed stage and one
or more output batches representing the product stage.
Multiple process units can be connected, building up more
complex flowsheets. An example of the relation between
batches, stages and process units is depicted in Figure 1.
The definition of J components gives the second aggre-
gation level. The term components in this work represent
Figure 1. Relation of batches, stages and process units -figure originally published in (Schach et al., 2024)
substances. New analytical measurement techniques, such
as SEM-based mineral liberation analysis, allow for the cal-
culation of multidimensional partition curves, taking more
than one particle property for the analysis of a separation
process into account. Statistical entropy was introduced as
a measure of separation efficiency that considers the whole
distribution of partition values to characterize multidimen-
sional separation processes (Buchmann et al., 2020 Schach
et al., 2019).
To describe comminution as one of the most energy-
intensive processes in the resource sector (Ballantyne and
Powell, 2014), Peuker et al. introduced an excess entropy
term in addition to conventional SEA, allowing the descrip-
tion of disperse particle properties as size and intergrowth
(Peuker et al., 2020). Fernandes et al. applied SEA, includ-
ing this extensive entropy term, to the comminution of
a gold-copper ore, taking different milling times and size
fractions into account (Fernandes et al., 2021). However,
the authors could not find a direct correlation between the
excess entropy term and the particle size.
Until now, statistical entropy analysis for processes for
raw materials takes only one of the following dimensions
into account: bulk concentrations, partition values from
separation processes or the disperse properties of particle
systems relevant for comminution. However, processing
routes for raw materials, including primary and secondary
materials, include all those aspects, and their relation to
each other determines the overall process efficiency. This
contribution introduces a standard notation for the statisti-
cal entropy analysis containing all the previously mentioned
dimensions. Describing those dimensions can improve
entropy analysis accuracy as part of, e.g., life cycle assess-
ment. Further, with the ability to describe comminution
and separation with one consistent measure, we showcase
how to use entropy analysis to optimize both processing
units simultaneously. Such a joined optimization could
reduce overgrinding and increase process efficiency.
METHODOLOGY
To understand the differences and relations between the
definitions of statistical entropy mentioned above, we have
to consider three levels of aggregation of a system mass
N000. The first level is the level of batches. A batch is a
homogeneous amount of material treated in a processing
plant in a homogeneous way. One process unit has one or
more input batches representing the feed stage and one
or more output batches representing the product stage.
Multiple process units can be connected, building up more
complex flowsheets. An example of the relation between
batches, stages and process units is depicted in Figure 1.
The definition of J components gives the second aggre-
gation level. The term components in this work represent
Figure 1. Relation of batches, stages and process units -figure originally published in (Schach et al., 2024)