Heap Leaching Simulation
8
Published by Maney Publishing (c) IOM Communications Ltd Simulation technology to support base metal ore heap leaching C. R. Bennett* 1 , D. McBride 1 , M. Cross 1 , J. E. Gebhardt 2 and D. A. Taylor 2 A simulation framework is outlined for the analysis of the operation of both the heap and the associated water balance circuit for the leaching of primary metal ores. The heap simulation is based on a detailed computational model of the leaching process. The process chemistry, including reactants in the gas–liquid–solid matrix, gas flow, variably saturated liquid flow, species transport in both phases, heat transport, and biomass growth and catalysis, is accounted for in models that are equally applicable to simple and complex geometries. The leaching models are contained within the PHYSICA computational modelling environment that includes a powerful multiphase computational fluid dynamic (CFD) solver enabling reactive flow simulation through arbitrarily complex geometries. Tools have been developed in one-, two- and three-dimensions to capture a variety of aspects of the leaching process behaviour. By careful choice of tools, the framework can be applied to a wide range of leaching problems from small scale (e.g. analysis of column tests and drip emitter spacing) through to full scale heap simulation. An optimised version of the heap leach model is itself embedded within a simulation environment that exploits the BILCO mass balance software to enable dynamic simulation of the water balance within the whole plant circuit. Keywords: Leaching, Bioleaching, Numerical modelling, Reactive transport Introduction Hydrometallurgical problems, such as stockpile leaching for metal recovery (Bartlett, 1998; Davenport et al., 2002), provide considerable challenges in the develop- ment of effective computational models owing to the wide range of physical and chemical phenomena present. These phenomena include a series of interacting physicochemical processes, including the transport of raffinate and air through the porous stockpile, a sequence of highly interdependent gas–liquid–solid reactions, including the impact of a bacterial population as a catalyst of the reaction sequence, and the generation and transport of thermal energy. In addition, there are considerable challenges in capturing and managing the data from the plant to parameterise the simulation and the simulation itself, which provides large amounts of detailed information throughout the heap and its lifetime. Typically, such problems concern large heaps (gen- erally with a width and depth of hundreds of metres) of low grade ore reacting over timescales that may be measured in months to years. This means that it is very difficult to evaluate the impact of process design and control systems on the operation of the heap in a reliable fashion. As such, a variety of tools are required to support process engineers in the optimal design and operation of stockpile leaching operations with respect to both overall recovery and efficiency. Unsurprisingly, there has been an enduring interest for over 25 years in the development of mathematical models of stockpile leaching processes to provide effective engineering management tools. For example, in the context of copper heap leaching, Wadsworth and co-workers (Braun et al., 1974; Madsen and Wadsworth, 1981) have played a major role in developing the concept of the shrinking core model (Szekely et al., 1976) to characterise the set of chemical reactions that comprise the main phenomena involved. This pioneering work was then utilised first by Cathles and Apps (1975) and Cathles and Schlitt (1980), and then by Paul et al. (1992a, b) to develop models of copper sulphide heap leaching. More recently, Casas et al. (1993, 1998) have developed a two-dimensional model of the process involving an explicit representation of the biological effects. Although the researchers of these models recognized all the phenomena that must be represented to characterise leaching effectively, a com- bination of limitations in numerical algorithms and computer technology forced a variety of simplifications to enable numerical solutions in practical simulation times. The multiphase transport phenomena represent a significant challenge in the modelling of stockpile leaching processes, and Ritchie and co-workers have 1 School of Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, Wales, UK 2 Process Engineering Resources, Inc., 1945 S 1100 E Ste 100, Salt Lake City, UT 84106, USA *Corresponding author, email [email protected] ß 2006 Institute of Materials, Minerals and Mining and The AusIMM Published by Maney on behalf of the Institute and The AusIMM Received 10 November 2005; accepted 13 December 2005 DOI 10.1179/174328506X91347 Mineral Processing and Extractive Metallurgy (Trans. Inst. Min. Metall. C) 2006 VOL 115 NO 1 41
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Transcript of Heap Leaching Simulation
Pub
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(c)
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Simulation technology to support base metalore heap leaching
C R Bennett1 D McBride1 M Cross1 J E Gebhardt2 and D A Taylor2
A simulation framework is outlined for the analysis of the operation of both the heap and the
associated water balance circuit for the leaching of primary metal ores The heap simulation is
based on a detailed computational model of the leaching process The process chemistry
including reactants in the gasndashliquidndashsolid matrix gas flow variably saturated liquid flow species
transport in both phases heat transport and biomass growth and catalysis is accounted for in
models that are equally applicable to simple and complex geometries The leaching models are
contained within the PHYSICA computational modelling environment that includes a powerful
multiphase computational fluid dynamic (CFD) solver enabling reactive flow simulation through
arbitrarily complex geometries Tools have been developed in one- two- and three-dimensions to
capture a variety of aspects of the leaching process behaviour By careful choice of tools the
framework can be applied to a wide range of leaching problems from small scale (eg analysis of
column tests and drip emitter spacing) through to full scale heap simulation An optimised version
of the heap leach model is itself embedded within a simulation environment that exploits the
BILCO mass balance software to enable dynamic simulation of the water balance within the whole
plant circuit
Keywords Leaching Bioleaching Numerical modelling Reactive transport
IntroductionHydrometallurgical problems such as stockpile leachingfor metal recovery (Bartlett 1998 Davenport et al2002) provide considerable challenges in the develop-ment of effective computational models owing to thewide range of physical and chemical phenomena presentThese phenomena include a series of interactingphysicochemical processes including the transport ofraffinate and air through the porous stockpile asequence of highly interdependent gasndashliquidndashsolidreactions including the impact of a bacterial populationas a catalyst of the reaction sequence and the generationand transport of thermal energy In addition there areconsiderable challenges in capturing and managing thedata from the plant to parameterise the simulation andthe simulation itself which provides large amounts ofdetailed information throughout the heap and itslifetime
Typically such problems concern large heaps (gen-erally with a width and depth of hundreds of metres) oflow grade ore reacting over timescales that may bemeasured in months to years This means that it is verydifficult to evaluate the impact of process design and
control systems on the operation of the heap in a reliablefashion As such a variety of tools are required tosupport process engineers in the optimal design andoperation of stockpile leaching operations with respectto both overall recovery and efficiency Unsurprisinglythere has been an enduring interest for over 25 years inthe development of mathematical models of stockpileleaching processes to provide effective engineeringmanagement tools
For example in the context of copper heap leachingWadsworth and co-workers (Braun et al 1974 Madsenand Wadsworth 1981) have played a major role indeveloping the concept of the shrinking core model(Szekely et al 1976) to characterise the set of chemicalreactions that comprise the main phenomena involvedThis pioneering work was then utilised first by Cathlesand Apps (1975) and Cathles and Schlitt (1980) andthen by Paul et al (1992a b) to develop models ofcopper sulphide heap leaching More recently Casas etal (1993 1998) have developed a two-dimensionalmodel of the process involving an explicit representationof the biological effects Although the researchers ofthese models recognized all the phenomena that must berepresented to characterise leaching effectively a com-bination of limitations in numerical algorithms andcomputer technology forced a variety of simplificationsto enable numerical solutions in practical simulationtimes The multiphase transport phenomena represent asignificant challenge in the modelling of stockpileleaching processes and Ritchie and co-workers have
1School of Engineering University of Wales Swansea Singleton ParkSwansea SA2 8PP Wales UK2Process Engineering Resources Inc 1945 S 1100 E Ste 100 Salt LakeCity UT 84106 USA
Corresponding author email crbennettswanseaacuk
2006 Institute of Materials Minerals and Mining and The AusIMMPublished by Maney on behalf of the Institute and The AusIMMReceived 10 November 2005 accepted 13 December 2005DOI 101179174328506X91347
Mineral Processing and ExtractiveMetallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 41
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Man
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made a significant contribution to this problem usingcommercial computational fluid dynamic (CFD) tech-nologies (Davis and Ritchie 1986 Pantelis and Ritchie1992 Anne and Pantelis 1997) Aside from usingmodels to assess the impact of the generation andtransport of heat in heap leach operations (Dixon andHendrix 1993a b Dixon 2000) Dixon and co-workershave also made significant contributions to full processmodels with simplified fluid mechanics Bouffard andDixon (2003) described work on refractory gold oresand Dixon (2003) and Dixon and Petersen (2003)examined chalcocite based ores Recently Leahy et al(2003 2004 2005) have developed models of chalcociteleaching processes involving unsaturated flow chemicalreactions component transport and thermal processesusing the CFX CFD software technology (wwwansyscom) While these and others have made importantcontributions to heap leach modelling the complexity ofthe process and the resulting mathematical modelformulations have so far resulted in limited success inthe development and application of fully comprehensivesimulation tools
The objectives of the work reported here include thedevelopment of a suite of simulation tools to support thecomprehensive computational modelling and processanalysis of heap leach systems as a basis for processdesign and optimisation
Heap leach simulation tool setThe main tools and component models contained withina simulation environment for the comprehensive model-ling and analysis of heap leaching systems are as follows
