DE LANGE, T. and VENTER, P.E. The use of simulated Tromp partition curves in developing the flowsheet
of plant extensions at Grootegeluk Coal Mine. APCOM 87. Proceedings of the Twentieth International Symposium
on the Application of Computers and Mathematics in the Mineral Industries. Volume 2: Metallurgy. Johannesburg,
SAIMM, 1987. pp. 295 - 311.
The Use of Simulation Tromp Partition Curves in
Developing the Flowsheet of Plant Extensions at
Grootegeluk Coal Mine
T. DE LANGE and P.E. VENTER
Grootegeluk Coal Mine, [scor Ltd, South Africa
Extensions to the beneficiation plant at the Grootegeluk Coal Mine are currently being planned in order to provide power station coal for Escom's Matimba Power Station, presently under construction. A simulation model was
developed on the Olivetti M-24 microcomputer to facilitate the development
of the envisaged flowsheet. The computer program simulates the heavy-medium
separation and screening unit operations. The model is based on the construction of the Tromp partition curve described by an arctangent function, allowing
ideal and non-ideal separations.
The paper discusses the determination of the parameters required by the
arctangent curve from standard process parameters such as Epm, Wolf cutpoint, Tromp cutpoint and screening efficiency. The accuracy and shortcomings of the model are discussed, while an overview of the application of the
model to evaluate borehole and bulk sample analyses is also given. It is concluded that the model is an invaluable aid to general flowsheet development.
Introduction
The Grootegeluk Coal Mine, situated in the
model involved,
Waterberg coal-field 20 km west of Ellis-
for both heavy-medium separation
ras,
and screening operations,
is
coal.
Iscor's
major source of
coking
The beneficiation plant treats some
000 t/h of raw coal from the Upper
3
yielding approximately
the
Ecca,
coking
coal and 24% of a middlings frac-
and bulk sampling campaigns were
launched
development
tons
The
Escom's
Matimba Power Station,
under construction,
coal
the
flowsheet
detailed
to
currently
design
to
facilitate
evaluation of borehole and bulk
sampling data.
This
paper
describes
the
heat value
of
simulation
the
as
of the
analyses
included,
was awarded to Iscor.
A computer model was developed as part
the
System demands
Extensive plant expansion became necessary when the contract to supply 12 x 106
of middlings
during
12%
Borehole
annum
and illustrates
application of the model
tion.
per
circuits
flowsheet development phase.
and
Middle
the accuracy of the model
envisaged
among others,
~
steps
flowsheet.
samples
sink/float analyses.
these
sets
of
data
been manipulated by hand
fractional densimetric
Mayer
curves.
THE USE OF SIMULATED TROMP PARTITION CURVES
the
fractional ash,
yield
be
in
specified on these
Conventionally,
would have
first
curves
to
and
Ideal cutpoints would then
utilized to calculate graphically
the
295
expected
yields at specified heat
values
or ash values.
However,
this
conventional method
had
the following disadvantages:
a)
The
method
was
the
tedious
and
time
into
tations; and
To
separations
while
practical
could
a)
compute blended washability data
different boreholes; and
the
organic
and
be
accept
model
in
order
disadvantages of the
the
available,
required
and
to
hand
raw data in
the
to draw washability
c)
curves
summarized
the heavy-medium
and
size
flowsheet
bulk
and
data,
thus
practically
orientated
than would have
been
plant
possible
Overview of existing models
The
specific
above,
an
parameters
requirements
together
as
discussed
with the given time con-
virtually excluded the use
existing simulator
l'DDSIM
using a his-
Wd.S
negotiating
from
University
package.
Prof.
of
the
the
R.P.
Al though
purchase
King<
of
1)
of
the
Witwatersrand,
the
package
coal beneficiation plant;
as it was still being prepared for distri-
allow a choice of Epm values, organic
bution.
and other parameters in
non-ideally,
cess
required
at each point in
,the
pro-
screening
process had to be
tated
the
by
choice
of
compute
the
excluded owing to
a)
inability to cater for the format
b)
equipment
screen analyses
of both products
The
available APPLE II + microcomputer
an
permit a step-by-step development
of
develop
step,
a logical flowline.
model
therefore had to be able
i.e.
decision was therefore taken to use
to
separation
involved,
purchasing and commissioning.
in order
each
by
which was unavailable
the time constraints
and
of
required
at that stage of the design; and
screening
sink/float
information
such packages,
c)
total
of
the raw data;
facili-
efficiencies;
stage,
The use of other simulation packages was
the
flowline. Simulation of the non-ideal
was not available at that
of
accumulated on the Grootegeluk coking
specific heavy-media separation
296
borehole
could be manipulated extensively,
and
ting partition factors,
order to simulate,
The
rate
Iscor
of standard process
from
permitting the development of a more accu-
separation unit processes by calcula-
efficiencies
d)
samples
straints,
simulate
tory
data
format
calculate the information
present results in a
supplied
otherwise.
