3908 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
obtain 75% and 25% curves. This procedure is repeated
for any chosen ‘split’ and split curves such as for 93.75%
and 6.25% of the data. Therefore, to quantify the break-
age variability of the samples, the JKMRC breakage model
(Equation 1) was fitted repeatedly to the data, using the
adopted technique.
Figure 3 shows the ExDWT data points with fitted
curves using the percentile curve model-fitting technique—
that is, by estimating the breakage parameters for each per-
centile range which minimised the sum of squares of the
differences between measured and modelled. The break-
age potential, A×b for fitted percentile curves are given in
Table 1.
Characterising pebbles of Sample C (or Sample D) by
the ExDWT indicates that the ore competence heteroge-
neity is smoothed out to some extent for these samples.
Typically, these spheroidal-shaped survivor particles should
comprise the most competent proportion of the initial feed.
A comparison between t10-Ecs plots of samples C and D
implies that the harder components are preferentially recy-
cled as pebbles which will accumulate in the charge inside
the mill and limit capacity. This is the expected effect for a
harder ore type. However, it seems that it also applies for a
harder component of any ore type. These percentile curves
can be used to estimate the proportion of different compe-
tences within the tested samples.
Stage 2—Defining Components and Estimating
Their Proportion
The breakage model parameters (A and b values) of the
percentile curves can be plotted as cumulative A×b dis-
tribution and then classified into Very Hard (A×b30),
Hard (30A×b38), Moderately Hard (38A×b43),
Medium (43A×b56), Moderately Soft (56A×b67),
Soft (67A×b127) and (Very Soft 127). This classifica-
tion is based on a historic database of more than 5,000
standard JKDWT (JKTech, 2018). Figure 4 illustrates how
the JKTech classification is used to estimate distribution of
competence with ExDWT data.
Figure 5 shows how competence is distributed within
each sample where cubic spline function can be used to
estimate through interpolation the exact A×b values given
in the classification. In this paper, three components were
defined as hard, medium and soft with proportion esti-
mated for each one (Table 2).
Stage 3—Estimating the A×b of Defined Components
Based on the ExDWT Data
Defining components as hard (A×b38), medium
(38A×b67) and soft (A×b67) offers three ranges or pop-
ulations. That is, the ExDWT data points for each sample
can be split into three populations if being fitted by two
curves with A×b=38 and A×b=67, called split functions.
The model parameters (A and b values) those generate
these split functions can be estimated by the Spline func-
tion for each sample. These estimates, “split function model
parameters” (Table 3) are used to split the ExDWT data
into three groups of hard, medium and soft. After grouping
the ExDWT data, Equation 1 can be fitted to each group
of competence to estimate its model parameters, A and b.
Figure 6 shows the JKMRC breakage model
(Equation 1) was fitted separately to three pre-defined
groups of competence (which were grouped based on the
model parameters given in Table 3) for all samples. The
Figure 2. The adopted fitting technique for generating comminution percentile curves
obtain 75% and 25% curves. This procedure is repeated
for any chosen ‘split’ and split curves such as for 93.75%
and 6.25% of the data. Therefore, to quantify the break-
age variability of the samples, the JKMRC breakage model
(Equation 1) was fitted repeatedly to the data, using the
adopted technique.
Figure 3 shows the ExDWT data points with fitted
curves using the percentile curve model-fitting technique—
that is, by estimating the breakage parameters for each per-
centile range which minimised the sum of squares of the
differences between measured and modelled. The break-
age potential, A×b for fitted percentile curves are given in
Table 1.
Characterising pebbles of Sample C (or Sample D) by
the ExDWT indicates that the ore competence heteroge-
neity is smoothed out to some extent for these samples.
Typically, these spheroidal-shaped survivor particles should
comprise the most competent proportion of the initial feed.
A comparison between t10-Ecs plots of samples C and D
implies that the harder components are preferentially recy-
cled as pebbles which will accumulate in the charge inside
the mill and limit capacity. This is the expected effect for a
harder ore type. However, it seems that it also applies for a
harder component of any ore type. These percentile curves
can be used to estimate the proportion of different compe-
tences within the tested samples.
Stage 2—Defining Components and Estimating
Their Proportion
The breakage model parameters (A and b values) of the
percentile curves can be plotted as cumulative A×b dis-
tribution and then classified into Very Hard (A×b30),
Hard (30A×b38), Moderately Hard (38A×b43),
Medium (43A×b56), Moderately Soft (56A×b67),
Soft (67A×b127) and (Very Soft 127). This classifica-
tion is based on a historic database of more than 5,000
standard JKDWT (JKTech, 2018). Figure 4 illustrates how
the JKTech classification is used to estimate distribution of
competence with ExDWT data.
Figure 5 shows how competence is distributed within
each sample where cubic spline function can be used to
estimate through interpolation the exact A×b values given
in the classification. In this paper, three components were
defined as hard, medium and soft with proportion esti-
mated for each one (Table 2).
Stage 3—Estimating the A×b of Defined Components
Based on the ExDWT Data
Defining components as hard (A×b38), medium
(38A×b67) and soft (A×b67) offers three ranges or pop-
ulations. That is, the ExDWT data points for each sample
can be split into three populations if being fitted by two
curves with A×b=38 and A×b=67, called split functions.
The model parameters (A and b values) those generate
these split functions can be estimated by the Spline func-
tion for each sample. These estimates, “split function model
parameters” (Table 3) are used to split the ExDWT data
into three groups of hard, medium and soft. After grouping
the ExDWT data, Equation 1 can be fitted to each group
of competence to estimate its model parameters, A and b.
Figure 6 shows the JKMRC breakage model
(Equation 1) was fitted separately to three pre-defined
groups of competence (which were grouped based on the
model parameters given in Table 3) for all samples. The
Figure 2. The adopted fitting technique for generating comminution percentile curves