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Marketdrivenmineplanning:Optimisingproductsportfolio,MuzoEmeraldminecasestudy
EnriqueRubio
MiningEngineeringDepartment,UniversidaddeChile
ABSTRACT
Mine planning is themining engineering that transforms a geological orebody into abusiness
promise that shall optimise shareholders value. Traditionally this process commenceswith the
geologicalmodellingstatingtheestimationoforeresources,thentheseresourcesaresubjecttoan
economic envelopewhich is after sequenceddefiningminingmethods and finally a production
schedule is computed inorder toprovide the financial team thebest offer togenerate the sales
contracts.Ingeneral,thismethodologyworksforcommoditiesandrawmaterialsinwhichformalcontracts are set among the producers and thebuyers. In the precious stonebusiness and in
particularintheemeraldbusinessthemarketismuchmoresegregatedanddifferentbuyersattend
emerald auctions to acquired package of emeralds thatwillbe later transform in any form of
jewellery.Thus,thebusinesschangesdependingonhowthedifferentemeraldpackagesareoffered
toasetofbuyers.Thischallengehasmotivatedtheauthortodeviceamineplanningmethodology
tointegratedifferentlevelsofoperationalhedgingtorespondtoamarketsegmentationthatcould
changeovertime.Inparticular,flexibilityhasbeendesignedandaddedto:thenumberofoperating
minesunderproduction, therateofdevelopment,preparationandproductionatanygiven time,
the adoption of an inclined draw point cavingmethod, and finally the automated production
controlsystem tocapture inreal time theemeraldproduction.Thedevicemethodology isunder
applicationby
Muzo
International
at
the
Muzo
underground
mine,
located
in
the
province
of
Boyac,Colombia.Thispaperdescribes the theoretical framework, theactual toolsdeveloped to
apply themethodology and full details regarding themine and plant design to transform an
artisanaloperationintothefirstworldemeraldfabric.
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INTRODUCTION
Themineplanningtraditionalprocessflowisasfollows:
Figure1Mineplanningtraditionalflowsheet
Inthepreciousstonebusinessatremendousfactorisplayedbytheintrinsicuncertaintycontained
in theunderlyingassetconcentrationasgradesand themarket inwhich thosegemstoneswillbe
finally commercialised. The following figure shows the market composition of the emerald
productionworldwide.
Figure2Worldwideemeraldproduction
Alsothepriceofemeraldsplayatremendousroleinvaluingdifferentmineplanningalternatives.
Thefollowingfigureshowsapricetrendovera35yearsperiod.
Figure3 35yearsemeraldprices,nationalgemstonecompany
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Atypi
Itissh
extrem
depen
Thefo
import
From
above,
qualit
20%ar
50%is
thefin
alcommerci
ownthatthe
ely volatile.
ingongem
lowingfigur
anttonotet
he totalmat
50%was cl
emeraldsa
eemeraldst
waste.The
lprice(see
alisationsche
Fi
rearesevera
Typically in
quality(size
eshowsthe
atcuttingan
Figur
erial recover
assified as
dgemsnam
atcanbetr
roductsoft
igure1).Crit
metomarke
ure4 Commestepsfrom
the emerald
,cut,clarity,
ercentageo
dpolishing
e5 Valuechai
d from the
aste. From
dChispero,
atedtobeco
ischainare
icalpointsar
3
temeraldsis
rcialisationsc
inetomark
business th
greenningle
eachpotent
as,inaverag
nMuzoemer
ineemeral
he remainin
thesecond2
meartificial
emeraldsgr
etherobberi
theonesho
eme,agents
etthatmake
rewillbe a
s,shape),C
ialproductf
e,a50%reco
ldmineproje
productof
g 50%, 10%
%arequalit
emeralds`,n
upedin lots
esatthemin
nbelow.
thewholee
t least three
ispero,Morr
omthemine
veryasapro
t
themethod
corresponds
yemeraldsn
amedPerma
forauction,
,theclassifi
eraldbusin
main produ
allaandPer
tomarket.I
cess.
logydescrib
to the high
amedMorra
andthelow
whichthen
ationstagea
ss
cts
a.
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est
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est
et
nd
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finally the auction.The engineering,development andmanagement should aim to control these
itemstoensurethesuccessandsustainabilityofthisbusiness.
In terms ofpricing,GemFieldsthe largestpublic emeraldproducing company reportshigh
variabilityasafunctionoftimeandunderlyingcontractsexistingbetweenthe intermediateagent
andthefinaljewellery.
Table1 SalesperAuction,Gemfieldreport2010
AUCTIONRESULTS
SUMMARY
JULY09
AUCTION
NOVEMBER09
AUCTION
MARCH10
AUCTION
JULY10
AUCTION
DECEMBER10
AUCTION
Dates 2024July2009 2327November2009 1115March2010 1923July2010 610December2010
Location London,England Johannesburg,S.A. Jaipur,India London,England Johannesburg,S.A.
