Note- The information contained in these slides is considered Note- The information contained in these slides is considered common knowledge to those schooled in the field and was not common knowledge to those schooled in the field and was not
collected from any one particular source. Acknowledgement is given collected from any one particular source. Acknowledgement is given to SME for model P.E. exams that provided guidance on subjects that to SME for model P.E. exams that provided guidance on subjects that
required coverage for students to prepare to pass the P.E.required coverage for students to prepare to pass the P.E.
Ore Grade RealitiesOre Grade Realities
• Very few ore deposits where the mineral or Very few ore deposits where the mineral or element of interest is only a minor percentage of element of interest is only a minor percentage of the total mass have a uniform grade throughout the total mass have a uniform grade throughout the orebody.the orebody.
• Example – A gold deposit has the following ore Example – A gold deposit has the following ore grade distributiongrade distribution– 6% is 1 to 4 grams/tonne6% is 1 to 4 grams/tonne– 12% is 4 to 6 grams/tonne12% is 4 to 6 grams/tonne– 30% is 6 to 10 grams/tonne30% is 6 to 10 grams/tonne– 36% is 10 to 12 grams/tonne36% is 10 to 12 grams/tonne– 16% is 12 to 20 grams/tonne16% is 12 to 20 grams/tonne– What is the average grade?What is the average grade?
Ore Grade DistributionsOre Grade Distributions
• Most minor element grade Most minor element grade distributions are highly skewed with distributions are highly skewed with a lot more low grade ore than high a lot more low grade ore than high grade oregrade ore
• Histograms capture that skewnessHistograms capture that skewness
• Average grades can be computed Average grades can be computed with a weighted average.with a weighted average.
Lets Give it a TryLets Give it a Try
• Midpoint of each grade categoryMidpoint of each grade category– 6% is about 2.5 grams/tonne6% is about 2.5 grams/tonne– 12% is about 5 grams/tonne12% is about 5 grams/tonne– 30% is about 8 grams/tonne30% is about 8 grams/tonne– 36% is about 11 grams/tonne36% is about 11 grams/tonne– 16% is about 16 grams/tonne16% is about 16 grams/tonne
Reality #2 Most Ore Deposits Reality #2 Most Ore Deposits are Polymetalicare Polymetalic
• Means there is more than 1 mineral Means there is more than 1 mineral of interestof interest– An orebody contains Cu, Zn, and PbAn orebody contains Cu, Zn, and Pb
• How do I put a value on the oreHow do I put a value on the ore– Best way is to sum the value of the Best way is to sum the value of the
componantscomponants
Summing the Value of Summing the Value of ComponentsComponents
• The ore contains 7% zinc, 1% Pb, 0.5% Cu in The ore contains 7% zinc, 1% Pb, 0.5% Cu in sulfide - sulfide - – The zinc will be floated, roasted, leached, The zinc will be floated, roasted, leached,
electrowonelectrowon• Suppose you have 85% recovery in flotation and then Suppose you have 85% recovery in flotation and then
85% recovery in the roast leach and 99% in electrowin85% recovery in the roast leach and 99% in electrowin
• Suppose zinc sells for 80 cents/lb, lead for 60 cents/lb, Suppose zinc sells for 80 cents/lb, lead for 60 cents/lb, and copper for $3/lband copper for $3/lb
• The roast leach process is about $80/ton of concentrateThe roast leach process is about $80/ton of concentrate
• Flotation process runs about $4.75/ton of ore for 3 Flotation process runs about $4.75/ton of ore for 3 productsproducts
Working on the Value of the Working on the Value of the ZincZinc
• Take the electrowining cost off of the Take the electrowining cost off of the sale price since they are in the same sale price since they are in the same unitsunits– 80 cents – 5 cents = 75 cents80 cents – 5 cents = 75 cents– But only 99% of the zinc in solution will be But only 99% of the zinc in solution will be
recovered for salerecovered for sale•75 * 0.99 = 0.7425 per lb of zinc in solution75 * 0.99 = 0.7425 per lb of zinc in solution
• To get the cost for the roast and leach To get the cost for the roast and leach on a lb of zinc basis I will need to know on a lb of zinc basis I will need to know the zinc content of the concentratethe zinc content of the concentrate
Zinc Concentrate GradeZinc Concentrate Grade
• In this deposit and most let us suppose the In this deposit and most let us suppose the zinc is in sphalerite ZnS.zinc is in sphalerite ZnS.– Sphalerite is about 64% zincSphalerite is about 64% zinc– Since so stuff that should not float will get into the Since so stuff that should not float will get into the
zinc concentrate let us suppose that 2% of the zinc concentrate let us suppose that 2% of the sulfides are chalcopyrite and 0.5% is pyrite and sulfides are chalcopyrite and 0.5% is pyrite and there is about 4% gangue mineral carry over.there is about 4% gangue mineral carry over.• Thus 97.5% of the sulfides in the concentrate are Thus 97.5% of the sulfides in the concentrate are
sphalerite.sphalerite.