(i) liquid flow and species transport includingdealing with variably saturated flow throughheterogeneous media
(ii) gas flow and species transport through hetero-geneous media with varying saturation levels
(iii) chemical reactions within and between masstransfer between the gas liquid and solid phasesincluding the dissolution of primary minerals ofinterest gangue reactions precipitation reac-tions regeneration of reagents within the liquidphase partitioning of species between liquidand gas phases eg oxygen and water vapour(evaporationcondensation)
(iv) bacterial catalysis of chemical reactions includ-ing bacterial population growth death andtransport andmultiple bacteria types for cata-lysis of different chemistry and potentially fordifferent temperature regimes
(v) heat transport including heat from chemicalreactions external weather effects and heattransport by movement of gas and liquid phases
(vi) modelling of the water balance in naturalenvironments with high and variable precipita-tion to ensure the efficacy of the arrangementsmade to cope with extreme weather andoperational events
(vii) data input and output and usability covering asuitable user interface for data input datamanagement including management of pastsimulations and data output in the form ofplots of species output in the pregnant leachsolution recovered from the modelled systemplots of mineral reactions and reagent use
against time contour plots showing remainingminerals and solution inventory in space and intime and animations showing system behaviourover time
In the present paper a simulation environment isoutlined to address all the above issues in a coherentfashion and in particular to manage the raw data andinformation associated with all aspects of the processrelevant to its analysis This environment is based onfour main software tools
(i) a CFD simulation software tool ndash in this casethe flow module of the PHYSICA multiphysicssimulation are employed (wwwphysicacouk)
(ii) a CFD modelling support environment toprovide geometry definition mesh generationand results visualisation tools ndash in this workFEMGV (wwwfemsyscouk) has been used
(iii) an interactive simulation toolkit for resolvingmass and material balances in complex flowsheets ndash the tool used here is Bilco (wwwprocessengcom)
A user environment to encapsulate the informationrequired for data rationalisation structuring andstorage in a database simulation set-up managementand results analysis ndash this is achieved here in theHeapNET environment (wwwprocessengcom) whichitself is built within Visual StudioNET using SQL as thecore database technology and employing Excel as aresults analysis tool
A representation of the heap leaching simulationtechnology is shown in Fig 1 HeapNET manages allthe communication with the other tools used within theenvironment Importantly it provides the user withopportunities to specify simulation scenarios to controlwhich simulation results are saved and then to dialoguewith the visualisation tool to obtain the graphical plots(and movies) The user is only aware of using theHeapNET user environment this generates a variety ofscripts dynamically to call the mesh generation visua-lisation and solver tools to build run and explore theresults of a simulation series for all applications but thefull 3D simulations (although this is currently underdevelopment)
The simulation tools currently consist of the following
(i) a 1D simulation of laboratory columns this is akey tool both with respect to parameterising aspecific ore with respect to reaction rates andalso as a vehicle for validation
1 Overview of HeapNET heap leach simulation technology
Bennett et al Simulation technology to support base metal ore heap leaching
42 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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(ii) a 2D slice simulation of full heaps this is wherea vertical plane through the heap using depthaveraged properties is used to examine a varietyof phenomena particularly the couplingbetween the liquid and gas flows and theemerging thermal distributions
(iii) the water balance model that contains a reduced3D model of the heap here the focus of the toolis on the evaluation of the solution distributionnot only through the heap but also in thecomplete circuit particularly to examine theimpact of operational strategies on pondvolumes against available capacity Scenariossuch as 100 year weather events andor draindown owing to operational malfunction are ofspecial interest to process operations
(iv) a full 3D model of the heap which captures thefull behaviour over its lifetime not only doesthis enable an ongoing audit of performance ofa heap and accurate prediction of its futureperformance but also enable the evaluation of anumber of future operational strategies for themost beneficial options with respect to anumber of possibly conflicting criteria
Each of the above tools has a specific role Obviouslytheir use is influenced by both the volume of data thatthey produce versus that which is required for a specificpurpose and the time taken for the computationsTypically
(i) the 1D simulation of laboratory column experi-ments involving a 150 day operation require2 min of elapsed time on a current generationPC
(ii) a 2D slice simulation involving three lifts over450 days operation could take on the order ofan hour with the same PC
(iii) the water balance model with the reduceddimension simplified heap leach model wouldtake about a minute for a dayrsquos worth ofoperation
(iv) the full 3D model with 250 K cells takes 4 hof simulation for each monthrsquos worth ofoperational time
Underlying computational modellingapproachThe computational modelling approach requires thesolution of coupled liquid and gas flows through porousmedia reactions between the phases and with thehost solid media resulting in the exchange of massand the generation or loss of heat These phenomenaare best modelled these days by CFD simulation toolsthat facilitate the modelling of flow based transportprocesses
The approach adopted here exploits the CFD modulewithin the multiphysics modelling software environmentPHYSICA which employs state of the art finite volumemethods on an unstructured mesh in one- two- andthree-dimensions and has the added benefit of runningscalably in parallel should simulation run times becomesignificant (wwwphysicacouk) Figure 2 illustrates thegeneric macrosolution procedure for the heap leachmodel
In the case of gold heap leaching by cyanide theprincipal reactions are cyanide with gold silver copperand gangue minerals There are no substantial thermaleffects and owing to the low oxygen requirements thesystem is not dependent on gas flow In this case theheat transport gas flow and bacteria tools are notrequired for an adequate gold heap model
In the case of copper sulphide ore leaching is highlydependent on bacterial activity to catalyse the dissolutionof copper through the generation of ferric (Fe3z) which isthe dominant reagent from ferrous ions (Fe2z) andoxygenMany of the reactions are exothermic and thermaleffects can be significant In this case a comprehensivemodel will depend on all of the above tools as oxygen andtherefore gas flow are of crucial importance
The representation of the component phenomenacomprising the phenomenological physical model andthe approach to their solution is briefly summarised inthe following sections However there are more detaileddiscussions of the model formulations and solutionstrategies described in Bennett et al (2003a b) Crosset al (2005) and McBride et al (2005a b)
Variably saturated liquid flowHeaps under leach are subject to an application of asolution of reactants and occasional rain events Heapsmay internally be made up of different ores leading toconsiderable heterogeneity leading to widely varyingflow conditions and therefore levels of saturation Otherphenomena that can influence flow conditions includedecrepitation of the substrate compaction precipitationof salts from the liquid phase and transport of fines (egclay) Compaction can to a certain extent be modelledthrough appropriate use of heterogeneity Decrepitationwould only be an issue where large proportions of thesolid phase are soluble which is not typical for thesekinds of problems addressed here Precipitation is easilymodelled and fines can be dealt with through the use ofappropriate rules
Flow through variably saturated porous media istypically characterised by the Richardsrsquo equation Themixed form of the Richardsrsquo equation is written in termsof two unknown variables moisture content h and thepressure head h where K is the hydraulic conductivity
LhLt
~+K(h)+hzLK(h)
Lz(1)
there are a number of potential models to use to describe
2 Heap leach model computational generic macrosolu-
tion procedure
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 43
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the unsaturated hydraulic conductivity The model mostcommonly employed by the hydrology community andused within in the present work is that of van Genuchten(1980) where the moisture h and hydraulic conductivityK are defined by
h~hresz
hsathres1zjahjneth THORNm hv0
hsat hcent0
( (2)
K~
Ksathhreshsathres
1=2
1 1hhreshsathres
1=m m( )2
(3)
where a and n are material parameters that affect theshape of the soil hydraulic functions and m5121n
The equation for solute transport through porousmaterials has been described by Bear (1972) Thetransport algorithm is coupled with the flow modulethrough the moisture content h and Darcy flux
qxi~k(h)L(hzz)
Lxiwhere z is the elevation head
Modelling this type of flow has presented somethingof a challenge to the computational communitySaturated and unsaturated flows have individually beenwell described but systems containing both saturatedand unsaturated regions offer considerable problemsVarious versions of the classical Richards equation havebeen proposed in the past and used to provide the basisof specific numerical solution procedures A methodoriginally suggested by Celia et al (1990) combined witha transformation and proposed by Pan and Wierenga(1995) has been shown to have the potential to be a fastnumerically robust scheme A computational procedurebased on an extension of the above method into a fullyunstructured context has been implemented for model-ling variably saturated flow in leach systems withvariable material properties and arbitrarily complexthree-dimensional geometries by McBride et al (2005b)and forms the basis of the liquid flow scheme for theheap leach models used in the present work
The production and consumption of species is givenby the reaction module and enters the transportequation as a source term S The continuity equationfor convectivendashdispersive transport of multiple solutes inporous media is given by
L(hCi)
Lt+(hD+Ci)z+(qCi)~Si (4)
where Ci is the concentration of species i in the solutionphase and Si the production or consumption of species iDij is the dispersion coefficient that only becomessignificant in fully saturated flows
Gas phase transportOxygen can be important in any system containingsignificant sulphurous minerals such as many copperores and pyrite containing ores In these leach environ-ments where oxygen is an important reagent a gastransport model will be crucial Although the primaryspecies transported via gas flow is oxygen water vapourcontrolled by condensation and evaporation may alsobe of interest Oxygen mainly enters the heap through