format.;
b)
expected yields at specified
maximising the usage of given
method. The model had to be able to
a)
compute
By using this model it is clear that the
efficiencies proved to
simulation
for
the extrapolation to
need therefore existed to utilize a
eliminate
charac-
ash, heat value or density cutpoints.
complicated and time consuming.
computer
The
be
expected
screening
The
operation.
evaluate borehole data (in addition
b)
ideal
induced,
screening
to the above) this model had to be able to
data could not be analyzed
only
a
computation of separation product
satisfactory depth, due to time limic)
or
teristics could then be facilitated.
consuming;
b)
compute full partition curves for either a
density
a model in-house.
The APPLE
and
was
later replaced by an Olivetti M-24.
to
METALLURGY: SIMULATION
The performance evaluation program
Modelling
an
Heavy-medium separation
Iscor
Grootegeluk
washer
performance
metallurgical
dy.
had been using a
This
program for
partition
coal
program is similar to
the
one
was therefore available for
the feed,
(This
to
the
(4,5):
to
a
=
t
the
P3»)
[1 ]
fitted
Tramp
partition factor
(ie.
probability that a coal particle
of a given density, d, will report to
the
the overflow ) ( %
metallurgical
samples of
sink-float
taken
=
d
density ( g/cm3
PI - P4
analysis.
conventional
way<
The
parameters describing the shape
general
shape
of
this
curve
(referred to as the fitted curve) is given
3) •
is referred to as the observed par-
=
)
of the specific separation curve.
Tromp partition factors are then
in
Arctan(P2(d
where
the
product and tailings are
calculated
according
observed
cutpoints
incorporation
of a coal washer,
applied
Discrete
the
to
PI - P4
the model.
Performance curve fitting
In order to determine
and
= lOO(PI
t
An extensive
errors and Wolf curve
performance
factors
following equation
weekly
database, including Tromp curve cutpoints,
into
curve
audits for some time alrea-
described by Wizzard(2).
probable
arctangent
fits
in
tition factors).
Figures
The use
01
1 and 4.
"he::
c;.';:".' Ji
,:~ent
function
dif-
100-r--------------------------------------------------------~
Hx; - Shift for asymmetry
~-----
1------
Ideal Epm - no asymmetry
~-------
WWg
o
1,490
1,470
1,450
1,510
DENSITY (g/ cm3)
FIGURE 1. Plot of the overflow Tramp distribution factor against density showing the development of
the HMS simulation model
Points A
B
C
I
W
Wg
=
=
(d",,,)
(d so ,5o) Tramp cutpoint
= (d'5,25)
(d;. t;) Arctan in flection point
True mass based Wolf cutpoint
= Two-dimensional Wolf cutpoint based on graphic integration
=
THE USE OF SIMULATED TROMP PARTITION CURVES
297
fers
from the method followed by Wizzavd,
who
made use of a
The
arc tangent
Weibull
approach
since it culminates in a
distribution.
is
preferred,
1000
of
iterations required from
to +/- 120,
correlation
a
b
=
=
two- dimensional
search, instead of four, thus reducing the
number
d = density (g/cm3)
whilst still
coefficients
c
=
objective
simple:
to
performance
starting
of the simulation model
reverse the
This meant
evaluation.
with
process
calculated results
and
tailings streams
avail-
have
been
Four
which
the
information
parameters and
is
obtain
a
of
distributed evenly on the
four parameters a, b, c and e. Finding the
of the
Arctan
immediately,
around
are
the
Le.
the
would solve parameter c
thus
to find.
equation,
making
ita
logical
The points (d2s ,25)
distributed
evenly
and
enough
inflection point in order
to
Transform
only
the
into
continuous
discrete
partition
intervals,
by
one point not yet defined.
Ideally,
one would endeavour to use the
means of integration;
Tromp cutpoint
in order to find the
apply
flection
and
the discrete partition factors
point
the
Ecart
Probable
Moyen
calculate
solve d2s and d 75 , since these values have
the simulated product
t~ilings
streams;
compare
the
simulated
and
(Epn) as a degree of
in-
to the feed stream washability data;
found
streams
to
sharpness
widespread application in the
to
coal
processing industry.
observed and refine the model;
the
historical
performance
with those desired on
the
new
Tramp cutpoint
At
this
stage
substitute
the
it
is
Tromp
not
possible
cutpoint
for
to
the
inflection point, because of the asymmetry
The influence of
~ach
of the parameters Pl
to P4 is better understood by rearranging
involved.
