There are several tools available for modeling coal preparation
plant performance. And
they all do a good job, but it is helpful to understand the basic
principles to understand what the results mean.
The following is a brief overview of how I perform process
simulation on a coal cleaning circuit.
This process was used for performing analysis of coal
preparation circuits in Alberta, British Columbia, China, Illinois,
India, Ohio, Pennsylvania, Utah, and West Virginia.
Several of these were comparing actual plant performance to a
predicted performance both past, present, and future.
Others were used to model a new circuit during engineering
and design.
The work is based on the fact that gravity based processes can be
simulated mathematically with three pieces of information. Two of
the pieces required to predict the clean coal yield and quality are
washability or sinkfloat tests on the coal and partition curves for
the various gravity cleaning devices.
COAL WASHABILITY
The washability of a coal is determined by sinkfloat testing.
The test is performed by placing a sample of coal in
progressively heavier specific gravity baths and scooping off the
material that floats.
This test shows how the quality and yield of the coal varies as the
specific gravity changes.
The data shows how one coal would separate at various
specific gravities. The
cumulative float at any float specific gravity is what a "perfect"
(theoretical) specific gravity separation would produce in the way
of clean coal yield and quality, with the cumulative sink being the
refuse from the perfect separation.
This test result will be used as the example for this manual.
A typical washability data is shown in Table 1.
In general the information in the yellow highlighted sections
comes from the analysis f the test data.
Other analysis information such as volatile matter or fixed
carbon can also be used.
This is typical of a steam coal analysis from North America.
Table 1 Example Washability Data
With the washability data and information about the preparation
plant equipment the performance can be predicted with a fairly good
accuracy. The
information needed on the equipment is the partition curves.
Each type of washing equipment has its own characteristic
performance curve, commonly referred to as a partition
(distribution) curve. They are also known as Tromp curves from the
work of Klaas F. Tromp from the Dutch State Mines Organization.
Typical curves are shown in
Figure 1. The term
"partition" derives from the fact that the equipment separates or
"partitions" the coal into two fractions, plus or minus the specific
gravity of separation.
Each curve is substantially independent of the density distribution
of the coal being washed.
The curve is dependent upon the size distribution of the feed
coal.
Figure 1 – Typical Partition Curves
There are two basic philosophies in dealing with the effect of
different size feeds.
One philosophy requires a unique partition curve for each size feed
and each separating gravity.
This procedure becomes very cumbersome and requires a large
file of curves. A new
or changed feed size requires the development of a new curve or
access to one in storage.
This is the procedure first developed by the USBM and
continued by the DOE, which have proceeded to sample and test
various plants and process equipment, and publish the results.
The second philosophy is based upon the work of the Dutch State
Mines organization which specifies that each family of curves can
be reduced to a single curve that defines the effects at low and
high gravities. This
curve can then be modified to any feed by adjusting the slope of the
center section. This is
generally referred to as a normalized curve and is based on +/ X
specific gravity units from a separating point, referenced as zero.
This second method is the method I and many others in the coal
industry use. As such,
we have a set of partition curves for different types of processing
equipment, and adjustment factors (called Ep's) for the center
sections. Ep is an
abbreviation for Ecart Probable Error (or sometimes moen) and is a
measure of the precision of separation.
It is defined as the specific gravity at which 25% of the
feed reports to clean coal (D25), minus the specific gravity at
which 75% reports to clean coal (D75), all divided by 2, or:
Ep = (D25  D75)/ 2
A low Ep (.02) indicates a very precise separation, and a high Ep
(.20) indicates a very inefficient separation.
Other factors such as error area, imperfection, and Tromp
area are, and have been, used by various preparation engineers.
From results experienced in the field, and comparing theoretical to
actual plant performance, some adjustments to this method of Ep have
been developed and a unique Ep calculation is done for each
equipment based on some adjustment factors.
Ep =F1*F2*(F3*SGF4)
Where:
F1:
Where F1 is calculated from the separating SG and the Ave
Size
Where Ave Size
uses Ave = e^{((ln(top)+ln(bot))/2)}
F2:
Prediction or guarantee, 1.0 if predicting performance, 1.25
if guaranteeing performance
F3:
empirical factors determined by testing and unique for each
equipment (generally)
F4:
empirical factors determined by testing and unique for each
equipment (generally)
The raw data I use was taken from old notes, then a regression
analysis was performed to fit a curve to the data to determine
general characteristics.
This was then used to calculate curves for each device based
on separating gravity and assumed Ep. This curve is then used to
calculate a unique curve from the input data.
Regression analysis was also performed on the impact of
average grain size to refine the F1 value.
The following pages present information for major equipment types
commonly found in coal preparation plants.
The attached spreadsheet ( SDM Process Sim) shows this data
in use with the typical washability presented above.
Using this information and assuming a dense media vessel for the
coarse and a wateronly
cyclone circuit for the fines the results are
Dense Media Vessel 

Sep.Gr. 
% Wt 
% Ash 
% S 

1.55 
Predicted 
78.70 
8.67 
1.16 
Theoretical 
80.38 
8.99 
1.17 

Wateronly Cyclone (2 Stage sink reclean) 

