Predicting Continuous Leach Performance
from Batch Data
An approach to non-ideal reactors and
scale- up of leaching systems
Presented by Lynton Gormely, P.Eng., Ph.D.
The Problem
• given lab scale batch results, predict conversion
•
(“extraction”) as a function of reactor configuration for
a commercial installation
historically, in autoclave design, we have always
sought continuous results in order to design a full
scale reactor, so no magic was required: simply
translate mini-pilot small scale continuous autoclave
leach curve to full scale, and allow a safety factor.
• the same approach is starting to be used more for
gold circuit design
2
• simplest lab leaching test is a small scale batch such
•
•
•
as a bottle roll or a Parr autoclave
the leaching duration of every particle in the reactor is
the same, and thus is well known
commercially, continuous reactors are most common
to obtain the highest utilisation of expensive
equipment
not all particles experience the same leach time in a
continuous reactor
– some leave early (“short circuiting”) some leave late (“dead
zones”)
3
• “short circuiting” and “dead zones” are terms
•
suggesting non-ideal reactor performance due to
poor mixing
however, even ideal reactors may exhibit a range of
particle ages leaving the reactor
– e.g., in a perfectly stirred tank reactor, each particle has the
same probability of leaving in a particular time segment, so
some “young” particles as well as some “old” particles will
always be found in the discharge
4
• so, we know from batch tests how a group of
•
5
particles of a single age leaches with time for a given
set of conditions (e.g., reagent concentration
changes with time)
but how do we translate this to a continuous reactor
with a range of particle ages, which may or may not
be known from theory, and for which reagent
concentrations are invariant with time, but perhaps
change with location in the reactor system?
Moving Forward
• we seek a procedure that can be used to scale up
laboratory results to predict commercial performance
without detailed knowledge of the heterogeneous
kinetic reaction rates and their dependence on
process variables
6
Residence Time Distributions
• need to know how long individual particles stay in the
•
reactor (which depends on reactor geometry,
entrance and exit conditions, and chance)
generally, earlier and later departures can be
organized into a distribution, with some departure
times (“ages”) occurring more frequently than others
• this is called a Residence Time Distribution, or Exit
Age Distribution of the fluid leaving the vessel(s)
7
Generic RTD curve
8
Dispersed Plug Flow Model
9
CSTR in series
10
Tracer Tests
• we can determine the RTD for a given vessel or
•
11
system, whether ideal or not, using a tracer test
in slurry systems, solids and liquid might demonstrate
different RTDs; separate tests may be desirable to
determine each, and get another measure of nonideality
Pulse Input Tracer Tests
• output gives RTD directly except for normalization
• QC check is determination of the tracer recovery
12
Leaching Particle Batch/Continuous
Kinetic Correspondence
• mental leap: extraction of a mineral particle of age t
•
in a CSTR is the same in a batch reactor of age t
generally, the concentration of the needed reactants
will be different, so extractions would differ, but:
– in many autoclave leaching processes, oxygen is a ratelimiting reactant (which is why we use an autoclave)
– in both batch lab and commercial operation, we maintain a
constant oxygen overpressure, and use high agitation to
ensure gas/liquid mass transfer is not controlling
13
– in cyanide leaching, we maintain a high NaCN level so that it
does not limit the cyanidation rate
• in both batch (bottle roll) and continuous commercial operation,
the cyanide may be made up periodically to ensure that it does
not limit the leach rate
– in cyanide leaching, enough aeration is provided so that the
solution dissolved oxygen level remains fairly constant,
eliminating this as a significant variable when comparing
batch and continuous operation
14
With Correspondence in
Kinetics Established
• use RTD and batch extraction information to predict
•
continuous performance in any kind of reactor
use the following equation:
fraction of
fraction of sulfur
sulfur
unoxidized in a
=
unoxidized in
all particles particle of age
the exit stream
15
in the exit
stream
fraction of exit
stream consisting
of particles of age
between t and t + ∆t between t and t + ∆t
Implementation for Design
• need batch leach curve and RTD for selected reactor
• theoretical RTDs are available for:
–
–
–
–
a single CSTR
any number of CSTRs in series
dispersed plug flow (pipeline) reactor
various combinations of the above
• if a theoretical RTD doesn’t work, develop an actual
RTD curve using tracer tests
16
Utility of Method
• this approach can account for any influence modeled
by the experimental batch curve, many of which are
theoretically intractable:
– changes in surface area due to changes in particle shape
during the course of the leach, preferential leaching in some
areas and directions
– particle breakage (if shear rates are similar)
– change in rate controlling step during course of batch
reaction, (e.g., due to effect of size on liquid-solid mass
transfer), as long as effect would be the same in both lab
and commercial reactors
17
Utility of Method (cont’d)
• any form of reaction kinetics
• galvanic effects
• particle settling in reactor, segregation in withdrawal,
agglomeration (non-ideal mixing) – there still will be a usable
RTD for the solids (may be different from the liquid)
• other non-idealities in RTD (dead space, short-circuiting)
• scale-up:
– effect on RTD – full-scale tracer test or predict from experience
– effect on batch performance – choose lab conditions which will not
be changed significantly at the commercial operating conditions
• e.g, if cyanidation is to be conducted at 0.5 g/L commercially, it should
be conducted at 0.5 g/L in the lab as well.
18
Example 1: batch-to-continuous
calculation for autoclave:
An operating 6 compartment autoclave was subjected to
a tracer test using a pulse injection of zinc solution. The
zinc concentration in the autoclave discharge was
determined in a series of samples so as to generate a
tracer curve. The data collected were as follows:
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20
The correction was necessary to allow for a baseline
zinc concentration already in the exit solution.