Type HigherQuality HigherQuality LowerQuality HigherQuality HigherQuality
Caratsoffered 1.36million 1.12million 28.90million 0.85million 0.87million
CaratsSold 1.36million 1.09million 22.80million 0.80million 0.75million
No.ofcompaniesplacingbids 23 19 25 37 32
Averageno.ofbidsperlot 10 13 8 18 16
No.oflotsoffered 27 19 56 27 19
No.oflotssold 26 14 49 24 18
Percentageoflotssold 96% 74% 88% 89% 95%
Percentageoflotssoldbyweight 99.8% 97.2% 78.9% 94.2% 86%
Percentageoflotssoldbyvalue 82% 76% 89% 87% 99%
Totalsalesrealisedatauction USD5.9million USD5.6million USD7.2million USD7.5million USD19.6million
Averagepercaratsalesvalue USD4.40percarat USD5.10percarat USD0.31percarat USD9.35percarat USD26.20percarat
These twosourcesofuncertaintycreateagreatdealofvolatilitywhenvaluatinganyof themain
componentsofthetraditionalmineplanningprocess.Therefore,tosetupamineplanningmodel
uponexpectedvaluesofpricesofmainoutcomeproductionand theproduction itselfwouldbe
extremelydangerous,
and
there
is
certainly
atremendous
gain
potential
as
well
as
aloss.
Thus,
a
differentmethodologyhasbeendevicedinordertoderivethemainmineplanningdecisionssuch
as economic envelop, mining sequence and production scheduling as a result of a portfolio
optimisation exercise inwhich the expected return over the investment aswell as its volatility
aretakenintoaccount.
PROPOSEDMETHODOLOGY
Efficient portfolio hasbeen discussed extensivelyby Samis et al (2006), andDavis andNewman
(2008),usingrealoptionsandquantifyingtheriskofdifferentminingstrategiesandalsoreviewing
value at riskmethod. In thispaper, the authorwanted togive a fresh review at theMarkowitz
method(1959)
and
complemented
by
Haugen
(1990)
and
Merton
(1990)
in
which
he
defines
a
frontierefficientoptimisationmethod toallocate resources to aportfolioofassetswithdifferent
returnover investmentandrisk.Themethodologyconsistsofcomputingthecrosscovarianceof
all thepossiblecombinationofassets inaportfolio tocompute themediumvariancespaceupon
whichagivenportfolio isefficient tobe invested in.So, for instance, in the following figure the
highlighteddotsrepresentaportfoliothat is inefficientsincetherearecombinationsofassetsthat
couldprovideahigherreturnforthesamecomputedaveragerisk.
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Notethattheriskinthiscontextisseenastheaveragevolatilityoftheunderlyingassetportfolio.
Then theminingapplicationwillbe tomimic severalminingdecisions suchasminingmethods,
productionrate,miningsequenceandproductionscheduleasifthesedecisionswherecomponents
of a portfolio. Then the covariances of different decisionswill define the variance of a given
decisionsubjecttotheotherstatussuchasmine,productionrate,sequenceandothers.
Figure6 Frontierefficientforportfoliooptimisation
Thefirststeptousethismethodologyistomodeltheprobabilitydistributionofthemainproducts
of interests, in the case of emeralds these productswouldbe heads orChisperos,Morralla and
Perma.Thefollowingfigureshowsprobabilitydensityfunctionsforthosethreepricestakenfora
givenhistoricaltimeinterval.
Figure7 Priceprobabilitydensityfunctionsfordifferentproducts
Thefollowingstepconsistsofmodellingthegradeconcentrationofthemainproducts(Chispero,
MorrallaandPerma)asaprobabilitydensityfunctionforeverydifferentminingmethodtouseas
anextraction
system.
The
following
figure
depictures
these
functions
for
agiven
mining
method.
Returnover
Investment
Risk
IneficientProjects
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Figure8 Gradesprobabilitydensityfunctionfordifferentproductsforagivenmineandminingmethod
Afterdefining the probabilitydistribution of themain sources of return volatility of interest to
integrateinthedecisionmodel,theassetportfolioshouldbedefined.Inthiscaseitcorrespondsto
define for every one of themines or sectors under study the possibleminingmethod. In other
words,beingamine 1 . .andalternativeminingmethods 1 . . ,anassetcanbedefinedasthecombinationofamineandamethodas .Thenthegradeofproductforthemineandthemethodcanbedefinedas , ,theexpectedpriceforproduct isdefinedas ,theminingrecoverycanbedefinedas , , theprocessingrecoverycanbedefinedas .For thedifferentproductsapricethatisdistributedfollowingaknowndensityfunctioncanbemodelled.Thenavaluefunctionisproposedasfollows.
, ,
, , ,(1)
Where:isthesellingcostofcuttingandpolishingofproductk,istheminingcostofminemusingextractionmethodu,istheproductivityofminemusingextractionmethoduNotethatgrades,pricesandmethodproductivityareallrandomvariableswithknownprobability
densityfunction.Thusthereturnovertheinvestmentiscomputedas:
, , , , , ,(2)
Where:isthefixedcostofmovingonetonoforefromminem.
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Then several simulations are performed over the defined random variables sampling the
probabilitydistributionthatdefinestheuncertaintyofgrades,pricesandmethodforagiventime
periodatthemine.Thentheexpectedrateofreturncanbedefinedas,foraportfolioofn assets , would be the covariance of asset i respect to j. Thus the average standarddeviationofagivenportfolioofcomponents
isdefinedas:
, .