% Wt 
% Ash 
% S 

1.70 
Predicted 
69.66 
8.77 
1.01 
Theoretical 
81.87 
8.39 
1.00 

Plant 

% Wt 
% Ash 
% S 

Predicted 
67.42 
8.71 
1.09 

Theoretical 
73.56 
8.69 
1.08 
PROCESS EQUIPMNENT
Baum Jig
Figure 2 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 2: Normaized Baum Jig Partition Curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 0.0118x^{3}
+ 0.1364x^{2} + 0.5221x + 0.6656
Middle: y = 0.2455x + 0.5032
Tail:
y = 0.0043x^{3}  0.0606x^{2} + 0.2896x +
0.5174
Using these functions and the following unique values for Baum jigs:
F1:
y = 0.0002x^{2}
 0.0243x + 1.2129
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.11
F4:
0.01
Figure 3 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 3: Normaized Baum Jig Partition Curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 0.0007x^{3}
+ 0.015x^{2} + 0.1185x + 0.3482
Middle: y = 0.25x + 0.5
Tail:
y = 0.0051x^{3}  0.064x^{2} + 0.2935x +
0.512
Using these functions and the following unique values for Fine Coal
(Batac) jigs:
F1:
y = 0.0013x^{2}  0.063x + 1.513
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.114
F4:
0.1
Figure 4 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 4: Normaized Baum Jig Partition Curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 0.0118x^{3}
+ 0.1364x^{2} + 0.5221x + 0.6656
Middle: y = 0.2455x + 0.5032
Tail:
y = 0.0043x^{3}  0.0606x^{2} + 0.2896x +
0.5174
Using these functions and the following unique values for
Mineral (Diaphragm) jigs:
F1:
y = 0.0013x^{2}  0.063x + 1.513
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.11
F4:
0.1
Figure 5 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 5 Normalized Dense Media Vessel Partition curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 0.0002x^{5}
+ 0.0042x^{4} + 0.0436x^{3} + 0.2231x^{2} +
0.5784x + 0.645
Middle: y = 0.25x + 0.5
Tail:
y = 0.002x^{5} + 0.0236x^{4}  0.0779x^{3}
 0.0265x^{2} + 0.5319x + 0.2983
Using these functions and the following unique values for dense
media vessels:
F1:
y = 3.7425x^{0.4676}
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.047
F4:
0.05
Figure 6 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 6 Normalized Dense Media Cyclone Partition curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 1E05x^{6}
+ 0.0005x^{5} + 0.0082x^{4} + 0.0685x^{3} +
0.3092x^{2} + 0.7224x + 0.7231
Middle: y = 0.25x + 0.5
Tail:
y = 0.0004x^{5}  0.0091x^{4} + 0.0882x^{3}
 0.4074x^{2} + 0.9152x + 0.1633
Using these functions and the following unique values for dense
media cyclones:
F1:
y = 0.0028x^{3} + 0.0598x^{2}  0.3723x + 1.5081
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.37
F4:
0.15
Figure 7 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 7 Normalized Wateronly Cyclone Partition curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 0.0051x^{3}
+ 0.0645x^{2} + 0.2954x + 0.5026
Middle: y = 0.0068x^{3} + 0.0265x^{2} + 0.2646x +
0.4971
Tail:
y = 0.0062x^{3}  0.0745x^{2} + 0.3301x +
0.5125
Using these functions and the following unique values for wateronly
cyclones:
F1:
y =
0.142Ln(x) + 0.8912
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.33
F4:
0.31
Tables
Figure 6 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 6 Normalized Dense Media Cyclone Partition curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 3E06x^{6}
+ 0.0001x^{5} + 0.0018x^{4} + 0.0147x^{3} +
0.0651x^{2} + 0.1498x + 0.347
Middle: y = 0.25x + 0.5
Tail:
y = 0.0004x^{3}  0.0109x^{2} + 0
0.095x + 0.6813
F1:
y = 0.0983Ln(x) + 1.1566
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.25
F4:
0.08
Figure 6 shows normalized partition curves for a heavy media vessel
at increasing separating gravities.
These curves are for adjusted by changing the Ep.
Figure 6 Normalized Spiral Concentrator Partition curve
By using regression analysis, functions for the both tails and the
mid section were determined.
Head: y = 3E06x^{6}
+ 0.0001x^{5} + 0.0018x^{4} + 0.0147x^{3} +
0.0651x^{2} + 0.1498x + 0.347
Middle: y = 0.25x + 0.5
Tail:
y = 0.0004x^{3}  0.0109x^{2} + 0.095x +
0.6813
F1:
y = 0.0983Ln(x) + 1.1566
F2:
1.00
Prediction or guarantee,
1.0 if predicting performance, 1.25 if guaranteeing
performance
F3:
0.25
F4:
0.08
o
40+
years’ experience in the mining industry with strong mineral
processing experience in Precious metals, copper, industrial
minerals, coal, and phosphate
o
Operational experience in precious metals, coal, and phosphate plus
in petrochemicals.
o
Extensive experience studies and feasibility in the US and
international (United States, Canada, Mexico, Ecuador, Columbia,
Venezuela, Chile, China, India, Indonesia, and Greece).