air injection or air convection via its exposed slopes Airflow will also influence the heat balance Air flow withinthe heap is subject to the same range of heterogeneousflow conditions as the liquid phase but in addition mustrespond to liquid flow and saturation There isessentially a one way coupling between liquid and gasphase flow (with liquid flow influencing gas flow but notthe reverse) through the alteration of the voidage owingto changing moisture levels
The basic continuity equation for gas phase flow is
LrgLt
zdiv rgvg
~Sg (5)
where rg is the gas density Sg a source term for gas andvg the gas velocity given by
vg~kinkg(S)
egmg+pgzrgg+z
(6)
with kin is the intrinsic permeability of the porous mediaeg is the volume fraction of the gas phase mg is the gasviscosity and kg(S) is the unsaturated permeability of thegas at liquid saturation (S) related to the liquidunsaturated permeability kl(S) by
kg(S)~1kl(S) (7)
the gas source term combines the effects of thermalgradients the mass of gas displaced by any change involume in the element owing to a change in liquid phasesaturation boundary conditions evaporation and con-densation and mass transfer between gas and liquidphases An equation of the same form as equation (4) isused to transport the species in the gas phase
Heat balanceFactors affecting heat balance in the heap are heatgenerated by chemical reactions the heat of liquid andgas entering the heap external temperature and solarradiation and evaporation and condensation
The heat balance in the heap can be solved using thetemperature conservation equation
L rcpT Lt
zdiv rucpT
~div K+ Teth THORNfrac12 zST (8)
where cp is the specific heat r the density u the velocityvector K the thermal conductivity T the temperatureand ST any heat source incorporating heat of reactionevaporation and condensation raffinate and gas tem-perature and weather effects
A single lsquomixturersquo temperature is calculated for thewhole system with properties dependent on averagethermal properties based on the solid liquid and gasfractions present in each element Heat energy generated(or lost) from all of the implemented chemical reactionsis then converted into a temperature rise
Chemical reactionsMineral reactions are solved by dividing the ore intodiscrete size fractions with characteristic radii andmineral concentrations Solid reaction kinetics aremodelled using a shrinking core reaction to link porediffusion and rate kinetics both being heavily dependenton the particle diameter then solved for each mineralacross a set of size fractions The equation used tocalculate the rate of dissolution of a particular mineral is
Bennett et al Simulation technology to support base metal ore heap leaching
44 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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given by
drm
dt~
3rm
4pr2o
Mi
rorexi
DeffcoAm
3Deffrocoz2(rorm)r2m(1ep)Am
(9)
where ro is the initial particle radius rm the currentmineral radius Am comes from the kinetic rate equationfor the current mineral R is the gas constant T thetemperature in Kelvin Deff the effective rock diffusioncoefficient ep the rock voidage rore the ore density Mi
the molecular weight of the mineral and xi the massfraction of the mineral
The value of Am comes from the general expressionfor the kinetic rate equations such as those produced byPaul et al (1992a b) where the general form is
db
dt~A exp (B=RT) (10)
where b is the fraction of mineral reacted and A and Bare functions of the individual kinetic rate equation
Liquid phase reactions including precipitation aremodelled using individual kinetics for each reaction
Bacteria kineticsIn copper sulphide and pyrite systems bacteria drive theoxidation of ferrous ions to the primary reactant offerric and also oxidise sulphur to form acid There maybe some resident population of bacteria such asacidothiobacillus ferro-oxidans naturally occurring inthe heap but in the case of copper heap leaching it iscommon to inoculate the reactant solution
There are numerous bacteria species that catalysethese reactions so it is difficult to model individualspecies Instead bacteria are modelled as generic ferrousor sulphur oxidisers Each bacteria species can exist inthe liquid phase or attached to mineral surfaces and cantransfer between the two states allowing the bacteria tobuild up a healthy population and spread through theheap when the conditions are conducive The specificmodel implemented in the present work is not dissimilarfrom that of Leahy et al (2005) using ideas originallydrawn from Neuburg et al (1991) and developed byPetersen and Dixon (2003)
Data input and output and usabilityVisual StudioNET technologies can be used to create auser interface that wraps around the core simulation
code to provide an environment that is tailored to therequirements of the particular model This enablesfeatures of the model that do not concern the user tobe hidden and allows the required data input to bebroadly accessible through forms The same approachcan be stretched to govern databases of simulation setsand manage data output which can be in the form ofspreadsheets contour plots and even animationsthrough the use of appropriate visualisation softwareMore details of the user environment design andperformance are described in Gebhardt et al (2005)
For complex 3D geometries building the discretiseddomain or mesh that describes the problem requiresadditional third party mesh generation tools in thepresent work FEMGV (wwwfemsyscouk) was usedfor both this task and the results visualisation
Applications
Column simulationA common practice in testing minerals for heap leachsuitability is column testing Typically these tests arecarried out in a combination of columns from 005 mdiameter and 15 m high to 2 m in diameter and up to6 m high The experimentally measured parameters aretypically the grade of the ore the particle size distribu-tion and the bulk density (equivalently the voidage)Column tests results provide the rate of flow andcontents of the pregnant solution throughout the leachcycle These tests are ideal for parameterising andvalidating the core model as they are performed underwell controlled conditions Typically the model isparameterised using the small scale laboratory testsand validated on data from a 2 m column test Becausethe solution flow is greatly simplified in these cases themain emphasis is on validating the chemical componentsof the model
The example presented here is for a run of minechalcocite ore in a 6 m tall column under ferric (Fe3z)leach Air is pumped in through the base so that there isplentiful oxygen Over the course of the test the ferricsolution is applied on a cycle of 90 days on 30 days off30 days on then a final rest period of 10 days The orecontains 065 copper in the form of chalcocite (Cu2S)2 pyrite with a particle size distribution whose averagediameter is in the order of 10 cm The solution appliedcontains 4 g L21 of ferric and is at pH 08
There has been significant interest in modellingchalocite heap leaching in recent times and so one
3 Copper recovery against time
4 Copper and ferric output from column
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 45
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would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
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ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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Man
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IOM
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mun
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ions
Ltd
made a significant contribution to this problem usingcommercial computational fluid dynamic (CFD) tech-nologies (Davis and Ritchie 1986 Pantelis and Ritchie1992 Anne and Pantelis 1997) Aside from usingmodels to assess the impact of the generation andtransport of heat in heap leach operations (Dixon andHendrix 1993a b Dixon 2000) Dixon and co-workershave also made significant contributions to full processmodels with simplified fluid mechanics Bouffard andDixon (2003) described work on refractory gold oresand Dixon (2003) and Dixon and Petersen (2003)examined chalcocite based ores Recently Leahy et al(2003 2004 2005) have developed models of chalcociteleaching processes involving unsaturated flow chemicalreactions component transport and thermal processesusing the CFX CFD software technology (wwwansyscom) While these and others have made importantcontributions to heap leach modelling the complexity ofthe process and the resulting mathematical modelformulations have so far resulted in limited success inthe development and application of fully comprehensivesimulation tools
The objectives of the work reported here include thedevelopment of a suite of simulation tools to support thecomprehensive computational modelling and processanalysis of heap leach systems as a basis for processdesign and optimisation
Heap leach simulation tool setThe main tools and component models contained withina simulation environment for the comprehensive model-ling and analysis of heap leaching systems are as follows
(i) liquid flow and species transport includingdealing with variably saturated flow throughheterogeneous media
(ii) gas flow and species transport through hetero-geneous media with varying saturation levels
(iii) chemical reactions within and between masstransfer between the gas liquid and solid phasesincluding the dissolution of primary minerals ofinterest gangue reactions precipitation reac-tions regeneration of reagents within the liquidphase partitioning of species between liquidand gas phases eg oxygen and water vapour(evaporationcondensation)
(iv) bacterial catalysis of chemical reactions includ-ing bacterial population growth death andtransport andmultiple bacteria types for cata-lysis of different chemistry and potentially fordifferent temperature regimes
(v) heat transport including heat from chemicalreactions external weather effects and heattransport by movement of gas and liquid phases
(vi) modelling of the water balance in naturalenvironments with high and variable precipita-tion to ensure the efficacy of the arrangementsmade to cope with extreme weather andoperational events
(vii) data input and output and usability covering asuitable user interface for data input datamanagement including management of pastsimulations and data output in the form ofplots of species output in the pregnant leachsolution recovered from the modelled systemplots of mineral reactions and reagent use
against time contour plots showing remainingminerals and solution inventory in space and intime and animations showing system behaviourover time
In the present paper a simulation environment isoutlined to address all the above issues in a coherentfashion and in particular to manage the raw data andinformation associated with all aspects of the processrelevant to its analysis This environment is based onfour main software tools
(i) a CFD simulation software tool ndash in this casethe flow module of the PHYSICA multiphysicssimulation are employed (wwwphysicacouk)
(ii) a CFD modelling support environment toprovide geometry definition mesh generationand results visualisation tools ndash in this workFEMGV (wwwfemsyscouk) has been used