However,
asymmetry
is known,
for,
Equation [1] as follows:
by using
assumed
Arctan[b (d - c)] + e
[2]
where
the
if
the
it can be
linear
degree
of
corrected
relationship
to apply in the centre region
of
the partition curve.
Wolf cutpoint
overflow
Tromp distribution
as before(%)
298
degree
consider finding them as well. This leaves
Parameter solving
=
describing the
inflection point,
plant.
t
would be
simulated Tromp partition curve;
replace
=a
e
partition curve, are required to solve the
(d7 5 , 75)
data
t
symmetrical
parameter
points,
PI to P4 ;
those
g)
Under
in-
asymmetry of the partition curve
choice
curve
f)
parameter
required to solve the four parameters
Solve
el
=
root
Determine
d)
point
of the arctan
that
This was approached as follows:
c)
e
of
found.
b)
of
equal to 50, in which case c would be
and
one had to work backwards until the
product
a)
sharpness
equal to the Tromp cutpoint)
The
able,
shift
conditions,
higher.
was
describing
horizontal
flection
+/-
0,995
parameter
separation
obtaining
of
overall efficiency parameter
factor,
When
integrating the top error area
from
the left of the curve and at the same time
METALLURGY: SIMULATION
integrating
the
right,
arrives at the point of equal
one
bottom area
from
the
error area intersection. Under synmetrical
condi tions ,
cide
try,
=
= 50,25
- 377,2 x
tI
50.
x
=Abscissa of inflection point
= Tramp cutpoint - Wolf cutpoint
the larger the extent of asynme-
the
larger will be the
between these two cutpoints.
gration
from
two sides is
difference
Since
inte-
nothing
else
The
relationship is considered signifi-
cant with a coefficient of correlation
0,91 as exemplified in Figure 2.
than a two-dimensional version of the Wolf
more,
cutpoint calculation, it followed that the
would expect that with
the
equal to 50.
difference between the Tramp and Wolf
cutpoints was a key in the search for
the
is
inflection point. Therefore, the relationship between the difference in the
and Wolf
the
cutpoints and
inflection
point
the abscissa
had
to
be
means
if
no
asynmetry is
determined
one
tI would be
The constant in Equation [3]
acceptably close to
this
theoretical
value, at 50,25.
Sharpness of separation
of
esta-
In
order
to obtain the ordinat,e
inflection point,
relationship was
Further-
present,
x =0,
of
Tromp
blished.
This
[3]
where
this intersection will coin-
with the Tramp cutpoint at t
However,
tI
by
of linear regression on 25 observa-
tions as
cessary
parameter e,
of
the
it is ne-
to find the horizontal difference
between this point and the Tramp cutpoint,
defined as follows:
54
....
o
ti
~
§ 46
'';:::
;::l
:9
b<JJ
;a 42
0-
B
o....
E-
:::
o
38
.:;::
1i:l
:>
o
34
+
30;---~--~--~--~--~--~--~--~--~--~--~--~--~~
-0,002
0,01
0,014
0,018
0,006
Tramp cutpoint - Wolf cutpoint (g/cml)
0,002
o Included
0,022
0,026
+ Excluded
FIGURE 2. Plot of the difference between Tramp and Wolf cutpoints against the distribution factors of
the Arctan inflection point.
Liner regression: t;
=
50,25 - 377,2 x (correlation coefficient
THE USE OF SIMULATED TROMP PARTITION CURVES
=
0,91)
299
[4]
XI = dI - dso
metrically
around an imaginary axis lying
in an opposite direction from ds 0 than the
This
can
slope
be done
by
determining
the
in the linear section of the parti-
inflection point,
tance,
found
difference,
asymmetry:
which
is already known (tr -
Therefore, d 7 s and dz 5 may be
XI.
tion curve and applying it to the vertical
dI, but with equal dis-
by compensating for this
shift
in
50). Assuming that the linear relationship
holds from dz 5 to d75,
m,
the slope,
is
= ds
XI - Epm
[10]
dzs = dso - XI + Epll
[11]
d7 5
0
-
given as:
and
m
= (75
- 25) I (d75
-
dzs)
[5]
For coal processing, m is always negative.
Applying
Probable
the
definition of
the
Ecart
Moyen to coal beneficiation,
Solving arctan parameters
The
we
a., b, c and e may now
parameters
solved by assigning the following
find:
be
initial
values:
Epm = (d.z 5 - d? 5) I 2
(positive)
[6 ]
= 100 Ire
[12]
=
=
dI
[13]
tI
[14]
leaving
b to be solved by substitution in
a
and
subst,i tution
thereof
into
Equation
[5], we find m in terms of Epm:
ID
= -25
c
e
I hpn
[7]
[2] with (d,t) = (d7S. 75).