Then theabove formulation canbeoptimisedbyminimising the standarddeviation subject toa
givenminimumexpectedrateofreturnandassuming thattheportionsof theportfolioshouldaddatthemost1,beingthepercentageofcapitaltodevelopasseti.CASE
STUDY:
THE
MUZO
STRATEGIC
PLANNING
EmeraldMuzominesarelocated815moverseaintheWestDepartmentofBoyac,Colombia.The
population of this zone is about approximately 15,000 people. The zone has special
geological/metamorphicfeatures thatfacilitated theemeraldgenesis.Inspiteof therewasmining
from1540bySpaniardsconquers,itwasonlyinthe60sthatbiggeremeraldvolumesstartedtobe
produced.Thehistoryofminingmethodsatthiszoneisasfollows:
19601970:surfacemining.19701985:surfaceminingwithminingloaders.1985current:undergroundmining(tunnels,shaftsandchimneys).
Figure9 BoyacDepartmentinColombia
Themine operationuntil 2009wasdivided into a series of shafts:PuertoArturo,Tequendama,
Catedral,Retorno1andVolver,where therewere severalartisanalminingcontractorswhodid
notregisterneitherproductioninformationnorplansortopographicfeatures.Thefigureshowsa
3Dmapoftheminingatthemomentoffinding.
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Figure10 3Dlayoutoftheminebackin2009
TheownersofthemineCoexminasS.A.madethedecisionbackin2009toassociatewithaNorth
American investment consortiumCrestInvestment to take over the operation through an option
contracttochangethewaythemineoperatedandpursuedamassiveemeraldproductionreducing
therobberiesfrom50%oftheactualproductiondownto10%.Inordertoimplementthisobjective
CrestInvestment contracted the Chilean engineering company REDCO Mining Consultants to
conceptuallydesign, implementandoperatea solution thatcouldmatch thebudgetingand time
constraintsoftheowners.
Thechallengewasdividedintofourmainareasofdevelopment:
1.Modifythecurrentdriftingminingmethodintoamoremassiveandcontrolledminingsystem
2.Implementawirelesstrackingundergroundsystem
3.Implement
an
optical
sorting
plant
to
automate
the
emerald
classification
and
cleaning
process
4.Modifythemineplanningprocessandproductioncontrolsystems
Alternativeminingmethods
Driftting
ThemethodthatwasusedinthepastatMuzoconsistedoffollowingtheinstinctofdifferentmine
contractors without taking samples or any geological observations that could facilitate any
engineeringprocedureatthefield.
Driftandfill
BecauseoftheoccurrenceofsuccessfulproductioninTequendamamineduetotheidentificationof
a geological emeraldbelt, itwasnecessary to incur in subsequentdeepeningproduction levels,
whichconstantlyweakenedtheinfrastructureofthemineinlevelsR1Inf.,S1R1Inf.,S2R1Inf.Due
to this, was proceeded to design and build a concrete slab that could support the vertical
andhorizontal forcespresent in the sector, the locationof itand its schematicdesignare shown
inthefollowingfigure.
Tqdama
R2 R1
Volver
Catedral
Puerto Arturo
3D Model
Mine Shafts [m] Drifts [m]
Tequendama246 2487
Parturo 154 718
Retorno1 83 1176
Volvere 239 1744
Retorno2 215 476
Catedral 139 1145
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Figure11 Constructionscheme:constructionsite(left),design(right)
Besides the two activitiesdescribed above, a rehabilitationprogrammewas implemented all over
haulage tunnels,replacing timberpoolssupport inpoorconditionaccording toacostmanagement
and a priorities strategy that would not interrupt the production of emeralds and kept their
stabilityoutofrisk.
Inclineddraw
point
caving
The design of the exploitation method involves the construction of loading stabs, facing
perpendicularlythegeologicalproductivezone,andconnectedthroughamainhaulagelevel.This
patternisrepeatedverticallyifageologicalandstructuralproductivecontinuityzoneisverified.
Figure12Mineralisedzoneprofile
Theplanviewoftheproposedminedesignforthisexploitationmethodisshowninthefollowing
figure.ForTequendama,theaccessshafttotheproductivelevelsindepthwillbemadethroughthe
CL04shaft,becauseofitsconvenientlocationinhardrock,whichgivesanappropriatesupportfor
undergroundminingandgoodworkperformance.
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Figure13 Productionlevelplanview
ForCatedralandPuertoArturomines,implementingthesamesystemofexploitationaccordingto
theshownandmodelledgeologicalbehaviourisplanned.
Aproductionsummary2010,withtheinformationaccumulateduntil7January,2011,thelastday
of the REDCO teamwork in the operation of theMuzo emeraldmine.During thementioned
period,about280,000caratsofemeraldmaterialwereproduced,corresponding toapproximately
350 tulasandapproximately52,800carrs,withanaverageofabout32carrspermetreofmining
advance. The main productive activities were carried out at Level Tequendama R1Inf. and
SubR1Inf,level11S1CatedralandLevel12PuertoArturo.
Table2Operationperformanceindicators,2010
Units Q12010 Q2.2010 Q3.2010 Q4.2010
ROM*Operation (Tonnes) 3,820 4,663 6,382 3,286
ROM*MxZone (Tonnes) 2,674 2,798 4,468 3,244
Drifting (m) 222 223 390 264
ROM*Production (carats) 121,244 60,637 16,850 80,760
Grade (c/t) 45,3 21,7 3,8 18,3
*ROM:runofminematerial
The following figureshows theoperationalperformancemeasured in termsofdrifting,carrsand
tulas,itisnotedthat50%oftheactivityisconcentratedinTequendama,35%inPuertoArturoand
15%inCatedralandVolver.