(iii) an interactive simulation toolkit for resolvingmass and material balances in complex flowsheets ndash the tool used here is Bilco (wwwprocessengcom)
A user environment to encapsulate the informationrequired for data rationalisation structuring andstorage in a database simulation set-up managementand results analysis ndash this is achieved here in theHeapNET environment (wwwprocessengcom) whichitself is built within Visual StudioNET using SQL as thecore database technology and employing Excel as aresults analysis tool
A representation of the heap leaching simulationtechnology is shown in Fig 1 HeapNET manages allthe communication with the other tools used within theenvironment Importantly it provides the user withopportunities to specify simulation scenarios to controlwhich simulation results are saved and then to dialoguewith the visualisation tool to obtain the graphical plots(and movies) The user is only aware of using theHeapNET user environment this generates a variety ofscripts dynamically to call the mesh generation visua-lisation and solver tools to build run and explore theresults of a simulation series for all applications but thefull 3D simulations (although this is currently underdevelopment)
The simulation tools currently consist of the following
(i) a 1D simulation of laboratory columns this is akey tool both with respect to parameterising aspecific ore with respect to reaction rates andalso as a vehicle for validation
1 Overview of HeapNET heap leach simulation technology
Bennett et al Simulation technology to support base metal ore heap leaching
42 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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Man
ey P
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IOM
Com
mun
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ions
Ltd
(ii) a 2D slice simulation of full heaps this is wherea vertical plane through the heap using depthaveraged properties is used to examine a varietyof phenomena particularly the couplingbetween the liquid and gas flows and theemerging thermal distributions
(iii) the water balance model that contains a reduced3D model of the heap here the focus of the toolis on the evaluation of the solution distributionnot only through the heap but also in thecomplete circuit particularly to examine theimpact of operational strategies on pondvolumes against available capacity Scenariossuch as 100 year weather events andor draindown owing to operational malfunction are ofspecial interest to process operations
(iv) a full 3D model of the heap which captures thefull behaviour over its lifetime not only doesthis enable an ongoing audit of performance ofa heap and accurate prediction of its futureperformance but also enable the evaluation of anumber of future operational strategies for themost beneficial options with respect to anumber of possibly conflicting criteria
Each of the above tools has a specific role Obviouslytheir use is influenced by both the volume of data thatthey produce versus that which is required for a specificpurpose and the time taken for the computationsTypically
(i) the 1D simulation of laboratory column experi-ments involving a 150 day operation require2 min of elapsed time on a current generationPC
(ii) a 2D slice simulation involving three lifts over450 days operation could take on the order ofan hour with the same PC
(iii) the water balance model with the reduceddimension simplified heap leach model wouldtake about a minute for a dayrsquos worth ofoperation
(iv) the full 3D model with 250 K cells takes 4 hof simulation for each monthrsquos worth ofoperational time
Underlying computational modellingapproachThe computational modelling approach requires thesolution of coupled liquid and gas flows through porousmedia reactions between the phases and with thehost solid media resulting in the exchange of massand the generation or loss of heat These phenomenaare best modelled these days by CFD simulation toolsthat facilitate the modelling of flow based transportprocesses
The approach adopted here exploits the CFD modulewithin the multiphysics modelling software environmentPHYSICA which employs state of the art finite volumemethods on an unstructured mesh in one- two- andthree-dimensions and has the added benefit of runningscalably in parallel should simulation run times becomesignificant (wwwphysicacouk) Figure 2 illustrates thegeneric macrosolution procedure for the heap leachmodel
In the case of gold heap leaching by cyanide theprincipal reactions are cyanide with gold silver copperand gangue minerals There are no substantial thermaleffects and owing to the low oxygen requirements thesystem is not dependent on gas flow In this case theheat transport gas flow and bacteria tools are notrequired for an adequate gold heap model
In the case of copper sulphide ore leaching is highlydependent on bacterial activity to catalyse the dissolutionof copper through the generation of ferric (Fe3z) which isthe dominant reagent from ferrous ions (Fe2z) andoxygenMany of the reactions are exothermic and thermaleffects can be significant In this case a comprehensivemodel will depend on all of the above tools as oxygen andtherefore gas flow are of crucial importance
The representation of the component phenomenacomprising the phenomenological physical model andthe approach to their solution is briefly summarised inthe following sections However there are more detaileddiscussions of the model formulations and solutionstrategies described in Bennett et al (2003a b) Crosset al (2005) and McBride et al (2005a b)
Variably saturated liquid flowHeaps under leach are subject to an application of asolution of reactants and occasional rain events Heapsmay internally be made up of different ores leading toconsiderable heterogeneity leading to widely varyingflow conditions and therefore levels of saturation Otherphenomena that can influence flow conditions includedecrepitation of the substrate compaction precipitationof salts from the liquid phase and transport of fines (egclay) Compaction can to a certain extent be modelledthrough appropriate use of heterogeneity Decrepitationwould only be an issue where large proportions of thesolid phase are soluble which is not typical for thesekinds of problems addressed here Precipitation is easilymodelled and fines can be dealt with through the use ofappropriate rules
Flow through variably saturated porous media istypically characterised by the Richardsrsquo equation Themixed form of the Richardsrsquo equation is written in termsof two unknown variables moisture content h and thepressure head h where K is the hydraulic conductivity
LhLt
~+K(h)+hzLK(h)
Lz(1)
there are a number of potential models to use to describe
2 Heap leach model computational generic macrosolu-
tion procedure
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 43
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Ltd
the unsaturated hydraulic conductivity The model mostcommonly employed by the hydrology community andused within in the present work is that of van Genuchten(1980) where the moisture h and hydraulic conductivityK are defined by
h~hresz
hsathres1zjahjneth THORNm hv0
hsat hcent0
( (2)
K~
Ksathhreshsathres
1=2
1 1hhreshsathres
1=m m( )2
(3)
where a and n are material parameters that affect theshape of the soil hydraulic functions and m5121n
The equation for solute transport through porousmaterials has been described by Bear (1972) Thetransport algorithm is coupled with the flow modulethrough the moisture content h and Darcy flux
qxi~k(h)L(hzz)
Lxiwhere z is the elevation head
Modelling this type of flow has presented somethingof a challenge to the computational communitySaturated and unsaturated flows have individually beenwell described but systems containing both saturatedand unsaturated regions offer considerable problemsVarious versions of the classical Richards equation havebeen proposed in the past and used to provide the basisof specific numerical solution procedures A methodoriginally suggested by Celia et al (1990) combined witha transformation and proposed by Pan and Wierenga(1995) has been shown to have the potential to be a fastnumerically robust scheme A computational procedurebased on an extension of the above method into a fullyunstructured context has been implemented for model-ling variably saturated flow in leach systems withvariable material properties and arbitrarily complexthree-dimensional geometries by McBride et al (2005b)and forms the basis of the liquid flow scheme for theheap leach models used in the present work
The production and consumption of species is givenby the reaction module and enters the transportequation as a source term S The continuity equationfor convectivendashdispersive transport of multiple solutes inporous media is given by
L(hCi)
Lt+(hD+Ci)z+(qCi)~Si (4)
where Ci is the concentration of species i in the solutionphase and Si the production or consumption of species iDij is the dispersion coefficient that only becomessignificant in fully saturated flows
Gas phase transportOxygen can be important in any system containingsignificant sulphurous minerals such as many copperores and pyrite containing ores In these leach environ-ments where oxygen is an important reagent a gastransport model will be crucial Although the primaryspecies transported via gas flow is oxygen water vapourcontrolled by condensation and evaporation may alsobe of interest Oxygen mainly enters the heap through
air injection or air convection via its exposed slopes Airflow will also influence the heat balance Air flow withinthe heap is subject to the same range of heterogeneousflow conditions as the liquid phase but in addition mustrespond to liquid flow and saturation There isessentially a one way coupling between liquid and gasphase flow (with liquid flow influencing gas flow but notthe reverse) through the alteration of the voidage owingto changing moisture levels
The basic continuity equation for gas phase flow is
LrgLt
zdiv rgvg
~Sg (5)
where rg is the gas density Sg a source term for gas andvg the gas velocity given by
vg~kinkg(S)
egmg+pgzrgg+z
(6)
with kin is the intrinsic permeability of the porous mediaeg is the volume fraction of the gas phase mg is the gasviscosity and kg(S) is the unsaturated permeability of thegas at liquid saturation (S) related to the liquidunsaturated permeability kl(S) by
kg(S)~1kl(S) (7)
the gas source term combines the effects of thermalgradients the mass of gas displaced by any change involume in the element owing to a change in liquid phasesaturation boundary conditions evaporation and con-densation and mass transfer between gas and liquidphases An equation of the same form as equation (4) isused to transport the species in the gas phase
Heat balanceFactors affecting heat balance in the heap are heatgenerated by chemical reactions the heat of liquid andgas entering the heap external temperature and solarradiation and evaporation and condensation
The heat balance in the heap can be solved using thetemperature conservation equation
L rcpT Lt
zdiv rucpT
~div K+ Teth THORNfrac12 zST (8)
where cp is the specific heat r the density u the velocityvector K the thermal conductivity T the temperatureand ST any heat source incorporating heat of reactionevaporation and condensation raffinate and gas tem-perature and weather effects