Solving for asymmetry
The
horizontal
difference
between
the
Refinement of parameters
Tromp cutpoint and the inflection point is
'fhe
above
therefore:
owing
to
Equation
[8]
5Ql
parameters
the
found
dr,
Equation [12].
may now
be
narrow
in terms of the Tramp cutpoint,
by
[12]
rearranging [4]:
IJlade
IJlade
in
in
Furthermore, an additional
dr and d 7 5 lie in a
ds 0,
band on the curve.
is
based
on
an
Since Equation
assumption,
the
additional point required must lie closely
to
dI=dso+XI
[9]
the
curve
of
Solving d 75 and d25
The
approximation
[3] and the assumption
the points dz s,
inflection point,
refined,
be
point on the Tromp curve is required since
m
The
must
end points
tributed
symmetrically around
dso.
research
has shown that the Epm tends
disOur
to
the
distribution
in order to incorporate the
overall
observed
Ecart Probable is generally not
of
here,
efficiency.
~ximum
The
distribution factor
effect
was
chosen
e.g. (1,24 ; 99), referred to as
dM
and tH.
An
i terati ve procedure is then followed
shift according to the extent of asymmetry
whereby the four calculated data pairs are
present
substituted into Equation
300
and that it is
distributed
sym-
[2],
according
METALLURGY: SIMULATION
to following four equations:
b
=a
T
= Tan[(t7s-e)/a]
(d-c) Arctan[b(d-c)] + e(d-c)
[15]
a(ln[1+b2 (d-c)2)
d 7s -c
a
[19]
2b
=
[16)
which results into
(17]
TJ
=
[20]
T(dJ-l }-T(dJ )
Arctan[b (dr.!: - c)]
dJ - dJ-I
and
where
TJ is the discrete partition factor
for the Jth interval.
c = dso - Tan[(tso - el/a]
[18]
Size separation
b
Apling
sure
applied in the order as shown.
It
was found that the set of parameters
( 1985) describes a method t.o
the performance of screens, ( 6
meawhich
)
is
essentially the same as that
followed
those
in
the coal washer
program.
cases where the originally observed parti-
In
this
tion factors were fitted adequately by the
screen aperture is plotted on the ordinate
arctan
axis instead of the density.
converge
found
within
curve.
in
5
iterations
However ,
the
in
divergence
cases where
the
observed
partition curve had exhibited a low
ciency
This
was
tail in the lower density
effi-
situation
was
and
method the natural logaritmn
5
Following
it
was
The
screening
rectified by limiting
the
Tramp
thus achieving
a meta-stable convergence.
general
(See Figures
form
of
the
to
simulate
Apling
non-ideal
operations too by means of
partition
similar
in
the exemplary work of
decided
laboratory.
number of iterations to 2,
for the
of
distribution curve.)
region.
tail can often be ascribed to analy-
tical errors made in the
3
performance
curve
and to
follow
route to the one described
generating
the
partition
the
a
above
curve.
A
problem at hand was that very little plant:
Discrete partition factors
The
arctan curve describes
partition factor.
densi ty
continuous
practice,
discrete
intervals are used to obtain
partition
thus
In
a
factors.
calculated
midpoint
The partition
factor
is associated wi th
of the density interval.
the
It
Tromp
curve
across
the
interval in order to obtain the
discrete
T
arctan curve, then
method
of
computing
performance
been
implemented.)
undersize
since
the
screening
had not been
The
available were
Apling's
used
at.
(It has since
only
process
therefore
screen efficiency and
(i)
(ii) the
nominal cutpoint.
density
simulated
Model assumptions
As
less
required
the integral
curve
Grootegeluk at that stage.
is
partition factor for that partirepresents
available,
parameters
cular interval.
If
was
the
therefore necessary to integrate the simulated
history
of
the
information was
available
to describe the partition
accurately,
than
curve
the following assumptions had
to be made (see Figure 3):
THE USE OF SIMULATED TROMP PARTITION CURVES
301
100 .-------------------------------------------------------~_,
~
'§
~
80
J-.
.2u
oj
'-
c
.9
::l 60
oD
"5en
:.a
0-
E 40
0
J-.
f-<
~
0
A
c
J-.
<l)
;0-
0
20
o ~----~----~--~----_r~--~----~--~~--~--~_r~~
2,2
2,0
2,4
2,6
fn (Screen size) (mm)
2,8
3,0
FIGURE 3. Plot of the overflow Tromp distribution factor against the natural logarithm of screen size
showing the development of the screening simulation model.