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Figure14 Productionanddrifting
Figure15Miningoperationandproductivity
Figure16 Operationalperformance
10.000
20.000
30.000
40.000
50.000
60.000
70.000
0
20
40
6080
100
120
140
160
180
Dec,
09
Jan,
10
Feb,
10
Mar,
10
Apr,
10
May,
10
Jun,
10
Jul,
10
Aug,
10
Sep,
10
Oct,
10
Nov,
10
Dec,
10
Jan,
11
Pro
duc
tion
(carats
)
Dri
ftin
gDev
elopmentan
dPreparation
(m)
CA(m) VO(m) PA(m) TQ (m) Production(Carats)
0
1.000
2.000
3.000
4.000
5.000
6.000
7.000
Dec,
09
Jan,
10
Feb,
10
Mar,
10
Apr,
10
May,
10
Jun,
10
Jul,
10
Aug,
10
Sep,
10
Oct,
10
Nov,
10
Dec,
10
Jan,
11
OperationAct
ivit
y(carrs)
TQ(carrs) PA(carrs) VO(carrs) CAT(carrs)
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Notethattowardstheendoftheyearthemineproductionwasmoreconcentratedintothemineralised
zone,which isnotwider than2.5m.Thus inNovemberandDecemberof2010, therewasahigher
emeraldproductionandlesscarrsmoved.Thisindicatesthatthetraceoflithologiesandmetasomatic
evidencefoundonthehangingwallaretremendouslyrelevantfortheemeraldproduction.
Undergroundproductionmanagementsystem
This project involves the installation of an underground network based on fibre cables and
extremelyresistantwiresforelectricity,opticalsealedswitchesandwirelessaccesspoints,inPuerto
ArturoandTequendamamines,inordertoprovidevideomonitoringservice,trackingpeopleand
carrs,IPtelephonyandsensornetworksystemsinsidethemine.
Thesystemconsistsofasetofnetworkingequipment,cameras,specialcables,tagsandelectronic
tags,sensorsandotherdevices,allwithmaximumprotectionstandards forundergroundmining
conditions and high quality and continuity of service. Approximately one hundredmetres of
compoundcable,and500metresofredcablewithspecialcoverage,asetofapproximately30high
resolutionvideocameras,200tagsfortracking,20wirelessaccesspointsandantennashighfingertips
willbe implemented.Fixedcameraswillbe installedat intersectionsofmovementcorridors, fixedcameraswithvariablefocusinarrivalplaces,shaftsandextractionpointsandeasymountingcameras
forextractionpointsandadvancementtunnels,whichwillbeilluminatedbyinfrared,forlowlight
conditions. The samewireless network infrastructure allows having sevenmobile phones, three
insideofeachmineandoneinthesurfacetomaintaincommunicationswiththeengineersincharge
of theoperationatall times.Particularly inFigure17 it ispossible toappreciate the locationof the
networkcomponentscontrolinTequendamaandPuertoArturomines.
Figure17 ProductioncontrolsystematTequendamaandPuertoArturomines
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AcontrolroomisplannedtobeimplementedonthesecondfloorofthePuertoArturooffices,with
avideosurveillanceserver,whichwillmonitorandrecord the informationof thecameras.There
willbe a computer displaying the position of carrs and people in real time (online), through a
trackingapplicationthatwillusethesignalemittedbythetagsinsidethemine.
Theproject
also
includes
the
future
addition
of
sensors
to
expand
the
network
infrastructure
coverage.
The information that they will deliver will be processed through an application, optimising the
operationalactivities.Thesystemhasbeendesignedinamodularfashion,aimingtomeettheneedsof
coverageasthemineexpands,anditisthereforeconsideredtohavepartsforimmediateextensions.
ProcessingplantfortheMUZOoperation
InordertofacilitatetheclassificationandcleaningprocessofemeraldsfromthePuertoArturoand
Tequendamamines,itwillbenecessarytoestablishamanagementsystemtostockmobilemineral
containers, a storage silo, discharge grills and pick hammers for the oversize and a feedbelt
totheprocessingplant.
10tonnes
containers
Near theentranceaccessesofTequendamaandPuertoArturomines10 tonnescontainerswillbe
located, tobecarriedby trucksequipped for thatpurposeand taken to the feedsilo.Afterbeing
unloaded,thecontainerswillgobacktobefilledattheoutputofbothmines.
Roadconnectionwithsilofeeder
Tocarrythecontainersfromthetwomentionedmines,theroadsconnectingtheminesandthesilo
mustbeenabledandrepaired.
PuertoArturo:Theroadbehindtheminefacilitiesmustbeconstructedtoconnecttothefeedsilo.Tequendama:Itisnecessarytorepairtheroadtothefeedsilo,becauseoftheimportantslope.
Surfacesilo
The construction of a silo to store the ore extracted from Tequendama and Puerto Arturo is
planned.Thesilomustbecapableofgivingautonomytotheprocessofopticalsortingforatleast
threehours,anditwillalsoensureanadequateconstantsupplyforthenextprocess.TheSiloisalso
usedtostorethematerialincasedamagemightoccurintheprocessingplant.
Gridsizeselection
Thesortingplantwillprocessmaterialoflessthanfourinchesinsize,soitisnecessarythatthegrid
has that aperture setting.Thiswill ensure themineralmoves the following process having the
appropriateparticlesize.
