Incremental Separation

This method sorts by the provided direction prior to incrementally removing and discarding the first fraction (of the remaining fractions) and recalculating the mass-composition and recovery of the portion remaining. This is equivalent to incrementally applying a perfect separation (partition) at every interval edge.

The returned data can be used to assess the amenability of a fractionated sample (in the dimension of the sample).

This concept is only applicable in a single dimension where the mass-composition (sample) object is an interval index.

The example will use a dataset that represents a sample fractionated by size.

import logging

import pandas as pd
import plotly

from elphick.geomet import IntervalSample
from elphick.geomet.datasets.sample_data import size_by_assay

logging.basicConfig(level=logging.INFO,
                    format='%(asctime)s %(levelname)s %(module)s - %(funcName)s: %(message)s',
                    datefmt='%Y-%m-%dT%H:%M:%S%z')

Create the sample

The sample is a MassComposition object

df_data: pd.DataFrame = size_by_assay()
df_data

		mass_dry	fe	sio2	al2o3
size_retained	size_passing
0.850	2.000	3.3	64.15	2.04	2.68
0.500	0.850	9.9	64.33	2.05	2.23
0.150	0.500	26.5	64.52	1.84	2.19
0.075	0.150	2.5	62.65	2.88	3.32
0.045	0.075	8.8	62.81	2.12	2.25
0.000	0.045	49.0	55.95	6.39	6.34

The size index is of the Interval type, maintaining the fractional information.

mc_size: IntervalSample = IntervalSample(df_data, name='Sample', moisture_in_scope=False)
mc_size.data

	mass_dry	Fe	SiO2	Al2O3
size
[0.85, 2.0)	3.3	64.15	2.04	2.68
[0.5, 0.85)	9.9	64.33	2.05	2.23
[0.15, 0.5)	26.5	64.52	1.84	2.19
[0.075, 0.15)	2.5	62.65	2.88	3.32
[0.045, 0.075)	8.8	62.81	2.12	2.25
[0.0, 0.045)	49.0	55.95	6.39	6.34

Incrementally Separate

Leverage the method to return the incremental perfect separation in the size dimension. Here we will “de-slime” by discarding the smallest (lowest) sizes incrementally.

results: pd.DataFrame = mc_size.ideal_incremental_separation(discard_from="lowest")
results

		mass_dry	Fe	SiO2	Al2O3
size_cut-point	attribute
0.850	composition	3.300	64.150000	2.040000	2.680000
0.500	composition	13.200	64.285000	2.047500	2.342500
0.150	composition	39.700	64.441864	1.908992	2.240705
0.075	composition	42.200	64.335711	1.966517	2.304645
0.045	composition	51.000	64.072451	1.993000	2.295216
0.000	composition	100.000	60.092450	4.147530	4.277160
0.850	recovery	0.033	0.035228	0.016231	0.020677
0.500	recovery	0.132	0.141209	0.065164	0.072293
0.150	recovery	0.397	0.425734	0.182728	0.207979
0.075	recovery	0.422	0.451798	0.200088	0.227385
0.045	recovery	0.510	0.543778	0.245069	0.273677
0.000	recovery	1.000	1.000000	1.000000	1.000000

Repeat the process but by discarding the coarser sizes.

results_2: pd.DataFrame = mc_size.ideal_incremental_separation(discard_from="highest")
results_2

		mass_dry	Fe	SiO2	Al2O3
size_cut-point	attribute
2.000	composition	100.000	60.092450	4.147530	4.277160
0.850	composition	96.700	59.953981	4.219452	4.331665
0.500	composition	86.800	59.454873	4.466889	4.571371
0.150	composition	60.300	57.228905	5.621327	5.617910
0.075	composition	57.800	56.994429	5.739896	5.717301
0.045	composition	49.000	55.950000	6.390000	6.340000
2.000	recovery	1.000	1.000000	1.000000	1.000000
0.850	recovery	0.967	0.964772	0.983769	0.979323
0.500	recovery	0.868	0.858791	0.934836	0.927707
0.150	recovery	0.603	0.574266	0.817272	0.792021
0.075	recovery	0.578	0.548202	0.799912	0.772615
0.045	recovery	0.490	0.456222	0.754931	0.726323

Plot Grade-Recovery

fig = mc_size.plot_grade_recovery(target_analyte='Fe')
fig.update_layout(height=800)
fig

Discard the highest (coarsest) sizes. As expected the response differs.

fig = mc_size.plot_grade_recovery(target_analyte='Fe', discard_from="highest")
fig.update_layout(height=800)

Plot Amenability

The Amenability Index (AI) will generally range between zero and one, but can in fact be legitimately negative. The closer the AI is to 1.0, the more amenable the ore is to separation of that particular gangue component relative to the target analyte. The AI is shown in the legend (in brackets).

The plot below suggests that SiO2 is marginally more amenable than Al2O3 across the spectrum of yield for this sample.

fig = mc_size.plot_amenability(target_analyte='Fe')
fig.update_layout(height=800)
# noinspection PyTypeChecker
plotly.io.show(fig)

Discard the highest (coarsest) sizes. As expected the response differs. The Amenability indices are negative indicating a downgrade, rather than an upgrade. This demonstrates that desliming is a plausible pathway to beneficiating this sample, while “coarse scalping” is not.

fig = mc_size.plot_amenability(target_analyte='Fe', discard_from="highest")
fig.update_layout(height=800)
fig