Points A = (d,5.2')
B = (dsll"o) Tramp cutpoint (15,3 mm)
C = (d",,,)
= (d" t) Arctan inflection point (18,5 mm)
(1)
The nominal cut size of the screen is
~luivalent
to the size where material
to
vary between 75 and 92% instead of the
90% assumed initially.
has a 90% probability of reporting to
the overflow, i. e.
( 2)
The
(]g 0
Parameter solving
•
vertical range of the
undersize
distribution is between 0 and 90% •
(3 )
The
inflection
point of
curve coincides with
(4)
(5 )
The
oversize
the
Based on
a
(]go.
[21]
ranges
distribution
according to assumptions (1) and
The lower size limit, dL, is taken as
parameter c is defined as
cannot be used
since
the
logarithm of 0 is not defined.)
Based
available
on
the
all
largely valid.
was
found
historical
data
these
assumptions
are
further work was
done
As
that the ordinate
of
1,25.
the abscissa of the inflection
=
[22]
In (~o)
e
= 90
This
[23]
leaves only b yet to be
determined.
the
coincide
with the nominal size but differs within a
ratio between 1,0 and
c
(3)
and
li ttle
inflection point does not always
302
= 180 /7r
and
(Zero
is
Tramp
between 90 and 100% ,
2.
a
defined as
the smallest size fraction divided by
it
assumption (2) parameter
Tramp undersize efficiency
By defining f as
Futhermore,
point tend
(24)
METALLURGY: SIMULATION
and substituting into [19], the error area
interval
of true tmdersize separation, Eu,
EffuT
may be
calculated as follows:
Eu
= af
[25]
f2)
undersize
100f,
area
the
preselected
discrete partition factors
may
once
again be calculated as discussed previous-
2b
by
until
Discrete partition factors
The
Furthermore,
EffUR is less than a
used
tolerance.
Arctan(-bf) + ef
+ a In( 1 + 1>2
halving routine was
defining
the
as the rectangular
Tramp undersize
ly.
Once
obtained,
these are applied to
total
the
size intervals of the feed stream
block
order
to generate the overflow
in
(product)
and underflow (tailings) streams.
efficiency,
EffuT, may be defined as
Model accuracy
EffuT
=
[26]
100f - Eu
Heavy-medium separation model
f
A typical
By
entering
efficiency EffuR,
required
a
b
iteration until EffuR
vary
between
0,1
can
undersize
shown
simulated partition
Figure
in
be
solved by
partition
= EffuT.
Since b can
calculated
and 2000
a
geometric
program.
factors
4,
with
and the
the
can
be seen that
lS
observed
fitted
by the performance
It
curve
curve
evaluation
both
the
100lF======e=~~==~::::;:::::~==~----------------------1
Simulated
O;---~--~-.---r--'---~-'~-.---r--,---,--,~-,~~--4
1,2
1,24
1,28
1,32
1,36
1,4
1,44
1,48
l
Density (gl cm )
o Observed
FIGURE 4. Plot of overflow Tramp distribution factor against density showing the accuracy of the HMS
model
Observed Determined from sampling.
Fitted
Curve generated by the performance evaluation program.
Simulated Curve generated by the HMS simulation model.
THE USE OF SIMULATED TROMP PARTITION CURVES
303
simulated
the
and fitted curve
observed
density
points
region,
fonns of interpolation than
deviate
from
accurate
in
high
linear fonn that was used. Recent investi-
only
by more or
the
less
equal
amounts.
gations
at
Grootegeluk
logarithmic
The
accuracy
of
the
heavy-med.ium
accurate,
showed
while
interpolation
Lagrange polynomials yields
Figures
6 to 8,
results.
between
simulated
various
confidence
being
and actual
detennined
evaluation
others,
program.
errors
values
the
by
perfonnance
These
latter
results,
and
are further summarized in
Table
is no doubt that other simulators
Acceptable accuracies were obtained· only
in
those
cases where it
experience
showed
that
in
were considered accurate enough for the
particular application, with the advantage
nominal
cutpoint
that only process paramaters are utilized.
parti tion
The
instead of 90%.
cutpoint
for
predicting
may be enhanced by
the
compensating
the difference between the
cutpoint
value
and
is
mass based
more
or
Wolf
graphical
cutpoint.
less
fixed
This
for
the
had
could
of
be
ordinates
of
made
acceptable
when
the
was replaced
with
the
the
true
of inflection was
used
and
In other words,
This is
(dI ,tI )
of
course
since usage of
the
the inflection point
concept
in
obtained
be known.
factor
from
Further work
cases
inflection,
factor
limiting
novel
other
cutpoint
to
known
MiS
that the assumptions
accuracies
in
by using
Size separation model
might achieve better accuracies, but these
accuracy
more
unpredictable
the screen model were valid.
1.