Secondaryreductionhammer
Asthegridwillhavefourinchesaperture,aflexiblesecondaryreductionsystemwithahydraulic
hammer isnecessary.Thehammershallreduce thesizeofallparticlesexceeding four inches. Its
actionisdirectlyonthegrill.Itisimportanttomentionthatitisexpectedthatonly5%oftheoreis
greaterthanfourinches.Thefollowingfigureshowsthehammer:
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Figure18Hydraulichammer
Silowall
The storage silowas located immediatelybelow thewallwhere the trucksunload theore from
minesTequendamaandPuertoArturoand thewallhasbeenbuilt toprovidemaximumsecurity
forthetruckstodownloadandtobepartofthesilodescribedabove.
Extractionbelt
Tocarrytheorefromthesilofeedertotheopticalsortingplant,itisnecessarytoinstallabeltformineral
movement,asshowninthefigurebelow.Thismainbeltshouldhavetwostraps,onethatcarrytheore
tothenewprocessingplantandanothertosendtheoretotheexistingprocessingplant.
Opticalsortingplant
TheMuzoprocessingplantwasdesignedforatreatmentcapacityof250[tpd]consideringthatthe
plantoperatestenhoursperday,beingoperatedandmonitoredfromacontrolroomlocated ina
differentplantequipmentsector.Itmainlyconsistsoftwoopticalsortingequipment,twoscreeners
forselectionofsize,twowashinganddryingtrays,andtransferbelts.Somesmallequipmentwhich
purchaseispending,are:belts,transferchutes,generators,compressors,blowers,amongothers.
Figure19 Longitudinalviewofthesortingplant
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Thepl
beobs
sortin
Sorter
The o
materi
10 37 19 9.
GEMThisso
and
its
GEMlThisso
andits
ntwillbelo
ervedfrom t
plant.
e granulom
lintofourfr
1[mm] +37
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ineCOLORrterclassified
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catedinside
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try of the
actionstoco
[mm]
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[mm]
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thetwosmall
0
kg.
Machine
thetwobigg
0kg.Machin
completely
om.The foll
ine is quite
sider:
rfractionsan
of
5
KVA.
Figure20
rfractionsa
of5KVA.
Figure21 15
lockedshed
wing isab
variable; th
dtheircapaci
GEMfineC
ditscapacit
GEMlargeC
ndcontrolle
iefdescripti
refore itwa
yis8[TPH].I
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is8[TPH].I
LOR
dbyvideoc
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s determine
tsdimensions
sdimensions
merasthat
entused in
to divide
are4.6x2.3[
are4.6x2.3[
ill
he
he
],
],
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Screeners
Thesemachines split themineral in four fractions, the fourmachines correspond to theSandvik
LF1030screener,1.0x3.0[m],andtotalweightof3,000kg.Eachonehastwoenginesof6.6[kW].
Figure22 Screenerslocation(screener1=H1)
Airblower
It isnecessary towash themineral toremovedirtanddust,and thenproceed toblow the same
product toremovewater from thewashingprocess.Soneed twomachinesareneeded todeliver
500[cfm],withapressureof100[mbar].Eachofthesemachineshasacapacityof7.5[HP].
Figure23 Lowcapacityblower
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AirexComm
moistu
connec
Gener
Below
ractorodas also p
reproductt
tedtothetw
linfrastructisamapoft
oposed the
eparticlesej
oopticalsort
ureelocationof
installation
ect,thismac
ingequipme
Figure
theelements
Figure25 17
f an exhau
hinemustbe
ts.
24 Airextract
describeda
eneralinfrast
t fan to co
locatedont
or
ove:
ucture
trol airborn
eroofofthe
dust and
hangarand
he
be
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Productionsecurityarea
The production security area is a highly secure area within the mining complex in which
productiontakesplace.Thisareawasconceivedtobecontrolledbycamerasatalltimesandgated
lockingtheaccessforpeoplenotrelatedtotheoperation.Themainareasare:
MainaccessgateandpersonnelscreeningControlaccesstoTequendamaandPuertoArturoPlantwarehouseEngineeringandproductioncontrolroom
THEMINEPLANNINGPROCESS
Ascanbeseen,thebusinessvaluechaincanbesetinacircleconnectingthestagesofexploration,
design,productionplanning,miningoperations,productioncontrol,sorting,polishing,andfinally
themarketsale.Becauseofthestrategicobjectivesofthecompanythatownsthemine,theguiding
operation shouldbebased on the strategy ofmarket positioning, conditioning the exploration,
operationandtherestofthechain.
Figure26 Strategicmethodology
OneimportantaspectofplanningMuzowastofindthegradedistributionofemeraldssurrounding
ageologicalcontactformedinahydrothermalandpostmetasomaticmetamorphicprocess.Below
isthe
genetic
model
in
the
Muzo
emerald
mine
and
the
conceptual
summary
of
the
mines
geologicalmapping.
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Figure27 Geneticmodel
AstudyoffieldgeologyhasbeenperformedforeachmineoftheMuzoComplextoidentifytheareas
wheretheemeraldsarelocated.Basedonthisdata,thefollowingprovisionoflithologieswasidentified:
Figure28 GeologicalprofileMuzoemeraldmine
CarbonateBlackShale(BS):
Carbonatedshalewithaveragehardness. Itshowsnosignsofposthumoustectonicsandmineralisation.Typicallyknownas liso
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FragmentedBlackShale(FS)
ShalewithfoldingVeinswithcalciteandpyriteThepyritezonescanbeseenindisseminatedform.