• And 96% of the concentrate is sulfideAnd 96% of the concentrate is sulfide
Now lets get the roast leach Now lets get the roast leach cost on a recovered zinc basiscost on a recovered zinc basis
• $80/ton of concentrate that is 59.9% $80/ton of concentrate that is 59.9% zinczinc– 2000 lbs * 0.599 = 1198 lbs of zinc2000 lbs * 0.599 = 1198 lbs of zinc– But only 85% of that will be recoveredBut only 85% of that will be recovered
– Cost per recovered lb of zinc = 80/1018 = Cost per recovered lb of zinc = 80/1018 = 0.079 or 7.9 cents per lb0.079 or 7.9 cents per lb
• Value of zinc in concentrateValue of zinc in concentrate– 74.25 cents – 7.9 cents = 66.35 cents/lb in 74.25 cents – 7.9 cents = 66.35 cents/lb in
concentrateconcentrate
Now Lets Get the Value of Zinc Now Lets Get the Value of Zinc in the Rockin the Rock
• Zinc in concentrate is worth 66.35 cents Zinc in concentrate is worth 66.35 cents per lbper lb
• 85% of the zinc in the rock is recovered in 85% of the zinc in the rock is recovered in concentrate soconcentrate so– 66.35 * 0.85 = 56.4 cents per lb66.35 * 0.85 = 56.4 cents per lb
• Rock is 7% zincRock is 7% zinc– 2000 lbs/ton * 0.07 = 140 lbs of zinc2000 lbs/ton * 0.07 = 140 lbs of zinc– At 56.4 cents/lbAt 56.4 cents/lb– 140 * 0.564 = $78.96 for the zinc 140 * 0.564 = $78.96 for the zinc
Now Lets Value the LeadNow Lets Value the Lead
• Lets assume the lead is in GalenaLets assume the lead is in Galena– PbS is 86.6% leadPbS is 86.6% lead– Galena will be floated into a concentrate Galena will be floated into a concentrate
(96.5% recovery)(96.5% recovery)– Smelted in a Blast Furnace $100/ton of Smelted in a Blast Furnace $100/ton of
concentrate (95% recovery)concentrate (95% recovery)– Electrorefined for about 10 cents/lb Electrorefined for about 10 cents/lb
(99% recovery)(99% recovery)
Start by getting value of Start by getting value of unrefined leadunrefined lead
• Lead is 60 cents per lbLead is 60 cents per lb
• It cost 10 cents per lb to refineIt cost 10 cents per lb to refine– That leaves 50 cents per lbThat leaves 50 cents per lb
• But recovery is 99%But recovery is 99%– 50 * .99 = 49.5 cents per lb of unrefined 50 * .99 = 49.5 cents per lb of unrefined
lead bullion from the blast furnacelead bullion from the blast furnace
Lets get the Grade of the Lets get the Grade of the Concentrate Going to the Blast Concentrate Going to the Blast FurnaceFurnace• Lets assume about 10% impurity in the concentrate Lets assume about 10% impurity in the concentrate
– meaning 90% of the concentrate is Galena– meaning 90% of the concentrate is Galena• Galena is 86.6% LeadGalena is 86.6% Lead• Thus the concentrate has 2000lbs/ton * .9 * 0.866 Thus the concentrate has 2000lbs/ton * .9 * 0.866
= 1559 lbs of lead= 1559 lbs of lead– 95% will be recovered in the blast furnace95% will be recovered in the blast furnace– 1559 * 0.95 = 1481 lbs of recoverable lead1559 * 0.95 = 1481 lbs of recoverable lead
• Concentrate Processing is $100/ton / 1481 lbs/ton Concentrate Processing is $100/ton / 1481 lbs/ton = 0.068 or 6.8 cents per lb= 0.068 or 6.8 cents per lb
• Lead in concentrate is thus worth 49.5 cent/lb – 6.8 Lead in concentrate is thus worth 49.5 cent/lb – 6.8 cents/lb = 42.7 cents/lbcents/lb = 42.7 cents/lb
