Computer Aided Mine Design Computer Aided Mine Design Part III Cut-Off/Equipment Part III Cut-Off/Equipment

InteractionsInteractions

©Dr. B. C. Paul 2000©Dr. B. C. Paul 2000

©Dr. B. C. Paul Summer 2003©Dr. B. C. Paul Summer 2003

Where We Are AtWhere We Are At• We Developed a Block Model of Our We Developed a Block Model of Our

Deposit GeologyDeposit Geology• We Built Some Economics Assumptions We Built Some Economics Assumptions

Over the ModelOver the Model– Often Requires us to approximate a Break-Even COVOften Requires us to approximate a Break-Even COV

• We Determined Our Ultimate Pit at the We Determined Our Ultimate Pit at the Final SlopeFinal Slope– We used our knowledge of the minable reserve size to We used our knowledge of the minable reserve size to

crudely calculate our mine size and ratecrudely calculate our mine size and rate

• We Determined Our Pit Sequences out to We Determined Our Pit Sequences out to the Ultimate Pit at Working Slopethe Ultimate Pit at Working Slope

• We Made Practical Adjustments to the We Made Practical Adjustments to the Computer Aided Pit SequenceComputer Aided Pit Sequence

Size the Mine Equipment – Life Size the Mine Equipment – Life – and COV– and COV• It was necessary to make approximations It was necessary to make approximations

on all of these things to get this faron all of these things to get this far– Example – When got Economic Block Model had Example – When got Economic Block Model had

to guess basic costs to find out which blocks had to guess basic costs to find out which blocks had enough mineral to pay for processingenough mineral to pay for processing• Ie we applied a break-even COVIe we applied a break-even COV• The pit routines took only blocks that could also carry The pit routines took only blocks that could also carry

the stripping coststhe stripping costs– Example – Had to have some idea how things Example – Had to have some idea how things

were going to be done to know costs for BECOVwere going to be done to know costs for BECOV– Example – Had to have idea of mining rate to Example – Had to have idea of mining rate to

pick reasonable increments for staged pits in pick reasonable increments for staged pits in the sequencethe sequence

Now Time to Refine and Now Time to Refine and FinalizeFinalize• Break-Even COVs and SRs made sure that Break-Even COVs and SRs made sure that

all material carried the direct costs of all material carried the direct costs of productionproduction

• Costs are composed of Fixed and Direct Costs are composed of Fixed and Direct CostsCosts– Direct costs occur when mining is done and in Direct costs occur when mining is done and in

proportion to amount doneproportion to amount done• Our break-even parameters coveredOur break-even parameters covered

– Fixed costs occur for being thereFixed costs occur for being there• Foreman, taxes, purchase of equipmentForeman, taxes, purchase of equipment

What Break-Even DoesWhat Break-Even Does

• Break-Even ensures that no action will Break-Even ensures that no action will be taken that costs more than it can be taken that costs more than it can earnearn

• Break-Even does not cover fixed costsBreak-Even does not cover fixed costs– Subtle accounting mistake takes fixed costs Subtle accounting mistake takes fixed costs

and distribute them evenly to every ton and distribute them evenly to every ton minedmined

• Average Grade and Earnings above Strip Average Grade and Earnings above Strip must be great enough to cover the fixed must be great enough to cover the fixed costscosts

What a Cut-Off Grade Must What a Cut-Off Grade Must DoDo• Must make sure don’t loose money Must make sure don’t loose money

by mining (Break-Even)by mining (Break-Even)• Must make sure that the average Must make sure that the average

grade of the ore mined is high grade of the ore mined is high enough to cover the fixed costsenough to cover the fixed costs

• Doing one does not ensure the otherDoing one does not ensure the other– Ie must check both Cut-Offs and pick the Ie must check both Cut-Offs and pick the

higher of the twohigher of the two

BECOV Does Not Guarantee BECOV Does Not Guarantee Maximized NPVMaximized NPV• Lane and Henning Showed COV should be Lane and Henning Showed COV should be

adjusted through life of mine for maximum NPVadjusted through life of mine for maximum NPV

• Start with the Grade Tonnage Relationship for Start with the Grade Tonnage Relationship for the next increment of “ore”? to be taken and the next increment of “ore”? to be taken and then calculate the COV to use on that incrementthen calculate the COV to use on that increment– We know this because we have staged pitsWe know this because we have staged pits

• Best COV is one of six COVs to be calculatedBest COV is one of six COVs to be calculated

Understanding What Comes Understanding What Comes NextNext• Most delivery of market ready product requires Most delivery of market ready product requires

purchase of equipment for several stepspurchase of equipment for several steps– Mining Equipment to remove ore from the groundMining Equipment to remove ore from the ground– Concentrator Equipment to pick out the pay mineral Concentrator Equipment to pick out the pay mineral

from other stufffrom other stuff• Usually involves crushing the ore and putting it through a Usually involves crushing the ore and putting it through a

separator that learn about in 420 Mineral Processingseparator that learn about in 420 Mineral Processing– Refining EquipmentRefining Equipment