In a series of batch experiments on a refractory gold
ore, the following batch leach information was
generated. Calculate the sulfur oxidation that can be
expected from the autoclave when operating under
the conditions of the tracer test.
21
Batch oxidation results at 185oC and 30% solids:
22
23
First, we normalize the tracer curve, so that the
area under the curve is 1. The area under the
zinc curve is determined by graphical
integration (essentially, the trapezoidal rule).
The area for a particular time is the area
between that time and the next time in the
series.
24
25
To normalize, all the zinc concentrations are divided by the area so
determined. When the area under the normalized curve is determined
again, it is indeed 1.
26
Now we have to deal with the batch data.
There is not a batch data point for each time
interval used to generate the tracer curve.
We must assign a % oxidation to each time
value. It would be best to curve fit the batch
results and pick the values off the curve, but
here, we have simply linearly interpolated
the missing numbers.
27
28
29
In the final columns, we form the product of the batch
oxidation and the fraction of the exit stream with that age (the
area assigned to that time). These are accumulated to
achieve our predicted sulfur oxidation percentage for the
continuous autoclave, in this case, 62%.
fraction of
fraction of sulfur
fraction of exit
sulfur
unoxidized in a
stream consisting
unoxidized in
the exit stream
30
=
all particles
in the exit
stream
of particles of age
particle of age
between t and t + ∆t between t and t + ∆t
31
Example 2: cyanide leach bottle roll
• batch data from Lakefield bottle roll test
• RTD assumes theoretical continuous stirred tank
•
32
reactors (CSTR) in series (we don’t have a tracer
test)
using the theoretical model for RTD will allow us to
predict the effect of residence time and number of
tanks on gold extraction in the commercial system
Bottle Roll Test Results –
Test MB-14
33
RTD from Theory: Tanks in Series
Model
N ( Nθ )
− Nθ
E=
e
( N − 1)!
N −1
34
Number of tanks
Total residence time
9
60 h
Time
interval
35
2h
i
time(i)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
h
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
Dim'
less
time
E
areas
0.03
0.07
0.10
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
0.40
0.43
0.47
0.50
0.53
0.57
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.02
0.04
0.07
0.12
0.17
0.24
0.32
0.42
0.52
0.62
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.02
0.02
Constrained Spline Interpolation
batch
wtd
cum
results
fraction
fraction
Au ext
Au ext
0
0.129323
0.250931
0.357109
0.444422
0.532306
0.62106
0.706865
0.785903
0.854355
0.908401
0.944222
0.958
0.959423
0.960726
0.961909
0.96297
0.963909
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.02
0.02
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.002
0.004
0.008
0.013
0.021
0.032
0.045
0.062
0.082
Number of tanks
Total residence time
9
60 h
Time
interval
36
2h
i
time(i)
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
h
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
Dim'
less
time
E
areas
0.60
0.63
0.67
0.70
0.73
0.77
0.80
0.83
0.87
0.90
0.93
0.97
1.00
1.03
1.07
1.10
1.13
1.17
0.73
0.83
0.93
1.02
1.09
1.16
1.20
1.24
1.25
1.26
1.24
1.22
1.19
1.14
1.09
1.03
0.97
0.91
0.02
0.03
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
Constrained Spline Interpolation
batch
wtd
cum
results
fraction
fraction
Au ext
Au ext
0.964724
0.965417
0.965985
0.966428
0.966745
0.966936
0.967
0.966625
0.965544
0.96382
0.961519
0.958703
0.955438
0.951787
0.947815
0.943586
0.939164
0.934614
0.02
0.03
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.105
0.132
0.162
0.195
0.230
0.267
0.306
0.346
0.386
0.426
0.466
0.505
0.543
0.579
0.614
0.646
0.677
0.705
Number of tanks
Total residence time
9
60 h
Time
interval
37
2h
i
time(i)
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
h
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
Dim'
less
time
E
areas
1.20
1.23
1.27
1.30
1.33
1.37
1.40
1.43
1.47
1.50
1.53
1.57
1.60
1.63
1.67
1.70
1.73
1.77
0.84
0.78
0.71
0.65
0.59
0.53
0.48
0.43
0.38
0.34
0.30
0.26
0.23
0.20
0.17
0.15
0.13
0.11
0.03
0.03
0.02
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.00
Constrained Spline Interpolation
batch
wtd
cum
results
fraction
fraction
Au ext
Au ext
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.03
0.02
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.00
0.00
0.00
0.731
0.755
0.777
0.797
0.816
0.832
0.847
0.860
0.872
0.882
0.892
0.900
0.907
0.913
0.919
0.923
0.927
0.931
Number of tanks
Total residence time
9
60 h
Time
interval
2h
i
time(i)
101
102
103
104
105
106
107
108
109
110
h
202
204
206
208
210
212
214
216
218
220
Dim'
less
time
E
areas
3.37
3.40
3.43
3.47
3.50
3.53
3.57
3.60
3.63
3.67
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.0000
38
Constrained Spline Interpolation
batch
wtd
cum
results
fraction
fraction
Au ext
Au ext
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.93
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.951
95.1%
0.951
0.951
0.951
0.951
0.951
0.951
0.951
0.951
0.951
39
40
41
Example 3: Validation (McLaughlin
Autoclave)
• Khosrow obtained a paper on McLaughlin (first gold
•
•
42
autoclave, now defunct) providing comparable batch
and continuous data
we performed the same calculations as outlined
previously on the data with the results shown in the
next two slides
the agreement is pretty good between batch and
continuous, and this starts to give us some
confidence that the assumptions have validity, and
that the method works
43
44