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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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Typically in

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erial recover

assified as

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aste. From

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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

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GEMlThisso

andits

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rfractionsa

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Figure21 15

lockedshed

wing isab

variable; th

dtheircapaci

GEMfineC

ditscapacit

GEMlargeC

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yis8[TPH].I

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ill

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],

],

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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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21

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


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


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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25

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



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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26

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]

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