Stockwork(SK)
BlackshalecarbonateVeinletsofalbite,calciteDisseminatedpyriteVeinsupto20[cm]thickwithalbite/calcite(averagethickness10[cm])Maycontainemeralds
ClayZone(CZ)
GrayrockwithhighlyalteredrocktexturedofbrecciaAreseenhealthyandalteredcrystalsofalbiteanddolomiteCrumblesinyourhandDisseminatedpyriteSomelaminarorbandedareasavailableYoucansubmitmmangularclastsofblackshaleSomecarbonatedareas
Carbonatedbreccia(CB)
VerysoftblackshalethatcrumblesinyourhandAlbite
veins
(altered
to
clay)
and
disseminated
pyrite
ClaymatrixOverayearofmineproductiongeologicalmapsweresetupinordertofindthemainconcentration
ofemeraldproductionatdifferent levelsofeachmine:PuertoArturo,CatedralandTequendama.
ThefollowingfigureillustratesthefindingsatTequendamamine.
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Figure29 EmeraldfindingsandgeologyatTequendama
Thetypicalgeologicalcrosssectionsoftheminesarepresentedasfollows:
Figure30 Geologicalmapping
Geophysics
The aim of this study was to test the resistivity geophysical techniques, IP and resistivity
tomography, todetermine itsapplicability in theexplorationofemeraldmines,and therebyhelp
reducetheuncertaintyofoccurrenceofemeralds.
WithresistivityandIP,twostudieswereconducted,500[m]longeach.Datawasrecordedinthetime
domain, dipoledipole configuration, the distancebetween the electrodeswas 50metres (a = 50),
progresswasmadeatevery25metres,therewere6levelsdeep(n=6)(110mdepthofinvestigation)
andanintegrationtimeof2secondswasused.Intotaltherewere950metreslinearsurfacecovered.
Inresistivitytomography10 linesof45to90metreswerestudied.Datawasrecordedinthetime
domain,dipoledipoleconfiguration,thedistancebetweenthestakeswas5metres(a=5),upto13
levelsdeepwererecorded(n=13)equivalentto15to20metresdepthofinvestigationandusean
integrationtimeof0.5seconds.Intotaltherewere630metreslinear,ofwhich505metresoccurred
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22
in the interiorof tunnelsand125metresat the surface, these last90,plus35 testandcalibration
samples.We used a team scores IRIS SYSCALPro model. Below there is one of the specific
outcomefiguresforTequendamamine,themostproductiveminein2010.Itispossibletoidentify
the lithological contact between structures of different hardness, allowing to identify sectors
concentratingthehighprobabilityofoccurrenceofemeralds.
Figure
312D
resistivity
model
TQ
R1Inf
sector.
Carbonaceous
shale
and
wet
(pink),
shale,
drierandmoreestablished(blue,yellowandorange)
Geochemistry
Takingthemainobjectiveofdefiningasystemofeffectiveprospectingandexplorationthatallows
increasedemeraldrecoverywithrespecttothenumberofblocks inproduction, it isof interestto
findarelationshipbetweenthegeophysicalresults,mineralogy,chemicalelementsandoccurrence
of emeralds. Based on this idea, a complete search for equipment that can help obtaining the
spectrum ofmineralogical and chemical elements in rock samples, to create a complete system
characterisationandidentificationofareasofhighemeraldprobabilitymustbeconducted.Theuse
of technologies such as fluorescence andXraydiffraction (XRF andXRD)hasbeen considered.
Someoftheresultsfor12samplesanalysedinthelaboratory,arepresentedinthefollowingtable.
Table3 Samplesdetailandcriticalelementscontent
N Sample Si
(%)
Al
(%)
Fe
(%)
Ca
(%)
Mg
(%)
S
(%)
Na
(%)
K
(%)
Ti
(%)
P
(%)
Mn
(%)
Sr
(%)
Zn
(%)
Cu
(%)
Cr
(PPM)
Ba
(%)
1 TQDR1i_SASN 36,4 10,3 4,6 2,6 6,3 5,7 0,3 0,4 0,3 0,1 0,0 0,2 0,0 937,0 0,1
2 TQDR1iB03 20,3 7,2 4,8 26,4 5,5 7,3 1,7 1,1 0,3 0,1 0,1 0,0 0,1 0,0 786,0 0,0
3 TQDR1iB01 40,0 11,0 3,2 12,9 4,5 3,0 6,3 0,1 0,5 0,4 0,1 0,0 0,0 0,0 458,0 0,1
4 TQDR1iSAS 39,2 10,5 2,2 14,6 4,1 1,6 6,3 0,2 0,4 0,6 0,1 0,0 0,0 0,0 511,0 0,0
5 CATN11Cx01
(ClayZone)
0,0 0,2 3,3 29,9 19,4 0,6 0,0 0,0 0,0 0,0 0,1 0,0 0,0 0,0 162,0 0,0
6 CATN11Cx01
(ClayZone)
0,0 0,3 6,5 28,1 18,6 6,5 0,0 0,0 0,0 0,0 0,1 0,0 0,0 0,0 481,0 0,0
7 TWDR1iSAS
NCx01
25,1 7,2 6,5 24,4 1,5 8,6 4,1 0,1 0,3 0,2 0,1 0,0 0,0 0,1 519,0 0,0
8 B03(LeftWall) 33,0 8,2 4,5 14,3 8,0 5,0 4,1 0,2 0,3 0,4 0,1 0,0 0,1 0,0 739,0 0,1
9 B03(RightWall) 22,2 6,3 6,2 26,9 3,3 7,9 3,5 0,1 0,2 0,1 0,1 0,0 0,1 0,0 459,0 0,0
10 R1iB03(1) 40,8 10,1 4,6 14,9 3,6 5,7 6,1 0,1 0,5 0,3 0,1 0,0 0,0 0,1 815,0 0,1
11 R1iB01 29,1 9,6 7,0 16,3 6,4 11,2 3,0 1,4 0,4 0,1 0,1 0,0 0,7 0,0 939,0 0,2
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12 M
Q Q Q
ORALLA
uadrant1:M
uadrant2:R
uadrant3:M
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1
DolomiteCaMg(CO3
CalciteCaCO3
BerylBe3Al2(SiO3)6
5,4 1,7 2,8
F
EmeraldIdodelandreal
alitywithe
odelandreal
2 3
)2
44,5 1,6
igure32 Grap
Figure3
(1.957*10^3
ityagreewit
eraldoccurr
ityagreeon
4 5
AlbiteNaAlSi3
UraloliteCa2B
Pyrite FeS2
23
,7 0,5 0,0
hXraydiffrac
Predicted
m
xNa/K)+(3
hemeraldso
enceofMorr
henonoccu
6 7
O8
e4(PO4)3(OH)35(H2O)
0,0 0,0 0,
tionresults
odel
.01*10^2xA
ccurrence.