A single lsquomixturersquo temperature is calculated for thewhole system with properties dependent on averagethermal properties based on the solid liquid and gasfractions present in each element Heat energy generated(or lost) from all of the implemented chemical reactionsis then converted into a temperature rise
Chemical reactionsMineral reactions are solved by dividing the ore intodiscrete size fractions with characteristic radii andmineral concentrations Solid reaction kinetics aremodelled using a shrinking core reaction to link porediffusion and rate kinetics both being heavily dependenton the particle diameter then solved for each mineralacross a set of size fractions The equation used tocalculate the rate of dissolution of a particular mineral is
Bennett et al Simulation technology to support base metal ore heap leaching
44 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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lishe
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ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
given by
drm
dt~
3rm
4pr2o
Mi
rorexi
DeffcoAm
3Deffrocoz2(rorm)r2m(1ep)Am
(9)
where ro is the initial particle radius rm the currentmineral radius Am comes from the kinetic rate equationfor the current mineral R is the gas constant T thetemperature in Kelvin Deff the effective rock diffusioncoefficient ep the rock voidage rore the ore density Mi
the molecular weight of the mineral and xi the massfraction of the mineral
The value of Am comes from the general expressionfor the kinetic rate equations such as those produced byPaul et al (1992a b) where the general form is
db
dt~A exp (B=RT) (10)
where b is the fraction of mineral reacted and A and Bare functions of the individual kinetic rate equation
Liquid phase reactions including precipitation aremodelled using individual kinetics for each reaction
Bacteria kineticsIn copper sulphide and pyrite systems bacteria drive theoxidation of ferrous ions to the primary reactant offerric and also oxidise sulphur to form acid There maybe some resident population of bacteria such asacidothiobacillus ferro-oxidans naturally occurring inthe heap but in the case of copper heap leaching it iscommon to inoculate the reactant solution
There are numerous bacteria species that catalysethese reactions so it is difficult to model individualspecies Instead bacteria are modelled as generic ferrousor sulphur oxidisers Each bacteria species can exist inthe liquid phase or attached to mineral surfaces and cantransfer between the two states allowing the bacteria tobuild up a healthy population and spread through theheap when the conditions are conducive The specificmodel implemented in the present work is not dissimilarfrom that of Leahy et al (2005) using ideas originallydrawn from Neuburg et al (1991) and developed byPetersen and Dixon (2003)
Data input and output and usabilityVisual StudioNET technologies can be used to create auser interface that wraps around the core simulation
code to provide an environment that is tailored to therequirements of the particular model This enablesfeatures of the model that do not concern the user tobe hidden and allows the required data input to bebroadly accessible through forms The same approachcan be stretched to govern databases of simulation setsand manage data output which can be in the form ofspreadsheets contour plots and even animationsthrough the use of appropriate visualisation softwareMore details of the user environment design andperformance are described in Gebhardt et al (2005)
For complex 3D geometries building the discretiseddomain or mesh that describes the problem requiresadditional third party mesh generation tools in thepresent work FEMGV (wwwfemsyscouk) was usedfor both this task and the results visualisation
Applications
Column simulationA common practice in testing minerals for heap leachsuitability is column testing Typically these tests arecarried out in a combination of columns from 005 mdiameter and 15 m high to 2 m in diameter and up to6 m high The experimentally measured parameters aretypically the grade of the ore the particle size distribu-tion and the bulk density (equivalently the voidage)Column tests results provide the rate of flow andcontents of the pregnant solution throughout the leachcycle These tests are ideal for parameterising andvalidating the core model as they are performed underwell controlled conditions Typically the model isparameterised using the small scale laboratory testsand validated on data from a 2 m column test Becausethe solution flow is greatly simplified in these cases themain emphasis is on validating the chemical componentsof the model
The example presented here is for a run of minechalcocite ore in a 6 m tall column under ferric (Fe3z)leach Air is pumped in through the base so that there isplentiful oxygen Over the course of the test the ferricsolution is applied on a cycle of 90 days on 30 days off30 days on then a final rest period of 10 days The orecontains 065 copper in the form of chalcocite (Cu2S)2 pyrite with a particle size distribution whose averagediameter is in the order of 10 cm The solution appliedcontains 4 g L21 of ferric and is at pH 08
There has been significant interest in modellingchalocite heap leaching in recent times and so one
3 Copper recovery against time
4 Copper and ferric output from column
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 45
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would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
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Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
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ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
(ii) a 2D slice simulation of full heaps this is wherea vertical plane through the heap using depthaveraged properties is used to examine a varietyof phenomena particularly the couplingbetween the liquid and gas flows and theemerging thermal distributions
(iii) the water balance model that contains a reduced3D model of the heap here the focus of the toolis on the evaluation of the solution distributionnot only through the heap but also in thecomplete circuit particularly to examine theimpact of operational strategies on pondvolumes against available capacity Scenariossuch as 100 year weather events andor draindown owing to operational malfunction are ofspecial interest to process operations
(iv) a full 3D model of the heap which captures thefull behaviour over its lifetime not only doesthis enable an ongoing audit of performance ofa heap and accurate prediction of its futureperformance but also enable the evaluation of anumber of future operational strategies for themost beneficial options with respect to anumber of possibly conflicting criteria
Each of the above tools has a specific role Obviouslytheir use is influenced by both the volume of data thatthey produce versus that which is required for a specificpurpose and the time taken for the computationsTypically
(i) the 1D simulation of laboratory column experi-ments involving a 150 day operation require2 min of elapsed time on a current generationPC
(ii) a 2D slice simulation involving three lifts over450 days operation could take on the order ofan hour with the same PC
(iii) the water balance model with the reduceddimension simplified heap leach model wouldtake about a minute for a dayrsquos worth ofoperation
(iv) the full 3D model with 250 K cells takes 4 hof simulation for each monthrsquos worth ofoperational time
Underlying computational modellingapproachThe computational modelling approach requires thesolution of coupled liquid and gas flows through porousmedia reactions between the phases and with thehost solid media resulting in the exchange of massand the generation or loss of heat These phenomenaare best modelled these days by CFD simulation toolsthat facilitate the modelling of flow based transportprocesses
The approach adopted here exploits the CFD modulewithin the multiphysics modelling software environmentPHYSICA which employs state of the art finite volumemethods on an unstructured mesh in one- two- andthree-dimensions and has the added benefit of runningscalably in parallel should simulation run times becomesignificant (wwwphysicacouk) Figure 2 illustrates thegeneric macrosolution procedure for the heap leachmodel
In the case of gold heap leaching by cyanide theprincipal reactions are cyanide with gold silver copperand gangue minerals There are no substantial thermaleffects and owing to the low oxygen requirements thesystem is not dependent on gas flow In this case theheat transport gas flow and bacteria tools are notrequired for an adequate gold heap model
In the case of copper sulphide ore leaching is highlydependent on bacterial activity to catalyse the dissolutionof copper through the generation of ferric (Fe3z) which isthe dominant reagent from ferrous ions (Fe2z) andoxygenMany of the reactions are exothermic and thermaleffects can be significant In this case a comprehensivemodel will depend on all of the above tools as oxygen andtherefore gas flow are of crucial importance
The representation of the component phenomenacomprising the phenomenological physical model andthe approach to their solution is briefly summarised inthe following sections However there are more detaileddiscussions of the model formulations and solutionstrategies described in Bennett et al (2003a b) Crosset al (2005) and McBride et al (2005a b)
Variably saturated liquid flowHeaps under leach are subject to an application of asolution of reactants and occasional rain events Heapsmay internally be made up of different ores leading toconsiderable heterogeneity leading to widely varyingflow conditions and therefore levels of saturation Otherphenomena that can influence flow conditions includedecrepitation of the substrate compaction precipitationof salts from the liquid phase and transport of fines (egclay) Compaction can to a certain extent be modelledthrough appropriate use of heterogeneity Decrepitationwould only be an issue where large proportions of thesolid phase are soluble which is not typical for thesekinds of problems addressed here Precipitation is easilymodelled and fines can be dealt with through the use ofappropriate rules
Flow through variably saturated porous media istypically characterised by the Richardsrsquo equation Themixed form of the Richardsrsquo equation is written in termsof two unknown variables moisture content h and thepressure head h where K is the hydraulic conductivity
LhLt
~+K(h)+hzLK(h)
Lz(1)
there are a number of potential models to use to describe
2 Heap leach model computational generic macrosolu-
tion procedure
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 43
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
the unsaturated hydraulic conductivity The model mostcommonly employed by the hydrology community andused within in the present work is that of van Genuchten(1980) where the moisture h and hydraulic conductivityK are defined by
h~hresz
hsathres1zjahjneth THORNm hv0
hsat hcent0
( (2)
K~
Ksathhreshsathres
1=2
1 1hhreshsathres
1=m m( )2
(3)
where a and n are material parameters that affect theshape of the soil hydraulic functions and m5121n
The equation for solute transport through porousmaterials has been described by Bear (1972) Thetransport algorithm is coupled with the flow modulethrough the moisture content h and Darcy flux
qxi~k(h)L(hzz)
Lxiwhere z is the elevation head
