Engineering Theory of Leaching An approach to non-ideal reactors and scale- up of pressure leaching systems Presented by Lynton Gormely, P.Eng., Ph.D.
The Problem given lab scale batch results, predict conversion as a function of reactor size for a commercial installation historically, 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. 2
Scale-up we have to be able to accurately predict how each variable affects the process outcome we need to be in control of the major variables for the process difficulties occur when we cannot make this prediction in going from laboratory results to commercial scale 3
Major Process Variables Temperature Reagent concentrations, eg: pulp density oxygen overpressure acid Mass transfer rates: gas-liquid liquid-solid Time batch vs continuous environment (hence, flow patterns in reactor) 4
Major Process Variables (cont d) Temperature is usually subject to control by heat exchange or manipulating initial conditions Reagent concentrations can be controlled or predicted relative to process performance by way of mass balance Mass transfer rates: agitation systems tend to be engineered so that marginal increases in agitation are of little benefit 5
Major Process Variables (cont d) Time: while a small-scale batch operation can be managed to have a residence time distribution that is theoretically tractable, commercial-scale continuous operations may be more complex, and not subject to theoretical modeling this area of uncertainty must be dealt with in commercial reactor sizing from small-scale batch data measured in terms of residence time distributions 6
Moving Forward 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 7
Residence Time Distributions Need to know how long individual molecules 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) We will consider only steady-state flow of a single fluid, without density change 8
9 Generic RTD curve
Ideal and Non-Ideal Distributions Ideal: can be easily and accurately modelled with just a few parameters, eg: Continuous Stirred Tank Reactor (CSTR, perfectly mixed reactor) CSTRs in series plug flow reactor dispersed plug flow reactor Non-ideal: distribution must be modeled assuming a combination of ideal types, because internal flows cannot be characterized as either perfectly mixed or dispersed plug flow 10
11 Dispersed Plug Flow Model
12 CSTR in series
Tracer Tests Can determine RTD for a given vessel or system whether ideal or not Two common types: pulse input step input In slurry systems, solids and liquid might demonstrate different RTDs; separate tests may be desirable to determine each, and get another measure of nonideality 13
Pulse Input Tracer Tests Often easiest to execute Output gives RTD directly except for normalization QC check is determination of the tracer recovery 14
Step Input Tracer Test Requires the ability to make a continuous tracer injection for several residence times Output gives the integral of RTD, except for normalization QC check to ascertain that exit concentration equals the inlet concentration at the end of the test 15
Fluid Behaviour in a Reactor Two concepts that determine reaction kinetics Degree of segregation of a fluid: characterizes extent to which mixing occurs on the microscopic (individual molecules) or macroscopic (clumps of molecules) level microfluid: free mixing among molecules is easy macrofluid: liquid is available only as a large number of small sealed packets Earliness of mixing: whether a fluid mixes early or late as it flows through a vessel macrofluids would tend to exhibit late mixing 16
Fluid Behaviour and Batch Reactor Kinetics For mixed batch reactors with either microfluid or macrofluid, reaction slows with time as reactants are consumed 17
Microfluid Behaviour and CSTR Kinetics All reactants are at their exit (ie, low) concentrations Reactants entering are immediately diluted to exit concentrations by perfect mixing Reactions therefore take place at a relatively low rate, as dictated by reactant concentrations 18
Macrofluid Behaviour and CSTR Kinetics Reactant concentrations do not immediately drop to a low value, but decrease as they would in a batch reactor Extent of reaction in each of the millions of little aggregates in the reactor depends only on length of stay Equally true for any aggregate in the exit stream 19
Macrofluid Behaviour and CSTR Kinetics (cont d) Fractional conversion in the exit stream is determined by summing the conversions of all the aggregates fraction of reactant = unreactedin the exit stream in all the aggregates exit stream fraction of reactant fraction of exit remaining in an streamconsisting aggregateof age of aggregatesof age between t and t + t between t and t + t 20
Leaching Particle Batch/Continuous Kinetic Correspondence Mental leap: conversion of a mineral particle of age t in a CSTR is the same in a batch reactor Generally, the concentration of the needed reactants will be different, so conversions 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 21
Leaching Particle Batch/Continuous Kinetic Correspondence (cont d) Then if the rate-limiting step is the diffusion from bulk solution to the particle surface, driving force should be the same for lab and commercial operation because overpressure is the same, solution concentration is the same, and the concentration at the surface is about zero In many other processes, oxidation by ferric is rate-limiting and the ratio of ferric to ferrous can be maintained by oxygen overpressure, so that the kinetics in batch and continuous operation should be similar Reaction rate drops over the course of the batch reaction, but only due to disappearance of oxidizable surface, not depletion of a dissolved reagent 22
With Correspondence in Kinetics Established Use RTD and batch information to predict continuous performance in any kind of reactor Use previously developed equation for macrofluids where, in this case, an aggregate in the fluid is a leaching particle fraction of reactant = unreactedin the exit stream in all the aggregates exit stream fraction of reactant fraction of exit remaining in an streamconsisting aggregateof age of aggregatesof age between t and t + t between t and t + t 23
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 24
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, due to effect of size on liquid-solid mass transfer, as long as effect would be the same in both lab and commercial reactors 25
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 set lab test conditions and commercial design where batch performance is unaffected by scale 26
Example batch-to-continuous calculation: 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: 27
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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. 29
30 Batch oxidation results at 185 o C and 30% solids:
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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. If the time intervals are large, this can bias the residence time to lower values, and yield a lower predicted oxidation. This happens because the each trapezoid is assigned to the lower time bound rather than the average of the upper and lower time bound. A better procedure in this case would be to plot the areas so determined at the mean of the respective time interval. 32
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34 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.
35 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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38 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%.
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