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
5 so, we know from batch tests how a group of 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
8 Generic RTD curve
9 Dispersed Plug Flow Model
10 CSTR in series
Tracer Tests we can determine the RTD for a given vessel or 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 11
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 sulfur unoxidized in the exit stream = in all stream the particles exit fraction of sulfur fraction of exit unoxidized in a streamconsisting particle of age of particles of age between t and t + t between t and t + t 15
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: 19
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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
22 Batch oxidation results at 185 o C and 30% solids:
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24 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.
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26 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.
27 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.
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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 sulfur = unoxidized in the exit stream allparticles in the exit stream fraction of sulfur fraction of exit unoxidized in a streamconsisting particle of age of particles of age between t and t + t between t and t + t 30
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Example 2: cyanide leach bottle roll batch data from Lakefield bottle roll test RTD assumes theoretical continuous stirred tank 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 32
33 Bottle Roll Test Results Test MB-14
RTD from Theory: Tanks in Series Model E = N( N θ ) N 1 Nθ ( N 1)! e 34
Number of tanks 9 Total residence time 60 h Time interval i time(i) Dim'less time 2 h Constrained Spline Interpolation E areas batch wtd cum results fraction fraction Au ext Au ext h 0 0 - - - 0-0.000 1 2 0.03 0.00 0.00 0.129323 0.00 0.000 2 4 0.07 0.00 0.00 0.250931 0.00 0.000 3 6 0.10 0.00 0.00 0.357109 0.00 0.000 4 8 0.13 0.00 0.00 0.444422 0.00 0.000 5 10 0.17 0.00 0.00 0.532306 0.00 0.000 6 12 0.20 0.00 0.00 0.62106 0.00 0.000 7 14 0.23 0.01 0.00 0.706865 0.00 0.000 8 16 0.27 0.02 0.00 0.785903 0.00 0.001 9 18 0.30 0.04 0.00 0.854355 0.00 0.002 10 20 0.33 0.07 0.00 0.908401 0.00 0.004 11 22 0.37 0.12 0.00 0.944222 0.00 0.008 12 24 0.40 0.17 0.01 0.958 0.01 0.013 13 26 0.43 0.24 0.01 0.959423 0.01 0.021 14 28 0.47 0.32 0.01 0.960726 0.01 0.032 15 30 0.50 0.42 0.01 0.961909 0.01 0.045 16 32 0.53 0.52 0.02 0.96297 0.02 0.062 17 34 0.57 0.62 0.02 0.963909 0.02 0.082 35
Number of tanks 9 Total residence time 60 h Time interval i time(i) Dim'less time 2 h Constrained Spline Interpolation E areas batch wtd cum results fraction fraction Au ext Au ext h 18 36 0.60 0.73 0.02 0.964724 0.02 0.105 19 38 0.63 0.83 0.03 0.965417 0.03 0.132 20 40 0.67 0.93 0.03 0.965985 0.03 0.162 21 42 0.70 1.02 0.03 0.966428 0.03 0.195 22 44 0.73 1.09 0.04 0.966745 0.04 0.230 23 46 0.77 1.16 0.04 0.966936 0.04 0.267 24 48 0.80 1.20 0.04 0.967 0.04 0.306 25 50 0.83 1.24 0.04 0.966625 0.04 0.346 26 52 0.87 1.25 0.04 0.965544 0.04 0.386 27 54 0.90 1.26 0.04 0.96382 0.04 0.426 28 56 0.93 1.24 0.04 0.961519 0.04 0.466 29 58 0.97 1.22 0.04 0.958703 0.04 0.505 30 60 1.00 1.19 0.04 0.955438 0.04 0.543 31 62 1.03 1.14 0.04 0.951787 0.04 0.579 32 64 1.07 1.09 0.04 0.947815 0.03 0.614 33 66 1.10 1.03 0.03 0.943586 0.03 0.646 34 68 1.13 0.97 0.03 0.939164 0.03 0.677 35 70 1.17 0.91 0.03 0.934614 0.03 0.705 36
Number of tanks 9 Total residence time 60 h Time interval i time(i) Dim'less time 2 h Constrained Spline Interpolation E areas batch wtd cum results fraction fraction Au ext Au ext h 36 72 1.20 0.84 0.03 0.93 0.03 0.731 37 74 1.23 0.78 0.03 0.93 0.02 0.755 38 76 1.27 0.71 0.02 0.93 0.02 0.777 39 78 1.30 0.65 0.02 0.93 0.02 0.797 40 80 1.33 0.59 0.02 0.93 0.02 0.816 41 82 1.37 0.53 0.02 0.93 0.02 0.832 42 84 1.40 0.48 0.02 0.93 0.01 0.847 43 86 1.43 0.43 0.01 0.93 0.01 0.860 44 88 1.47 0.38 0.01 0.93 0.01 0.872 45 90 1.50 0.34 0.01 0.93 0.01 0.882 46 92 1.53 0.30 0.01 0.93 0.01 0.892 47 94 1.57 0.26 0.01 0.93 0.01 0.900 48 96 1.60 0.23 0.01 0.93 0.01 0.907 49 98 1.63 0.20 0.01 0.93 0.01 0.913 50 100 1.67 0.17 0.01 0.93 0.01 0.919 51 102 1.70 0.15 0.01 0.93 0.00 0.923 52 104 1.73 0.13 0.00 0.93 0.00 0.927 53 106 1.77 0.11 0.00 0.93 0.00 0.931 37
Number of tanks 9 Total residence time 60 h Time interval i time(i) Dim'less time 2 h Constrained Spline Interpolation E areas batch wtd cum results fraction fraction Au ext Au ext h 101 202 3.37 0.00 0.00 0.93 0.00 0.951 102 204 3.40 0.00 0.00 0.93 0.00 0.951 103 206 3.43 0.00 0.00 0.93 0.00 0.951 104 208 3.47 0.00 0.00 0.93 0.00 0.951 105 210 3.50 0.00 0.00 0.93 0.00 0.951 106 212 3.53 0.00 0.00 0.93 0.00 0.951 107 214 3.57 0.00 0.00 0.93 0.00 0.951 108 216 3.60 0.00 0.00 0.93 0.00 0.951 109 218 3.63 0.00 0.00 0.93 0.00 0.951 110 220 3.67 0.00 1.0000 0.951 95.1% 38
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Example 3: Validation (McLaughlin Autoclave) Khosrow obtained a paper on McLaughlin (first gold 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 42
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