Modelling this type of flow has presented somethingof a challenge to the computational communitySaturated and unsaturated flows have individually beenwell described but systems containing both saturatedand unsaturated regions offer considerable problemsVarious versions of the classical Richards equation havebeen proposed in the past and used to provide the basisof specific numerical solution procedures A methodoriginally suggested by Celia et al (1990) combined witha transformation and proposed by Pan and Wierenga(1995) has been shown to have the potential to be a fastnumerically robust scheme A computational procedurebased on an extension of the above method into a fullyunstructured context has been implemented for model-ling variably saturated flow in leach systems withvariable material properties and arbitrarily complexthree-dimensional geometries by McBride et al (2005b)and forms the basis of the liquid flow scheme for theheap leach models used in the present work
The production and consumption of species is givenby the reaction module and enters the transportequation as a source term S The continuity equationfor convectivendashdispersive transport of multiple solutes inporous media is given by
L(hCi)
Lt+(hD+Ci)z+(qCi)~Si (4)
where Ci is the concentration of species i in the solutionphase and Si the production or consumption of species iDij is the dispersion coefficient that only becomessignificant in fully saturated flows
Gas phase transportOxygen can be important in any system containingsignificant sulphurous minerals such as many copperores and pyrite containing ores In these leach environ-ments where oxygen is an important reagent a gastransport model will be crucial Although the primaryspecies transported via gas flow is oxygen water vapourcontrolled by condensation and evaporation may alsobe of interest Oxygen mainly enters the heap through
air injection or air convection via its exposed slopes Airflow will also influence the heat balance Air flow withinthe heap is subject to the same range of heterogeneousflow conditions as the liquid phase but in addition mustrespond to liquid flow and saturation There isessentially a one way coupling between liquid and gasphase flow (with liquid flow influencing gas flow but notthe reverse) through the alteration of the voidage owingto changing moisture levels
The basic continuity equation for gas phase flow is
LrgLt
zdiv rgvg
~Sg (5)
where rg is the gas density Sg a source term for gas andvg the gas velocity given by
vg~kinkg(S)
egmg+pgzrgg+z
(6)
with kin is the intrinsic permeability of the porous mediaeg is the volume fraction of the gas phase mg is the gasviscosity and kg(S) is the unsaturated permeability of thegas at liquid saturation (S) related to the liquidunsaturated permeability kl(S) by
kg(S)~1kl(S) (7)
the gas source term combines the effects of thermalgradients the mass of gas displaced by any change involume in the element owing to a change in liquid phasesaturation boundary conditions evaporation and con-densation and mass transfer between gas and liquidphases An equation of the same form as equation (4) isused to transport the species in the gas phase
Heat balanceFactors affecting heat balance in the heap are heatgenerated by chemical reactions the heat of liquid andgas entering the heap external temperature and solarradiation and evaporation and condensation
The heat balance in the heap can be solved using thetemperature conservation equation
L rcpT Lt
zdiv rucpT
~div K+ Teth THORNfrac12 zST (8)
where cp is the specific heat r the density u the velocityvector K the thermal conductivity T the temperatureand ST any heat source incorporating heat of reactionevaporation and condensation raffinate and gas tem-perature and weather effects
A single lsquomixturersquo temperature is calculated for thewhole system with properties dependent on averagethermal properties based on the solid liquid and gasfractions present in each element Heat energy generated(or lost) from all of the implemented chemical reactionsis then converted into a temperature rise
Chemical reactionsMineral reactions are solved by dividing the ore intodiscrete size fractions with characteristic radii andmineral concentrations Solid reaction kinetics aremodelled using a shrinking core reaction to link porediffusion and rate kinetics both being heavily dependenton the particle diameter then solved for each mineralacross a set of size fractions The equation used tocalculate the rate of dissolution of a particular mineral is
Bennett et al Simulation technology to support base metal ore heap leaching
44 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
given by
drm
dt~
3rm
4pr2o
Mi
rorexi
DeffcoAm
3Deffrocoz2(rorm)r2m(1ep)Am
(9)
where ro is the initial particle radius rm the currentmineral radius Am comes from the kinetic rate equationfor the current mineral R is the gas constant T thetemperature in Kelvin Deff the effective rock diffusioncoefficient ep the rock voidage rore the ore density Mi
the molecular weight of the mineral and xi the massfraction of the mineral
The value of Am comes from the general expressionfor the kinetic rate equations such as those produced byPaul et al (1992a b) where the general form is
db
dt~A exp (B=RT) (10)
where b is the fraction of mineral reacted and A and Bare functions of the individual kinetic rate equation
Liquid phase reactions including precipitation aremodelled using individual kinetics for each reaction
Bacteria kineticsIn copper sulphide and pyrite systems bacteria drive theoxidation of ferrous ions to the primary reactant offerric and also oxidise sulphur to form acid There maybe some resident population of bacteria such asacidothiobacillus ferro-oxidans naturally occurring inthe heap but in the case of copper heap leaching it iscommon to inoculate the reactant solution
There are numerous bacteria species that catalysethese reactions so it is difficult to model individualspecies Instead bacteria are modelled as generic ferrousor sulphur oxidisers Each bacteria species can exist inthe liquid phase or attached to mineral surfaces and cantransfer between the two states allowing the bacteria tobuild up a healthy population and spread through theheap when the conditions are conducive The specificmodel implemented in the present work is not dissimilarfrom that of Leahy et al (2005) using ideas originallydrawn from Neuburg et al (1991) and developed byPetersen and Dixon (2003)
Data input and output and usabilityVisual StudioNET technologies can be used to create auser interface that wraps around the core simulation
code to provide an environment that is tailored to therequirements of the particular model This enablesfeatures of the model that do not concern the user tobe hidden and allows the required data input to bebroadly accessible through forms The same approachcan be stretched to govern databases of simulation setsand manage data output which can be in the form ofspreadsheets contour plots and even animationsthrough the use of appropriate visualisation softwareMore details of the user environment design andperformance are described in Gebhardt et al (2005)
For complex 3D geometries building the discretiseddomain or mesh that describes the problem requiresadditional third party mesh generation tools in thepresent work FEMGV (wwwfemsyscouk) was usedfor both this task and the results visualisation
Applications
Column simulationA common practice in testing minerals for heap leachsuitability is column testing Typically these tests arecarried out in a combination of columns from 005 mdiameter and 15 m high to 2 m in diameter and up to6 m high The experimentally measured parameters aretypically the grade of the ore the particle size distribu-tion and the bulk density (equivalently the voidage)Column tests results provide the rate of flow andcontents of the pregnant solution throughout the leachcycle These tests are ideal for parameterising andvalidating the core model as they are performed underwell controlled conditions Typically the model isparameterised using the small scale laboratory testsand validated on data from a 2 m column test Becausethe solution flow is greatly simplified in these cases themain emphasis is on validating the chemical componentsof the model
The example presented here is for a run of minechalcocite ore in a 6 m tall column under ferric (Fe3z)leach Air is pumped in through the base so that there isplentiful oxygen Over the course of the test the ferricsolution is applied on a cycle of 90 days on 30 days off30 days on then a final rest period of 10 days The orecontains 065 copper in the form of chalcocite (Cu2S)2 pyrite with a particle size distribution whose averagediameter is in the order of 10 cm The solution appliedcontains 4 g L21 of ferric and is at pH 08
There has been significant interest in modellingchalocite heap leaching in recent times and so one
3 Copper recovery against time
4 Copper and ferric output from column
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 45
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
the unsaturated hydraulic conductivity The model mostcommonly employed by the hydrology community andused within in the present work is that of van Genuchten(1980) where the moisture h and hydraulic conductivityK are defined by
h~hresz
hsathres1zjahjneth THORNm hv0
hsat hcent0
( (2)
K~
Ksathhreshsathres
1=2
1 1hhreshsathres
1=m m( )2
(3)
where a and n are material parameters that affect theshape of the soil hydraulic functions and m5121n
The equation for solute transport through porousmaterials has been described by Bear (1972) Thetransport algorithm is coupled with the flow modulethrough the moisture content h and Darcy flux
qxi~k(h)L(hzz)
Lxiwhere z is the elevation head
Modelling this type of flow has presented somethingof a challenge to the computational communitySaturated and unsaturated flows have individually beenwell described but systems containing both saturatedand unsaturated regions offer considerable problemsVarious versions of the classical Richards equation havebeen proposed in the past and used to provide the basisof specific numerical solution procedures A methodoriginally suggested by Celia et al (1990) combined witha transformation and proposed by Pan and Wierenga(1995) has been shown to have the potential to be a fastnumerically robust scheme A computational procedurebased on an extension of the above method into a fullyunstructured context has been implemented for model-ling variably saturated flow in leach systems withvariable material properties and arbitrarily complexthree-dimensional geometries by McBride et al (2005b)and forms the basis of the liquid flow scheme for theheap leach models used in the present work
The production and consumption of species is givenby the reaction module and enters the transportequation as a source term S The continuity equationfor convectivendashdispersive transport of multiple solutes inporous media is given by
L(hCi)
Lt+(hD+Ci)z+(qCi)~Si (4)
where Ci is the concentration of species i in the solutionphase and Si the production or consumption of species iDij is the dispersion coefficient that only becomessignificant in fully saturated flows
Gas phase transportOxygen can be important in any system containingsignificant sulphurous minerals such as many copperores and pyrite containing ores In these leach environ-ments where oxygen is an important reagent a gastransport model will be crucial Although the primaryspecies transported via gas flow is oxygen water vapourcontrolled by condensation and evaporation may alsobe of interest Oxygen mainly enters the heap through