There
a
at
levels,
the
that
interpolation is by far
separation model is further exemplified in
representing the
the
introduced in this
a
cois
a
paper.
application at Grootegeluk at 0,003 g/cm3.
More research will therefore be
(See
to establish the relationship between more
Figure
1 - points W and
Wg).
The prediction of organic efficiency may
also
be
erilianced
by
utilizing
more
used
nominal size,
parameters,
Epm values etc.
Furthermore, there
Parameter
Absolute errors
Confidence level*
80%
50%
such
as
the
those
and
mentioned above.
Accuracy of HMS model
TABLE 1.
widely
necessary
95%
is no reason not
to
follow the same route as had been used
in
the
HMS
database
have
model,
where
been
apart from a lack
the
relevant
established.
This
of
a
parameters
had
only
Concentrate ash, %
0,24
0,48
1,00
become
Misplaced material,%
0,6
1,0
2,0
of the perfonnance evaluation program
Wolf cutpoint, g/cm3
0,002
0,004
0,006
screening operations.
Epm (Ecart)
0,001
0,002
0,004
Organic efficiency,%
1,6
3,0
9,0
lated partition curves are shown in Figure
Clean coal yield, %
0,5
0,9
1,4
5,
A typical plot of the fitted and
read as follows:
c~es
errors
of
the
typical
the simulated concentrate
ash
given
differed
in 50%
less than 0,24%
absolute
for
simu-
whilst Table 2 summarizes the relative
HMS
To
available after the bnplementation
(root mean squared)
parameters.
of
some
Relative errors are
since a logarithmic
transformation
was used to normalize the size ranges.
from the actual.
304
METALLURGY: SIMULATION
,.
~
100 ,,----------------------------------------------------~~
o
o ~~~~~~TrMT~~~TM~rnTrMTrn~rnTM~~~~TM~rnTM~~
1,0
1,5
2,2
3,3
5,0
7,4
11,0
16,4
Screen size (mm) (logarithmic scale)
o Observed
FIGURE 5. Plot of overflow Tromp distribution factor against screen size showing the accuracy of the
screening model
Observed Determined from sampling.
Fitted
Curve generated by the performance evaluation program.
Simulated Curve generated by the screening simulation model.
Accuracy of Screening Model
TABLE 2.
Upper
Ecca contains bright and dull coal,
suitable
Parameter
HMS
errors
coal.
for
For
the
production
mining operations,
of
coking
4
benches
have been developed, with bench 1 as overTramp cutpoint, mm
2,1%
burden.
bench
5,
Wolf
3,5%
exhibits too high a phosphorus content
to
cutpoint, mm
transition
zone,
be rendered suitable for the production of
11,9%
Epm (Ecart)
The
Tramp U/f efficiency, %
1,5%
Abs
coking
coal.
Olf yield, %
0,8% Abs
bright
coal and is only suitable for
Misplaced material, %
1,3%
Abs
The Middle Ecca contains no
prodL'Ction of power
station
coal.
the
This
is divided into mining benches 6
section
----~----~----~-------------
to 14, of which bench 14 will not be mined
Application of the model
as
Geology and mining
The
into
Upper and Middle
be
divided
Ecca
series,
Ten
were
stratigraphic
each
boreholes,
mining
while the Lower Ecca is not developed. The
zones
bench
drilled
coal
determine
wi th interbedded shale layers
with
of
into
samples.
The
the
spaced over the planned
operations for the next 40
series consists of 11
zone subdivided
layer,
13, is too thick.
Waterberg coal field can
the
the overlying sandstone
and
analysed,
years,
in order to
the quality and expected
raw
coal to be
treated
yield
in
the
envisaged beneficiation plant.
THE USE OF SIMULA;rED TROMP PARTITION CURVES
305
Borehole evaluation
The
borehole cores were crushed to -25
and
the
-0,5
Evaluation
done
the
of
fraction
DID
various zones from
tical data,
removed.
the borehole analyses
by using the model
to
was
reconstitute
the sample analy-
and subsequently the benches.
A modified version of the computer
was
DID
then
used
to
calculate,
in-situ characteristics;
(b)
mass
for
each
yields
at
a density of
2,0
ideally and non-ideally sepa-
,
at
other
densities
ranging
if the
pi t
is
yields
at
such
density where
be
eliminate
properly.
This
to
unusable excess
capacity
once
these production peaks had been passed.