alla,butthe
renceofem
8 9
Illite(K,
Bavenit
Quartz
1 0,0 0,0
lbite[%])
odeldoesn
ralds.
10 11
H3O)(Al,Mg,Fe)2(Si,Al)4O
eCa4Be2Al2Si9O26(OH)2
SiO2
0,0 477,0
otmatch.
12
10[(OH)2,(H2O)]
,0
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24
After the research process,we recommend testing equipment SAX (Bruker distributor), IGMO
(distributorofFEICompany)andSpectralInternationalInc,performingtestsonsamplessentfrom
themine,thendotheanalysisofwhattechnologyisbestbasedonthequalityandquantityofthe
results,andfinallydefinewhatisthemostappropriateequipmentfortheconditionsofuse.
MINEDESIGNANDPRODUCTIONPLANNINGBASEDIN
PORTFOLIOOPTIMISATION
Basedonthegeologicalgeneticmodelspresentedbeforeaprobabilitydistributionofgradesforthe
differentproductswereconstructedforthedifferentminesatdifferentwidths,withthemainaxis
being themetasomatic contact of hard and soft rock. Every singleminingwidth represents a
differentminingmethod.Sofortheartisanalmethodthewidthhappens tobe1.5m,forthedrift
andfill2.5mandforInclinedDrawPointCaving4.0m.Thefollowingtableshowsthelognormal
gradedistributionofChispero,MorrallaandPermaforallthreeminesfordifferentminingwidths.
Table4 Lognormaldistributionofgradesforthedifferentminesanddifferentminingmethods
GradesM1 GradesM2 GradesM3
Chispero A1 A2 A3 A1 A2 A3 A1 A2 A3
Media 1.10 0.41 0.36 1.44 0.92. 0.22 1.79 1.39 0.41
StandardDeviation 0.11 0.04 0.04 0.29 0.18 0.04 0.26 0.20 0.06
Moralla A1 A2 A3 A1 A2 A3 A1 A2 A3
Media 1.79 0.69 0.69 2.13 1.03 0.36 2.48 1.39
StandardDeviation 0.36 0.14 0.14 0.43 0.21 0.07 0.50 0.28 0.20
Perma
A1
A2
A3 A1 A2 A3 A1
A2
A3
Media 1.57 0.47 0.92 1.91 0.81 0.58 2.26 1.16 0.22
StandardDeviation 0.31 0.09 0.18 0.38 0.16 0.12 0.45 0.23 0.04
Thepricedistributionoveraoneyearperiodwastakenfrompublicreportsaswellasthe2010sales
performedbyCoexminas.Thepricedistributionperproductsisshowninthetablebelow:
Table5 Lognormaldistributionofpricestakenfromayearofmineproduction
Prices/products Chispero Morralla Perma
Media 6.68 5.01 3.91
StandardDeviation 0.07 0.10 0.06
Based on the above, several simulationswere performed to analyse at least 50 combinations of
miningmethods (drifting,driftand filland inclineddrawpointcaving) for thedifferentmining
areas.Thefollowingparametersofcostsandproductivitybymethodbymineareusedtocompute
therateofreturnofeverycombination.
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Table6 Parametersfortheportfoliooptimisation
M1 M2 M3
ProductivityMethod1(t/year) 18,000 12,000 12,000
ProductivityMethod
2(t/year) 60,000 42,000 32,400
ProductivityMethod3(t/year) 72,000 60,000 72,000
CostMethod1($/t) 600 400 500
CostMethod2($/t) 200 300 350
CostMethod3($/t) 100 140 180
MiningRecoveryofMethod1 0.3 0.3 0.3
MiningRecoveryofMethod2 0.4 0.4 0.4
MiningRecoveryofMethod3 0.5 0.5 0.5
ProcessRecovery 0.35 0.35 0.35
Mining
fixed
cost
($)
3,000,000
1,500,000
500,000
Sellingcost($/c) 20
Finally, the efficient frontier is computed for theMuzo Emeraldmines for the three different
operatingminesandforthreealternativeminingmethods.Therewasanintegerconstraintadded
tothemodeltoavoidsolutionssuchthatinaminetherecouldbetwocoexistentminingmethodsat
thesametime(Norstand,1999).Thefollowingchartshowstheresult.