Finding the Value of Lead in Finding the Value of Lead in RockRock
• 1 Ton of Rock is 1% Lead1 Ton of Rock is 1% Lead– 2000 lbs * 0.01 = 20 lbs of lead2000 lbs * 0.01 = 20 lbs of lead
• 96.5% of that will be recovered in 96.5% of that will be recovered in floatationfloatation– 20 lbs * 0.965 = 19.3 lbs of lead20 lbs * 0.965 = 19.3 lbs of lead
• At 42.7 cents/lbAt 42.7 cents/lb– 19.3 * 0.427 = $8.24 for the lead in a 19.3 * 0.427 = $8.24 for the lead in a
ton of Oreton of Ore
Now Lets Get the CopperNow Lets Get the Copper
• 0.5% Copper assumed in Chalcopyrite0.5% Copper assumed in Chalcopyrite– CuFeS2, 34.6% CopperCuFeS2, 34.6% Copper
• Copper is Floated with about 87% recoveryCopper is Floated with about 87% recovery
• The Concentrate is Smelted with 92% The Concentrate is Smelted with 92% recovery at a cost of $85/ton of recovery at a cost of $85/ton of concentrateconcentrate
• Blister Copper is electrorefined for about Blister Copper is electrorefined for about 10 cents per lb with about 99% recovery10 cents per lb with about 99% recovery
Get the value of Blister Get the value of Blister CopperCopper
• $3/lb market – 10 cents/lb to $3/lb market – 10 cents/lb to electrorefineelectrorefine– $2.90/lb as blister$2.90/lb as blister– Adjust for 99% recoveryAdjust for 99% recovery– 2.90*.99 = 2.87/lb2.90*.99 = 2.87/lb
Getting the Concentrate Grade Getting the Concentrate Grade so the Smelter cost can be so the Smelter cost can be converted to a cost/lbconverted to a cost/lb• Chalcopyrite is 34.6% CuChalcopyrite is 34.6% Cu
– Assume about 17% impuritiesAssume about 17% impurities– 34.6% *.83 = 28.7% Cu34.6% *.83 = 28.7% Cu
• A ton of concentrate cost $85 to process to blister A ton of concentrate cost $85 to process to blister copper in the smeltercopper in the smelter– 2000 lbs *.287 = 574 lbs in concentrate2000 lbs *.287 = 574 lbs in concentrate– 92% will be recovered92% will be recovered
• Cost per lbCost per lb– $85/ton / 528 lbs/ton = 0.161 or 16.1 cents per lb$85/ton / 528 lbs/ton = 0.161 or 16.1 cents per lb– $2.87/lb – 0.161 = $2.71 per lb in concentrate$2.87/lb – 0.161 = $2.71 per lb in concentrate
Working Back to the RockWorking Back to the Rock
• Rock is 0.5% CopperRock is 0.5% Copper– 2000 lbs *0.005 = 10 lbs of copper2000 lbs *0.005 = 10 lbs of copper– But only 87% of that will be recovered in But only 87% of that will be recovered in
the concentratorthe concentrator•10 * 0.87 = 8.7 lbs of copper10 * 0.87 = 8.7 lbs of copper
• Getting the valueGetting the value– 8.7 lbs/ton * $2.71/lb = $23.58 for the 8.7 lbs/ton * $2.71/lb = $23.58 for the
coppercopper
Totaling Things UpTotaling Things Up
• Zinc $78.96Zinc $78.96
• Lead $8.24Lead $8.24
• Copper $23.58Copper $23.58
• $110.78$110.78
• But we still have not charged off the cost But we still have not charged off the cost of running a 3 product concentrator $4.75of running a 3 product concentrator $4.75
• Looks like a nice valuable chunk of ore Looks like a nice valuable chunk of ore
That’s a lot of Calculations – That’s a lot of Calculations – Why Are You Doing This to Us?Why Are You Doing This to Us?