Bulk sample evaluation
kers
in
the existing
results
were
sensitivity
yields
analysis
on
the
DID
(b)
(c)
and
performed at
the
35,
25
and 15
IIIID,
30,
20 and
10
at 92% U/f efficiency;
feed preparation screens:
1
5,
3 and
at 75% U/f efficiency;
DID,
static bath HMS:
2,0
g/cm3
1,7; 1,8
at
0,025
1,9 and
90%
and
Epm
organic efficiency;
beneficiated by spirals to yield a product
were incorporated into the
computer
degradation screens:
fractions were assumed to be
the
simulations
Analytical
at 88% U/f efficiency;
(d)
of 20 MJ /kg and a discard of 4 MJ /kg;
fed into the
primary screens:
at other heat values (ranging
from 12 to 22 MJjkg).
plant.
following cutpoints:
IIIID,
obtained; and
cyclone HMS:
(e)
g/cm3
above
1,7;
1,8;
1,9 and 2,0
at 0,017 Epm and 90%
organic
efficiency.
calculations.
From
developed
designed for dual purposes in order to
a
product with a 20 MJjkg heat value is
results
to be
implied that certain plant modules had
(a)
between 1,8 and 2,0 ;
The -0, 5
ini tial production stages,
extensive
yields
(e)
during
and crushed by the primary Bradford brea-
rated;
(d)
occur,
Bulk samples were collected bench by bench
(a)
(c)
from the upper benches must
model
bench, the
g/crn3
peaks
the in-situ characteristics it was
possible to determine which benches
be mined without any beneficiation
from size reduction.
could
apart
From the sensitivity
From the above simulations the optimized
cutpoints
the
were chosen and correlated with
minimum and maximum
obtained
from
expected
the borehole
yields
evaluations.
and constant heat value analyses ( items d
Thus the average, minimum and maximum mass
and
flowrates
e
above) it
was
determined which
could be established
stream,
which
and the reticulation balance completed.
separate
flowline designed in
each
benches could be beneficiated together and
had to be beneficiated in
the
for
detail
plant modules.
Simulation results
Production constraints
Figure 9 shows a typical simulation
The constraints introduced by the simul ta-
performed
neous adherence to product quality control
bench 2, which contains 13% coking coal in
and pit development were also elicited, by
situ.
planning production,
of 1,8 g/crn
available
40
306
years.
blending options and
clean coal stocks for the
This
showed
that
next
production
on
g/cm
in
sample
results
from
shows that with pulp densities
It
3
3
bulk
study
in the cylcone plant and
the
static
maximum densities
bath
achievable
1,9
plant,
(the
with
con-
METALLURGY: SIMULATION
32.0
32.0
----
~ 20
;>,
u
t::
<l)
;:l
0'
<l)
<.'::
<l)
.!::
~
V
c:.:
10
-0,25
0,00
0,25
0,50
0;75
1,00
Absolute error (0/0 Ash)
1,25
1,50
1,75
~ Root mean square = 0,59%
FIGURE 6. Histogram showing the relative frequency distribution of absolute error in concentrate ash
values - HMS simulation model
50,-----------------------------------------------------,
-0,005
-0,004
-0,003
(222J
-0,002
-0,001
Absolute error
0,0
0,001
Root mean square = 0,0018
FIGURE 7. Histogram showing the frequency distribution of absolute error in Epm values - HMS simulation model
THE USE OF SIMULATED TROMP PARTITION CURVES
307
40.-------------------------------------------------,
36.0
30
~
-§
~
>.
u
c<1)
;:l
er
<1)
....
20
'<1)
.~
~
vp;::
10
-15,0
-12,0
-7,5
-10,0
-5,0
0,0
-2,5
5,0
2,5
Absolute error (070 organic efficiency)
~ Root mean square = 4,5070
FIGURE 8. Histogram showing the frequency distribution of absolute error in organic efficiency - HMS
simulation model
ventional
equipnent) ,
yield was 44,6%,
tent
of
the total expected
with a product ash
26,1% and a heat value
of
be
done by hand.
The developnent of
and
programming
con-
simulation
23,5
thereof took approximately 2 weeks.
model
the
the
MJ/kg. Since the contract specification is
35%
ash and a heat value of 20 MJ/kg,
was
clear
pulp
that either
higher
densities were required,
Conclusions
it
operating
or that
low ash coking coal stream had to be
(a)
a
stream,
sheet
density of 2,28 g/cm3 was
the
static bath plant,
obtain the desired product
would
in
or-deI'
quali ty.
(b)
to
only
This
than
ash
into
possible,
84%, compared to 80% previously.
flowsheet
the
180 separations were
course of 6 days,
different
taken
308
flowsheets.
performed in
prone
thus producing 145
This
would
available
considerably more
would
content would have been very acceptable at
Over
not
enabled the design engineers to
opportunity to exploit the
data
the
sample
meet their deadlines, but allowed the
vious
this case
of borehole and bulk
The availability of such a model
55,8%, which was 11% more than in the preIn
developnent as far as the eva-
analytical results were concerned.
have resulted into a total yield of
situation.
flow-
re-
quired in the cyclone plant and 2,05 g/cm3
in
here
invaluable for general
luation
10 shows that with the same feed
a
simulation model described
proved
bled
off in order not t,o discard valuable coal.