Figure34 EfficientfrontierfortheMuzoEmeraldmine
Itwas very interesting to see that for every combination of return and volatility the production
scheduleandminingmethodsperminechangeaccordingly.Thefollowingchartshowsthestrategy
ofminingmethodandproportionofproductioncontributingtothescheduleperminefordifferent
rateofreturnandvolatility.
0%
10%
20%
30%
40%
50%
60%
70%
0% 5% 10% 15% 20% 25%
Ex
pecte
dRateo
fRetu
rn
ReturnStandardDeviation
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Forinstancethefollowingconclusionscanbederivedfromtheanalysis:
1. Forahighreturnandhighvolatilityapproach,theproductionscheduleshouldconcentrateatTequendamamineusingdriftandfillmethodconcentratingover80%ofproduction.
2. For an intermediate return and medium volatility, the production schedule shouldconcentrate
at
Puerto
Arturo
with
Drift
and
Fill,
Catedral
with
Drift
and
Fill
and
TequendamawithInclinedDrawPointCaving.
3. For low returnbut also low risk approach the schedule should concentrate at PuertoArturowithDriftandFillmethod.
The following figure showsdifferentmining combinations,methodsand schedule that couldbe
usedatMuzofordifferentreturn/riskapproaches.
Figure35 Differentstrategiesandproductionschedulesdependingonthereturn/volatility decision
Basedotheaboveguidelinetheschedulefor2011ispresentedasfollows:
Figure36 Finalproposedproductionschedule
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A1_M1 A2_M1 A3_M1 A1_M2 A2_M2 A3_M2 A1_M3 A2_M3 A3_M3
%ofp
roductionunder
theoption
3% 12% 20% 25% 30% 50% 60% 61%
0
20
40
60
80
100
120
140
160
0
10,000
20,000
30,000
40,000
50,000
60,000
jan,
11
feb,
11
mar,
11
apr,
11
may,
11
jun,
11
jul,11
aug,
11
sep,
11
oct,11
nov,
11
dec,
11
RO
M(tp
d)/Headgrade(c/t)
Prod
uction(carats/month)
Carats ROM (tpd) Grade(c/t)
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CONCLUSIONSANDRECOMMENDATIONS
Themain conclusion that canbe obtained from the approach presented in this paper is that
uncertaintymodellingopensanewwayofperformingstrategicmineplanning.Itisnotpossibleto
integrate uncertainty into our production planning discipline if there are not clear and
understandablefinancialtoolsthatcanfacilitatethedecisionsmakerstoseethevalueofvariability.
Currently,thereisplentyofuncertaintymodellingmethodsavailablethatendupbeingusedasa
sensitivity analysisof a fixedproduction schedule.This ongoing researchhas shown thatwhen
adding uncertainty to themodelling of grades and prices the structuralmining decisionsmay
changeaccordinglybasedontheacceptanceofriskandreturn.
In terms of the specific results for theMuzomine it is interesting to outline that a couple of
modelling techniques together with a financial well known approach could contribute to the
delineationof theorebody, sequence,minedesignandproductionschedule from thevaluingof
optionsdowntogeology.
It isexpected that themining industryunderstands that thenewparadigmof strategicplanning
would
be
to
concentrate
much
on
the
market
and
how
the
financial
position
of
shareholders
could
facilitatethedelineationofourmineplanningdecisionsandnottheotherwayaround.
ACKNOWLEDGEMENTS
Theauthorwouldliketothankfirstofalltheorganisationsthatsupportedtheventuresummarised
inthispaperstartingwiththeUniversidaddeChileMiningDepartmentandtheAdvancedMining
TechnologyCentreforsupportingthetechnologyappliedinthisproject.Theauthorwouldalsolike
to thank the engineers of REDCOMining Consultants that took over the project in particular
GabrielPais,PamelaCastillo,DanielaSiuela,JorgeAros,ClaudioGuzmnand IgnacioMuoz.
Also,many thanks to the authors graduate students at the timeMarceloVargas and Fernando
Peirano
for
their
help
in
many
aspects
of
the
work
presented
in
this
paper.
Finally,
the
author
wouldliketothankallhisundergradstudentsthathelpedoutwithmanyshiftsattheMuzomine
andcontributedinagreatdealtothesuccessofthisproject.
REFERENCES
Haugen,RobertandNardinBaker,DedicatedStockPortfolios,JournalofPortfolioManagement,Summer1990,
pp.1722.[1]
Markowitz,Harry,PortfolioSelection:EfficientDiversificationofInvestments,JohnWiley&Sons,Inc.,1959.[2]
RobertC.Merton.ContinuousTimeFinance.Blackwell,1990.[3]
JohnNorstad.Anintroductiontoportfoliotheory.http://homepage.mac.com/j.norstad/finance,Apr1999.[4]
Samis,M.,Davis,G.A.,Laughton,D.,andPoulin,R.,2006,Valuinguncertainassetcashflowswhenthereareno
options:arealoptionsapproach,ResourcesPolicy30:285298.[5]
Davis,G.A.,NewmanA.M.,2008.ModernStrategicMinePlanning.ColoradoSchoolofMines.Workingpaper.[6]