air injection or air convection via its exposed slopes Airflow will also influence the heat balance Air flow withinthe heap is subject to the same range of heterogeneousflow conditions as the liquid phase but in addition mustrespond to liquid flow and saturation There isessentially a one way coupling between liquid and gasphase flow (with liquid flow influencing gas flow but notthe reverse) through the alteration of the voidage owingto changing moisture levels
The basic continuity equation for gas phase flow is
LrgLt
zdiv rgvg
~Sg (5)
where rg is the gas density Sg a source term for gas andvg the gas velocity given by
vg~kinkg(S)
egmg+pgzrgg+z
(6)
with kin is the intrinsic permeability of the porous mediaeg is the volume fraction of the gas phase mg is the gasviscosity and kg(S) is the unsaturated permeability of thegas at liquid saturation (S) related to the liquidunsaturated permeability kl(S) by
kg(S)~1kl(S) (7)
the gas source term combines the effects of thermalgradients the mass of gas displaced by any change involume in the element owing to a change in liquid phasesaturation boundary conditions evaporation and con-densation and mass transfer between gas and liquidphases An equation of the same form as equation (4) isused to transport the species in the gas phase
Heat balanceFactors affecting heat balance in the heap are heatgenerated by chemical reactions the heat of liquid andgas entering the heap external temperature and solarradiation and evaporation and condensation
The heat balance in the heap can be solved using thetemperature conservation equation
L rcpT Lt
zdiv rucpT
~div K+ Teth THORNfrac12 zST (8)
where cp is the specific heat r the density u the velocityvector K the thermal conductivity T the temperatureand ST any heat source incorporating heat of reactionevaporation and condensation raffinate and gas tem-perature and weather effects
A single lsquomixturersquo temperature is calculated for thewhole system with properties dependent on averagethermal properties based on the solid liquid and gasfractions present in each element Heat energy generated(or lost) from all of the implemented chemical reactionsis then converted into a temperature rise
Chemical reactionsMineral reactions are solved by dividing the ore intodiscrete size fractions with characteristic radii andmineral concentrations Solid reaction kinetics aremodelled using a shrinking core reaction to link porediffusion and rate kinetics both being heavily dependenton the particle diameter then solved for each mineralacross a set of size fractions The equation used tocalculate the rate of dissolution of a particular mineral is
Bennett et al Simulation technology to support base metal ore heap leaching
44 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
given by
drm
dt~
3rm
4pr2o
Mi
rorexi
DeffcoAm
3Deffrocoz2(rorm)r2m(1ep)Am
(9)
where ro is the initial particle radius rm the currentmineral radius Am comes from the kinetic rate equationfor the current mineral R is the gas constant T thetemperature in Kelvin Deff the effective rock diffusioncoefficient ep the rock voidage rore the ore density Mi
the molecular weight of the mineral and xi the massfraction of the mineral
The value of Am comes from the general expressionfor the kinetic rate equations such as those produced byPaul et al (1992a b) where the general form is
db
dt~A exp (B=RT) (10)
where b is the fraction of mineral reacted and A and Bare functions of the individual kinetic rate equation
Liquid phase reactions including precipitation aremodelled using individual kinetics for each reaction
Bacteria kineticsIn copper sulphide and pyrite systems bacteria drive theoxidation of ferrous ions to the primary reactant offerric and also oxidise sulphur to form acid There maybe some resident population of bacteria such asacidothiobacillus ferro-oxidans naturally occurring inthe heap but in the case of copper heap leaching it iscommon to inoculate the reactant solution
There are numerous bacteria species that catalysethese reactions so it is difficult to model individualspecies Instead bacteria are modelled as generic ferrousor sulphur oxidisers Each bacteria species can exist inthe liquid phase or attached to mineral surfaces and cantransfer between the two states allowing the bacteria tobuild up a healthy population and spread through theheap when the conditions are conducive The specificmodel implemented in the present work is not dissimilarfrom that of Leahy et al (2005) using ideas originallydrawn from Neuburg et al (1991) and developed byPetersen and Dixon (2003)
Data input and output and usabilityVisual StudioNET technologies can be used to create auser interface that wraps around the core simulation
code to provide an environment that is tailored to therequirements of the particular model This enablesfeatures of the model that do not concern the user tobe hidden and allows the required data input to bebroadly accessible through forms The same approachcan be stretched to govern databases of simulation setsand manage data output which can be in the form ofspreadsheets contour plots and even animationsthrough the use of appropriate visualisation softwareMore details of the user environment design andperformance are described in Gebhardt et al (2005)
For complex 3D geometries building the discretiseddomain or mesh that describes the problem requiresadditional third party mesh generation tools in thepresent work FEMGV (wwwfemsyscouk) was usedfor both this task and the results visualisation
Applications
Column simulationA common practice in testing minerals for heap leachsuitability is column testing Typically these tests arecarried out in a combination of columns from 005 mdiameter and 15 m high to 2 m in diameter and up to6 m high The experimentally measured parameters aretypically the grade of the ore the particle size distribu-tion and the bulk density (equivalently the voidage)Column tests results provide the rate of flow andcontents of the pregnant solution throughout the leachcycle These tests are ideal for parameterising andvalidating the core model as they are performed underwell controlled conditions Typically the model isparameterised using the small scale laboratory testsand validated on data from a 2 m column test Becausethe solution flow is greatly simplified in these cases themain emphasis is on validating the chemical componentsof the model
The example presented here is for a run of minechalcocite ore in a 6 m tall column under ferric (Fe3z)leach Air is pumped in through the base so that there isplentiful oxygen Over the course of the test the ferricsolution is applied on a cycle of 90 days on 30 days off30 days on then a final rest period of 10 days The orecontains 065 copper in the form of chalcocite (Cu2S)2 pyrite with a particle size distribution whose averagediameter is in the order of 10 cm The solution appliedcontains 4 g L21 of ferric and is at pH 08
There has been significant interest in modellingchalocite heap leaching in recent times and so one
3 Copper recovery against time
4 Copper and ferric output from column
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 45
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
given by
drm
dt~
3rm
4pr2o
Mi
rorexi
DeffcoAm
3Deffrocoz2(rorm)r2m(1ep)Am
(9)
where ro is the initial particle radius rm the currentmineral radius Am comes from the kinetic rate equationfor the current mineral R is the gas constant T thetemperature in Kelvin Deff the effective rock diffusioncoefficient ep the rock voidage rore the ore density Mi
the molecular weight of the mineral and xi the massfraction of the mineral
The value of Am comes from the general expressionfor the kinetic rate equations such as those produced byPaul et al (1992a b) where the general form is
db
dt~A exp (B=RT) (10)
where b is the fraction of mineral reacted and A and Bare functions of the individual kinetic rate equation
Liquid phase reactions including precipitation aremodelled using individual kinetics for each reaction
Bacteria kineticsIn copper sulphide and pyrite systems bacteria drive theoxidation of ferrous ions to the primary reactant offerric and also oxidise sulphur to form acid There maybe some resident population of bacteria such asacidothiobacillus ferro-oxidans naturally occurring inthe heap but in the case of copper heap leaching it iscommon to inoculate the reactant solution
There are numerous bacteria species that catalysethese reactions so it is difficult to model individualspecies Instead bacteria are modelled as generic ferrousor sulphur oxidisers Each bacteria species can exist inthe liquid phase or attached to mineral surfaces and cantransfer between the two states allowing the bacteria tobuild up a healthy population and spread through theheap when the conditions are conducive The specificmodel implemented in the present work is not dissimilarfrom that of Leahy et al (2005) using ideas originallydrawn from Neuburg et al (1991) and developed byPetersen and Dixon (2003)
Data input and output and usabilityVisual StudioNET technologies can be used to create auser interface that wraps around the core simulation
code to provide an environment that is tailored to therequirements of the particular model This enablesfeatures of the model that do not concern the user tobe hidden and allows the required data input to bebroadly accessible through forms The same approachcan be stretched to govern databases of simulation setsand manage data output which can be in the form ofspreadsheets contour plots and even animationsthrough the use of appropriate visualisation softwareMore details of the user environment design andperformance are described in Gebhardt et al (2005)
For complex 3D geometries building the discretiseddomain or mesh that describes the problem requiresadditional third party mesh generation tools in thepresent work FEMGV (wwwfemsyscouk) was usedfor both this task and the results visualisation
Applications
Column simulationA common practice in testing minerals for heap leachsuitability is column testing Typically these tests arecarried out in a combination of columns from 005 mdiameter and 15 m high to 2 m in diameter and up to6 m high The experimentally measured parameters aretypically the grade of the ore the particle size distribu-tion and the bulk density (equivalently the voidage)Column tests results provide the rate of flow andcontents of the pregnant solution throughout the leachcycle These tests are ideal for parameterising andvalidating the core model as they are performed underwell controlled conditions Typically the model isparameterised using the small scale laboratory testsand validated on data from a 2 m column test Becausethe solution flow is greatly simplified in these cases themain emphasis is on validating the chemical componentsof the model
The example presented here is for a run of minechalcocite ore in a 6 m tall column under ferric (Fe3z)leach Air is pumped in through the base so that there isplentiful oxygen Over the course of the test the ferricsolution is applied on a cycle of 90 days on 30 days off30 days on then a final rest period of 10 days The orecontains 065 copper in the form of chalcocite (Cu2S)2 pyrite with a particle size distribution whose averagediameter is in the order of 10 cm The solution appliedcontains 4 g L21 of ferric and is at pH 08