• Often the mineral is not what market wantsOften the mineral is not what market wants– Can sell copper, not chalcopyriteCan sell copper, not chalcopyrite

• Refining breaks down mineral to get specific target Refining breaks down mineral to get specific target elements for marketelements for market

– Market that Buys the Finished ProductMarket that Buys the Finished Product

Looking at Next TaskLooking at Next Task

• We are going to size our mining / We are going to size our mining / concentrating and refining equipmentconcentrating and refining equipment

• These things will determine how long it These things will determine how long it takes us to mine through stage pitstakes us to mine through stage pits– Also interacts with our fixed costs and our cut-Also interacts with our fixed costs and our cut-

off gradeoff grade

• Cut-Off grade determines how much of Cut-Off grade determines how much of what we mine really goes to processingwhat we mine really goes to processing– This too determines mine lifeThis too determines mine life

Possible Cut-Off GradesPossible Cut-Off Grades

• Lane assumes the objective is to make as much Lane assumes the objective is to make as much money as possible off the next increment but money as possible off the next increment but that the system has a bottleneck that limits how that the system has a bottleneck that limits how much it can handlemuch it can handle

• Could be mine is the limit - this gives BECOVCould be mine is the limit - this gives BECOV

• Could be concentrator is the limit - adds a Could be concentrator is the limit - adds a penalty for feeding marginally profitable material penalty for feeding marginally profitable material into a finite capacityinto a finite capacity

• Could be refinery or marketCould be refinery or market

Balancing Cut-Off GradesBalancing Cut-Off Grades

• With aide of grade-tonnage chart can pick With aide of grade-tonnage chart can pick off grades where capacity from more than off grades where capacity from more than one system is fully usedone system is fully used

• Could be mine and concentratorCould be mine and concentrator

• Could be mine and refinery or marketCould be mine and refinery or market

• Could be concentrator and refinery or Could be concentrator and refinery or marketmarket

• Could be all threeCould be all three

The Pick RulesThe Pick Rules

• Lane uses rules about size of COVs to pick Lane uses rules about size of COVs to pick the optimum from the listthe optimum from the list

• Process is based on an opportunity cost for Process is based on an opportunity cost for mining low grade ore and putting off earnings mining low grade ore and putting off earnings of high grade into the future where discounting of high grade into the future where discounting will minimize valuewill minimize value– If you were trying to get rich would you take a job If you were trying to get rich would you take a job

at McDonalds for $5.50 an hour when you could at McDonalds for $5.50 an hour when you could have a job that paid $125,000/year salary?have a job that paid $125,000/year salary?

The ProcessThe Process

• The pit is divided into push backs of ore that will The pit is divided into push backs of ore that will be mined in each planning period (often one be mined in each planning period (often one year)year)

• Optimum COV is selected for each planning Optimum COV is selected for each planning periodperiod

• The NPV is calculatedThe NPV is calculated

• Because NPV is a factor in the COVs the Because NPV is a factor in the COVs the process must be repeatedprocess must be repeated

• The process convergesThe process converges

What Lane-Henning DidWhat Lane-Henning Did

• Picked the COV for each pit stagePicked the COV for each pit stage• This determined how long it took the equipment This determined how long it took the equipment

to mine through that pitto mine through that pit– Collectively this set the mine lifeCollectively this set the mine life

• How Did we get the size of the mine fleet How Did we get the size of the mine fleet concentrator and refinery?concentrator and refinery?– We just made a guessWe just made a guess

• We use repeated calculations to find the best We use repeated calculations to find the best actual size for the equipmentactual size for the equipment– Each try the Lane Henning routine optimizes the COVsEach try the Lane Henning routine optimizes the COVs

Optimum SizeOptimum Size

Bang for the Buck(PVR)

Size of Mine

Economic Feasibility Line

This Size Range is Economic

This size is optimum

Added WorkAdded Work

• May also run scenarios with changes May also run scenarios with changes in markets or metal price to try to in markets or metal price to try to deal with riskdeal with risk

What We HaveWhat We Have

• This is Long Term Mine PlanThis is Long Term Mine Plan– Know ultimate size of pitKnow ultimate size of pit– Know the steps that will be followed to get thereKnow the steps that will be followed to get there– Know what equipment will be used to get there Know what equipment will be used to get there

and which rock will be handled as ore or wasteand which rock will be handled as ore or waste

• Intermediate and Short Range mine plans Intermediate and Short Range mine plans start providing detail of which equipment is start providing detail of which equipment is doing what where on what daydoing what where on what day– Won’t have lot of coverage on these topics in Won’t have lot of coverage on these topics in

this classthis class

Where Do We Go From HereWhere Do We Go From Here

• Next parts of course look at specific Next parts of course look at specific operations in more detailoperations in more detail

• Will examine how to design Will examine how to design production blasting rounds (tends to production blasting rounds (tends to emphasize quarry work)emphasize quarry work)

• Will look at Sizing and Selection of Will look at Sizing and Selection of Common Load and Haul EquipmentCommon Load and Haul Equipment– Trucks and ShovelsTrucks and Shovels