Figure
The
otherwise
detail
have
been
thus
arriving at a
final
that
should be much
to the development of
less
bottle-
necks and other design errors.
have
approximately 2 months if it had to
(c)
The
simulation accuracy achieved
by
METALLURGY: SIMULATION
>-3
~
w
Cl)
-<
tr1
:;0
c
(j
z
23
>-3
......
>-3
~
:;0
"1:J
~
o
:;0
>-3
tritl
:;
~
Cl)
o"!j
tr1
Cl)
c
:r:tr1
55,4
80,4
4,2
Tailings
r---
.1J~
S1,80
Tromp 1,80
Epm
0,018
Org Eft 95%
CV MJiI<g
%ROM
ASH%
LEGEND
24,6
76,2
5,7
47,4
49,2
15,3
22,8
20,2
25,6
+1
I
,
I
I
r8,7
31,9
21,2
S1,90
90%
Eff
+35
1mm
-35
46,5
16,2
12,8
100,0
56,1
iill"
I
ROM
7' 7 I Cut
-1
Eff 9 %
L--
1'&
-150 mm
Cut 35mm
Simulation study of blast 2/161 at conventional pulp densities
FIGURE 9.
o
30,8
83,7
2,9
43,9
68,1
8,5
44,6
26,1
23,5
Product
13,1
32,4
21,6
F 1,90
Tromp 1,90
Epm
0,012
Org Eft 95%
44,6% Yield
26,1% Ash
23,5 MJ/kg
FINAL
PRODUCT
o
z
c
~...,
~
......
[/J.
~
Cl
G
:;0
~
r<
~
tI:I
o
.....
w
44,2
83,6
3,1
Tailings
.....-
T~
S2,28
Tramp 2,28
Epm
0,020
Org Eff 95%
%ROM
ASH%
CV MJ/kg
LEGEND
14,7
81,3
4,0
47,4
49,2
15,3
32,7 '
34,8
20,3
+1
I
8,7
31,9
21,2
I
~
-1
7
+35
S2,05
Eft 90%
Cut lmm
46,5
16,2
100,0
56,1
12,8
ROM
lUfr
- 35
\: 7\:
Eft 9 %
L-
1"7
-150 mm
Cut 35mm
Simulation study of blast 21161 at optimum product qualities
FIGURE 10.
o
29,5
84,7
2,6
43,9
68,1
8,5
55,8
34,4
20,5
Product
14,4
35,1
20,5
F2,05
Tromp
2,05
Epm
0,015
Org Eft 95%
55,8% Yield
34,4% Ash
20,5 MJ/kg
FINAL
PRODUCT
the
model
was more than
acceptable
for
the application in which it
and GOTl'FRIED, B. S. The Department of
was
Energy's
used. Further refinement of the model
computer
to
achieve
adapt ion
left
as
higher
for
accuracies
to the research
computer
sidered
as
the primary
not
task
performance
FToc.
program.
of
1st
AIME, August 1983, ch
Coal Industry,
is
24, pp. 215 - 221.
organizations,
modelling is
washer
Conference on Use of Computers in the
and
other applications
coal
conof
a
3.
production engineer based on a mine.
K.F. New Methods of Computing
'I'Ra1P,
the
Washability of
Coal.
GlUckauf,
Vol 37, Feb 1937. pp 125-131,151-156.
Acknowledgements
4.
The
authors would like to thank the
agement
of
publish
this paper and the personnel from
the
Iscor Ltd for
man-
Ore dressing
section,
permission
Research
ERASMUS, T.C. The fitting of a smooth
curve
to
and
to
the experimentally
deter-
mined coordindates of a Tromp
curve.
Fuel
Report
Research Inst.
of S.A.
No. 4, 1973.
Development for their valuable assistance.
5.
Erasmus,
aid
KING,
R. P. and W<X>LLACXYIT, L. Compu-
ter-aided-engineering
processing.
in
of
a mathematical
Research Inst.
minerals
Fuel
of S.A. Report No. 8,
1975.
6.
APLING,
J.T. ,
KILI11EYER ,
R.P.
THE USE OF SIMULATED TROMP PARTITION CURVES
Measuring
A.C.
performances.
WIZZARD,
model.
GEE course, Uni v. of the
Witwatersrand, 1986.
2.
the
performance of a coal washer with the
References
1.
Predicting
T .C.
Mine
& Quarry,
screen
April
1985. pp 31 - 25.
311