1531
Working with Multi-Dimensional Particle Property Distributions
Thomas Buchwald, Edgar Schach, Ralf Ditscherlein, Urs A. Peuker
Institute of Mechanical Process Engineering and Mineral Processing,
Technische Universität Bergakademie Freiberg, Germany
ABSTRACT: Mineral processing deals with complex intergrown particles thus, the particle system consists
of individual particles of different size, shape and different mineral composition. To describe such a complex
system based on geo-metallurgicalw image data (Furat 2024), it is necessary to extend the concept of a particle
size distribution to a two- or multi-dimensional particle property distribution. To describe the related multi-
dimensional separation in ore processing, it is necessary to develop or define a multi-dimensional separation
function. This concept of multi-dimensional particle property distributions is introduced here as a new
quantitative toll, which key parameters allow a deeper insight and understanding of particle-based processes in
mineral processing, e.g., milling and all kind of physical separation.
INTRODUCTION
Modern manufacturing techniques are mandatory to create
high-tech materials. In the case of particle-related processes,
the basis are particle systems with precise specifications in
terms of composition i.e., purity and distinct characteris-
tics. To analyze multi-dimensional particle systems, it is
necessary to expand the concept of particle size distribution
to additional dimensions (Buchwald 2022, Schach 2023,
Buchwald 2024), creating a multi-dimensional particle
property distribution. This includes for example attributes
like size, shape, composition, and porosity. We will dem-
onstrate how to define and utilize property distributions
and their key parameters for the two-dimensional case,
along with managing and statistically processing raw par-
ticle data to establish reliable two- or multi-dimensional
distributions.
Describing multi-dimensional separation involves
formulating a separation function that can quantify the
success of separation of a particle system based on mul-
tiple properties. This is achievable by examining particle
data before and after the separation process. Using this
multi-dimensional separation function, we can identify
characteristic separation parameters, like the median, which
in two dimensions becomes a line. We’ll explore how to use
these graphs and the methods available for validating analy-
sis results (Schach 2019, Buchmann 2020).
Finally, from the multi-dimensional separation func-
tion, it is feasible to derive a one-dimensional separation
function for a multi-dimensional particle system, focusing
on separation based on one property. In the case of min-
eral processing the one-dimensional separation function
describes either the separation according size (classification)
or according composition (sorting).
Regarding application of the approach, on the one
hand the multi-dimensional separation is necessary to
obtain specified properties of the particle system and on
the other hand the multi-dimensional separation occurs
anyhow due to the interlinked separation criteria, separa-
tion mechanisms respectively (Damm 2024, Rhein 2023).
Dynamic density sorting in flow fields e.g., in a spiral sepa-
rator uses force balances involving drag, inertia and gravita-
tional forces, which all depend of both particle density and
particle size.
Working with Multi-Dimensional Particle Property Distributions
Thomas Buchwald, Edgar Schach, Ralf Ditscherlein, Urs A. Peuker
Institute of Mechanical Process Engineering and Mineral Processing,
Technische Universität Bergakademie Freiberg, Germany
ABSTRACT: Mineral processing deals with complex intergrown particles thus, the particle system consists
of individual particles of different size, shape and different mineral composition. To describe such a complex
system based on geo-metallurgicalw image data (Furat 2024), it is necessary to extend the concept of a particle
size distribution to a two- or multi-dimensional particle property distribution. To describe the related multi-
dimensional separation in ore processing, it is necessary to develop or define a multi-dimensional separation
function. This concept of multi-dimensional particle property distributions is introduced here as a new
quantitative toll, which key parameters allow a deeper insight and understanding of particle-based processes in
mineral processing, e.g., milling and all kind of physical separation.
INTRODUCTION
Modern manufacturing techniques are mandatory to create
high-tech materials. In the case of particle-related processes,
the basis are particle systems with precise specifications in
terms of composition i.e., purity and distinct characteris-
tics. To analyze multi-dimensional particle systems, it is
necessary to expand the concept of particle size distribution
to additional dimensions (Buchwald 2022, Schach 2023,
Buchwald 2024), creating a multi-dimensional particle
property distribution. This includes for example attributes
like size, shape, composition, and porosity. We will dem-
onstrate how to define and utilize property distributions
and their key parameters for the two-dimensional case,
along with managing and statistically processing raw par-
ticle data to establish reliable two- or multi-dimensional
distributions.
Describing multi-dimensional separation involves
formulating a separation function that can quantify the
success of separation of a particle system based on mul-
tiple properties. This is achievable by examining particle
data before and after the separation process. Using this
multi-dimensional separation function, we can identify
characteristic separation parameters, like the median, which
in two dimensions becomes a line. We’ll explore how to use
these graphs and the methods available for validating analy-
sis results (Schach 2019, Buchmann 2020).
Finally, from the multi-dimensional separation func-
tion, it is feasible to derive a one-dimensional separation
function for a multi-dimensional particle system, focusing
on separation based on one property. In the case of min-
eral processing the one-dimensional separation function
describes either the separation according size (classification)
or according composition (sorting).
Regarding application of the approach, on the one
hand the multi-dimensional separation is necessary to
obtain specified properties of the particle system and on
the other hand the multi-dimensional separation occurs
anyhow due to the interlinked separation criteria, separa-
tion mechanisms respectively (Damm 2024, Rhein 2023).
Dynamic density sorting in flow fields e.g., in a spiral sepa-
rator uses force balances involving drag, inertia and gravita-
tional forces, which all depend of both particle density and
particle size.