1011
Entropy Analysis for Raw Material Processes
Edgar Schach, Thomas Buchwald, Thomas Leißner, Urs Peuker
TU Bergakademie Freiberg Institute of Mechanical Processing and Mineral Processing
Raimon Tolosana Delgado
Helmholtz Institute Freiberg for Resource Technology
ABSTRACT: Several definitions of entropy have been used in literature to assess the efficiency of processes in
the raw material industry. These definitions are based on tracking substance- or material concentrations within
anthropogenic systems such as processing plants or analyzing partition values for characterizing separation
processes. This work presents a common framework for entropy analysis for particulate systems, combining
these existing definitions and, for the first time, taking the disperse state of particles, described by size and
intergrowth, into account. Consequently, the same characteristic measure can evaluate both comminution and
separation processes, allowing for combined optimization.
INTRODUCTION
Statistical entropy analysis has recently been applied in
the field of raw materials to analyze and compare different
processing routes and flowsheets. At least three concepts of
entropy can be identified, resulting in various interpreta-
tions and notations. In all cases, statistical entropy relates
to the entropy definition of information theory as a mea-
sure of uncertainty in a message or signal (Shannon, 1948).
Coming from the field of material flow analysis (Brunner
and Rechberger, 2003), Rechberger et al. first introduced the
statistical entropy analysis (SEA) based on a set of substance
concentrations and mass flows as a tool for decision-making
in the field of waste management and anthropogenic systems
in general (Rechberger, 2001 Rechberger and Brunner,
2002 Rechberger and Graedel, 2002). The SEA method
was further extended for various applications, e.g., analyz-
ing chemical compounds such as different molecules of the
same chemical element (Sobantka et al., 2014b, 2014a).
In the field of recycling and circular economy, statistical
entropy analysis was first applied by Martinez et al. to ana-
lyze a classification process of lithium-ion battery fractions
(Martínez et al., 2019), different processing routes for the
recycling of LIBs (Velazquez-Martinez et al., 2019) or the
recycling of thermoelectric devices (Velázquez-Martinez et
al., 2020). As conventional SEA could not describe circu-
lar economy scenarios as repair, reuse or remanufacturing,
Parchomenko et al. introduced two new aggregation levels
-functional components and products. Application of such
a multilevel SEA demonstrated that it could evaluate the
circularity of different circular economy strategies by iden-
tifying process steps with a negative impact on the circular-
ity and choosing the strategy with the lowest loss of product
functionality (Parchomenko et al., 2021, 2020).
All of the approaches mentioned above are based on
analyzing bulk concentrations of substances. However,
mechanical separation processes for particle systems, e.g.,
ores or shredded lithium-ion batteries, act on specific par-
ticle properties, including particle size (classification), sus-
ceptibility (magnetic separation), density or wettability
(flotation). Therefore, one approach to analyzing separation
processes is the partition curve, which is based on recover-
ing particle property classes instead of the concentration of
Entropy Analysis for Raw Material Processes
Edgar Schach, Thomas Buchwald, Thomas Leißner, Urs Peuker
TU Bergakademie Freiberg Institute of Mechanical Processing and Mineral Processing
Raimon Tolosana Delgado
Helmholtz Institute Freiberg for Resource Technology
ABSTRACT: Several definitions of entropy have been used in literature to assess the efficiency of processes in
the raw material industry. These definitions are based on tracking substance- or material concentrations within
anthropogenic systems such as processing plants or analyzing partition values for characterizing separation
processes. This work presents a common framework for entropy analysis for particulate systems, combining
these existing definitions and, for the first time, taking the disperse state of particles, described by size and
intergrowth, into account. Consequently, the same characteristic measure can evaluate both comminution and
separation processes, allowing for combined optimization.
INTRODUCTION
Statistical entropy analysis has recently been applied in
the field of raw materials to analyze and compare different
processing routes and flowsheets. At least three concepts of
entropy can be identified, resulting in various interpreta-
tions and notations. In all cases, statistical entropy relates
to the entropy definition of information theory as a mea-
sure of uncertainty in a message or signal (Shannon, 1948).
Coming from the field of material flow analysis (Brunner
and Rechberger, 2003), Rechberger et al. first introduced the
statistical entropy analysis (SEA) based on a set of substance
concentrations and mass flows as a tool for decision-making
in the field of waste management and anthropogenic systems
in general (Rechberger, 2001 Rechberger and Brunner,
2002 Rechberger and Graedel, 2002). The SEA method
was further extended for various applications, e.g., analyz-
ing chemical compounds such as different molecules of the
same chemical element (Sobantka et al., 2014b, 2014a).
In the field of recycling and circular economy, statistical
entropy analysis was first applied by Martinez et al. to ana-
lyze a classification process of lithium-ion battery fractions
(Martínez et al., 2019), different processing routes for the
recycling of LIBs (Velazquez-Martinez et al., 2019) or the
recycling of thermoelectric devices (Velázquez-Martinez et
al., 2020). As conventional SEA could not describe circu-
lar economy scenarios as repair, reuse or remanufacturing,
Parchomenko et al. introduced two new aggregation levels
-functional components and products. Application of such
a multilevel SEA demonstrated that it could evaluate the
circularity of different circular economy strategies by iden-
tifying process steps with a negative impact on the circular-
ity and choosing the strategy with the lowest loss of product
functionality (Parchomenko et al., 2021, 2020).
All of the approaches mentioned above are based on
analyzing bulk concentrations of substances. However,
mechanical separation processes for particle systems, e.g.,
ores or shredded lithium-ion batteries, act on specific par-
ticle properties, including particle size (classification), sus-
ceptibility (magnetic separation), density or wettability
(flotation). Therefore, one approach to analyzing separation
processes is the partition curve, which is based on recover-
ing particle property classes instead of the concentration of