There has been significant interest in modellingchalocite heap leaching in recent times and so one
3 Copper recovery against time
4 Copper and ferric output from column
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 45
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
would expect to see a good comparison between thepredicted and measured overall recovery and indeedFig 3 shows just such a match However more difficultto match is the daily recovery and composition of thepregnant solution leaving the column Figure 4 showsthat both the copper and the ferric in the pregnant leachsolution leaving the column are well matched althoughthere is some initial overestimation of copper recovery inthe first 20 days
Flow patterns in leaching ore dumped againstslope 2D slice simulationsAn example of using the 2D slice version of the model isfor two similar materials stacked against a slope asshown in Fig 5 The stack is 10 m high and 10 m acrossat the base The ore is basically the same run of minematerial as used in the previous example with thematerial in area 1 with a solid fraction of 65 and inarea 2 a solid fraction of 59 In addition the saturatedconductivity of area 1 is 00073 m s21 whereas in area 2it is 001 m s21 These values are illustrative of what canhappen with compression of the inner stack owing to theweight of the outer stack and settling through a leachcycle Solution is applied uniformly over the top face atan irrigation rate of 161026 m s21
The effect of having two slightly dissimilar materialsnext to each other is to produce a preferential flow pathat the boundary The solution flows faster along thewettest path This is shown clearly in Fig 6 Figure 7shows the water saturation through the system at steady
state As expected the area close to the wall on the lefthand side reaches as high as 70 saturation in thissimulation The toes of both stacks remain relatively dryand little leaching will occur here over time
3D simulation of whole heapThe results presented here are taken from a three-dimensional full heap simulation used to model a goldndashsilverndashcopper oxide ore under cyanide leach Figure 8shows part of the complex mesh required to represent asection of the full heap where the lifts are clearly visibleand the shading captures each of the areas under leach atthe same time Figure 9 shows solution application atthe top surface the flow pattern through a cross-sectionof the heap and the corresponding saturation at thebase As is clear there are considerable variations in thelevel of saturation within the heap which itself can havea significant impact on the recovery of gold
Figure 10 shows the CN concentration in solutionwithin a cross-section of the heap as well as the gold inthe solution and that retained within the ore Knowledgeof these distributions is important for a number ofreasons including
(i) assessing the inventory remaining within the heapand how it is held
(ii) considering changes to operating strategies torecover gold that has somehow become trappedwithin the heap ndash either in the solution or stillwithin the ore
Simulating water balance within plantA considerable proportion of the water within the wholeplant circuit is held within the heap It is therefore vitalto be able to accurately assess the solution distributionwithin the heap Obviously although this is possible toperform with the 3D model it is totally impractical forwater balance calculations that otherwise take a fewseconds for each hour of operation As such anapproach has been developed for gold oxide simulation(where air flow is not important) to simplify the 3D
6 Solution flow under steady state conditions
7 Saturation under steady state conditions
8 Computational mesh for full heap with separate
regions described by shade
5 Schematic of 2D slice model test case
Bennett et al Simulation technology to support base metal ore heap leaching
46 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
model specifically to capture all the important aspects ofthe process behaviour in an integrated yet sufficientlydiscriminating fashion to enable a water and concentra-tion balance (of gold silver copper and CN) to betracked throughout the plant (see Gebhardt et al 2005)An important feature here is the capture of the volumeof solution retained within the heap over time andhow this responds to precipitation and drain downevents In this context the simplified heap leach model ismerely a component model of the water balance circuit
simulation which is solved using the BILCO materialbalance software Using this software the authors havebeen able to provide accurate comparisons with fullplant operation over time as is illustrated in Fig 11
ConclusionsHeap leaching is a process that represents a considerablechallenge from the perspective of engineers who wish togain a holistic understanding of all the factors that
9 Solution and precipitation at base applied to top surface and through a cross-section of heap light shades show
more solution
10 Cross-section of heap showing CN in solution and Au in solution and in ore
Bennett et al Simulation technology to support base metal ore heap leaching
Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1 47
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
Pub
lishe
d by
Man
ey P
ublis
hing
(c)
IOM
Com
mun
icat
ions
Ltd
ultimately govern the effective operation of industrialscale heaps In recent years there has been a good dealof effort to develop process models that might supportminerals engineers in optimising heap leaching opera-tions It is not just that computational modelling of heapleach operations is very challenging owing to thecomplexity of the processes involved an accuraterepresentation of a wide range of simultaneously inter-acting physical and chemical phenomena is also requiredEven though core models of such processes can beassembled the issues of usability are not inconsiderable
The present work has described in overview oneattempt at the development of a core suite of computa-tional models based on advanced CFD technology toproduce a simulation software technology to enable theanalysis of a wide range of heap leaching processes froma number of perspectives
(i) 1D models of laboratory sized columns(ii) 2D slice models to evaluate a range of opera-
tional strategies in full heaps(iii) full 3D models to enable the tracking of every
aspect of operation of a heap and to character-ise the ongoing inventory within both the orematrix and the solution retained within the heap
(iv) simplified models within the context of a wholeplant water balance model to provide a basis forassessing the strategies to ensure that extremeevents (eg precipitation and drain down) donot cause problems with regard to capacity
The objectives of the present work have not onlyincluded developing successful models but also makingthem accessible to the minerals processing engineer It isbelieved that these technologies can offer considerablebenefits for real process optimisation through thestructured exploration of a large number of potentialscenarios in the order of at most days as opposed to thelong time scales (ie many months) and huge expenseinvolved in full scale tests
References1 Anne R D and Pantelis G Proc Int Conf on lsquoCFD in mineral
amp metal processing and power generationrsquo Melbourne Australia
1997 CSIRO 453ndash458
2 Bartlett R W in lsquoSolution miningrsquo 2nd edn 443 1998
Amsterdam The Netherlands Gordon amp Breach Science
Publishers
3 Bear J lsquoDynamics of fluids in porous mediarsquo 1972 New York
NY Elsevier
4 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoHydrometallurgy 2003rsquo (ed CA Young
et al) 315ndash319 2003a Warrendale PA TMS
5 Bennett C R Cross M Croft T N Uhrie J L Green C R
and Gebhardt J in lsquoCopper 2003 ndash Cobre 2003 Vol VI
Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
Vol VI 563ndash579 2003b Montreal PQ CIM
6 Bouffard S and Dixon D in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 275ndash288 2003 Warrendale PA The Metallurgical
Society of AIME
7 Braun R L Lewis A E and Wadsworth M E Metall Trans
1974 5 1717ndash1726
8 Casas J M Vargas T Martinez J and Moreno L in
lsquoBioleaching processesrsquo (ed AE Torma et al) Vol I 249ndash258
1993 Warrendale PA TMS
9 Casas J M Martinez J Moreno L and Vargas T Metall
Trans B 1998 29B 899ndash909
10 Cathles L M and Apps J A Metall Trans B 1975 6B 617ndash
624
11 Cathles L M and Schlitt W J in lsquoLeaching and recovering
copper from as-mined materialsrsquo (ed WJ Schlitt) 8ndash24 1980
New York NY SME-AIME
12 Celia M A Bouloutas E T and Zarba RL Water Resour
Res 1990 26 1483ndash1496
13 Cross M Bennett C R McBride D and Gebhardt J E CD
Proc Conf Computational modelling rsquo05 Cape Town South
Africa November 2005 MEI
14 Davenport W G L King M Schlesinger M and Biswas A K
lsquoExtractive metallurgy of copperrsquo 4th edn 2002 Amsterdam The
Netherlands Elsevier Science Pergamon Press
15 Davis G B and Ritchie A I M Appl Math Model 1986 10
314ndash322
16 Dixon D G Hydrometal 2000 58 27ndash41
17 Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA Young et al)
289ndash314 2003 Warrendale PA TMS
18 Dixon D G and Petersen J in lsquoCopper 2003 ndash Cobre 2003 Vol
VI Hydrometallurgy of copper (Book 2)rsquo (ed PA Riveros et al)
493ndash515 2003 Montreal PQ CIM
19 Dixon D G and Hendrix J L Metall Trans B 1993a 24B
157ndash169
20 Dixon D G and Hendrix J L Metall Trans B 1993b 24B
1087ndash1101
21 Gebhardt J E Taylor D A McBride D and Cross M Proc
Conf Process Systems rsquo05 Cape Town South Africa November
2005 MEI
22 Leahy M J Schwarz M P and Davidson M R Proc 3rd Int
Conf on lsquoCFD in the minerals and process industriesrsquo (ed MP
Schwarz) 581ndash586 2003 Vic Australia CSIRO
23 Leahy M J Davidson M R and Schwarz M P Proc Conf
BACMIN AusIMM Bendigo Vic Australia 2004 41ndash47
24 Leahy M J Davidson M R and Schwarz M P Miner Eng
2005 to be published
25 Madsen B W and Wadsworth M E lsquoA mixed kinetics dump
leaching model of ores containing a variety of copper sulfide
mineralsrsquo USBM Report of Investigations No 8547 USBM Salt
Lake City UT USA 1981 1ndash44
26 McBride D Cross M Croft N Bennett C R and Gebhardt
J in lsquoComputational analysis in hydrometallurgyrsquo (ed DG
Dixon and MJ Dry) 45ndash59 2005a Montreal PQ CIM
27 McBride D Cross M Croft T N Bennett C R and
Gebhardt J Int J Numer Meth Fluid Flow 2005b to be
published
28 Neuburg H Castillo J Herrera M Wiertz J Vargas T and
Badilla-Ohlbaum T Int J Min Process 1991 31 247ndash264
29 Pan L and Wierenga P J Water Resour Res 1995 31 925ndash931
30 Pantelis G and Ritchie I M Appl Math Model 1992 16 553ndash
560
31 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992a 23B 537ndash548
32 Paul B C Sohn H Y and McCarter M K Metall Trans B
1992b 23B 549ndash555
33 Petersen J and Dixon D G in lsquoHydrometallurgy 2003rsquo (ed CA
Young et al) 351ndash364 2003 Warrendale PA TMS
34 Szekely J Evans J W and Sohn H Y lsquoGas-solid reactionsrsquo
400 1976 New York NY Academic Press
35 Van Genuchten M T Soil Sci Am J 1980 44 892ndash898
11 Comparison of daily predicted and measured Au
recovery for early stages of heap operation
Bennett et al Simulation technology to support base metal ore heap leaching
48 Mineral Processing and Extractive Metallurgy (Trans Inst Min Metall C) 2006 VOL 115 NO 1