• These types of calculations are on the P.E. These types of calculations are on the P.E. examexam
• But Won’t Computer Programs do this for us?But Won’t Computer Programs do this for us?– In mine planning ore grades are kept in blocks and In mine planning ore grades are kept in blocks and
calculations like this are done to get the value per calculations like this are done to get the value per ton of the blockton of the block
– Most programs do not consider all recoveries and Most programs do not consider all recoveries and costs – you may have to adjust the market price costs – you may have to adjust the market price before you feed it to the programbefore you feed it to the program• If you don’t know what went into the cost you won’t be If you don’t know what went into the cost you won’t be
able to do it.able to do it.
What About Early Phase Ore What About Early Phase Ore Body Evaluation – Does it have Body Evaluation – Does it have to be this hairy?to be this hairy?• NoNo
• An approximation used for early An approximation used for early planning is to assign a polymetalic planning is to assign a polymetalic deposit an equivalent gradedeposit an equivalent grade– Our Zinc Lead Copper deposit might be Our Zinc Lead Copper deposit might be
defined as if all the value came from defined as if all the value came from ZincZinc
IllustratingIllustrating
• What if the entire $106.03 came What if the entire $106.03 came from Zinc – what grade would do from Zinc – what grade would do that?that?
Of Course to Do That I Had a Of Course to Do That I Had a Bunch of CalculationsBunch of Calculations
• Equivalent Grades sometimes use very Equivalent Grades sometimes use very crude datacrude data
• Example of an Equivalent Grade based on Example of an Equivalent Grade based on market price onlymarket price only– Lead was 1% but lead is 60 cents per lb Lead was 1% but lead is 60 cents per lb
instead of 80 cents/lbinstead of 80 cents/lb• 1%*60/80= 0.75% Zinc equivalent1%*60/80= 0.75% Zinc equivalent
– Copper was 0.5% but copper is $3/lbCopper was 0.5% but copper is $3/lb• 0.5% * 300/80 = 1.88% zinc equivalent0.5% * 300/80 = 1.88% zinc equivalent
Things to Note About Things to Note About Equivalent GradeEquivalent Grade
• People are not totally consistent as to People are not totally consistent as to what is and is not includedwhat is and is not included
• Equivalent Grade hides a multitude of Equivalent Grade hides a multitude of calculations – many parameters, calculations – many parameters, especially market prices change with especially market prices change with timetime– Thus equivalent grade is only good at one Thus equivalent grade is only good at one
point in time and for a specific set of point in time and for a specific set of assumptionsassumptions
Is It Any Good?Is It Any Good?
• YesYes• Early in the life of an orebody discovery Early in the life of an orebody discovery
our knowledge of ore grades can easily be our knowledge of ore grades can easily be plus or minus 25%plus or minus 25%– Differences in equivalent grade will usually be Differences in equivalent grade will usually be
well within 10% so the imprecision is within the well within 10% so the imprecision is within the uncertainty of our orebodyuncertainty of our orebody
• The fact that equivalent grade values get The fact that equivalent grade values get bad over time is not importantbad over time is not important– Early in the life we want to know whether the Early in the life we want to know whether the
orebody merits further attention now – we are orebody merits further attention now – we are not doing a long term plannot doing a long term plan
Now Its Your TurnNow Its Your Turn
• Do Assignment #2 on Orebody Sizes Do Assignment #2 on Orebody Sizes and Gradesand Grades
